Aristotelian Syllogisms: Difference between revisions
No edit summary |
No edit summary |
||
| (29 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
=First Figure Syllogisms= | Syllogism is the word in Aristotle's Greek that is translated "[[deduction]]." In English, the term has come to refer specifically to deductive arguments with two premises. Aristotle considered forms of argument that have the following features: | ||
*There are two premises. | |||
*All the propositions in the argument are of the form "Some/All SUBJECT are/aren't PREDICATE." | |||
*The subject term of the conclusion (called the ''major term'') is in one of the two premises (called the ''major premise''). | |||
*The predicate term of the conclusion (called the ''minor term'') is in the other premise (called the ''minor premise''). | |||
*There is a term (called the ''middle term'') that is present in both premises. | |||
He worked out that among the forms of argument with these features, 14 were valid deductions. The 14 forms of syllogism were later given names by Medieval logicians. We can call these the Aristotelian Syllogisms. | |||
He categorized these syllogisms into three "figures" depending on what role the middle term plays in the premises. In a ''First Figure'' syllogism the middle term is the subject of the major premise and the predicate of the minor. In the ''Second Figure'', the middle term is the predicate of both premises, and in the ''Third Figure'', it's the subject of both premises. | |||
Four of the valid syllogisms are in the First Figure. Aristotle called these the ''perfect syllogisms'', and he showed how the other 10 syllogisms could be ''reduced'' to one (or more) of these four. To reduce a syllogism is to prove that its conclusion is necessitated by its premises using the only the perfect syllogisms and [[immediate inferences]]. | |||
Aristotle also identified why the premises of these perfect syllogisms necessitate their conclusions. In the case of each argument form one premise is a universal proposition saying something about everything of a certain sort and the other premise tells us that something else is that sort of thing. The conclusion then applies the universal premise about all things of the sort to the thing that the other premise tells us is a member of that sort. If the universal premise is really true, and the thing in question really belongs to the relevant sort, then the universal premise will, of course, have to apply to that thing. | |||
=The Perfect (or First-Figure) Syllogisms= | |||
==Barbara== | ==Barbara== | ||
Barbara is the first figure syllogism composed of two universal affirmative premises and a universal affirmative conclusion as follows: | |||
{{Map|https://app.reasonspace.com/arguments/916b58e1-07e7-484c-adf9-2cb8897c1eb7}} | {{Map|https://app.reasonspace.com/arguments/916b58e1-07e7-484c-adf9-2cb8897c1eb7}} | ||
| Line 12: | Line 33: | ||
{{Map|https://app.reasonspace.com/arguments/9ea18ef3-9d6c-4d80-ae4e-7447ea4ee011}} | {{Map|https://app.reasonspace.com/arguments/9ea18ef3-9d6c-4d80-ae4e-7447ea4ee011}} | ||
= | =Second Figure Syllogisms= | ||
==Cesare== | |||
{{Map|https://app.reasonspace.com/submaps/e39e4348817443e09207784c738f4ee0}} | |||
See below for how this argument reduces to Celerant (inferences D and F). | |||
{{Map|https://app.reasonspace.com/submaps/afb3d284133041b2b2d69a150f5b9c18}} | |||
==Camestres== | |||
{{Map|https://app.reasonspace.com/submaps/1ec06c9d531d4fe8bf37d8afe0715470}} | |||
Reduction of Camestres to Celarent: | |||
{{Map|https://app.reasonspace.com/submaps/9716df7b263e42e794975cdc2824eda8}} | |||
==Festino== | |||
{{Map|https://app.reasonspace.com/submaps/505af1ffbefa4916aaae52b39bd704f6}} | |||
Reduction to Ferio: | |||
{{Map|https://app.reasonspace.com/submaps/dec1f42e54764f01b05d7b9027665046}} | |||
==Baroco== | |||
{{Map|https://app.reasonspace.com/submaps/caa45bfba37c4d3c8c34d0e548d63c08}} | |||
Reduction: | |||
{{Map|https://app.reasonspace.com/submaps/ad80d90a06d44661be6a6a7c8b147d19}} | |||
=Third Figure Syllogisms= | |||
==Darapti== | |||
{{Map|https://app.reasonspace.com/smaps/adf9016cfb6f41649e66f8c321dd6c13}} | |||
Reduction: | |||
{{Map|https://app.reasonspace.com/smaps/31c6cc2f68b34a5e9169755b8c82e135}} | |||
==Felapton== | |||
{{Map|https://app.reasonspace.com/smaps/41ad65f348d544ba9c08800fcac8e099}} | |||
Reduction: | |||
{{Map|https://app.reasonspace.com/smaps/0ea20e40e8ac44f8a9255d7a7aecd58c}} | |||
==Disamis== | |||
{{Map|https://app.reasonspace.com/smaps/7f43ec3ab1104f628ed6235b4ab6e61e}} | |||
Reduction: | |||
{{Map|https://app.reasonspace.com/smaps/8d38f9242dbb49a9bb580875bbb3cc6b}} | |||
==Datisi== | |||
{{Map|https://app.reasonspace.com/smaps/06b5bffa79714581b62b532ac688f344}} | |||
Reduction: | |||
{{Map|https://app.reasonspace.com/smaps/a6aa4a971cd6450e961b67db0d0580f0}} | |||
==Bocardo== | |||
{{Map|https://app.reasonspace.com/smaps/5d2911f1f5104c4d88258518c800f248}} | |||
Reduction: | |||
{{Map|https://app.reasonspace.com/smaps/e6e5d4b9277941c3b8ab5a53c839bd95}} | |||
==Ferison== | |||
{{Map|https://app.reasonspace.com/smaps/3f7ba1ecefa047f78832280bde866fdc}} | |||
Reduction: | |||
{ | {{Map|https://app.reasonspace.com/smaps/e96fc026ffa948aca83d77a5c69debc6}} | ||
| | |||
Latest revision as of 13:12, 2 September 2024
Syllogism is the word in Aristotle's Greek that is translated "deduction." In English, the term has come to refer specifically to deductive arguments with two premises. Aristotle considered forms of argument that have the following features:
- There are two premises.
- All the propositions in the argument are of the form "Some/All SUBJECT are/aren't PREDICATE."
- The subject term of the conclusion (called the major term) is in one of the two premises (called the major premise).
- The predicate term of the conclusion (called the minor term) is in the other premise (called the minor premise).
- There is a term (called the middle term) that is present in both premises.
He worked out that among the forms of argument with these features, 14 were valid deductions. The 14 forms of syllogism were later given names by Medieval logicians. We can call these the Aristotelian Syllogisms.
He categorized these syllogisms into three "figures" depending on what role the middle term plays in the premises. In a First Figure syllogism the middle term is the subject of the major premise and the predicate of the minor. In the Second Figure, the middle term is the predicate of both premises, and in the Third Figure, it's the subject of both premises.
Four of the valid syllogisms are in the First Figure. Aristotle called these the perfect syllogisms, and he showed how the other 10 syllogisms could be reduced to one (or more) of these four. To reduce a syllogism is to prove that its conclusion is necessitated by its premises using the only the perfect syllogisms and immediate inferences.
Aristotle also identified why the premises of these perfect syllogisms necessitate their conclusions. In the case of each argument form one premise is a universal proposition saying something about everything of a certain sort and the other premise tells us that something else is that sort of thing. The conclusion then applies the universal premise about all things of the sort to the thing that the other premise tells us is a member of that sort. If the universal premise is really true, and the thing in question really belongs to the relevant sort, then the universal premise will, of course, have to apply to that thing.
The Perfect (or First-Figure) Syllogisms
Barbara
Barbara is the first figure syllogism composed of two universal affirmative premises and a universal affirmative conclusion as follows:
Celarent
Darii
Ferio
Second Figure Syllogisms
Cesare
See below for how this argument reduces to Celerant (inferences D and F).
Camestres
Reduction of Camestres to Celarent:
Festino
Reduction to Ferio:
Baroco
Reduction:
Third Figure Syllogisms
Darapti
Reduction:
Felapton
Reduction:
Disamis
Reduction:
Datisi
Reduction:
Bocardo
Reduction:
Ferison
Reduction:
