more from Shaughan Lavine

### Single Idea 15926

#### [catalogued under 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic]

Full Idea

The distinctive feature of second-order logic is that it presupposes that, given a domain, there is a fact of the matter about what the relations on it are, so that the range of the second-order quantifiers is fixed as soon as the domain is fixed.

Gist of Idea

Second-order logic presupposes a set of relations already fixed by the first-order domain

Source

Shaughan Lavine (Understanding the Infinite [1994], V.3)

Book Reference

Lavine,Shaughan: 'Understanding the Infinite' [Harvard 1994], p.123

A Reaction

This sounds like a rather large assumption, which is open to challenge. I am not sure whether it was the basis of Quine's challenge to second-order logic. He seems to have disliked its vagueness, because it didn't stick with 'objects'.