Deduction - Revision history

GSalmieri at 17:41, 22 August 2025

2025-08-22T17:41:14Z

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	(If you just mechanically substitute the relevant words in for the letters p and q, you won't always 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.)		(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.)

	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.		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.

GSalmieri at 18:45, 2 September 2024

2024-09-02T18:45:32Z

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	[[file:deduction.png\|thumb\|center\|600px]]		[[file:deduction.png\|thumb\|center\|600px]]

	~~In assessing~~ whether a (~~seeming~~) deduction is valid, 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.		=Determining whether an inference is a (valid) deduction=

			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.

	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.		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.

	If the ~~deduction~~ is ~~valid~~ and the premises ~~are certain then~~ the ~~argument will make~~ the ~~conclusion certain~~. ~~If it is valid and all but one~~ of ~~the premises~~ are ~~certain, then it will elevate the conclusion~~ to the ~~epistemic status~~ of ~~the remaining premise. If more than one~~ of the premises ~~is uncertain, then the argument will give us less reason to believe~~ the conclusion ~~than we have to believe the least certain of its premises~~.		=Are deductive arguments better than other arguments?=

			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 "All S is P" or "No S is P") 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.


	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 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]].		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]].

GSalmieri at 18:36, 2 September 2024

2024-09-02T18:36:02Z

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	<blockquote>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)</blockquote>		<blockquote>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)</blockquote>

	The premises are the "things laid down" 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 ~~argument~~ in which the premises necessitate the conclusion''. That means that ~~it's an argument in which~~ the premises being true would make the conclusion ''have to be'' true. It will be easier to see what's meant by "necessitate" or "have to be" if we look at some examples.		The premises are the "things laid down" 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 "necessitate" or "have to be" if we look at some examples.

	=Example 1: "Barbara"=		=Example 1: "Barbara"=

GSalmieri: /* Example 2: "Modus Tollens" */

2024-09-02T18:02:19Z

Example 2: "Modus Tollens"

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	=Example 2: "Modus Tollens"=		=Example 2: "Modus Tollens"=

	Here are three maps that illustrate another form of argument, called [[Deductions_Involving_Complex_Propositions#Modus_Tollens]]:		Here are three maps that illustrate another form of argument, called [[Deductions_Involving_Complex_Propositions#Modus_Tollens\|modus tollens]]:

	{{Map\|https://app.reasonspace.com/arguments/9df82f8daf9f49c5b32f9a2b19a0d373}}		{{Map\|https://app.reasonspace.com/arguments/9df82f8daf9f49c5b32f9a2b19a0d373}}

GSalmieri: /* Example 2: "Modus Tollens" */

2024-09-02T18:02:04Z

Example 2: "Modus Tollens"

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	=Example 2: "Modus Tollens"=		=Example 2: "Modus Tollens"=

	Here are three maps that illustrate another form of argument, called [[~~Modus Tollens~~]]:		Here are three maps that illustrate another form of argument, called [[Deductions_Involving_Complex_Propositions#Modus_Tollens]]:

	{{Map\|https://app.reasonspace.com/arguments/9df82f8daf9f49c5b32f9a2b19a0d373}}		{{Map\|https://app.reasonspace.com/arguments/9df82f8daf9f49c5b32f9a2b19a0d373}}

GSalmieri: /* The strength of a deduction */

2024-08-30T21:23:31Z

The strength of a deduction

← Older revision		Revision as of 17:23, 30 August 2024
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	=The strength of a deduction=		=The strength of a deduction=

	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''.		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''.

	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.		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.

GSalmieri: /* The strength of a deduction */

2024-08-30T21:23:13Z

The strength of a deduction

← Older revision		Revision as of 17:23, 30 August 2024
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	=The strength of a deduction=		=The strength of a deduction=

	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]]. 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''.		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''.

	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.		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.

GSalmieri: /* The strength of a deduction */

2024-08-30T19:57:24Z

The strength of a deduction

← Older revision		Revision as of 15:57, 30 August 2024
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	=The strength of a deduction=		=The strength of a deduction=

	Unlike ~~the~~ sorts of inferences ~~that will be discussed in the remaining sections~~, deductive inferences do not differ from one another in strength. Either an inference is deductive, or it is not. However, there are some ~~arguments~~ that may seem like deductions ~~when they~~ are not. To differentiate between the genuine deductions and the imposters, logicians call the genuine ones ''valid'' ~~deductions~~ and ~~the imposters ''invalid'~~'. All valid deductive arguments have equally strong inferences, but this doesn’t mean that the arguments as a whole are equally strong, since their premises may still 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.		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]]. 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''.

	~~In assessing whether~~ a (~~seeming) deduction is valid, one needs to consider not only it's form,~~ but ~~also check~~ for ~~[[equivocation]] — i.e. cases where it may only seem to be an argument of a certain form because a term is being used in two different ways.~~

	~~If the deduction is valid and the premises are certain then the argument will make the conclusion certain. If it is valid and all but~~ one of the premises are certain, then it will elevate the conclusion to the epistemic status of the remaining premise. If more than one of the premises is uncertain, then the argument will give us less reason to believe the conclusion than we have to believe the least certain of its premises.

			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.

	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.		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.
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	[[file:deduction.png\|thumb\|center\|600px]]		[[file:deduction.png\|thumb\|center\|600px]]

	~~For the purposes of this course~~, it ~~is not necessary to memorize the samples of~~ valid ~~and invalid forms of~~ deductive ~~inference discussed in this section~~. ~~They do not exhaust all~~ the ~~possible deductive~~ forms, ~~nor~~ even ~~all the forms that we will encounter~~ this ~~semester. When dealing with a deductive argument, instead of trying to classify it under one of the forms we’ve discussed~~, 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. If the answer ~~isn’t~~ immediately obvious, try to make up an argument of the same form with true premises and a false conclusion.		In assessing whether a (seeming) deduction is valid, 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.

			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.

			If the deduction is valid and the premises are certain then the argument will make the conclusion certain. If it is valid and all but one of the premises are certain, then it will elevate the conclusion to the epistemic status of the remaining premise. If more than one of the premises is uncertain, then the argument will give us less reason to believe the conclusion than we have to believe the least certain of its premises.

	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 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]].		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 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]].

GSalmieri: /* Example 1: "Barbara" */

2024-08-29T23:29:33Z

Example 1: "Barbara"

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	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”.		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”.

	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]] 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.		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.

	=Example 2: "Modus Tollens"=		=Example 2: "Modus Tollens"=

GSalmieri: /* Example 1: "Barbara" */

2024-08-29T23:28:59Z

Example 1: "Barbara"

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	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”.		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”.

	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 [[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.		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]] 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.

	=Example 2: "Modus Tollens"=		=Example 2: "Modus Tollens"=