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Full Idea
Nowadays Russell's position is routinely put by saying that existence is what is expressed by the existential quantifier and only by that.
Gist of Idea
Existence is entirely expressed by the existential quantifier
Source
report of Bertrand Russell (On Denoting [1905]) by Colin McGinn - Logical Properties Ch.2
Book Ref
McGinn,Colin: 'Logical Properties' [OUP 2003], p.20
A Reaction
We must keep separate how you express existence, and what it is. Quantifiers seem only to be a style of expressing existence; they don't offer any insight into what existence actually is, or what we mean by 'exist'. McGinn dislikes quantifiers.
| 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] |