Single Idea 8079

[catalogued under 5. Theory of Logic / G. Quantification / 3. Objectual Quantification]

Full Idea

Aristotelian logic has two quantifiers of the subject ('all' and 'some'), and two ways to combine the subject with the predicate ('have', and 'have not'), giving four propositions: all-s-have-p, all-s-have-not-p, some-s-have-p, and some-s-have-not-p.

Gist of Idea

Aristotelian logic has two quantifiers of the subject ('all' and 'some')

Source

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

Book Reference

Devlin,Keith: 'Goodbye Descartes: the end of logic' [Wiley 1997], p.39


A Reaction

Frege seems to have switched from 'some' to 'at-least-one'. Since then other quantifiers have been proposed. See, for example, Ideas 7806 and 6068.

Related Ideas

Idea 7806 Boolos invented plural quantification [Boolos, by Benardete,JA]

Idea 6068 We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn]