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There are legitimate criticisms you can levy against set theory, but I'm starting to lose you here. I'm not really following your point anymore - this seems like arguing about whether or not mathematics is invented or discovered.

Are you trying to argue coming up with new definitions isn't worthwhile if the axioms don't have a foundation in reality? If so, why? If not, what are you saying?

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The original post is called "What even is a number?". The comment I replied to tried to answer that question with "some formalism".

What I'm saying is: questioning foundations leads you to new foundations. New foundations that you can then question all over again. It's turtles all the way down.

If you're actually looking to use math, this is a futile exercise. It works, so just use it. Essentially, I am re-iterating von Neumann's statement:

> In mathematics you don't understand things. You just get used to them.

In that case I'd agree with you. I'm not particularly keen on rehashing foundations of mathematics either.

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