>>13273139I don't. But that's irrelevant. Instead of attacking my credentials, try countering my points.
>>13273134Kronecker, Poincare, Weyl, Robinson, Goodstein, Nelson, Manin, Wildberger, Zeilberger, the intuitionists, the constructive school, just to name a few.
>>13273163>The question is if we want to count an answer as a mathematical at all if it can't be given in a formal system that's compatible with other math we'd like to be true (arithmetic)Nearly all of everyday mathematics that we learn and study is not given in a formal system. Formal systems only began in the 20th century. Mathematics was done long before that.
>What's the value of "have an answer mean" if those are not in a in principle formalizable systemIt means there is a convincing proof for the proposition. Whether it's done in a previously recognized as a standard formalizable system is a separate question.
> I want math to have models and if a statement can have models that take different truth valuesAnd what's stopping you?
>I don't want my informal "answers" to deny thisThey don't.
>>13273211An interesting fact to observe that all these "problems" proven to be independent of ZFC are pure set theory bullshit, which are untranslatable to arithmetic. Whitehead problem, (G)CH, Martin's axiom, etc. all are meaningless nonarithmetic formulas.
The only arithmetic independent propositions that we've found like Goodstein's theorem have convincing higher order proofs.
