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?
Gödel had proven that the classical semantics of truth was ill-defined. It came as a shock to him, because he found it hard to change his convictions in the nature of truth. If you define truth as the output of a computable function you are fine.
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The more standard take on this (at least from the authors I read) is that Gödel proved that almost all mathematical truths have no proof. Similarly Turing showed that almost all mathematical functions have no program.
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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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Essential! Entia sunt multiplicanda praeter necess itatem. More things must be presumed to exist than are absolutely necessary in your construction.
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s/necessitatem
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