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Full Idea
In order to express generality, Frege introduced quantifier notation.
Gist of Idea
Frege introduced quantifiers for generality
Source
report of Gottlob Frege (Begriffsschrift [1879]) by Joan Weiner - Frege
Book Ref
Weiner,Joan: 'Frege' [OUP 1999], p.44
A Reaction
This is the birth of predicate logic, beloved of analytical philosophers (but of no apparent interest to phenomenalists, deconstructionists, existentialists?). Generality is what you get from induction (which is, of course, problematic).
| 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] |