### Single Idea 18761

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

Full Idea

To get any advantage from moving to second-order logic, we need to assign to second-order variables a role different from merely ranging over collections made up of things the first-order variables range over.

Gist of Idea

Second-order variables need to range over more than collections of first-order objects

Source

Vann McGee (Logical Consequence [2014], 7)

Book Reference

'Bloomsbury Companion to Philosophical Logic', ed/tr. Horsten,L/Pettigrew,R [Bloomsbury 2014], p.47

A Reaction

Thus it is exciting if they range over genuine properties, but not so exciting if you merely characterise those properties as sets of first-order objects. This idea leads into a discussion of plural quantification.

Related Idea

Idea 18763
Basic variables in second-order logic are taken to range over subsets of the individuals **[Anderson,CA]**