>Yet still professional mathematicians have an underlying notion of truth outside of any axiom systems. I am certain about that, but it does not make my statem

>Yet still professional mathematicians have an underlying notion of truth outside of any axiom systems. I am certain about that, but it does not make my statement less true. I actually think that very few people believe in ZFC as either a formalist absolute or as an arbitrary set of rules. I think the most common view is that it enables other theories, that those mathematicians actually care about. The moment those theories rely directly on axioms things get difficult. I think the following quote describes quite well the state of ZFC: "The axiom of choice is obviously true, the well-ordering principle obviously false, and who can tell about Zorn's lemma?"