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	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1311</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1311"/>
		<updated>2025-12-10T17:40:26Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Arguments that it is Reasonable to Believe in God without an Argument that He exists */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7dfb69eda7d248578554179b849df565 Argument from the Insufficiency of Materialism]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2081feb796d040ac97f763eca74a85da Argument from the Insufficiency of Materialism (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Additional Arguments for the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c1a61e83fbc848e6977908b77eea6848 Argument from a Sense of Purpose]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/5284dc3042d64483bb6becdce43655c8 Argument from Sense of Purpose (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/03022277956e411cade81c834994470c Argument from Personal Incompetence]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/bd2ce0f738e74427ad1ebefdc513b460 Argument from Personal Incompetence (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/81f8608d5e39403192a966adbd569fa7 Argument from Religious Experience]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/d08fb590992c47f8904ecc9fa5407e6b Argument from Religious Experience (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/cf0bda3290d741f3a31ae7d5d57fd2a8 Argument from the Incompleteness of Science]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/6f5362a9953048d1b44de57f676117ea Argument from the Incompleteness of Science (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/b0c8fb23e30a4c0dba5b725d8f2282e0 Argument from Objective Morality]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/ffa9303df4774cdd8c5d8ef1321960b0 Argument from Objective Morality (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;br /&gt;
&lt;br /&gt;
=Arguments that it is Reasonable to Believe in God without an Argument that He exists=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/d0a29f56663e4b9488e6cb38e39f91ee Pascal's Wager (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7b094827f1da4a2583e6c0fcf4a9ed06 James's argument that people are entitled to their religious beliefs (even if they lack evidence for them)]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/551e72749ca7418595cfdeb91b4c2ffe Plantinga's objection to the evidentialist objection to theism]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/e5d50dd50deb4b2c83be3d9c45a572ff Plantinga's core argument that the belief in God is properly basic for some people]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/8cc3638d96364ca99f274c20d0c5b6b7 Plantinga's argument with his own objection and his response to it]&lt;br /&gt;
*[https://app.reasonspace.com/submaps/5ef321028fe540fc9ffd8a86984598b1 Kant's Argument that you should believe in God]&lt;br /&gt;
**[https://app.reasonspace.com/submaps/addba74f7d4b4aa286511d223b2252dd Kant's argument simplified]&lt;br /&gt;
&lt;br /&gt;
=Relevant arguments concerning Epistemological Standards=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/3a5edf16dee04edda979cf6a166f3514 Clifford's Argument for Evidentialism (with James's objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c67c96d2e2644296b27d04dbad6b00bf James's arguments that our emotions entitle us to form certain beliefs (even with insufficient evidence)]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/078b3e74e8a047e9b1ff588a31ba8278 James's argument with objections]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fd6ad82d7a234db8a0128020fd2c3c15 Arguments for and against James's principle]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/37a70286bf304974944f32901d838d32 Locke on love of truth]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/7ac209598b7f474e860b0f2dc7f1d836 Plantinga's objection to classical foundationalism]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/4e998b5670d24ed19d32fd272c80368c Argument that unfounded propositions are not possible (in the epistemological sense of this term)]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1310</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1310"/>
		<updated>2025-10-09T20:17:10Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Relevant arguments concerning Epistemological Standards */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7dfb69eda7d248578554179b849df565 Argument from the Insufficiency of Materialism]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2081feb796d040ac97f763eca74a85da Argument from the Insufficiency of Materialism (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Additional Arguments for the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c1a61e83fbc848e6977908b77eea6848 Argument from a Sense of Purpose]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/5284dc3042d64483bb6becdce43655c8 Argument from Sense of Purpose (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/03022277956e411cade81c834994470c Argument from Personal Incompetence]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/bd2ce0f738e74427ad1ebefdc513b460 Argument from Personal Incompetence (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/81f8608d5e39403192a966adbd569fa7 Argument from Religious Experience]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/d08fb590992c47f8904ecc9fa5407e6b Argument from Religious Experience (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/cf0bda3290d741f3a31ae7d5d57fd2a8 Argument from the Incompleteness of Science]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/6f5362a9953048d1b44de57f676117ea Argument from the Incompleteness of Science (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/b0c8fb23e30a4c0dba5b725d8f2282e0 Argument from Objective Morality]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/ffa9303df4774cdd8c5d8ef1321960b0 Argument from Objective Morality (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;br /&gt;
&lt;br /&gt;
=Arguments that it is Reasonable to Believe in God without an Argument that He exists=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/d0a29f56663e4b9488e6cb38e39f91ee Pascal's Wager (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7b094827f1da4a2583e6c0fcf4a9ed06 James's argument that people are entitled to their religious beliefs (even if they lack evidence for them)]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/551e72749ca7418595cfdeb91b4c2ffe Plantinga's objection to the evidentialist objection to theism]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/e5d50dd50deb4b2c83be3d9c45a572ff Plantinga's core argument that the belief in God is properly basic for some people]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/8cc3638d96364ca99f274c20d0c5b6b7 Plantinga's argument with his own objection and his response to it]&lt;br /&gt;
&lt;br /&gt;
=Relevant arguments concerning Epistemological Standards=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/3a5edf16dee04edda979cf6a166f3514 Clifford's Argument for Evidentialism (with James's objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c67c96d2e2644296b27d04dbad6b00bf James's arguments that our emotions entitle us to form certain beliefs (even with insufficient evidence)]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/078b3e74e8a047e9b1ff588a31ba8278 James's argument with objections]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fd6ad82d7a234db8a0128020fd2c3c15 Arguments for and against James's principle]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/37a70286bf304974944f32901d838d32 Locke on love of truth]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/7ac209598b7f474e860b0f2dc7f1d836 Plantinga's objection to classical foundationalism]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/4e998b5670d24ed19d32fd272c80368c Argument that unfounded propositions are not possible (in the epistemological sense of this term)]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1309</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1309"/>
		<updated>2025-10-09T20:16:04Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7dfb69eda7d248578554179b849df565 Argument from the Insufficiency of Materialism]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2081feb796d040ac97f763eca74a85da Argument from the Insufficiency of Materialism (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Additional Arguments for the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c1a61e83fbc848e6977908b77eea6848 Argument from a Sense of Purpose]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/5284dc3042d64483bb6becdce43655c8 Argument from Sense of Purpose (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/03022277956e411cade81c834994470c Argument from Personal Incompetence]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/bd2ce0f738e74427ad1ebefdc513b460 Argument from Personal Incompetence (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/81f8608d5e39403192a966adbd569fa7 Argument from Religious Experience]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/d08fb590992c47f8904ecc9fa5407e6b Argument from Religious Experience (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/cf0bda3290d741f3a31ae7d5d57fd2a8 Argument from the Incompleteness of Science]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/6f5362a9953048d1b44de57f676117ea Argument from the Incompleteness of Science (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/b0c8fb23e30a4c0dba5b725d8f2282e0 Argument from Objective Morality]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/ffa9303df4774cdd8c5d8ef1321960b0 Argument from Objective Morality (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;br /&gt;
&lt;br /&gt;
=Arguments that it is Reasonable to Believe in God without an Argument that He exists=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/d0a29f56663e4b9488e6cb38e39f91ee Pascal's Wager (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7b094827f1da4a2583e6c0fcf4a9ed06 James's argument that people are entitled to their religious beliefs (even if they lack evidence for them)]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/551e72749ca7418595cfdeb91b4c2ffe Plantinga's objection to the evidentialist objection to theism]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/e5d50dd50deb4b2c83be3d9c45a572ff Plantinga's core argument that the belief in God is properly basic for some people]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/8cc3638d96364ca99f274c20d0c5b6b7 Plantinga's argument with his own objection and his response to it]&lt;br /&gt;
&lt;br /&gt;
=Relevant arguments concerning Epistemological Standards=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/3a5edf16dee04edda979cf6a166f3514 Clifford's Argument for Evidentialism (with James's objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c67c96d2e2644296b27d04dbad6b00bf James's arguments that our emotions entitle us to form certain beliefs (even with insufficient evidence)]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/078b3e74e8a047e9b1ff588a31ba8278 James's argument with objections]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fd6ad82d7a234db8a0128020fd2c3c15 Arguments for and against James's principle]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/37a70286bf304974944f32901d838d32 Locke on love of truth]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/7ac209598b7f474e860b0f2dc7f1d836 Plantinga's objection to classical foundationalism]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1308</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1308"/>
		<updated>2025-09-19T19:57:31Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Teleological Arguments */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7dfb69eda7d248578554179b849df565 Argument from the Insufficiency of Materialism]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2081feb796d040ac97f763eca74a85da Argument from the Insufficiency of Materialism (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Additional Arguments for the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c1a61e83fbc848e6977908b77eea6848 Argument from a Sense of Purpose]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/5284dc3042d64483bb6becdce43655c8 Argument from Sense of Purpose (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/03022277956e411cade81c834994470c Argument from Personal Incompetence]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/bd2ce0f738e74427ad1ebefdc513b460 Argument from Personal Incompetence (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/81f8608d5e39403192a966adbd569fa7 Argument from Religious Experience]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/d08fb590992c47f8904ecc9fa5407e6b Argument from Religious Experience (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/cf0bda3290d741f3a31ae7d5d57fd2a8 Argument from the Incompleteness of Science]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/6f5362a9953048d1b44de57f676117ea Argument from the Incompleteness of Science (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/b0c8fb23e30a4c0dba5b725d8f2282e0 Argument from Objective Morality]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/ffa9303df4774cdd8c5d8ef1321960b0 Argument from Objective Morality (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1307</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1307"/>
		<updated>2025-09-18T21:51:03Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Arguments Against the Existence of God */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7dfb69eda7d248578554179b849df565 Argument from the Insufficiency of Materialism]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2081feb796d040ac97f763eca74a85da Argument from the Insufficiency of Materialism (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Additional Arguments for the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c1a61e83fbc848e6977908b77eea6848 Argument from a Sense of Purpose]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/5284dc3042d64483bb6becdce43655c8 Argument from Sense of Purpose (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/03022277956e411cade81c834994470c Argument from Personal Incompetence]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/bd2ce0f738e74427ad1ebefdc513b460 Argument from Personal Incompetence (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/81f8608d5e39403192a966adbd569fa7 Argument from Religious Experience]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/d08fb590992c47f8904ecc9fa5407e6b Argument from Religious Experience (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/cf0bda3290d741f3a31ae7d5d57fd2a8 Argument from the Incompleteness of Science]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/6f5362a9953048d1b44de57f676117ea Argument from the Incompleteness of Science (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/b0c8fb23e30a4c0dba5b725d8f2282e0 Argument from Objective Morality]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/ffa9303df4774cdd8c5d8ef1321960b0 Argument from Objective Morality (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1306</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1306"/>
		<updated>2025-09-18T21:50:51Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Additional Arguments for the Existence of God */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7dfb69eda7d248578554179b849df565 Argument from the Insufficiency of Materialism]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2081feb796d040ac97f763eca74a85da Argument from the Insufficiency of Materialism (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Additional Arguments for the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c1a61e83fbc848e6977908b77eea6848 Argument from a Sense of Purpose]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/5284dc3042d64483bb6becdce43655c8 Argument from Sense of Purpose (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/03022277956e411cade81c834994470c Argument from Personal Incompetence]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/bd2ce0f738e74427ad1ebefdc513b460 Argument from Personal Incompetence (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/81f8608d5e39403192a966adbd569fa7 Argument from Religious Experience]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/d08fb590992c47f8904ecc9fa5407e6b Argument from Religious Experience (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/cf0bda3290d741f3a31ae7d5d57fd2a8 Argument from the Incompleteness of Science]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/6f5362a9953048d1b44de57f676117ea Argument from the Incompleteness of Science (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/b0c8fb23e30a4c0dba5b725d8f2282e0 Argument from Objective Morality]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/ffa9303df4774cdd8c5d8ef1321960b0 Argument from Objective Morality (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1305</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1305"/>
		<updated>2025-09-18T21:50:33Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/7dfb69eda7d248578554179b849df565 Argument from the Insufficiency of Materialism]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2081feb796d040ac97f763eca74a85da Argument from the Insufficiency of Materialism (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Additional Arguments for the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/c1a61e83fbc848e6977908b77eea6848 Argument from a Sense of Purpose]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/5284dc3042d64483bb6becdce43655c8 Argument from Sense of Purpose (with Objections)]&lt;br /&gt;
* [ https://app.reasonspace.com/submaps/03022277956e411cade81c834994470c Argument from Personal Incompetence]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/bd2ce0f738e74427ad1ebefdc513b460 Argument from Personal Incompetence (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/81f8608d5e39403192a966adbd569fa7 Argument from Religious Experience]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/d08fb590992c47f8904ecc9fa5407e6b Argument from Religious Experience (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/cf0bda3290d741f3a31ae7d5d57fd2a8 Argument from the Incompleteness of Science]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/6f5362a9953048d1b44de57f676117ea Argument from the Incompleteness of Science (with Objections)]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/b0c8fb23e30a4c0dba5b725d8f2282e0 Argument from Objective Morality]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/ffa9303df4774cdd8c5d8ef1321960b0 Argument from Objective Morality (with Objections)]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1304</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1304"/>
		<updated>2025-09-18T21:43:13Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1303</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1303"/>
		<updated>2025-09-18T21:42:46Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments&lt;br /&gt;
* [https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1302</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1302"/>
		<updated>2025-09-18T21:42:18Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;=Cosmological Arguments for the Existence of God=&lt;br /&gt;
*[https://app.reasonspace.com/submaps/e2d45621d8964a8486ad702b6fb003c7 Simpleminded Cosmological Argument]&lt;br /&gt;
*[https://app.reasonspace.com/arguments/99a7b52356fa42d28b42167bd1d2fd6e Simpleminded Cosmological Argument with Objections]&lt;br /&gt;
&lt;br /&gt;
==Thomas Aquinas' First Three Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 Thomas Aquinas' First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 Thomas Aquinas' First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 Thomas Aquinas' Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 Thomas Aquinas' Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a Thomas Aquinas' Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 Thomas Aquinas' Third Way with Objections]&lt;br /&gt;
&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
=Teleological Arguments&lt;br /&gt;
*[https://app.reasonspace.com/arguments/e7c041704be14042ad428c682af76040 Schematic Teleological Argument for God (with Objections)&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b Thomas Aquinas' Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/9d54a0ee1f7244958b2dbbd1b2a1178d Fine Tuning Argument with Objections and Dilemma]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/007d4d9499fb4161b487210b88151b31 Two Alternative Explanations of the Teleological Structure of Living Things]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Miracles=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/eb9c22f30ccc41b0b0dbd717ec80f907 Argument that Jesus' Resurrection proves the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Ontological Arguments=&lt;br /&gt;
* [https://app.reasonspace.com/arguments/6a710136d68147a19cbd55f4040d4e8c Anselm's Ontological Argument]&lt;br /&gt;
* [https://app.reasonspace.com/arguments/c1653cf9b0414f2582f465955a27b4ab *Descartes' Ontological Argument (with Objections)]&lt;br /&gt;
&lt;br /&gt;
=Arguments from Consciousness=&lt;br /&gt;
*[https://app.reasonspace.com/arguments/b8e0d3d812bc41bdb46bb5a78e494c50 Locke's Argument for the Existence of God]&lt;br /&gt;
&lt;br /&gt;
=Arguments Against the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ce3ed6d79acc4224ac8bef4ed4fefbcb The Problem of Evil]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/53ce511029c240a8a0dca637c49cfb43 The Problem of Evil with Objections]&lt;br /&gt;
&lt;br /&gt;
=Thomas Aquinas' Five Ways of Proving the Existence of God=&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1301</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1301"/>
		<updated>2025-09-18T18:38:37Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;==Thomas Aquinas' Five Ways of Proving the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/d3810df1ea80468a9b7e79d1f6e8cfa7 The First Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4e16f02b053146ee958da7cf2e99e086 The First Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/ad27f9e5bc98499ea783e12a90216a55 The Second Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/4866def271154c41837c6d79c5435492 The Second Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/4bb6f75908844b91a8f84c85e3ec617a The Third Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/2b0bc430e4e54e4391b7e227f48f7729 The Third Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/14fad158976441fb9a2b2af7100667e3 The Fourth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/053077724f5a4385ba3225190dd98699 The Fourth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/df1aabecbb4a46428a24c99caaca5f0b The Fifth Way]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/cd5cff45643f4dd88c9e206a1e1d6f7b The Fifth Way with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/51f2debb5ba442cd9ff6099338ab43df All Five Ways]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/aabca02b45424f0db717e48480052a28 All Five Ways with Objections]&lt;br /&gt;
==William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/e93ad063b6524c389e293830fc25432b The Kalam Syllogism]&lt;br /&gt;
* [https://app.reasonspace.com/smaps/3f1251f675564653b3149b5c27a6460c Craig's whole Kalam Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/82a472cfd33f4fefa80c531b96018bdf Craig's whole Kalam Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/5c85c0cf967a429bb79e8ee61f74cc83 Craig's Argument that the Cause of the Universe is Outside of Time]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/38f2e57244dc462585bd0f666f4d7234 Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation]&lt;br /&gt;
&lt;br /&gt;
==The &amp;quot;Fine Tuning&amp;quot; Argument==&lt;br /&gt;
* [https://app.reasonspace.com/submaps/25f40dfd7f374d889e48eed68e7e4056 William Lane Craig's Version of the Fine Tuning Argument]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/863661aa5f474045893420708e878f07 Fine Tuning Argument with Objections]&lt;br /&gt;
* [https://app.reasonspace.com/submaps/2e78af72be35456aa4c321151d2ede81 Reductio ad Absurdum: the Finely-Tuned God Argument]&lt;br /&gt;
** [https://app.reasonspace.com/arguments/22c39966f381496ab1641f4286b04d6c Fine Tuning Argument with Objections and Finely-Tuned God Argument]&lt;br /&gt;
&lt;br /&gt;
==Paley's Teleological Argument==&lt;br /&gt;
* [https://app.reasonspace.com/smaps/83695359de0d450087b18a6eeaf000f6 Paley's Watchmaker Analogy]&lt;br /&gt;
** [https://app.reasonspace.com/submaps/fb8d37d14bf24d3aae4e670b90c90b93 Paley's Watchmaker Analogy with Objection]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1300</id>
		<title>Maps Concerning the Existence of God</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Maps_Concerning_the_Existence_of_God&amp;diff=1300"/>
		<updated>2025-09-18T18:38:00Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: Created page with &amp;quot;Arguments Concerning the Existence of God Thomas Aquinas' Five Ways of Proving the Existence of God The First Way The First Way with Objections The Second Way The Second Way with Objections The Third Way The Third Way with Objections The Fourth Way The Fourth Way with Objections The Fifth Way The Fifth Way with Objections All Five Ways All Five Ways with Objections William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God The Kalam Syllogism Craig's who...&amp;quot;&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Arguments Concerning the Existence of God&lt;br /&gt;
Thomas Aquinas' Five Ways of Proving the Existence of God&lt;br /&gt;
The First Way&lt;br /&gt;
The First Way with Objections&lt;br /&gt;
The Second Way&lt;br /&gt;
The Second Way with Objections&lt;br /&gt;
The Third Way&lt;br /&gt;
The Third Way with Objections&lt;br /&gt;
The Fourth Way&lt;br /&gt;
The Fourth Way with Objections&lt;br /&gt;
The Fifth Way&lt;br /&gt;
The Fifth Way with Objections&lt;br /&gt;
All Five Ways&lt;br /&gt;
All Five Ways with Objections&lt;br /&gt;
William Lane Craig's &amp;quot;Kalam&amp;quot; Cosmological Argument for the Existence of God&lt;br /&gt;
The Kalam Syllogism&lt;br /&gt;
Craig's whole Kalam Argument&lt;br /&gt;
Craig's whole Kalam Argument with Objections&lt;br /&gt;
Craig's Argument that the Cause of the Universe is Outside of Time&lt;br /&gt;
Craig's Argument that the Cause of the Universe is Outside of Time with Objection that the Kalam Syllogism is an Equivocation&lt;br /&gt;
The &amp;quot;Fine Tuning&amp;quot; Argument&lt;br /&gt;
William Lane Craig's Version of the Fine Tuning Argument&lt;br /&gt;
Fine Tuning Argument with Objections&lt;br /&gt;
Reductio ad Absurdum: the Finely-Tuned God Argument&lt;br /&gt;
Fine Tuning Argument with Objections and Finely-Tuned God Argument&lt;br /&gt;
Paley's Teleological Argument&lt;br /&gt;
Paley's Watchmaker Analogy&lt;br /&gt;
Paley's Watchmaker Analogy with Objection&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1299</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1299"/>
		<updated>2025-09-18T18:37:43Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Epistemic status]]&lt;br /&gt;
* [[Objections]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
** [[Aristotelian Syllogisms]]&lt;br /&gt;
** [[Deductions Involving Complex Propositions]]&lt;br /&gt;
* [[Assessing Arguments in ReasonSpace]]&lt;br /&gt;
* [[Inference to the Best Explanation]]&lt;br /&gt;
* [[Fallacies]]&lt;br /&gt;
* [[How to map arguments from a text]]&lt;br /&gt;
* [[How to build an argument map in ReasonSpace]]&lt;br /&gt;
* [[Map Library]]&lt;br /&gt;
** [[Maps Concerning the Existence of God]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1298</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1298"/>
		<updated>2025-09-18T18:37:35Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Epistemic status]]&lt;br /&gt;
* [[Objections]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
** [[Aristotelian Syllogisms]]&lt;br /&gt;
** [[Deductions Involving Complex Propositions]]&lt;br /&gt;
* [[Assessing Arguments in ReasonSpace]]&lt;br /&gt;
* [[Inference to the Best Explanation]]&lt;br /&gt;
* [[Fallacies]]&lt;br /&gt;
* [[How to map arguments from a text]]&lt;br /&gt;
* [[How to build an argument map in ReasonSpace]]&lt;br /&gt;
* [[Map Library]]&lt;br /&gt;
** [Maps Concerning the Existence of God]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Deduction&amp;diff=1297</id>
		<title>Deduction</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Deduction&amp;diff=1297"/>
		<updated>2025-08-22T17:41:14Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[https://plato.stanford.edu/entries/aristotle/ Aristotle], the first logician, defined deduction as follows: &lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;A deduction is an argument in which, certain things being laid down, something other than these necessarily comes about through them. (''Topics'' I.1 100a25-27)&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The premises are the &amp;quot;things laid down&amp;quot; and the conclusion is what comes about necessarily through them, so another way to put Aristotle's definition is to say that ''a deduction is an [[inference]] in which the premises necessitate the conclusion''. That means that the premises' being true would make the conclusion ''have to be'' true. It will be easier to see what's meant by &amp;quot;necessitate&amp;quot; or &amp;quot;have to be&amp;quot; if we look at some examples.&lt;br /&gt;
&lt;br /&gt;
=Example 1: &amp;quot;Barbara&amp;quot;=&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/916b58e1-07e7-484c-adf9-2cb8897c1eb7}}&lt;br /&gt;
&lt;br /&gt;
Let’s focus on the first of these examples, Argument U. Proposition 1 tells us that all birds are animals, and Proposition 2, adds that all parrots are birds, so if we were to deny Proposition 3, it would amount to our saying &amp;quot;All birds are animals, and here's a type of bird that isn't.&amp;quot; We'd be caught in a contradiction. This is the sense in which Inference U necessitates Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is not because of anything special about the subject matter that the premises necessitate the conclusion. If we changed the argument to be about Volkswagens, cars, and Jettas, rather than birds, animals, and parrots, the premises would still necessitate the conclusion in exactly the same way. The same holds if we changed the argument to make it about musicians, matadors, and marriage counselors. In this last case, both premises would be false, but if they were true (that is, if all musicians were matadors and all matadors were marriage counselors), then the conclusion would have to be true: all musicians would ''have to'' be marriage counselors. What makes the deduction work doesn’t have to do with the subject matter of the propositions involved, but with their structure and interrelation. This is called the ''form'' of the argument. &lt;br /&gt;
&lt;br /&gt;
Argument V (in the map above) has the same form as Argument U. If you don’t see this immediately, try rewriting the phrase “need food” with “are things that need food” or “are food-needers”.&lt;br /&gt;
&lt;br /&gt;
In order to focus on the forms of deductive arguments rather than their content, Aristotle introduced the practice of using letters to stand for the subjects and predicates of the propositions, leaving behind only words like “some”, “all”, “no”, “is” and “not” (and their variants). Argument W (in the map above) uses letters in this way to display the Form of argument shared by Arguments U and V. It is one of the [[Aristotelian_Syllogisms |forms identified by Aristotle]], and it was named [[Aristotelian_Syllogisms#Barbara|Barbara]] by Medieval Philosophers who studied his logic. You can replace the capital letters S, M, and P with any terms you like, and you'll get a deductive argument.&lt;br /&gt;
&lt;br /&gt;
=Example 2: &amp;quot;Modus Tollens&amp;quot;=&lt;br /&gt;
&lt;br /&gt;
Here are three maps that illustrate another form of argument, called [[Deductions_Involving_Complex_Propositions#Modus_Tollens|modus tollens]]:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/9df82f8daf9f49c5b32f9a2b19a0d373}}&lt;br /&gt;
&lt;br /&gt;
Arguments X and Y share the same form, which is described in Argument Z. The letters &amp;quot;p&amp;quot; and &amp;quot;q&amp;quot; (in Argument Z) stand for whole propositions in the other two arguments, as shown in the table below. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Argument X'''&lt;br /&gt;
|'''Argument Y'''&lt;br /&gt;
|'''Argument Z'''&lt;br /&gt;
|-&lt;br /&gt;
|It is raining now.&lt;br /&gt;
|Daddy likes coffee.&lt;br /&gt;
|p&lt;br /&gt;
|-&lt;br /&gt;
|I feel wet.&lt;br /&gt;
|I've seen daddy drink coffee.&lt;br /&gt;
|q&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
(If you just mechanically substitute the relevant words in for the letters p and q, you won't always get grammatical sentences, so you need to edit the wording a bit. But with a little bit of practice, it's easy to see which arguments fall into this form.)&lt;br /&gt;
&lt;br /&gt;
The propositions in a modus tollens argument can be thought of as complex propositions. The first premise is relating two other propositions (p and q) telling you that if the first is true, then the other also is. The second premise is telling you that the second proposition (q) is not true, and the conclusion is that the first one (p) isn't true either. The premises might be false, but if they are true, then the conclusion would have to be.&lt;br /&gt;
&lt;br /&gt;
=The strength of a deduction=&lt;br /&gt;
&lt;br /&gt;
Unlike other sorts of inferences, deductive inferences do not differ from one another in strength. Either an inference is deductive, or it is not. However, there are some forms argument that may seem like deductions but are not. We can call these [[Deductive_Fallacies|deductive fallacies]].  To differentiate between the genuine deductions and the imposters, logicians call the genuine ones ''valid'', and they call any argument that isn't a deduction (but which someone might mistake for one) ''invalid''.&lt;br /&gt;
&lt;br /&gt;
All valid deductive arguments have equally strong inferences, but this doesn’t mean that the arguments are equally strong taken as wholes. The can differ in strength because their premises may differ in epistemic status. Thus, the two things to do in evaluating a deductive argument are to determine whether it is valid and to assess the premises. &lt;br /&gt;
&lt;br /&gt;
Deduction is the most studied form of argument and many valid deductive argument forms have been identified. Even without knowing these forms explicitly, one can often tell simply by asking oneself whether the premises and conclusion of an argument are related in such a manner as to preclude any scenario under which the premises would be true and the conclusion false.  &lt;br /&gt;
&lt;br /&gt;
Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
=Determining whether an inference is a (valid) deduction=&lt;br /&gt;
&lt;br /&gt;
To determine whether an inference is a (valid) deduction, one needs to consider whether it has a (valid) [[deductive form]]. One can memorize the forms, and try to apply them, but even without doing this, you simply ask yourself whether the premises and conclusion are so related that it is impossible for the conclusion to be false, if the premises are true. Sometimes the answer will be immediately obvious. If it's not, try to make up an argument of the same form with true premises and a false conclusion. If you can make one up, then the argument isn't a valid deduction. If you can't, then there's a good chance that it is. &lt;br /&gt;
&lt;br /&gt;
Even when the argument seems to have a valid deductive form like [[Barbara]] or [[Modus Tollens]], one has to check for the fallacy of [[equivocation]], since if a word appears with different meanings in different parts of an argument, the argument may not really have the form it appears to.&lt;br /&gt;
&lt;br /&gt;
=Are deductive arguments better than other arguments?=&lt;br /&gt;
&lt;br /&gt;
You might have gotten the impression from this section that deductive arguments are better than other kinds of arguments. There’s a respect in which this is true: their inferences are stronger. However, an argument is only as good as its premises, and the premises of deductions always either include universal propositions (of the &amp;quot;All S is P&amp;quot; or &amp;quot;No S is P&amp;quot;) or complex propositions that asserting something about the relations between other propositions. Premises of both of these types are often difficult to know to be true. So a deduction is usually the easy part of a larger chain of arguments, in which earlier non-deductive arguments establish the premises needed for the deduced conclusion.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
deductions are (for the most part, at least) generalizations, all (or nearly all) of which are established by other forms of argument. Given this, is it more accurate to view deduction as the easier and more straightforward part of a process whose more difficult part is the arguments that establish the general propositions used as premises in the deductions. The primary form of argument by which these general propositions are established is [[induction]].&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1296</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1296"/>
		<updated>2025-08-22T17:36:12Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Assessing objections in ReasonSpace */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that articulates a reason for rejecting another argument. It does this by objecting to one of the argument's premises or inferences. The objection as formulating as an argument a reason for giving the relevant premise or inference a low [[Assessing_Arguments_in_ReasonSpace|assessment]]. &lt;br /&gt;
&lt;br /&gt;
In [https://app.reasonspace.com ReasonSpace] an objection is represented by a red octagon with a red arrow pointing from it to the premise or inference that is being objected to. Each objection will have at least one premise, connected to it by black arrow (in the same way premises are connected to other arguments).&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded (or otherwise week) and therefore is of no (or little) value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
In these examples we argued that a premise is false. But a proposition doesn't have to be false to be unfounded or week. We just have to not be in a position to know that it's true. Here's a map that objects to a premise on these grounds.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/680b23346f374ef4a596cb11685ad142}}&lt;br /&gt;
&lt;br /&gt;
Objection B gives an ''argument'' that Proposition 2 is unknown. We could also have an objection that atterts this more directly, as in the map below:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/89c147f7f3ed4dd499c223c0945e5584}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]]. Here are two examples:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/c9ba87e0321f4bc8b94775604c4c85f8}}&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/b7ec631838ae4978af3aba15512105e8}}&lt;br /&gt;
&lt;br /&gt;
=Assessing objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
To assess an objection, you have to assess all of the objections premises and the objecting inference (represented by the red octagon). You assess the premises, as you would assess any other premise, by determining its [epistemic status]. You assess the objecting inference considering how damaging the objection would be to the premise or inference objected ''if all of the objection's premises were certain''. &lt;br /&gt;
&lt;br /&gt;
Assess the objecting inference in the right-most region of the assessment scale, if being certain of its premises would put you in a position to entirely reject the objection's target. (To entirely reject an premise is to regard it as [unfounded], and to entirely reject an inference is to regard it as a [non-sequitur].) On the opposite extreme, you should assess the objecting inference as a non-sequitur (in the left-most region of the assessment scale) if you found that being certain that the objection's premises were true would give you no reason to reject the objection's target. If you think that being certain of the objection's premises would give you some reason to doubt the objection's target, but not strong enough reason to reject it entirely, then assess the objecting inference somewhere in the middle two regions of the scale (depending on how strong you think the reason is).&lt;br /&gt;
&lt;br /&gt;
The system will calculate a strength for the objection as a whole based on the strengths you assign to the objection's premises and the objecting inference, and the system's assessment of the objection will then place an upper limit on the assessment of the objection's target. This limit will appear as a red shaded area at the right of the target's assessment scale.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Epistemic_status&amp;diff=1295</id>
		<title>Epistemic status</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Epistemic_status&amp;diff=1295"/>
		<updated>2025-08-22T17:35:50Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Epistemic Status as Relative to an Audience and Objective */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;[[file:Epistemic_status.png|thumb|700px]]&lt;br /&gt;
In evaluating arguments, it is necessary to determine the epistemic status of each premise—where it falls along the scale running from ignorance to knowledge.&lt;br /&gt;
&lt;br /&gt;
In some unusual cases, we might be able to specify this to such a fine degree of resolution that we can assign a number to it, and different scales have been devised for assigning such numbers. In most cases, however, this is not possible, and we distinguish epistemic statuses more coarsely using terms like “unfounded”, “possible”, “probable”, and “certain”. In order to get clearer on epistemic status, we will need to discuss each of these terms. &lt;br /&gt;
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=Between Knowledge and Ignorance=&lt;br /&gt;
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To get a sense of the continuum between knowing something and being wholly ignorant of it, it helps to consider some examples. Let’s start with the following scenario: While walking across the quad one day at 8:00am, you see someone at a distance whom you almost recognize as your acquaintance Bob, but you lose sight of him before you can be sure. If you had gotten a better look at the man and recognized him as Bob, then you would know that Bob was on the quad at 8:00am. As things stand, however, you do not know it. Still, you are not in the same position with respect to the proposition “Bob was on the quad at 8:00am” as you would be if you hadn’t seen what you did. Your experience on the quad gives you some ''reason'' to believe the proposition, without making you ''certain'' of it.  &lt;br /&gt;
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Notice that you might go on to use this proposition in arguments. Suppose, for example, that a bank robbery was committed in Dallas at 8:03 and Bob was suspected of being behind the wheel of the getaway car. If you knew that Bob was on the quad at 8:00, you could be certain, via the following argument, that these allegations are false.&lt;br /&gt;
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{{Map|https://app.reasonspace.com/arguments/6676e764-6cfb-4f6c-af5a-830115c9852e}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
As things stand, however, you do not know Proposition 2, and so you do not know the conclusion, Proposition 3. But, because you have some reason to believe Proposition 2, you have some reason to believe the conclusion as well. Perhaps, then, you should go to the police and make a statement. If you do, how much weight should the police give to your testimony? Let’s consider some of the questions that they might ask you (and that you could ask of yourself):&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt; For how long did you see him? At what distance? How good was the visibility? Did you focus on him, or was he in the periphery of your vision? How familiar are you with Bob’s appearance in the first place? Is it based on vision alone that you think you recognized him, or did you hear his voice as well, or smell that unusual cologne that he’s always wearing?&amp;quot; &amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In addition to these questions, you might also consider how distinctive Bob’s appearance is: is he someone who is easily recognized in a crowd, or someone who can easily be mistaken for someone else? Notice that for each of these questions there is a range of possible answers, and that how sure you could be that Bob was on the quad depends on where along that range your answer falls. &lt;br /&gt;
&lt;br /&gt;
Another way in which you might have some reason to believe something without being certain of it is by remembering it vaguely. This would be the case with someone who did see Bob on the quad recently and recognized him but couldn’t recall with certainty ''when'' the encounter occurred. To get a sense of the considerations that are relevant to determining the epistemic status for this person of the proposition that Bob was on the quad at 8:00am, we could make up a list of questions similar to those that we considered above for the case of seeing Bob on the quad. A third way that one might come to have an intermediate epistemic status with respect to a proposition is by inferring it from earlier propositions. In the example we’ve just been considering, your conclusion that Bob couldn’t have been behind the wheel of the getaway car has such a status because it is inferred from uncertain premises. But there are inferences in which, even if the premises are certain, the conclusion cannot be inferred with certainty. Later, when we consider some of these types of arguments in greater detail, we will get a sense of the factors that would lead to the conclusions being nearer to or further from certainty.&lt;br /&gt;
&lt;br /&gt;
=Certainty= &lt;br /&gt;
&lt;br /&gt;
Let’s start with '''certainty'''. We’ve been using this word a lot in the last few paragraphs, in a way that makes it seem to be nearly synonymous with “knowledge”. Understanding the relation between these two concepts will help us to understand epistemic status better. To be ''certain'' of a proposition is to ''regard it as knowledge'', as opposed to regarding it as doubtful. When you are certain of something you act on it and draw inferences from it confidently, whereas when you are uncertain you are more tentative, always keeping in mind the possibility that the proposition is false and planning for that contingency. In this sense, people are sometimes certain of things unreasonably. A fervent racist, for example, might not hesitate to act on his belief. However, when we speak of certainty as an epistemic status, we are referring not to the way a person actually does regard the proposition but to the way it is ''reasonable'' for him to regard it. We might call this ''rational certainty'' or ''objective certainty'' (as opposed to subjective certainty). In any case, this is how I am going to use the word “certain” going forward. &lt;br /&gt;
&lt;br /&gt;
There are some disputes among epistemologists about the relationship between certainty and knowledge. However, the following is comparatively uncontroversial: ''the beliefs that a person is entitled to classify as knowledge and those that he is entitled to classify as certain are the same''. The difference between classifying them as certain and classifying them as knowledge is that, in classifying them as certain, he is contrasting them specifically with beliefs that have a lower epistemic status and is focusing on the fact that he is in a position to act on these beliefs and to draw inferences on these beliefs without hesitation.&amp;lt;Ref&amp;gt;Among the disputed issues are whether it is possible to be certain of something that one doesn’t actually know and whether it is possible to know something without being certain of it.&amp;lt;/Ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In thinking about the different epistemic statuses, it is often helpful to consider how they come up in the criminal justice process, when police officers, judges, and juries often need to weigh evidence, and specify how sure they are of various propositions. The concept of “certainty” is central to criminal trials, where the jury is instructed to return a guilty verdict only if they are certain that the defendant is guilty—only, to use a familiar phrase, if his guilt has been established “beyond a reasonable doubt.” In general, we can think of certainty as the state we are in with respect to a proposition when there is no reasonable doubt about it. Thus, the proposition that Bob was on the quad is not certain because there is a reasonable doubt about it: you didn’t get a good enough look at the person in question to eliminate the possibility that it was someone else who vaguely resembled Bob. Whereas, if you had seen Bob clearly and heard and recognized his voice, these doubts would have been assuaged, and you could be certain that Bob was on the quad.  &lt;br /&gt;
&lt;br /&gt;
Of course, there are still doubts that someone might raise here, based on such farfetched scenarios as Bob impersonators, holograms, or hallucinogens; but most of us, in most contexts, would consider such doubts ''unreasonable'', and certainly they would be ruled out as unreasonable in court (unless there was some specific evidence for them in a certain situation). As you might imagine, there is room for argument about what sorts of doubts are reasonable in what contexts and about when we have certainty. Indeed, some philosophers think that there is very little about which we can be genuinely certain—that there is very little that we really know—while others think that we know a great deal. We will have occasion to discuss this debate later. For now, let’s put this issue aside and proceed on the assumption that we can be certain of such things as that the people we see in front of us are really there. This is an assumption that we all do make in our daily lives.&lt;br /&gt;
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=Probability=&lt;br /&gt;
&lt;br /&gt;
If a proposition fails to be certain, it may still be '''probable'''. A proposition is probable if the evidence is strong enough that it is more likely to be true than not, so that it is reasonable to assume it provisionally, while still making allowances for the possibility that it is false. For example, suppose that on your way to class you and one of your classmates, who you don’t know well, both stopped at an ATM to make a withdrawal and you happened to see his receipt and notice that the balance was $602.47. Half an hour later, during the class, it would be probable that this was still his balance. Since you have been with him in the intervening time, you would know that he hasn’t made any further withdrawals or deposits or used a debit card. But you could not be certain of the balance, since you do not know whether anyone else has access to the account, or whether any previous transactions were posted to the account during this period; and you know that these sorts of events regularly happen with bank accounts. Still, because thirty minutes is so short a time, the odds are against any of these things having happened in this period, so it is more likely than not that the balance has remained the same. &lt;br /&gt;
&lt;br /&gt;
I discussed earlier how juries are instructed to convict in criminal cases only when they are certain that the defendant is guilty. In civil cases (that is, lawsuits) there is a less rigorous standard and only probability is required. In legal terms, a jury should find for the plaintiff and order the defendant to pay damages if “the preponderance of the evidence” favors the plaintiff’s case. This means: if the plaintiff’s case is more likely to be true than false, given all the evidence presented.&amp;lt;ref&amp;gt; It is worth reflecting on the reason for this difference between criminal and civil law. In a criminal case, what is being decided is whether a person deserves to be punished, and it would be a grave injustice to punish him for a crime he didn’t commit, so it is important to be certain that he is guilty. In a civil case, however, what is being disputed is which of the two parties should have to bear a certain cost. For example, I might sue you for $1,000 to repair my car, claiming that you caused the damages. In this case, the court needs to decide between forcing you to pay the money and leaving me to pay it. And, if the preponderance of the evidence favors the conclusion that you caused the damage, then even if the jurors had some reasonable doubts, it would be unjust of them to leave me to pay for the damage that you probably caused.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
=Possibility=&lt;br /&gt;
A proposition that is not probable may still qualify as '''possible'''. To call a proposition “possible” in the relevant sense is to say that there is ''some reason'' to believe it and that it is, therefore, reasonable to regard it as something that “might be” true and to consider it in our thinking. Thus, in the example above concerning Bob, it is at least possible that he was on the quad at 8:00am (even if it turns out that it is not probable). He ''might'' have been there. &lt;br /&gt;
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Perhaps you’re thinking that “anything is possible” and that you would be in a position to say that Bob “might have been on the quad” even if you hadn’t had the experience of seeing someone who you thought you recognized as him there. There is a sense of the word “possible” in which you could say that it was possible that Bob was on the quad, even if you hadn’t had the experience, but there is another sense of the word in which this would be false. And it is this sense—let’s call it ''epistemic possibility'' that is relevant for our present purposes.  &lt;br /&gt;
&lt;br /&gt;
To see this, imagine calling the police to tell them of the possibility that Bob was on the quad at 8:00am, three minutes before the robbery in Dallas. They would ask you ''why'' you thought it was possible, and they would not react favorably if you responded that “anything’s possible”. They would have quite a different response, however, if you told them about your experience of thinking you recognized him. (Indeed, this report could prove quite useful to them. If Bob has been claiming that he was on the quad at that time, your report could make this alibi considerably more credible.)  &lt;br /&gt;
&lt;br /&gt;
There are other contexts in which we can see the idea of epistemic possibility at work in the law. We are all familiar with the idea of a “suspect”—that is, of a person whom the police think ''might'' have committed a certain crime, and whom they set to work investigating. There may be a number of suspects for a given crime but notice that the police don’t regard ''everyone'' as a suspect, nor do they consider everyone who had the opportunity and ability to commit it a suspect, unless there are only a few such people. In general, the police need some specific reason to suspect someone of a crime, and likewise, we need some specific reason to suspect a proposition of being true—that is, to classify it as “possible”.&lt;br /&gt;
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=Unfounded Propositions=&lt;br /&gt;
Epistemically possible propositions are to be contrasted with '''unfounded''' ones. A proposition is unfounded when there is no reason to believe it. This is the status of things that you make up out of thin air—for example, that there are monsters under your bed, that your roommate committed a murder five years ago, or that his second cousin once lived in Dallas. Some of these propositions are more far-fetched than others—there are no such things as monsters, and very few people commit murders, but many people live in Dallas. However, all these propositions have in common that you have ''no reason'' to think they are true, or even to consider them, and the proper course of action is to dismiss them out of hand. &lt;br /&gt;
&lt;br /&gt;
Because we have no reason to believe them, unfounded premises can offer ''no support whatsoever'' to any conclusions that we might infer from them. Thus, unfoundedness is the lowest epistemic status. &lt;br /&gt;
&lt;br /&gt;
In some cases, we not only have no reason to believe that a proposition is true, we actually have reason to believe that it is false. This happens when the proposition contradicts something that we know (or have reason to believe) to be true. For example, if you knew that your roommate only had one second cousin and that she spent her whole life in Wyoming, you would know that the proposition that she lives in Dallas was false—or, to put it more simply, you would know that she did not live in Dallas. (By the same token, if it were ''probable'' that she had spent her whole life in Wyoming, it would be probable that she didn’t live in Dallas.) In certain respects, propositions that are certainly or probably false can be thought of as having an even lower status than that of unfounded propositions. However, as far as their value as premises is concerned, an unfounded premise is no better than one that is certainly false: neither gives us any reason at all to believe any conclusion. &lt;br /&gt;
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=The Continuum=&lt;br /&gt;
[[File:Epistemic_status_explanations.png|thumb|right|700px]]&lt;br /&gt;
Thus, we can think of the continuum of epistemic statuses as running from unfounded to certain, with the “possible” and “probable” denoting ranges in between. Of course, among the propositions which are possible, some will be nearer to being probable than others, and, within the probable propositions, some will be nearer than others to being certain. To capture this, we often use the words “probable” and “certain” in a comparative (rather than absolute) sense and say that one proposition is “more probable” or “more certain” than another. This should not be taken to imply that either proposition is probable or certain. For example, when two propositions are merely possible, one may nevertheless be more probable than the other. A proposition is probable in the absolute (rather than comparative) sense when it is more probable that it is true than that it is false—or, as we put it earlier when the preponderance of the evidence favors it. And a proposition is certain (in the absolute rather than the comparative sense), when it is no longer epistemically possible that it is false (that is, when it has been established beyond a reasonable doubt). &lt;br /&gt;
&lt;br /&gt;
We often assert propositions tentatively, indicating that they are probable rather than certain, by qualifying them with the adverb “probably” (for example, “Bob was probably on the quad”), and we usually assert possibilities by saying that they “may” or “might be” the case (“Bob may have been on the quad”).&lt;br /&gt;
&lt;br /&gt;
Additionally, the fact that a conclusion can be inferred from false premises does not give us any reason to believe that the conclusion is also false. In fact, you can take any true proposition and make up arguments that infer it from false premises. Here’s an example: &lt;br /&gt;
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{{Map|https://app.reasonspace.com/arguments/af530bd519ab4020927aa2b1fb8217ea}}&lt;br /&gt;
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Since the premises are false this argument doesn’t give us any reason to believe that pigs are mammals, but it certainly doesn’t show that they’re ''not'' mammals!&lt;br /&gt;
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=Epistemic Status as Objective Relative to a Subject=&lt;br /&gt;
&lt;br /&gt;
To be known is to be known to ''someone'', and different people know different things. If you're assessing an argument to figure out whether it puts you in a position to tell that its conclusion is true, what matters about the premises is whether ''you'' know them. But if you're giving an argument to someone else to help them tell that the conclusion is true, it won't do you any good to use premises that you're certain of if the other person has no way to tell that they're true. An argument is a reason for ''someone'' to believe its conclusion, and how strong the argument is for that someone will depend on the epistemic status the premises have for that someone. Let's call the someone &amp;quot;the subject.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
The epistemic status of a proposition is relative to a subject, in the sense that the same proposition will have different statuses for different subjects. Consider the proposition &amp;quot;Lightning just struck the bell tower.&amp;quot; This would be ''certain'' for a subject who saw the lightning strike the tower, and ''unfounded'' for another subject who has no idea that a lightning storm is even taking place. And it might be ''possible'' for a third subject who saw lightning strike in the area, but doesn't know what building it hit. &lt;br /&gt;
&lt;br /&gt;
But even though the proposition has different epistemic statuses relative to these different subjects, its status is not ''subjective'' in the sense of being determined by the subject's feelings or opinions. &lt;br /&gt;
&lt;br /&gt;
We must take care, however, not to confuse a proposition’s epistemic status for an a subject with how firmly the subject believes it. By the firmness of a belief, I mean how steadfast the person is in holding it. We can think of this as how easy it would be to talk someone out of the belief. The stronger a proposition’s epistemic status is, the more steadfast it is reasonable to be in believing it. It would be unreasonable of someone to get talked out of something he knows to be true. (Indeed, if he was talked out of it, we would probably conclude that he didn’t really ''know'' it in the first place.) However, people can sometimes be quite firm in beliefs that have a very low epistemic status. One example would be a fervent racist who, despite all the evidence to the contrary, persists in the belief that the members of other races are inferior to members of his own. Another example would be a self-deceived husband who clings to the belief that his wife is faithful to him, despite strong evidence that she is having an affair. &lt;br /&gt;
&lt;br /&gt;
One way to formulate the distinction between firmness of belief and epistemic status is to say that the former is ''subjective'' and the latter ''objective''. Something is subjective if it is determined by someone’s feelings or opinions. It is objective if it is determined by the facts. Though different people know different things, whether a particular person knows something or not is not determined simply by whether he ''thinks'' or ''feels like'' he knows it, since many people think they know things that they don’t. Nor is something’s epistemic status for someone a matter of his feelings or opinions about it. The epistemic status of a proposition for a given person is determined by facts about such things as the observations he has made and the arguments he has.  &lt;br /&gt;
&lt;br /&gt;
When evaluating arguments for certain purposes, is important to consider the (subjective) firmness of an audience’s beliefs. The more firmly the audience believes the premises of an argument, the more persuasive it will find the argument. So, if we were interested in arguments primarily for the purposes of persuading other people, we would have to evaluate the premises with an eye to how firmly the audience believes them. This is how we might proceed in a rhetoric class or if we were considering whether to use an argument in an advertisement or a political campaign. However, this is not why we are interested in arguments in this class. We are interested in arguments because inference is a crucial ''means of knowledge''. From this point of view, what makes an argument good is not that it persuades anyone of anything, but that it puts the audience in a position to know that the conclusion is true (or else brings the audience close to such a position). Therefore, what is relevant to us when assessing premises is not how strongly the audience believes them, but what their epistemic status is for the audience. &lt;br /&gt;
&lt;br /&gt;
And the audience we are primarily interested in is ourselves. After all, we are studying arguments because we want to assess the arguments on which our own beliefs are based and to reach new knowledge. Therefore, when assessing the premises of the arguments we consider in this class, you should be focused on the epistemic status of these premises ''for you''. Do you know the premises to be true? Are you entirely ignorant as to whether they’re true? Or does your state with respect to them fall somewhere along the continuum between knowledge and ignorance? If so, where along that continuum? &lt;br /&gt;
&lt;br /&gt;
One thing to keep in mind when assessing propositions, is that you can't be sure of something if you don't understand it. If someone makes a claim using a lot of impressive technical terminology that you don't understand, then you're not in a position to know that the claim is true. You're not even in a position to think that its possibly or probably true, if you don't understand at all what the claim means. So in assessing it, you'd have to mark it as unfounded. In doing so, you're not necessarily saying that the person making the claim is mistaken or that he did something wrong. You're just saying that ''you'' are not in a position to treat the claim as knowledge or even as a hypothesis: given your state of knowledge, you're unable to use this proposition as a grounds to reach any further conclusions.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1294</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1294"/>
		<updated>2025-08-22T16:15:10Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Strength of Inferences */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1293</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1293"/>
		<updated>2025-08-22T16:14:21Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Strength of Inferences */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1292</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1292"/>
		<updated>2025-08-22T16:13:32Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1291</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1291"/>
		<updated>2025-08-22T16:12:59Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|1000px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1290</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1290"/>
		<updated>2025-08-22T16:12:22Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1289</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1289"/>
		<updated>2025-08-22T16:11:52Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|left|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1288</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1288"/>
		<updated>2025-08-22T16:11:31Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|left|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1287</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1287"/>
		<updated>2025-08-22T16:11:09Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|left|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1286</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1286"/>
		<updated>2025-08-22T16:10:57Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|left|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|left|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1285</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1285"/>
		<updated>2025-08-22T16:10:34Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Why Some Arguments are Stronger than Others */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|left|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1284</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1284"/>
		<updated>2025-08-22T16:08:18Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Arguments as Ways of Knowing */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—a term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard me say in class that the reading was assigned. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3, labeled A and B. Each argument has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3. Argument A's premises only put you in a position to know Proposition 3, when ''when they're combined''.&lt;br /&gt;
&lt;br /&gt;
The same goes for Argument B. Neither Proposition 4 nor Proposition 5 considered''on its own'', would put you in a position to know Proposition 3, but ''combining'' Propositions 4 and 5 does put you in a position to know it. Notice, also that it's not just ''any'' combination of premises that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only two specific combinations of these four premises amount to ''ways of knowing'' that Proposition 3 is true. And each of these combinations is a distinct ''argument'' for the proposition.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was his discovery that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1283</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1283"/>
		<updated>2025-08-22T15:56:50Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Arguments as Ways of Knowing */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—A term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the ''premises'' of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard the reading mentioned in class. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3. Each has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3, but ''when they're combined'', Propositions 1 and 2 do put you in a position to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
Likewise, knowing that I said that this article was assigned, wouldn't let you know that it really was assigned unless you also knew that I have the power to assign articles. After all, a random person's saying that the article was assigned wouldn't ''make it assigned''. But (since I'm the professor of the class) ''my'' saying something's assigned actually assigns it. But just knowing that I have this power to assign things merely by saying they're assigned wouldn't put you in a position to know that this article was assigned, unless you also knew that I said this article was assigned. So neither Proposition 4 or 5 ''on its own'' puts you in a position to know Proposition 3, but ''in combination'' Propositions 4 and 5 do put you in a position to know this.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
So these two arguments (labeled A and B above) give us ''two ways'' of knowing Proposition 3. Each way involved combining premises. Notice, also that it's not just ''any'' combination of Propositions 1, 2, 4, and 5 that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only certain specific combinations do the trick.&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was discovering that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1282</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1282"/>
		<updated>2025-08-22T15:53:16Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* The Ubiquity of Argument and the Value of Logic */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—A term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the /premises/ of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard the reading mentioned in class. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3. Each has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3, but ''when they're combined'', Propositions 1 and 2 do put you in a position to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
Likewise, knowing that I said that this article was assigned, wouldn't let you know that it really was assigned unless you also knew that I have the power to assign articles. After all, a random person's saying that the article was assigned wouldn't ''make it assigned''. But (since I'm the professor of the class) ''my'' saying something's assigned actually assigns it. But just knowing that I have this power to assign things merely by saying they're assigned wouldn't put you in a position to know that this article was assigned, unless you also knew that I said this article was assigned. So neither Proposition 4 or 5 ''on its own'' puts you in a position to know Proposition 3, but ''in combination'' Propositions 4 and 5 do put you in a position to know this.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
So these two arguments (labeled A and B above) give us ''two ways'' of knowing Proposition 3. Each way involved combining premises. Notice, also that it's not just ''any'' combination of Propositions 1, 2, 4, and 5 that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only certain specific combinations do the trick.&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was discovering that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. When people express arguments, they often leave premises unstated. We can call these &amp;quot;implicit premises.&amp;quot; I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The square brackets around Proposition 3, indicate that it's an implicit premise. &lt;br /&gt;
&lt;br /&gt;
Why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1281</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1281"/>
		<updated>2025-08-22T15:47:13Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* The Ubiquity of Argument and the Value of Logic */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—A term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the /premises/ of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard the reading mentioned in class. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3. Each has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3, but ''when they're combined'', Propositions 1 and 2 do put you in a position to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
Likewise, knowing that I said that this article was assigned, wouldn't let you know that it really was assigned unless you also knew that I have the power to assign articles. After all, a random person's saying that the article was assigned wouldn't ''make it assigned''. But (since I'm the professor of the class) ''my'' saying something's assigned actually assigns it. But just knowing that I have this power to assign things merely by saying they're assigned wouldn't put you in a position to know that this article was assigned, unless you also knew that I said this article was assigned. So neither Proposition 4 or 5 ''on its own'' puts you in a position to know Proposition 3, but ''in combination'' Propositions 4 and 5 do put you in a position to know this.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
So these two arguments (labeled A and B above) give us ''two ways'' of knowing Proposition 3. Each way involved combining premises. Notice, also that it's not just ''any'' combination of Propositions 1, 2, 4, and 5 that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only certain specific combinations do the trick.&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was discovering that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. People rarely say all of the premises of their arguments out loud. I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
And why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1280</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1280"/>
		<updated>2025-08-22T15:45:40Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Arguments as Ways of Knowing */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—A term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the /premises/ of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard the reading mentioned in class. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3. Each has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3, but ''when they're combined'', Propositions 1 and 2 do put you in a position to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
Likewise, knowing that I said that this article was assigned, wouldn't let you know that it really was assigned unless you also knew that I have the power to assign articles. After all, a random person's saying that the article was assigned wouldn't ''make it assigned''. But (since I'm the professor of the class) ''my'' saying something's assigned actually assigns it. But just knowing that I have this power to assign things merely by saying they're assigned wouldn't put you in a position to know that this article was assigned, unless you also knew that I said this article was assigned. So neither Proposition 4 or 5 ''on its own'' puts you in a position to know Proposition 3, but ''in combination'' Propositions 4 and 5 do put you in a position to know this.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
So these two arguments (labeled A and B above) give us ''two ways'' of knowing Proposition 3. Each way involved combining premises. Notice, also that it's not just ''any'' combination of Propositions 1, 2, 4, and 5 that would put you in a position to know Proposition 3. The combination of Propositions 1 and 4 wouldn't do it, and neither would the combination of Propositions 2 and 5. Only certain specific combinations do the trick.&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments. For example, one of Benjamin Franklin's claims to fame was discovering that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something—to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise, and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. And often people don't say all of the premises of their arguments out loud. I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
And why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1279</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1279"/>
		<updated>2025-08-22T15:34:10Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Arguments as Ways of Knowing */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—A term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the /premises/ of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard the reading mentioned in class. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3. Each has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing that the article is linked to in the calendar entry, wouldn't put you in a position to know that it was assigned reading, if you didn't also know that the items linked in the entries are assigned readings. And, of course, knowing that the items linked in the entries are assigned readings wouldn't put you in a position to know that this article was assigned, if you didn't also know that it was linked. So neither Proposition 1 nor Proposition 2 ''on its own'' puts you in a position to know Proposition 3, but ''when they're combined'', Propositions 1 and 2 do put you in a position to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
Likewise, &lt;br /&gt;
&lt;br /&gt;
 knowing that I said that this article was assigned, wouldn't let you know that it really was assigned unless you knew that I have the power to assign articles. After all, a random person's saying that the article was assigned wouldn't ''make it assigned''. But (since I'm the professor of the class) my ''saying'' something's assigned actually assigns it. Again, if you knew that anything I said was assigned is thereby assigned, it wouldn't put you in a position to know (3), that this article was assigned, unless you also knew that I said that this article was assigned. Notice also that it's not just ''any'' combination of Propositions 1, 2, 4, and 5 that puts one in a position to know Proposition 3. Combining Proposition 1 or 2 with 4 or 5 wouldn't do it. It's the specific ''combination'' of &lt;br /&gt;
&lt;br /&gt;
t's only the specific combinations of Propositions 1 and 2, and 4 and 5, that provide ways to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments—some of them very impressive. One of Benjamin Franklin's claims to fame was discovering that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something--to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise, and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. And often people don't say all of the premises of their arguments out loud. I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
And why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1278</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1278"/>
		<updated>2025-08-22T15:07:58Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Assessing objections in ReasonSpace */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that articulates a reason for rejecting another argument. It does this by objecting to one of the argument's premises or inferences. The objection as formulating as an argument a reason for giving the relevant premise or inference a low [[Assessing_Arguments_in_ReasonSpace|assessment]]. &lt;br /&gt;
&lt;br /&gt;
In [https://app.reasonspace.com ReasonSpace] an objection is represented by a red octagon with a red arrow pointing from it to the premise or inference that is being objected to. Each objection will have at least one premise, connected to it by black arrow (in the same way premises are connected to other arguments).&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded (or otherwise week) and therefore is of no (or little) value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
In these examples we argued that a premise is false. But a proposition doesn't have to be false to be unfounded or week. We just have to not be in a position to know that it's true. Here's a map that objects to a premise on these grounds.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/680b23346f374ef4a596cb11685ad142}}&lt;br /&gt;
&lt;br /&gt;
Objection B gives an ''argument'' that Proposition 2 is unknown. We could also have an objection that atterts this more directly, as in the map below:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/89c147f7f3ed4dd499c223c0945e5584}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]]. Here are two examples:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/c9ba87e0321f4bc8b94775604c4c85f8}}&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/b7ec631838ae4978af3aba15512105e8}}&lt;br /&gt;
&lt;br /&gt;
=Assessing objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
To assess an objection, you have to assess all of the objections premises and the objecting inference (represented by the red octagon). You assess the premises, as you would assess any other premise, by determining its [epistemic status]. You assess the objecting inference considering how damaging the objection would be to the premise or inference objected 'if all of the objection's premises were certain'.&lt;br /&gt;
&lt;br /&gt;
 &lt;br /&gt;
&lt;br /&gt;
considering how damaging the objection would be to the premise or inference objected to, ''if all of the objection's premises were certain''.&lt;br /&gt;
&lt;br /&gt;
Objections are assessed like other arguments. One assesses each of the objection's premises &lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1277</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1277"/>
		<updated>2025-08-22T15:07:21Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Assessing objections in ReasonSpace */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that articulates a reason for rejecting another argument. It does this by objecting to one of the argument's premises or inferences. The objection as formulating as an argument a reason for giving the relevant premise or inference a low [[Assessing_Arguments_in_ReasonSpace|assessment]]. &lt;br /&gt;
&lt;br /&gt;
In [https://app.reasonspace.com ReasonSpace] an objection is represented by a red octagon with a red arrow pointing from it to the premise or inference that is being objected to. Each objection will have at least one premise, connected to it by black arrow (in the same way premises are connected to other arguments).&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded (or otherwise week) and therefore is of no (or little) value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
In these examples we argued that a premise is false. But a proposition doesn't have to be false to be unfounded or week. We just have to not be in a position to know that it's true. Here's a map that objects to a premise on these grounds.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/680b23346f374ef4a596cb11685ad142}}&lt;br /&gt;
&lt;br /&gt;
Objection B gives an ''argument'' that Proposition 2 is unknown. We could also have an objection that atterts this more directly, as in the map below:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/89c147f7f3ed4dd499c223c0945e5584}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]]. Here are two examples:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/c9ba87e0321f4bc8b94775604c4c85f8}}&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/b7ec631838ae4978af3aba15512105e8}}&lt;br /&gt;
&lt;br /&gt;
=Assessing objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
To assess an objection, you have to assess all of the objections premises and the objecting inference (represented by the red octagon). You assess the premises, as you would assess any other premise, by determining its [epistemic status]. You assess the objecting inference considering how damaging the objection would be to the premise or inference objected 'if all of the objection's premises were certain'.&lt;br /&gt;
&lt;br /&gt;
 &lt;br /&gt;
&lt;br /&gt;
considering how damaging the objection would be to the premise or inference objected to, _if all of the objection's premises were certain_.&lt;br /&gt;
&lt;br /&gt;
Objections are assessed like other arguments. One assesses each of the objection's premises &lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1276</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1276"/>
		<updated>2025-08-22T15:06:50Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that articulates a reason for rejecting another argument. It does this by objecting to one of the argument's premises or inferences. The objection as formulating as an argument a reason for giving the relevant premise or inference a low [[Assessing_Arguments_in_ReasonSpace|assessment]]. &lt;br /&gt;
&lt;br /&gt;
In [https://app.reasonspace.com ReasonSpace] an objection is represented by a red octagon with a red arrow pointing from it to the premise or inference that is being objected to. Each objection will have at least one premise, connected to it by black arrow (in the same way premises are connected to other arguments).&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded (or otherwise week) and therefore is of no (or little) value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
In these examples we argued that a premise is false. But a proposition doesn't have to be false to be unfounded or week. We just have to not be in a position to know that it's true. Here's a map that objects to a premise on these grounds.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/680b23346f374ef4a596cb11685ad142}}&lt;br /&gt;
&lt;br /&gt;
Objection B gives an ''argument'' that Proposition 2 is unknown. We could also have an objection that atterts this more directly, as in the map below:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/89c147f7f3ed4dd499c223c0945e5584}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]]. Here are two examples:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/c9ba87e0321f4bc8b94775604c4c85f8}}&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/b7ec631838ae4978af3aba15512105e8}}&lt;br /&gt;
&lt;br /&gt;
=Assessing objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
To assess an objection, you have to assess all of the objections premises and the objecting inference (represented by the red octagon). You assess the premises, as you would assess any other premise, by determining its [epistemic status]. You assess the objecting inference considering how damaging the objection would be to the premise or inference objected 'if all of the objection's premises were certain'.&lt;br /&gt;
&lt;br /&gt;
 &lt;br /&gt;
&lt;br /&gt;
considering how damaging the objection would be to the premise or inference objected to, 'if all of the objection's premises were certain'. &lt;br /&gt;
&lt;br /&gt;
Objections are assessed like other arguments. One assesses each of the objection's premises &lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1275</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1275"/>
		<updated>2025-08-22T14:18:47Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that articulates a reason for rejecting another argument. Specifically it gives a reason for rejecting a premise or inference of the earlier argument. &lt;br /&gt;
&lt;br /&gt;
In ReasonSpace an objections is represented by a red octagon with a red arrow pointing to the premise or inference that is being objected to. Each objection will have at least one premise, connected to it in the same way that orem more or&lt;br /&gt;
&lt;br /&gt;
 is a weakness in another argument. An objection can be aimed at a premise or an inference. In [https://app.reasonspace.com ReasonSpace] objections are represented by red octagons.&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded and therefore is of no value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
In these examples we argued that a premise is false. But a proposition doesn't have to be false to be unfounded or week. We just have to not be in a position to know that it's true. Here's a map that objects to a premise on these grounds.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/680b23346f374ef4a596cb11685ad142}}&lt;br /&gt;
&lt;br /&gt;
Objection B gives an ''argument'' that Proposition 2 is unknown. We could also have an objection that atterts this more directly, as in the map below:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/89c147f7f3ed4dd499c223c0945e5584}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]]. Here are two examples:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/c9ba87e0321f4bc8b94775604c4c85f8}}&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/b7ec631838ae4978af3aba15512105e8}}&lt;br /&gt;
&lt;br /&gt;
=Assessing arguments with objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1274</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1274"/>
		<updated>2025-08-16T23:07:01Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Objections to inferences */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that there is a weakness in another argument. An objection can be aimed at a premise or an inference. In [https://app.reasonspace.com ReasonSpace] objections are represented by red octagons.&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded and therefore is of no value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
In these examples we argued that a premise is false. But a proposition doesn't have to be false to be unfounded or week. We just have to not be in a position to know that it's true. Here's a map that objects to a premise on these grounds.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/680b23346f374ef4a596cb11685ad142}}&lt;br /&gt;
&lt;br /&gt;
Objection B gives an ''argument'' that Proposition 2 is unknown. We could also have an objection that atterts this more directly, as in the map below:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/89c147f7f3ed4dd499c223c0945e5584}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]]. Here are two examples:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/c9ba87e0321f4bc8b94775604c4c85f8}}&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/arguments/b7ec631838ae4978af3aba15512105e8}}&lt;br /&gt;
&lt;br /&gt;
=Assessing arguments with objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1273</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1273"/>
		<updated>2025-08-16T22:52:36Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Objections to premises */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that there is a weakness in another argument. An objection can be aimed at a premise or an inference. In [https://app.reasonspace.com ReasonSpace] objections are represented by red octagons.&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded and therefore is of no value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
In these examples we argued that a premise is false. But a proposition doesn't have to be false to be unfounded or week. We just have to not be in a position to know that it's true. Here's a map that objects to a premise on these grounds.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/680b23346f374ef4a596cb11685ad142}}&lt;br /&gt;
&lt;br /&gt;
Objection B gives an ''argument'' that Proposition 2 is unknown. We could also have an objection that atterts this more directly, as in the map below:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/89c147f7f3ed4dd499c223c0945e5584}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=Assessing arguments with objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1272</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1272"/>
		<updated>2025-08-16T22:45:07Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Objections to premises */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that there is a weakness in another argument. An objection can be aimed at a premise or an inference. In [https://app.reasonspace.com ReasonSpace] objections are represented by red octagons.&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded and therefore is of no value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map of an argument with an objection that one of the premises is false.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
Of course, Proposition 4 is just the opposite of Proposition 1, so someone who believed this argument is likely to just reject Proposition 4 and be unmoved by this objection. So a more convicting form of the objection might give more of an argument against Proposition 4, rather than just asserting the opposite. Here's an example.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/48105ef66a014df3a101a05128f54b46}}&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=Assessing arguments with objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1271</id>
		<title>Objections</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Objections&amp;diff=1271"/>
		<updated>2025-08-16T22:39:28Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;An objection is an argument that there is a weakness in another argument. An objection can be aimed at a premise or an inference. In [https://app.reasonspace.com ReasonSpace] objections are represented by red octagons.&lt;br /&gt;
&lt;br /&gt;
=Objections to premises=&lt;br /&gt;
&lt;br /&gt;
An objection to a premise is an argument that the premise is unfounded and therefore is of no value in establishing any further conclusion. The objection can show this either by showing that the premise is false, or else by showing that we are in no position to know (or have any reason to believe) that it is true.&lt;br /&gt;
&lt;br /&gt;
Here is an example of a map with an objection to a premise on the grounds that it is untrue:&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/900d5cf08c3e428b8c3f8078089712c6}}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=Objections to inferences=&lt;br /&gt;
&lt;br /&gt;
An objection to an inference is an argument that the inference is a non-sequitur, or (failing that) that it is not very strong. This means that it aims to show that even if one knew the premises of the inference to be true, the premises wouldn't give one a reason to think that the conclusion is true.  Often such objections work by identifying the inference as a known [[Fallacies| fallacy]].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
=Assessing arguments with objections in ReasonSpace=&lt;br /&gt;
&lt;br /&gt;
Objections in ReasonSpace are represented as arguments with one or more propositions leading into the red hexagon, which represents the objecting inference. To assess an objection, first assess each of its premises as you would assess any other proposition. Then assess the objecting inference. To assess this inference, assume (for the sake of argument) that all of its premises are true, and then consider how damaging this would be to the proposition or inference being objected to. If the objection's premises being true would thoroughly undermine the item being objected to (showing that the premise us unfounded or the inference a non sequitur), then assess the objecting inference in the right-most region of the scale. If the premises' being true wouldn't at all undermine the item being objected to, then assess the objecting inference in the leftmost region of the scale (as a non sequitur). If the premises' being true would be damaging, but not fatal to the item being objected to, then assess the objecting inference somewhere in the middle two regions of the scale (depending on just how damaging you think it is).&lt;br /&gt;
&lt;br /&gt;
Assessing an objection will add a limit to how highly you can assess the item objected to. This limit will appear as a red shaded area at the right of the assessment scale of the relevant item.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1270</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1270"/>
		<updated>2025-08-16T21:29:49Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Epistemic status]]&lt;br /&gt;
* [[Objections]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
** [[Aristotelian Syllogisms]]&lt;br /&gt;
** [[Deductions Involving Complex Propositions]]&lt;br /&gt;
* [[Assessing Arguments in ReasonSpace]]&lt;br /&gt;
* [[Inference to the Best Explanation]]&lt;br /&gt;
* [[Fallacies]]&lt;br /&gt;
* [[How to map arguments from a text]]&lt;br /&gt;
* [[How to build an argument map in ReasonSpace]]&lt;br /&gt;
* [[Map Library]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Single_Culprit_Fallacy&amp;diff=1269</id>
		<title>Single Culprit Fallacy</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Single_Culprit_Fallacy&amp;diff=1269"/>
		<updated>2025-08-10T22:16:16Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Consider the following argument.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/755f10640666473c9cc7830bba28708a}}&lt;br /&gt;
&lt;br /&gt;
Proposition 1 is clearly true. Proposition 2 is also true. There are in fact tens of thousands of murders in the US on an average year. Moreover, the premises are related to one another such that we could deduce ''some'' conclusion from them, but the Inference A is clearly a [[non sequitur]]: the premises give us ''no reason'' to believe Proposition 3.&lt;br /&gt;
&lt;br /&gt;
From the premises we can conclude that there was at least one murderer in the USA last year. But we can't deduce that there was any ''single murderer'' that committed ''all the murders.'' The premises don't give us any information about how many of the murders were committed by the same person. For all they say, every murder might have been committed by a different murderer. And, going by our background knowledge of criminology, this is a lot more likely than that there was some single serial killer responsible for all the murders. More likely than either of these alternatives is that there were many murderers, and that some of them committed multiple murders. Any judgment we make about how many murderers there probably were is going to depend on such background knowledge, nothing in the premises suggests one way or another, and the premises certainly don't give us any reason to think that the murders were all committed by any one person. &lt;br /&gt;
&lt;br /&gt;
This argument commits what we can call the ''single culprit fallacy''. Let's describe it more generally. One premise tells us that a phenomenon of a certain sort (e.g. murder) cannot exist without a being of a certain sort (e.g. a murderer) to cause it. The second premise tells us that phenomena of that sort do exist. Then the conclusion says that there is a being of the relevant sort that causes ''all'' of the relevant phenomena.&lt;br /&gt;
&lt;br /&gt;
{{Map|https://app.reasonspace.com/submaps/0ae85bfffc494680afab416d645fd08f}}&lt;br /&gt;
&lt;br /&gt;
We could conclude from the premises that ''at least one'' being of the relevant sort exists, but not that there's a ''single'' such being causing ''all'' of the relevant phenomena. That's a [[non sequitur]]. To reach any conclusion about how many such beings there are, and about which of the phenomena are caused by the same being (and which by other beings of the same type) we'd need more information than is included in these premises.&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1268</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1268"/>
		<updated>2025-08-10T22:04:44Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* Strength of Inferences */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—A term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the /premises/ of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard the reading mentioned in class. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3. Each has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing (1), that the article is linked to in the calendar entry, wouldn't put you in a position to know (3), that it was assigned reading, if you didn't also know (2), that the items linked in the entries are assigned readings. And, of course, knowing (2), that the items linked in the entries are assigned readings, wouldn't put you in a position to know (3), that this article was assigned, if you didn't also know (2), that it was linked. Likewise, knowing (4), that I said that this article was assigned, wouldn't let you know that it really was assigned unless you knew (5), that I have the power to assign articles. After all, a random person's saying that the article was assigned wouldn't ''make it assigned''. But (since I'm the professor of the class) my ''saying'' something's assigned actually assigns it. Again, if you knew (5), that anything I said was assigned is thereby assigned, it wouldn't put you in a position to know (3), that this article was assigned, unless you also knew (4), that I said that this article was assigned. Notice also that it's not just ''any'' combination of Propositions 1, 2, 4, and 5 that puts one in a position to know Proposition 3. Combining Proposition 1 or 2 with 4 or 5 wouldn't do it. It's only the specific combinations of 1 and 2, and 4 and 5, that provide ways to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments—some of them very impressive. One of Benjamin Franklin's claims to fame was discovering that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something--to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise, and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. And often people don't say all of the premises of their arguments out loud. I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
And why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole fatuous. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1267</id>
		<title>Arguments</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Arguments&amp;diff=1267"/>
		<updated>2025-08-10T21:59:15Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: /* The Ubiquity of Argument and the Value of Logic */&lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;The word &amp;quot;argument&amp;quot; is most often used to refer to a heated conversation in which people disagree. We speak about a couple having an argument, or about a Thanksgiving dinner that's ruined by relatives who won't stop arguing about politics. But there's another, related meaning of the word &amp;quot;argument,&amp;quot; which is the more prevalent meaning in fields like philosophy, law, and rhetoric. When people are having an argument, we can speak of the ''arguments'' that each of them is making. For example consider the following brief dialogue in which Angela and Ben are arguing about abortion:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
Angela: How can you be opposed to laws banning abortion?!&lt;br /&gt;
&lt;br /&gt;
Ben: Easy, I respect the right to bodily autonomy! Laws against abortion severely limit pregnant women's bodily autonomy. &lt;br /&gt;
&lt;br /&gt;
Angela: But, abortion is ''murder'', and murder should always be illegal.&lt;br /&gt;
&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
In this brief exchange, Ben and Angela each give the other a reason for accepting a different answer to the question &amp;quot;Should abortion be illegal?&amp;quot; Each of these reasons is an ''argument'' in the sense of that word in which it is used in philosophy (and allied fields). Put roughly: an argument is a reason for believing something, and it is made up of other beliefs. We can represent Ben and Angela's arguments graphically in what is called an ''argument map'':&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 1: Ben and Angela's Arguments Concerning Anti-Abortion Laws'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/c0211ac351954f419f23e51661d3dbd4}}&lt;br /&gt;
|-&lt;br /&gt;
|Ben's argument is labeled &amp;quot;B&amp;quot;, and Angela's is labeled &amp;quot;A&amp;quot;.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This article is about arguments (in this sense of the word). We'll discuss what arguments are, their role in thinking, how argument maps can be used to illustrate their structure, and how we can assess arguments to determine how strong they are.&lt;br /&gt;
&lt;br /&gt;
=Arguments as Ways of Knowing=&lt;br /&gt;
&lt;br /&gt;
We most often speak about arguments in the contexts of disagreements (as in Ben and Angela's disagreement about abortion) or when people are trying to persuade one another. But arguments are made even in conversations where people do not disagree, and we form arguments in our own minds, even when there is no one around to convince of anything. Consider, for example, how you know that the article you're reading now is an assigned reading for Lecture 3 of the Introduction to Philosophy class you're taking. Most likely, you know it by means of the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 2: How you know that this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/954799ffc18046bba07a32106da18533}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This argument isn't about convincing anyone of anything. It is simply ''how you know'' something in the first place. You know that this article is assigned for Lecture 3 ''by knowing'' two other things: that this article is linked in the calendar entry for the lecture and that everything linked in a calendar entry for a lecture is a required reading for the lecture. When you ''combine'' your knowledge of these two facts, they lead to the further knowledge that this article is assigned for the lecture.&lt;br /&gt;
&lt;br /&gt;
On the map, each fact is depicted in a rectangle and labeled with a number. I'll refer to the contents of such boxes as propositions—A term I'll explain below. For now we can say that you in Argument A, you come to know Proposition 3 by combining your knowledge of Propositions 1 and 2. We call Propositions 1 and 2 the /premises/ of Argument A. &lt;br /&gt;
&lt;br /&gt;
Some of you might have come to know that this reading was assigned without knowing these premises—without having looked at or thought about the calendar at all. You may have simply heard the reading mentioned in class. If so, you wouldn't know Proposition 3 by Argument A, but rather by Argument B, which is pictured alongside it the map below:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 3: Two ways in which you can know this article is assigned for Lecture 3'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/arguments/760afa1e180d4baa8a0b5a760189ea66}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Here we see two separate arguments for Proposition 3. Each has two premises, which combine to give you a ''way of knowing'' the same fact. Notice, that in each argument the two premises ''work together'' to enable you to know the Proposition 3. Knowing (1), that the article is linked to in the calendar entry, wouldn't put you in a position to know (3), that it was assigned reading, if you didn't also know (2), that the items linked in the entries are assigned readings. And, of course, knowing (2), that the items linked in the entries are assigned readings, wouldn't put you in a position to know (3), that this article was assigned, if you didn't also know (2), that it was linked. Likewise, knowing (4), that I said that this article was assigned, wouldn't let you know that it really was assigned unless you knew (5), that I have the power to assign articles. After all, a random person's saying that the article was assigned wouldn't ''make it assigned''. But (since I'm the professor of the class) my ''saying'' something's assigned actually assigns it. Again, if you knew (5), that anything I said was assigned is thereby assigned, it wouldn't put you in a position to know (3), that this article was assigned, unless you also knew (4), that I said that this article was assigned. Notice also that it's not just ''any'' combination of Propositions 1, 2, 4, and 5 that puts one in a position to know Proposition 3. Combining Proposition 1 or 2 with 4 or 5 wouldn't do it. It's only the specific combinations of 1 and 2, and 4 and 5, that provide ways to know Proposition 3.&lt;br /&gt;
&lt;br /&gt;
In the grand scheme of things, Proposition 3 is not a particularly important piece of knowledge, and Arguments A and B aren't very impressive pieces of reasoning. But many life-saving truths were first reached by arguments—some of them very impressive. One of Benjamin Franklin's claims to fame was discovering that affixing a lightning rod to the roof of a building would prevent the building from being damaged by lightning. Here's a map of how he knew it:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 4: How Benjamin Franklin Knew His Lightning Rod Would Work'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/arguments/c8675d75d9904f56ac7528ad25cbffc4}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The last few arguments we've discussed are ways in which someone ''knows'' something. Of course, if you knew something by means of one of these arguments, you might tell the argument to others in order to convince them of what you know. This may be what Ben and Angela are ''trying'' to do in our earlier example, in which they're arguing with one another about laws prohibiting abortion. He tells her how he thinks he knows that there should not be such laws, and she responds by telling him how she thinks that she knows that there should be. Of course, they cannot both be right, so at least one of them must not really know and the relevant argument must not really be a ''way of knowing''. There must be something wrong with at least one of their arguments. For example, one of their premises might be false. But even if one of the arguments is faulty, it is still an ''attempt at knowing''. The point of the argument is to help us ''tell'' whether laws prohibiting abortion are wrong or right.&lt;br /&gt;
&lt;br /&gt;
Later in this article we'll discuss how to evaluate arguments, but the first point to bear in mind when evaluating them is that they are attempts to help you to ''know'' something--to put you in a position ''to tell that it is true.'' Some arguments take us all the way there, but arguments that don't might still prove useful (by bringing us closer to knowledge than we'd otherwise be).&lt;br /&gt;
&lt;br /&gt;
=The Ubiquity of Argument and the Value of Logic=&lt;br /&gt;
&lt;br /&gt;
You argue throughout the day every day, and you've been doing it since you were a small child. It's one of the things you learned to do as you learned to speak. Here are some examples from my young son. When he was two years old and I told him that it was his Grandfather's birthday, and said &amp;quot;Probably Grandpa will eat cake and walk around the sun.&amp;quot; Presumably he thinks that ''everyone'' does these things on his birthday, because he's observed that this is what happens on birthdays in his Montessori classroom. His reasoning can be represented as follows: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 5: My Two-Year-Old Son's Argument about his Grandfather's Birthday'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/63d6fb7560fa4971ab0f1dc72010f77c}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
The following year in school he started grinding coffee beans as a classroom exercise, and bringing the grounds home in a little baggie. One morning he told me that he'd bring some coffee grounds home for his mother, because she likes coffee. I asked if I liked coffee too and he replied: &amp;quot;Well, I've never seen you drink coffee, so I think that you don't like it.&amp;quot; We might think of him as making the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 6: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 1)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/237ec69f9d9643888062964255beb79b}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
But I don't think this map quite captures how he was thinking, because he doesn't normally assume just from the fact that he hasn't seen someone do something that the person doesn't like doing it. And often people don't say all of the premises of their arguments out loud. I think this is the argument he was actually using:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 7: My Three-Year-Old Son's Argument that I Don't Like Coffee (version 2)'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/c4aaea9e1cd144948b7bf98022910813}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
And why did he assume that he would have seen me drink coffee, if I liked it? I don't know, but there are some good reasons he might have had for thinking this, as illustrated in this map:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 8: Reconstruction of Reasons My Three-Year-Old Son has for Thinking that I Don't Like Coffee'''&lt;br /&gt;
|-&lt;br /&gt;
| {{Map|https://app.reasonspace.com/submaps/41572b4f89664ecf9a335af1ffa42e89}}&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
I've given these examples to illustrate how commonplace arguing is, even among very young children. It's something that we all learn to do in our first years of life, as part of learning how to speak and think. During this same period, we learn how to walk and how to grasp and manipulate objects. But we learn all of these things ''implicitly''—that is, without naming in words what we are doing and how we are doing it. You learned many words before you knew the word “word,” and you learned how to put words together into sentences before you had the word “sentence” or words for the parts of speech (much less for the rules of grammar). You also learned how to walk, without yet knowing the word &amp;quot;walk,&amp;quot; much less knowing words for the parts of your legs or for specific types of steps or for flexing and unflexing various muscles. You may have never thought much about ''how'' to walk, but if you’ve ever had physical therapy to recover from an injury or taken a movement class as part of learning how to dance or to act, you may have learned to analyze the act of walking into (named) component parts. Doing so gives you more control over the way you walk. When athletes train, they often learn to analyze movements they learned as a child into simpler movements, and this process gives them finer-grained control over their movements. It is likewise possible to gain greater control of your thinking by analyzing complex thought processes into the simpler components that make them up. The discipline that does this is called ''logic'', and one crucial part of it is the skill of analyzing arguments into their parts and assessing them, individually.&lt;br /&gt;
&lt;br /&gt;
=Anatomy of an Argument=&lt;br /&gt;
==Propositions==&lt;br /&gt;
&lt;br /&gt;
Before saying anything more about arguments, it will be helpful to say a bit about propositions, which are the smaller units of thought from which arguments are built. They're the things represented by the rectangles in our argument maps. A ''proposition'' is the sort of thought that is capable of being true or false, of being believed or disbelieved, and of being asserted or denied. Such thoughts are expressed by declarative sentences. Here are some examples:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''1.''' Healthy grass is green.&lt;br /&gt;
 &lt;br /&gt;
'''2.''' O. J. Simpson killed Nicole Brown.&lt;br /&gt;
&lt;br /&gt;
'''3.''' Twice two is four. &lt;br /&gt;
&lt;br /&gt;
'''4.''' Twice two is five. &lt;br /&gt;
&lt;br /&gt;
'''5.''' Many diseases are caused by bacteria. &lt;br /&gt;
&lt;br /&gt;
'''6.''' Stalin was evil. &lt;br /&gt;
&lt;br /&gt;
'''7.''' Joe Biden is the 46th President of the United States. &lt;br /&gt;
&lt;br /&gt;
'''8.''' Either Donald Trump or Kamala Harris will win the 2024 Presidential election.&lt;br /&gt;
&lt;br /&gt;
'''9.''' The Senate should have convicted Donald Trump in both of his impeachment trials.&lt;br /&gt;
&lt;br /&gt;
'''10.''' Hillary Clinton would have been an awful president.&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
The proposition is not the same thing as the sentence expressing it, because the same thought can be expressed by different sentences. For example, here are several different ways of expressing Proposition 3 from the list above:&lt;br /&gt;
&lt;br /&gt;
&amp;lt;blockquote&amp;gt;&lt;br /&gt;
'''3a.''' Twice two is four.&lt;br /&gt;
&lt;br /&gt;
'''3b.''' Two times two is four.&lt;br /&gt;
&lt;br /&gt;
'''3c.''' 2 x 2 = 4&lt;br /&gt;
&lt;br /&gt;
'''3d.''' Deux fois deux c'est quatre.&lt;br /&gt;
&lt;br /&gt;
'''3e.''' 兩次兩次是四次。&lt;br /&gt;
&amp;lt;/blockquote&amp;gt;&lt;br /&gt;
&lt;br /&gt;
Sentences 3a and 3b are two different ways of expressing the same proposition in English. 3c is a way of expressing it in mathematical notation, 3d is a way of expressing it in French, and 3e is a way of expressing it in Chinese. &lt;br /&gt;
&lt;br /&gt;
Another reason why a proposition is not the same thing as a sentence is that propositions can be expressing as parts of more complex sentences that include multiple propositions. For example, here’s a sentence expressing both Propositions 9 and 10 from the list above: &amp;quot;Even though Hillary Clinton would have been an awful president, the Senate should have convicted Donald Trump at both of his impeachment trials.&amp;quot;&lt;br /&gt;
&lt;br /&gt;
Some of the propositions from the list above are uncontroversially true and others are uncontroversially false. I expect that everyone in the class will agree that Propositions 1, 3, 5 and 7 are true and that Proposition 4 is false. We will probably disagree over some of the others—with some students thinking they’re true and others thinking they’re false. &lt;br /&gt;
&lt;br /&gt;
Some of you may think that some of the propositions we may disagree over aren’t ''really'' the sort of things that can be true or false at all. In particular, some of you may think this about Propositions 6, 9, and 10, because these propositions express evaluations. Some people think that evaluations aren’t the sorts of things that can be true or false. But even if you think this, you’ll have noticed that many people ''believe'' or ''disbelieve'' each of these propositions (and many other evaluations) as though they were true or false, and they make arguments to try to convince other people that these propositions are true or false. So, to understand their role in arguments you’ll have to treat them as the sort of thing that can be true or false.&lt;br /&gt;
&lt;br /&gt;
==Definition of Argument and the Conventions of Argument Mapping==&lt;br /&gt;
&lt;br /&gt;
As the term is used in philosophy, an '''argument''' is a set of related propositions (called '''premises''') that is given as a reason for believing a further proposition (called the '''conclusion'''). Consider, for example, the following simple argument:&lt;br /&gt;
 Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.&lt;br /&gt;
&lt;br /&gt;
Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.  &lt;br /&gt;
&lt;br /&gt;
There are a few ways in which we can represent an argument that makes its structure clearer. One popular way is called ''standard form''. Here’s what the argument we have been discussing looks like in standard form:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''1.''' Whoever murdered Carl had access to his rose garden at midnight.&lt;br /&gt;
'''2.''' Only Natalie had access to Carl’s rose garden at midnight.&lt;br /&gt;
|-&lt;br /&gt;
| '''3.''' Natalie murdered Carl.&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the '''inference'''—the mental act of moving in thought from the premises to the conclusion. &lt;br /&gt;
&lt;br /&gt;
In this class we'll occasionally see arguments laid out in standard form, but we'll mostly use argument maps (as we did earlier in this article). Here’s a map of the same argument with annotations, indicating what each element in the map means. &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|[[file:Map_9_Annotated.png|thumb|center|700px|]]&lt;br /&gt;
|-&lt;br /&gt;
|[https://app.reasonspace.com/submaps/d784fd01d2ef446abe5ef5be1d22783b View this map on ReasonSpace]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter (we call this the *inference symbol*). Thin lines connect the inference symbol's round bottom to the boxes containing the premises, and a thicker line with an arrow at the end connects the symbol's top to the box containing the conclusion.&amp;lt;ref&amp;gt;All the maps in this article, are made with [http://app.reasonspace.com ReasonSpace]. There are a few competing conventions for argument mapping, so you may sometimes find maps drawn or labeled a bit differently elsewhere.&amp;lt;/ref&amp;gt; &lt;br /&gt;
&lt;br /&gt;
The standard form is more compact, but argument mapping enables us to visualize the relationships between multiple arguments. &lt;br /&gt;
&lt;br /&gt;
Both ways of representing the argument highlight make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. &lt;br /&gt;
&lt;br /&gt;
Notice that it is only when we take them ''together'' that Propositions 1 and 2 give us a reason to believe Proposition 3. If you knew that only Natalie had access to Carl's rose garden at midnight, then learning that whoever killed Carl must have had access to the rose garden would put you in a position to tell that Natalie was the murderer. But if you didn't know anything about who had access to the rose garden, then learning that whoever committed the murderer had access, wouldn't give you any reason to suspect Natalie. Likewise, if you already knew that the killer had to have access to the rose garden, then learning that Natalie was the only one with access would put you in a position to know that she did it. But if you didn't know anything linking the rose garden to the murder, then learning that Natalie was the only one with access to it wouldn't give you any reason to suspect her of the crime. Only when the premises are put together do they link Natalie to the crime, that's what makes these ''two'' premises into a ''single'' argument. &lt;br /&gt;
&lt;br /&gt;
The map represents this relationship by having the lines from the two premises go to a single inference symbol (labeled A) from which a single arrow points to the conclusion.&lt;br /&gt;
&lt;br /&gt;
==Relations Between Arguments in Complex Maps==&lt;br /&gt;
&lt;br /&gt;
With this terminology under our belts, we can look at and discuss more complex maps that show relations between arguments.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
One way in which arguments can be related is by sharing the same conclusion. Here’s an example:&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 10'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/05c4582aace9476883878b49e3fce664}}&lt;br /&gt;
|}&lt;br /&gt;
Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. We already discussed how Propositions 1 and 2 have to be put together before either provides a reason for ''suspecting'' that Natalie murdered Carl. But if you know that both of these propositions are true, you're in a position to ''know'' that Natalie is the murderer regardless of whether you know any of Propositions 4–6. Likewise, if you knew Propositions 4–6, they'd put you in a position to know that Natalie did it, even if you didn't know Proposition 1 or 2. But you would need to know ''all three'' Propositions 4, 5, and 6, for them to put you in a position to know that Natalie was guilty; no one or two of them would do it alone.&amp;lt;ref&amp;gt;Propositions 4 and 6 taken together without Proposition 5 wouldn't even give you a reason to suspect Natalie. Knowing Propositions 4 and 5, without knowing 6, would give you a strong reason to suspect Natalie (since it would mean that she's one of only two people who could have done it), but adding Proposition 6 upgrades the argument from one that would make Natalie a suspect to one that proves that she's the murderer.&amp;lt;/ref&amp;gt;&lt;br /&gt;
&lt;br /&gt;
A second way arguments can be related is that a premise of one argument can be the conclusion of another, forming a chain. Here’s an example of that: &lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 11'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/95c077a9e8454fdfad9181e21a21ecd5}}&lt;br /&gt;
|}&lt;br /&gt;
Notice that Argument A (from Map 9) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C, and one of C's premises is a conclusion of a further argument, labeled D. So, we can think of D, C, and A as a chain of arguments, with Proposition 3 as their ultimate conclusion. (Or, to put it another way, we can think of D, C, and A as making up a three-step argument for Proposition 3. And, we can think of Propositions 2 and 8 as intermediate conclusions of this larger argument.)&lt;br /&gt;
&lt;br /&gt;
=Why Some Arguments are Stronger than Others=&lt;br /&gt;
&lt;br /&gt;
Mapping an argument is a way of analyzing it—breaking it up into its parts and showing how those parts fit together into a whole. The point of analyzing an argument is that it makes it easier for us to then ''assess'' the argument. When we assess an argument, we are asking how strongly it supports the conclusion—how good a reason it gives us to think that the conclusion is true. The strongest arguments are ''ways of knowing'' their conclusions—or, in other words, they give us a way to ''tell that the their conclusions are true''.&lt;br /&gt;
&lt;br /&gt;
If an argument supports its conclusion strongly enough to establish it as knowledge, the argument is called '''conclusive''' and is said to be a '''proof''' or to '''prove''' the conclusion. &amp;lt;Ref&amp;gt;People often call arguments that they come up with proofs if they think the arguments prove their conclusions, and sometimes these names catch on, but that doesn’t mean that the arguments ''really'' prove the conclusions. We have to assess them for ourselves to see.&amp;lt;/Ref&amp;gt; These arguments are especially valuable. On the opposite extreme would be an argument that gives us no reason to believe the conclusion and so leaves us no closer to knowing it than we were before. There is no special name for such arguments, but let’s call them '''fatuous''' (meaning silly and pointless) because they don’t accomplish ''any'' of what an argument should do.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Argument.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Many arguments fall in between these two extremes. That’s because knowledge isn’t an all-or-nothing affair. There is a whole spectrum between really knowing a proposition and being entirely ignorant of it. &lt;br /&gt;
&lt;br /&gt;
[[file:Knowledge_vs_Ignorance.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
Consider the proposition “Natalie murdered Carl,” which was the conclusion of many of the arguments in the maps we looked at earlier. Suppose that this proposition is true and that you’re a detective investigating Carl’s murder. When you begin the case, you may have no idea who killed Carl, and no reason to suspect Natalie; indeed, you might not even know who Natalie is. So, the proposition would be at the extreme left end of the scale pictured above. But as the investigation proceeds and you learn more about Carl’s life and death, at some point you encounter some evidence pointing to Natalie and you formulate the theory that she did it. At first, it might not be much evidence. We certainly wouldn’t say that you ''know'' she killed him or even that you ''believe'' it (or have reason to believe it), she may not even be your prime suspect, but she is now ''a'' suspect, so we wouldn’t say that you’re totally ignorant of her having murdered him. The proposition is now somewhere on the scale to the right of ignorance but to the left of the half-way mark.&lt;br /&gt;
&lt;br /&gt;
Eventually, as you accumulate more evidence, she becomes the lead suspect. Now if you had to bet, you’d say that she did it, and you’d have good reasons to support your bet. We might say you believed she did it, but that you don’t ''know'' it yet. Eventually, you accumulate enough evidence to be certain that she did it. Now the proposition has progressed to the right-most region on the scale—you know it. &lt;br /&gt;
&lt;br /&gt;
We can call a proposition's position along this continuum in the mind of a given person, the proposition's '''[[epistemic status]]''' for that person, and give names to the regions along the continuum. We call a proposition '''[[certain]]''' when we think that we ''know'' it to be true. On the other extreme, we can call a proposition '''[[unfounded]]''' if we have no reason to think it's true. We call a proposition '''[[possible]]''' (in one sense of that word) when we have reason to suspect that it might be true. And we call a proposition '''[[probable]]''' when the evidence makes it more likely to be true than not.&lt;br /&gt;
&lt;br /&gt;
[[file:epistemic_status.png|thumb|center|500px]]&lt;br /&gt;
&lt;br /&gt;
So in the example above, before the investigation starts you have no evidence to even suggest that Natalie may have murdered Carl. The proposition wouldn't even occur to you, but if for some reason it did, the proposition would be unfounded for you. Later when you find evidence that makes her a suspect, the proposition becomes possible, and as the evidence mounts it becomes probable and ultimately certain.&lt;br /&gt;
&lt;br /&gt;
The evidence that you accumulate could be spelled out in the form of arguments, and it is these arguments that advance us along the continuum from ignorance to knowledge (or from an unfounded proposition to a certain one). An argument that’s strong enough to &lt;br /&gt;
make its conclusion ''certain'' is a conclusive argument or proof. An argument that doesn’t give us ''any'' of the way towards certainty is worthless. But many arguments take us part of the way—they give us ''some'' reason to ''believe'' the conclusion without giving us conclusive reason. We can speak of an argument as being stronger or weaker, depending on how close it is to being conclusive.&lt;br /&gt;
&lt;br /&gt;
Notice that in the scale for epistemic status, knowledge and certainty are represented by a range and not by a point. This is because, even among the things we know, we sometimes think of ourselves as being ''more certain'' of some things than we are of others. We sometimes think this even when we're not ''uncertain'' of the less certain things; and we might think of ourselves as knowing the more certain things better than we know the less certain ones. For example, I expect that you know both that Joe Biden is the 46th President of the United States and that twice two equals four. (For my part, I'm certain of both things.) But you might regard yourself as ''more certain'' that twice two is four than you are that Biden is the 46th President, because you can imagine bizarre scenarios in which you're the victim of some elaborate hoax and Biden isn't ''really'' the President, but it's hard to imagine any scenario under which you could be mistaken that twice two is four. Some people think that there is almost nothing that they really ''know'' or can be ''certain'' of because they cannot completely rule out such hoaxes, and epistemologists think a lot about what to make of such [[skeptical scenarios]]. In ordinary reasoning however, we often take ourselves to ''know'' (or to be ''certain'' of) something without thinking that there is nothing better known (or more certain) than it. And this is what is allowed for by representing knowledge and certainty as a range rather than a point on our scales. Similarly, to say that an argument is conclusive is just to say that it’s strong ''enough'' to establish its conclusion as knowledge. It is not to say that there could not be some other argument that is even stronger. &lt;br /&gt;
&lt;br /&gt;
There are two factors that contribute to the strength of an argument: the strengths of its premises and the strength of its inference. So, to assess an argument we need to assess each premise and each inference. &lt;br /&gt;
&lt;br /&gt;
==Strength of premises==&lt;br /&gt;
&lt;br /&gt;
The strongest premises are ones that we can be certain of independently of knowing the conclusion. In order for an argument to be conclusive, all of its premises must be like this. On the other extreme, if any of an argument's premises is unfounded (or if we know the premise to be false), that makes the argument worthless. An argument with premises that are ''possible'' or ''probable'' cannot prove its conclusion, but it can still offer some support for it. For example, to return to the case of Carl's murder, if we were certain that whoever murdered Carl had access to his rose garden at midnight, and it was probable that Natalie was the only person who had this access, that would make it probable that Natalie was the murderer. &lt;br /&gt;
&lt;br /&gt;
This is illustrated in the assessment of our Familiar Argument A, below.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_1.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The scales placed in the box for Propositions 1 and 2 indicate the epistemic status of those propositions. The scale in the box for Proposition 1 has a mark in the rightmost region indicating that that proposition is certain. Proposition 2’s scale shows that the proposition is probable. And the scale for the Argument as a whole shows that it is strong enough to render the conclusion probable. &lt;br /&gt;
&lt;br /&gt;
Since the case of Natalie and Carl is fictitious, there’s no way for us to actually assess the premises. The epistemic statuses in the map above are made up (as is everything else in the example). To assess an actual premise one needs to consider how strong one's reasons to believe the premise are ''independent of one's belief in the conclusion''. This last qualification is important. It can take some reflection to recognize which of our beliefs are based on which others, so it's easy to regard as a premise something that we're only convinced of because we already believe the conclusion. This is called [[circular reasoning]].&lt;br /&gt;
&lt;br /&gt;
==Strength of Inferences==&lt;br /&gt;
&lt;br /&gt;
The strength of an argument depends not only on the strength of its premises, but also on the strength of its ''inference''. There are different [[types of inferences]] which we'll discuss over the semester, and learning about the types is a great aid in assessing specific inferences. Here I'll just make a few general remarks. &lt;br /&gt;
&lt;br /&gt;
In order for an argument to support its conclusion at all, the premises need to be related to one another and to the conclusion in such a manner that, the premises being true would make the conclusion likely to be true. In the very strongest inferences, the premises are related to one another and to the conclusion in such a manner that one would be caught in a contradiction if one held that the premises were true, but that the conclusion was false. This is the case with many of the inferences we've looked at in this article, including Inference A (in Map 9). Proposition 1 tells us a characteristic of Carl's murderer—namely that the murderer could access the rose garden at midnight. Proposition 2 tells us that only Natalie has this characteristic. If both propositions are true, then it ''has to be'' that Natalie is the murderer. There's no room for any alternative. Inference A is ''as strong as any inference could be''. Inferences like this are called '''[[deductions]]''' and are said to ''necessitate'' their conclusions. &lt;br /&gt;
&lt;br /&gt;
Deduction is the type of argument that has been most studied by logicians. All deductive arguments follow one of a number of ''forms'', which one can learn and train oneself to recognize. Since every deduction is as strong as an inference can be, no deduction can be stronger than any other. Thus, on a scale representing the strength of inferences, we must represent deduction, not as a range, but as a point on the far right.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
[[file:deduction.png|thumb|center|600px]]&lt;br /&gt;
&lt;br /&gt;
Let's add our assessment of Inference A as a deduction into our assessment of Inference A into our map of Argument A: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 9'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/smaps/0ad59e33b3434d96865df2350e2d4d7e}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_A_Assessment_2.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Notice that, though Inference A is a deduction, Argument A as a whole is still not conclusive. This is because Premise 2 is merely probable, rather than certain. The strength of the argument as a whole depends on the strength of ''all'' its elements, whereas the strength of the inference is independent of the strength of the premises. That’s illustrated by the following maps:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 12'''&lt;br /&gt;
|'''Map 13'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/1f4a6db8-37a3-4d02-b9b4-44749176a0b9}}&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/3c6b4d76-04ff-4219-8a2e-3e7b7c468e40}}&lt;br /&gt;
|-&lt;br /&gt;
|[[File:Argument_H_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|[[File:Argument_I_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
:&lt;br /&gt;
&lt;br /&gt;
Here we have two arguments (H and I) that are both fatuous for opposite reasons. In Argument H we have two awful premises—premises that no one has any reason to believe and that we all know to be false. But ''inference'' H is as strong as can be—it's a deduction. Propositions 17 and 18 are false, but ''if they were true'', then Proposition 19 would ''have to be'' true also. Nonetheless, the unfounded premises make the argument as a whole worthless. As it happens the conclusion, like the premises, is obviously false. Notice that if we changed Proposition 18 to say &amp;quot;All insects lay eggs&amp;quot; and Proposition 19 to say &amp;quot;All birds lay eggs,&amp;quot; the argument would then have a true conclusion and one true premise, in addition to having an inference that's as strong as can be. Nonetheless, it would still be fatuous, because Proposition 17 remains unfounded (indeed obviously false), and an argument can be no stronger than its weakest part.&lt;br /&gt;
&lt;br /&gt;
Both premises of Argument I are certain, but the argument is fatuous because Inference I is so bad. There's no relation at all between the premises and the conclusion, so even if we know the premises to be true, they can't give us any reason at all to even suspect that the conclusion might be true. You can’t infer anything about Carl and Natalie from premises about birds and insects. Inferences this bad are called '''[[non_sequitur|non sequiturs]]'''.&lt;br /&gt;
&lt;br /&gt;
An inference does not need to be a deduction to put one in a position to know its conclusion. Consider the following argument: &lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 14'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/fbdcd9761a1043f8aaaf94c6a70c88bb}}&lt;br /&gt;
|[[File:Argument_J_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
This is like Argument A from Map 9, except that we've replaced Proposition 1, which said that Carl's murderer had access to his rose garden, with a premise that allows for an extremely remote possibility of someone committing the murder without having had access. Because of this, unlike Inference A, Inference J is not a deduction. But it is still a very strong inference. To judge just how strong it is, we'd have to rely on some background knowledge of the situation. For example, if among Carl's associates were people who were at the cutting edge of crossbow marksmanship, we might regard it as a possibility that the murderer is someone other than Natalie—someone who has an unprecedented level of skill with the weapon. But, in most contexts, such speculation would be unfounded. In this case, Inference J is strong enough that being certain of its premises would put us in a position to be certain of its conclusion. That's how I assessed it on the scale above.&lt;br /&gt;
&lt;br /&gt;
Incidentally, instead of thinking of Proposition 22 as an alternative premise to Proposition 1 in an argument to the same conclusion, we might think of Proposition 22 as part of how we know that Proposition 1 is true, as illustrated in the following map.&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
| '''Map 15'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/submaps/ed74d8c90a3c418eb9435215133bdc5d}}&lt;br /&gt;
|[[File:Arguments_K_and_A_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
This amounts to a different way of mapping what is in essence the same line of reasoning.&lt;br /&gt;
&lt;br /&gt;
In any case, whether we focus on Argument K (in this most recent map) or on Argument J (in the map above it), the point remains the same. The inference isn't a deduction, but it's strong enough that being certain of its premises would put us in a position to be certain of its conclusion. We can call such inferences '''[[compelling]]'''.&lt;br /&gt;
&lt;br /&gt;
[[file:Strength_of_an_Inference.png|thumb|center|650px]]&lt;br /&gt;
&lt;br /&gt;
Even inferences that aren’t compelling can be useful. Consider the following argument:&lt;br /&gt;
&lt;br /&gt;
{| class=&amp;quot;wikitable&amp;quot;&lt;br /&gt;
|'''Map 16'''&lt;br /&gt;
|-&lt;br /&gt;
|{{Map|https://app.reasonspace.com/maps/156b41a4-a850-469b-9a7c-8665f4f3c2e6}}&lt;br /&gt;
|[[File:Argument_L_Assessment.png|thumb|center|500px]]&lt;br /&gt;
|}&lt;br /&gt;
&lt;br /&gt;
Inference L isn’t compelling, but it’s not bad, either. If you knew the premises to be true, this argument wouldn’t put you in a position to ''know'' the conclusion, but (unless you had other relevant knowledge of Estelle), it ought to lead you to regard it as ''probable'' that Estelle can speak English.&lt;br /&gt;
&lt;br /&gt;
==The Strength of an Argument as a Whole==&lt;br /&gt;
&lt;br /&gt;
To review then, arguments range in strength from fatuous to conclusive, with conclusive arguments being the ones that are strong enough to establish their conclusions as knowledge (in other words, to make them certain). The strength of an argument is determined by the strength of its premises and of its inference. The strength of a premise is its [[epistemic status]]. The highest epistemic status is knowledge or certainty, and the lowest is that of a proposition one is either wholly ignorant of or knows to be false. We called this status &amp;quot;unfounded.&amp;quot; The strength of an inference is determined by the relationship between the premises and the conclusion, and this is separate from whether the premises are true. The weakest inferences are called non-sequiturs and the strongest are called compelling.&lt;br /&gt;
[[file:Three_Scales.jpg|thumb|center|650px]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1266</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1266"/>
		<updated>2024-09-30T02:22:24Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Epistemic status]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
** [[Aristotelian Syllogisms]]&lt;br /&gt;
** [[Deductions Involving Complex Propositions]]&lt;br /&gt;
* [[Assessing Arguments in ReasonSpace]]&lt;br /&gt;
* [[Inference to the Best Explanation]]&lt;br /&gt;
* [[Fallacies]]&lt;br /&gt;
* [[How to map arguments from a text]]&lt;br /&gt;
* [[How to build an argument map in ReasonSpace]]&lt;br /&gt;
* [[Map Library]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1265</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1265"/>
		<updated>2024-09-30T02:21:31Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
** [[Aristotelian Syllogisms]]&lt;br /&gt;
** [[Deductions Involving Complex Propositions]]&lt;br /&gt;
* [[Epistemic status]]&lt;br /&gt;
* [[Assessing Arguments in ReasonSpace]]&lt;br /&gt;
* [[Map Library]]&lt;br /&gt;
* [[Inference to the Best Explanation]]&lt;br /&gt;
* [[How to map arguments from a text]]&lt;br /&gt;
* [[How to build an argument map in ReasonSpace]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1264</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1264"/>
		<updated>2024-09-30T02:21:22Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
** [Aristotelian Syllogisms]]&lt;br /&gt;
** [[Deductions Involving Complex Propositions]]&lt;br /&gt;
* [[Epistemic status]]&lt;br /&gt;
* [[Assessing Arguments in ReasonSpace]]&lt;br /&gt;
* [[Map Library]]&lt;br /&gt;
* [[Inference to the Best Explanation]]&lt;br /&gt;
* [[How to map arguments from a text]]&lt;br /&gt;
* [[How to build an argument map in ReasonSpace]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1263</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1263"/>
		<updated>2024-09-30T02:19:37Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
* [[Epistemic status]]&lt;br /&gt;
* [[Assessing Arguments in ReasonSpace]]&lt;br /&gt;
* [[Map Library]]&lt;br /&gt;
* [[Inference to the Best Explanation]]&lt;br /&gt;
* [[How to map arguments from a text]]&lt;br /&gt;
* [[How to build an argument map in ReasonSpace]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
	<entry>
		<id>http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1262</id>
		<title>Main Page</title>
		<link rel="alternate" type="text/html" href="http://reasonspace.s432.sureserver.com/index.php?title=Main_Page&amp;diff=1262"/>
		<updated>2024-09-30T02:15:51Z</updated>

		<summary type="html">&lt;p&gt;GSalmieri: &lt;/p&gt;
&lt;hr /&gt;
&lt;div&gt;Argument Mapping is a technique for visualizing [[arguments]], including the connections between them.&lt;br /&gt;
&lt;br /&gt;
[https://app.reasonspace.com ReasonSpace] is a tool for [[How_to_build_an_argument_map_in_ReasonSpace|building]] argument maps and [[Assessing_Arguments_in_ReasonSpace|assessing]] the arguments in them.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For more information on arguments and mapping, see the following pages: &lt;br /&gt;
* [[Arguments]]&lt;br /&gt;
* [[Deduction]]&lt;br /&gt;
* [[Epistemic status]]&lt;/div&gt;</summary>
		<author><name>GSalmieri</name></author>
	</entry>
</feed>