Single Idea 18845

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI]

Full Idea

Someone who is sympathetic to the thesis that the totality of sets is not well-defined ought to concede that we have no reason to think that the Power Set Axiom is true.

Gist of Idea

If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom

Source

Ian Rumfitt (The Boundary Stones of Thought [2015], 9.6)

Book Reference

Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.292


A Reaction

The point is that it is only this Axiom which generates the vast and expanding totality. In principle it is hard, though, to see what is intrinsically wrong with the operation of taking the power set of a set. Hence 'limitation of size'?