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0 pointshyperpape9mo ago0 comments

This ignores the fact that it is not so easy to find natural interesting statements that are independent of ZFC.

Statements that are independent of ZFC are a dime a dozen when doing foundations of mathematics, but they're not so common in many other areas of math. Harvey Friedman has done interesting work on finding "natural" statements that are independent of ZFC, but there's dispute about how natural they are. https://mathoverflow.net/questions/1924/what-are-some-reason...

In fact, it turns out that a huge amount of mathematics does not even require set theory, it is just a habit for mathematicians to work in set theory. https://en.wikipedia.org/wiki/Reverse_mathematics.

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Xcelerate9mo ago

Yeah, I’m quite familiar with Friedman’s work. I mentioned him and his Grand Conjecture in another comment.

> This ignores the fact that it is not so easy to find natural interesting statements that are independent of ZFC.

I’m not ignoring this fact—just observing that the sheer difficulty of the task seems to have encouraged mathematicians to pursue other areas of work beside foundational topics, which is a bit unfortunate in my opinion.

hyperpapeOP9mo ago

I agree most working mathematicians have limited interest in foundational topics. To me, that seems harmless enough.

> approximate those aspects of physical reality that are primarily relevant to the endeavors of humanity.

This is the comment that made me think that you were saying we needed more work on foundations for math as it is used in the sciences, and that doesn't match my understanding. Did I read it differently than you meant it?

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