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Philosophical aspects of logic and set theory; truth status of mathematical axioms; Philosophy of Mathematics; philosophical aspects of mathematics in general; relation of mathematics to philosophy; etc. Consider also posting at http://philosophy.stackexchange.com/, where philosophy-of-mathematics is one of the most popular tags.

10 votes

Philosophical Question related to Largest Known Primes

I think you are mis-understanding the purpose of the "largest prime" list. There are areas of mathematics in which we genuinely do not know how to generate or catalogue the objects of certain types. P …
5 votes

Are there examples of nonconstructive metaproofs?

If the proof system is recursively axiomatizable, this situation cannot occur. If there exists a proof of $\Theta$, there exists an algorithm to find that proof. Namely, search the recursively enumer …
David Harris's user avatar
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4 votes

How do they verify a verifier of formalized proofs?

One simple suggestion no-one seems to have mentioned is to have the verifier prove itself correct. Obviously, this cannot really give any assurance that the verifier is correct, since if the verifier …
David Harris's user avatar
  • 3,475
2 votes

Why is it OK to rely on the Fundamental Theorem of Arithmetic when using Gödel numbering?

Here is a way to think about it. When you use something like Fund Theorem of Arithmetic to prove Godel numbering, you are referring to the abstract set $\mathbf N$, which "exists". The Fundamental The …
David Harris's user avatar
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