Do Gödel Incompleteness theorems have any influence on the possibility of constructing / finding a "Theory of Everything" ?
But the theorems are about mathematical theories and no existing physical theory is completely mathematical. I don't mean that their mathematical formalisms can't be made rigorous, what I mean is that they also have a conceptual background which is not included in the calculational scheme. They are not pure mathematics.
A related question that might shed some light in this issue is: there could be a complete correspondence between physical reality and mathematical objects? Notice, however, that even if this turns out to be true, the question is not settled down, since there is the possibility of our "Axiomatic Theory of Everything" not being expressive enough to formalize the natural numbers and in this case Gödel's hypothesis would not apply.
So, what do you think?