Editing Term logic (section)

== Singular terms ==
For Aristotle, the distinction between singular{{Citation needed|date=July 2022}} and universal is a fundamental [[metaphysical]] one, and not merely [[grammatical]]. A singular term for Aristotle is [[substance theory|primary substance]], which can only be [[predicate (grammar)|predicate]]d of itself: (this) "Callias" or (this) "Socrates" are not predicable of any other thing, thus one does not say ''every Socrates'' one says ''every human'' (''De Int.'' 7; ''Meta.'' D9, 1018a4). It may feature as a grammatical predicate, as in the sentence "the person coming this way is Callias". But it is still a ''logical'' subject.

He contrasts universal (''katholou'')<ref name="katholouLSJ">{{LSJ|kaqo/lou|καθόλου|ref}}.</ref> secondary substance, genera, with primary substance, particular (''kath' hekaston'')<ref name="katholouLSJ"/><ref>{{LSJ|e(/kastos|καθ' ἕκαστον|shortref}}.</ref> specimens. The formal nature of [[Universal (metaphysics)|universals]], in so far as they can be generalized "always, or for the most part", is the subject matter of both scientific study and formal logic.<ref>They are mentioned briefly in the ''De Interpretatione''.  Afterwards, in the chapters of the ''Prior Analytics'' where Aristotle methodically sets out his theory of the syllogism, they are entirely ignored.</ref>

The essential feature of the [[syllogism]] is that, of the four terms in the two premises, one must occur twice. Thus

:All Greeks are '''men'''
:All '''men''' are mortal.

The subject of one premise, must be the predicate of the other, and so it is necessary to eliminate from the logic any terms which cannot function both as subject and predicate, namely singular terms.

However, in a popular 17th-century version of the syllogism, [[Port-Royal Logic]], singular terms were treated as universals:<ref>Arnauld, Antoine and Nicole, Pierre; (1662) ''La logique, ou l'art de penser''. Part 2, chapter 3</ref>

:All men are mortals
:All Socrates are men
:All Socrates are mortals

This is clearly awkward, a weakness exploited by Frege in his devastating attack on the system.

The famous syllogism "Socrates is a man ...", is frequently quoted as though from Aristotle,<ref>For example: Kapp, ''Greek Foundations of Traditional Logic'', New York 1942, p.&nbsp;17, Copleston ''[[A History of Philosophy (Copleston)|A History of Philosophy]]'' Vol. I., p.&nbsp;277, [[Bertrand Russell|Russell]], ''A History of Western Philosophy'' London 1946 p.&nbsp;218.</ref> but in fact, it is nowhere in the ''[[Organon]]''. [[Sextus Empiricus]] in his ''Hyp. Pyrrh'' (Outlines of Pyrronism) ii. 164 first mentions the related syllogism "Socrates is a human being, Every human being is an animal, Therefore, Socrates is an animal."

=== The three figures ===

Depending on the position of the middle term, Aristotle divides the syllogism into three kinds: syllogism in the first, second, and third figure.<ref>{{cite book |title=The Cambridge Companion to Aristotle |page=35 |quote=At the foundation of Aristotle's syllogistic is a theory of a specific class of arguments: arguments having as premises exactly two categorical sentences with one term in common.}}</ref> If the Middle Term is subject of one premise and predicate of the other, the premises are in the First Figure. If the Middle Term is predicate of both premises, the premises are in the Second Figure. If the Middle Term is subject of both premises, the premises are in the Third Figure.<ref>{{cite book |author=Robin Smith |title=Aristotle: Prior Analytics |page=XVIII }}</ref>

Symbolically, the Three Figures may be represented as follows:<ref>{{cite book|author=Henrik Legerlund|title=Modal Syllogistics in the Middle Ages|page=4}}</ref>

{| class="wikitable"
|-
!
! First figure
! Second figure
! Third figure
|-
|
| Predicate&nbsp;— Subject
| Predicate&nbsp;— Subject
| Predicate&nbsp;— Subject
|-
| Major premise
| A ------------ B
| B ------------ A
| A ------------ B
|-
| Minor premise
| B ------------ C
| B ------------ C
| C ------------ B
|-
| Conclusion
| A ********** C
| A ********** C
| A ********** C
|}

=== The fourth figure ===
<blockquote>In Aristotelian syllogistic (''Prior Analytics'', Bk I Caps 4-7), syllogisms are divided into three figures according to the position of the middle term in the two premises. The fourth figure, in which the middle term is the predicate in the major premise and the subject in the minor, was added by Aristotle's pupil [[Theophrastus]] and does not occur in Aristotle's work, although there is evidence that Aristotle knew of fourth-figure syllogisms.<ref>{{cite book|last1=Russell|first1=Bertrand|title=Cambridge essays, 1888-99|last2=Blackwell|first2=Kenneth|publisher=Routledge|year=1983|isbn=978-0-04-920067-8|page=411}}</ref></blockquote>