[cwzwarich]

> Generally speaking, nobody claims that the axioms of set theory are true in any ordinary sense of the word true.

Mathematical platonism is a pretty widely held belief, at least amongst pure mathematicians. From Hardy's A Mathematician's Apology,

"I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply the notes of our observations."

A lot of set theorists will speculate about the truth of axioms beyond the standard axioms of ZFC, e.g. large cardinal hypotheses or projective determinacy.