more from JP Burgess / G Rosen

### Single Idea 9933

#### [catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets]

Full Idea

The paradoxes only seem to arise in connection with Frege's logical notion of extension or class, not Cantor's mathematical notion of set. Cantor never assumed that every condition determines a set.

Gist of Idea

The paradoxes are only a problem for Frege; Cantor didn't assume every condition determines a set

Source

JP Burgess / G Rosen (A Subject with No Object [1997], III.C.1.b)

Book Reference

Burgess,J/Rosen,G: 'A Subject with No Object' [OUP 1997], p.224

A Reaction

This makes the whole issue a parochial episode in the history of philosophy, not a central question. Cantor favoured some sort of abstractionism (see Kit Fine on the subject).