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Full Idea
Frege treated 'everything' as basic, and suggested ways of recasting propositions containing other quantifiers so that this was the only one remaining. He recast 'something' as 'at least one thing', and defined this in terms of 'everything' and 'not'.
Gist of Idea
Frege reduced most quantifiers to 'everything' combined with 'not'
Source
report of Gottlob Frege (Begriffsschrift [1879]) by Gregory McCullogh - The Game of the Name 1.6
Book Ref
McCulloch,Gregory: 'The Game of the Name' [OUP 1989], p.19
A Reaction
Extreme parsimony seems highly desirable in logic as well as ontology, but it can lead to frustrations, especially over the crucial question of the existence of things quantified over. See Idea 6068.
Related Idea
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] |