[hyperpape]

"why mathematics don't have to do with experience" is too strong. Nothing you just said implies that math isn't intimately connected to empirical predictions in some way. What it shows is that contrary to Jules' earlier statements, there's no statement by statement correspondence--for any given mathematical statement, you can't find an interesting empirical prediction you associate with it.

[abrezas]

I don't believe they are entirely independent, but there's nothing you can look outside your window that will change any mathematical theorem.

[jules]

I agree with this statement (depending on how you interpret "change": if the world was different we may have been lead to prove different theorems), and nothing I've said previously contradicts it.

[jules]

I never claimed that, in fact I said precisely the opposite:

> Of course this isn't always the most interesting test

[hyperpape]

Substitute non-trivial for interesting. For instance, a calculation of pi to 50 digits will map to the same test as a calculation of pi to 51 digits. But the claims have different content so they should map to different tests!

[jules]

So?

(By the way, they do map to different tests if you view it as a statement in constructive logic, rather than geometry.)

[hyperpape]

They don't map to distinct empirical tests.

And that's the basic requirement for a semantic theory: map distinct statements to distinct contents.