Single Idea 10007

[catalogued under 5. Theory of Logic / G. Quantification / 2. Domain of Quantification]

Full Idea

Quantifiers have two functions in communication - to range over a domain of entities, and to have an inferential role (e.g. F(t)→'something is F'). In ordinary language these two come apart for singular terms not standing for any entities.

Gist of Idea

Quantifiers for domains and for inference come apart if there are no entities


Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], 6.3)

Book Reference

-: 'Philosophical Review 114' [Phil Review 2005], p.218

A Reaction

This simple observations seems to me to be wonderfully illuminating of a whole raft of problems, the sort which logicians get steamed up about, and ordinary speakers don't. Context is the key to 90% of philosophical difficulties (?). See Idea 10008.

Related Ideas

Idea 10008 Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber]

Idea 13818 If we allow empty domains, we must allow empty names [Bostock]