Single Idea 18843

[catalogued under 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets]

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.