User blog comment:Pellucidar12/Proof length function/@comment-1605058-20161226131313

I agree with the first (bolded) paragraph. Proof theory gives us precisely the tools to deduce statements from other ones in a truth-preserving way (this property is called the soundness of deduction rules).

However, I'm entirely not sure what the second paragraph is supposed to mean. Okay, we take every possible proof of size n (with the description there will be infinitely many proofs of given size, but it can be fixed, so I'm ignoring this issue), and then... what? "take the function we proved to grow fastest"? What does "fastest" mean? And then this function depends on the number n. So is this really a family of functions or what?