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Results tagged with mathematical-philosophy
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user 9896
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.
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 …
- 3,475
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 …
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 …
- 3,475
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 …
- 3,475