Single Idea 14459

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility]

Full Idea

The Axiom of Reducibility says 'There is a type of a-functions such that, given any a-function, it is formally equivalent to some function of the type in question'. ..It involves all that is really essential in the theory of classes. But is it true?

Clarification

'a-functions' are all the functions which can take object a as an argument

Gist of Idea

Reducibility: a family of functions is equivalent to a single type of function

Source

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

Book Reference

Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.191


A Reaction

I take this to say that in the theory of types, it is possible to reduce each level of type down to one type.