more from Bob Hale

Single Idea 19296

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

Full Idea

Contrary to what Quine supposes, it is neither necessary nor desirable to interpret bound higher-order variables as ranging over sets. Sets are a species of object. They should range over entities of a completely different type: properties and relations.

Gist of Idea

If second-order variables range over sets, those are just objects; properties and relations aren't sets


Bob Hale (Necessary Beings [2013], 08.2)

Book Reference

Hale,Bob: 'Necessary Beings' [OUP 2013], p.182

A Reaction

This helpfully clarifies something which was confusing me. If sets are objects, then 'second-order' logic just seems to be the same as first-order logic (rather than being 'set theory in disguise'). I quantify over properties, but deny their existence!