Well, you know the answer to that. The foundational crisis was never resolved; it just turned out not to have practical implications, >
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in the opinion of most mathematicians. Various flavors of constructivists, intuitionists, finitists, etc. think it does have implications >
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What's this from?
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Email I just wrote to a calculus student complaining about the “proofs” in the textbook.
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It’s not relationship with physical reality that’s at issue wrt mathematical proofs; it’s what it means to be rigorous, to deliver certainty
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You can’t rigorously prove the Fundamental Theorem of Calculus without a rigorous treatment of the reals, and you can’t do that without >
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Have you taken an intro course in analysis? Covers same material as undergrad calculus, except the proofs have fewer lies in them.
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What I am saying is substantively uncontroversial; I’m just being rude about it.
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Mmm…. the analogy with religion is humorous, but accurate I think; there’s no irony in the thrust of the explanation.
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The “proofs” in calculus are not that; they’re handwavey arguments meant to give some vague intuition. Which is fine—but should be honest.
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