more from this thinker | more from this text
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 Ref
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]
8079 | Aristotelian logic has two quantifiers of the subject ('all' and 'some') [Aristotle, by Devlin] |
7742 | Frege reduced most quantifiers to 'everything' combined with 'not' [Frege, by McCullogh] |
7730 | Frege introduced quantifiers for generality [Frege, by Weiner] |
6061 | Existence is entirely expressed by the existential quantifier [Russell, by McGinn] |
6069 | 'Partial quantifier' would be a better name than 'existential quantifier', as no existence would be implied [McGinn] |
11115 | 'All horses' either picks out the horses, or the things which are horses [Jubien] |
13392 | Philosophers reduce complex English kind-quantifiers to the simplistic first-order quantifier [Jubien] |
13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
8312 | It is better if the existential quantifier refers to 'something', rather than a 'thing' which needs individuation [Lowe] |