more from C. Anthony Anderson

### Single Idea 18763

#### [catalogued under 5. Theory of Logic / G. Quantification / 5. Second-Order Quantification]

Full Idea

Under its now standard principal interpretation, the monadic predicate variables in second-order logic range over subsets of the domain on individuals.

Gist of Idea

Basic variables in second-order logic are taken to range over subsets of the individuals

Source

C. Anthony Anderson (Identity and Existence in Logic [2014], 1.5)

Book Reference

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.59

A Reaction

This is an interpretation in which properties are just sets of things, which is fine if you are a logician, but not if you want to talk about anything important. Still, we must play the game. Boolos introduced plural quantification at this point.

Related Idea

Idea 18761
Second-order variables need to range over more than collections of first-order objects **[McGee]**