Reply #56: There seems to be little common ground here

[Boojatta]

1) Given that "absolute knowledge" means in mathematics "proven for a given set of things under certain axioms"

To prove FLT, Wiles didn't introduce a grab bag of assumptions including such things as the Riemann hypothesis. He started from theorems that were available to him because those theorems had already been proved using the ordinary foundations of mathematics. Do you deny that there is such a thing as the ordinary foundations of mathematics? Do you think that things analogous to relative consistency proofs play a major role in all branches of mathematics?

2) Why do we want to express the claim in terms of evidence?

I'm simply introducing a broader concept that includes as a special case the more restricted concept of "evidence" that you seem to prefer. This is done frequently in mathematics. For example, we might apply an "expansion" factor to something in a general sense that includes as possible subcases: expansion, contraction, and no change.

It doesn't carry any more information to rephrase everything in some kind of bastardized notion of evidence that bears no relation to the meaning of evidence in the real world, so why say "evidence" rather than "proven"?

Many people will tell you that there aren't infinitely many different numbers that have exactly the same magnitude. To them, the word "number" is bastardized when used in the phrase "complex number." Furthermore, you can rephrase any theorem involving complex numbers so that you are only talking about real numbers. So you can make a claim analogous to your claim about not carrying more information.