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Full Idea
One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'.
Gist of Idea
There are at least five unorthodox quantifiers that could be used
Source
Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3)
Book Ref
'Philosophy of Logic: an anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.39
A Reaction
[compressed - just listed for reference, if you collect quantifiers, like collecting butterflies]
| 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] |