Full Idea
We are doomed to postulate an infinite sequence of successively stronger axiom systems as we try to spell out what is involved in iterating the power set operation 'as far as possible'.
Gist of Idea
The iterated conception of set requires continual increase in axiom strength
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 9.3)
Book Reference
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.277
A Reaction
[W.W. Tait is behind this idea] The problem with set theory, then, especially as a foundation of mathematics, is that it doesn't just expand, but has to keep reinventing itself. The 'large cardinal axioms' are what is referred to.