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Full Idea
Since Frege and Russell were mainly interested in formalizing mathematics, the only quantifiers they needed were the universal and existential one.
Gist of Idea
The universal and existential quantifiers were chosen to suit mathematics
Source
Scott Soames (Philosophy of Language [2010], 1.22)
Book Ref
Soames,Scott: 'Philosophy of Language' [Princeton 2010], p.23
| 15878 | Some quantifiers, such as 'any', rule out any notion of order within their range [Harré] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
| 15534 | We could quantify over impossible objects - as bundles of properties [Lewis] |
| 15156 | The universal and existential quantifiers were chosen to suit mathematics [Soames] |
| 6068 | We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn] |
| 15138 | Not all quantification is objectual or substitutional [Williamson] |
| 8711 | Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend] |
| 18771 | Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA] |