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Single Idea 15138

[filed under theme 5. Theory of Logic / G. Quantification / 7. Unorthodox Quantification ]

Full Idea

We should not assume that all quantification is objectual or substitutional.

Gist of Idea

Not all quantification is objectual or substitutional

Source

Timothy Williamson (Truthmakers and Converse Barcan Formula [1999], §2)

Book Ref

-: 'Dialectica' [-], p.262


The 9 ideas with the same theme [non-classical ways of referring to the quantity of objects]:

Some quantifiers, such as 'any', rule out any notion of order within their range [Harré]
There are at least five unorthodox quantifiers that could be used [Tharp]
Boolos invented plural quantification [Boolos, by Benardete,JA]
We could quantify over impossible objects - as bundles of properties [Lewis]
The universal and existential quantifiers were chosen to suit mathematics [Soames]
We need an Intentional Quantifier ("some of the things we talk about.."), so existence goes into the proposition [McGinn]
Not all quantification is objectual or substitutional [Williamson]
Intuitionists read the universal quantifier as "we have a procedure for checking every..." [Friend]
Stop calling ∃ the 'existential' quantifier, read it as 'there is...', and range over all entities [Anderson,CA]