I'm sorry if this belongs rather to the /phil/ section. I just want to discuss this topic and I guess, it has to do with math anyway.

Some groups like the "New Atheits" and/or the so called "Intuitionists" (and the late Wittgenstein, too) think that you can make the following assumption:
"p is true" = "There is a proof for p [within a formal system]".

If it is impossible to provide a proof for p in principle, then you can claim that p is neither true nor false. Its just "undecidable".

My question is:
After the results of Tarski and Kurt Gödel, can we really still hold this assumption?

We see that "p is true" must be something different from "there is a proof for p" as there are some true statement of which the proof doesn't exist. We cannot define "truth" within a formal system and need some relation to something without the system itself. A semantic model.
In the light of this insights, the position that identified true with provability makes a lot less sense to me and many others.

Anyway, as far as I read, the critique of the inuitionists on the rule of double negation and the law of excluded middle relais a lot on the hidden premisse that "truth" and "can be proofen" is the same.
So, there viewpoint seems much less plausible anymore.

What do you think, anon?