### Single Idea 18956

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

Full Idea

The natural understanding of first-order logic is that in writing down first-order schemata we are implicitly asserting their validity, that is, making second-order assertions. ...Thus even quantification theory involves reference to classes.

Gist of Idea

Asserting first-order validity implicitly involves second-order reference to classes

Source

Hilary Putnam (Philosophy of Logic [1971], Ch.3)

Book Reference

Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.32

A Reaction

If, as a nominalist, you totally rejected classes, presumably you would get by in first-order logic somehow. To say 'there are no classes so there is no logical validity' sounds bonkers.

Related Idea

Idea 18951
For scientific purposes there is a precise concept of 'true-in-L', using set theory **[Putnam]**