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Single Idea 18953

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

Full Idea

In modern notation we can consider potential logical principles that Aristotle never considered because of his general practice of looking at inferences each of whose premises involved exactly two class-names.

Gist of Idea

Modern notation frees us from Aristotle's restriction of only using two class-names in premises

Source

Hilary Putnam (Philosophy of Logic [1971], Ch.3)

Book Ref

Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.26

A Reaction

Presumably you can build up complex inferences from a pair of terms, just as you do with pairs in set theory.

The 15 ideas with the same theme [Aristotle's original account of formal syllogistic logic]:

639 Socrates developed definitions as the basis of syllogisms, and also inductive arguments [Socrates, by Aristotle]
22272 Aristotle's later logic had to treat 'Socrates' as 'everything that is Socrates' [Potter on Aristotle]
9405 Square of Opposition: not both true, or not both false; one-way implication; opposite truth-values [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]
8071 Aristotle listed nineteen valid syllogisms (though a few of them were wrong) [Aristotle, by Devlin]
18953 Modern notation frees us from Aristotle's restriction of only using two class-names in premises [Putnam]
13643 Aristotelian logic is complete [Shapiro]
23505 Aristotelian logic cannot express 'Everyone loves someone' [White,RM]
13913 The four 'perfect syllogisms' are called Barbara, Celarent, Darii and Ferio [Engelbretsen/Sayward]
13914 Syllogistic logic has one rule: what is affirmed/denied of wholes is affirmed/denied of their parts [Engelbretsen/Sayward]
18913 Traditional term logic struggled to express relations [Engelbretsen]