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Full Idea
In the intuitionist version of quantification, the universal quantifier (normally read as "all") is understood as "we have a procedure for checking every" or "we have checked every".
Gist of Idea
Intuitionists read the universal quantifier as "we have a procedure for checking every..."
Source
Michèle Friend (Introducing the Philosophy of Mathematics [2007], 5.5)
Book Ref
Friend,Michèle: 'Introducing the Philosophy of Mathematics' [Acumen 2007], p.122
A Reaction
It seems better to describe this as 'verificationist' (or, as Dummett prefers, 'justificationist'). Intuition suggests an ability to 'see' beyond the evidence. It strikes me as bizarre to say that you can't discuss things you can't check.
| 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] |