I have just discovered (during homeschooling) that my children are being taught at school that infinitely many numbers exist. Where do I have to send my petitions against this devastating creationist pre-Hilbertian falsehood?
Yes, that's backward. The parts of mathematics that worked have always been only the computable ones. Gödel and Turing have shown that all the other parts are woo
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Certainly not denying the computable functions 'work', but it seems we have discovered a much larger class of functions that we may reason about.
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Yes, there is an abundance of things we can say about things that cannot exist.
End of conversation
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this isn’t true, though. in particular the axiom of choice is provably consistent, but generally deals with uncomputable functions. you can be philosophically opposed to it, but it is not accurate to say that godel/turing showed it is woo
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