more from Bertrand Russell

Single Idea 14461

[catalogued under 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets]

Full Idea

It is right (in its main lines) to say that there is a reduction of propositions nominally about classes to propositions about their defining functions.

Gist of Idea

Propositions about classes can be reduced to propositions about their defining functions

Source

Bertrand Russell (Introduction to Mathematical Philosophy [1919], XVII)

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.193


A Reaction

The defining functions will involve the theory of types, in order to avoid the paradoxes of naïve set theory. This is Russell's strategy for rejecting the existence of sets.