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Single Idea 9403

[filed under theme 4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic ]

Full Idea

Since to belong, to belong of necessity, and to be possible to belong are different, ..there will be different deductions for each; one deduction will be from necessary terms, one from terms which belong, and one from possible terms.

Gist of Idea

There are three different deductions for actual terms, necessary terms and possible terms

Source

Aristotle (Prior Analytics [c.328 BCE], 29b29-35)

Book Ref

Aristotle: 'Prior Analytics', ed/tr. Smith,Robin [Hackett 1989], p.13

A Reaction

Fitting and Mendelsohn cite this as the earliest thoughts on modal logic. but Kneale and Kneale say that Aristotle got into a muddle, and so was unable to create a workable system.

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]