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.