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Single Idea 14461

[filed under theme 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 Ref

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.


The 6 ideas with the same theme [sets whose membership is defined by a concept]:

A class is, for Frege, the extension of a concept [Frege, by Dummett]
Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA]
The 'no classes' theory says the propositions just refer to the members [Russell]
Propositions about classes can be reduced to propositions about their defining functions [Russell]
Realisms like the full Comprehension Principle, that all good concepts determine sets [Read]
The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine]