more on this theme     |     more from this thinker

Single Idea 8080

[filed under theme 4. Formal Logic / A. Syllogistic Logic / 1. Aristotelian Logic ]

Full Idea

Aristotle identified four 'figures' of argument, based on combinations of Subject (S) and Predicate (P) and Middle term (M). The addition of 'all' and 'some', and 'has' and 'has not' got the property, resulted in 256 possible syllogisms, 19 of them valid.

Gist of Idea

Aristotelian identified 256 possible syllogisms, saying that 19 are valid

Source

report of Aristotle (Prior Analytics [c.328 BCE]) by Keith Devlin - Goodbye Descartes Ch.2

Book Ref

Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.42

A Reaction

[Compressed version of Devlin] What Aristotle did was astonishing, and must be one of the key ideas of western civilization, even though a lot of his assumptions have been revised or rejected.

The 15 ideas from 'Prior Analytics'

13819 Aristotle's said some Fs are G or some Fs are not G, forgetting that there might be no Fs [Bostock on Aristotle]
22271 Aristotle was the first to use schematic letters in logic [Aristotle, by Potter]
11060 Aristotelian syllogisms are three-part, subject-predicate, existentially committed, with laws of thought [Aristotle, by Hanna]
18909 Aristotelian sentences are made up by one of four 'formative' connectors [Aristotle, by Engelbretsen]
8080 Aristotelian identified 256 possible syllogisms, saying that 19 are valid [Aristotle, by Devlin]
13912 Aristotle replaced Plato's noun-verb form with unions of pairs of terms by one of four 'copulae' [Aristotle, by Engelbretsen/Sayward]
18896 Aristotle places terms at opposite ends, joined by a quantified copula [Aristotle, by Sommers]
3300 Aristotle's logic is based on the subject/predicate distinction, which leads him to substances and properties [Aristotle, by Benardete,JA]
8079 Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin]
18911 Linguistic terms form a hierarchy, with higher terms predicable of increasing numbers of things [Aristotle, by Engelbretsen]
11149 Affirming/denying sentences are universal, particular, or indeterminate [Aristotle]
11148 Deduction is when we suppose one thing, and another necessarily follows [Aristotle]
9403 There are three different deductions for actual terms, necessary terms and possible terms [Aristotle]
14641 A deduction is necessary if the major (but not the minor) premise is also necessary [Aristotle]
8071 Aristotle listed nineteen valid syllogisms (though a few of them were wrong) [Aristotle, by Devlin]