Final theory in Physics: a mathematical existence proof?

Some time ago, I read something like this about the issue of "a final theory" in Physics:

"Concerning the physical laws, we have several positions as scientists

1. 
   
   

   There are no fundamental physical laws. At the most elementary level, the Universe/Multiverse is essentially chaotic and anarchical. There are no such laws.

   
   


2. 
   

   There are a continuous sequence of more and more precise theories, but there is no a final theory. Physics will be always evolving from one approximate theory to another bigger and more accurate. In the end, we will be also able to find a better theory and additional levels of complexity or reality.

   
   


3. 
   

   There is a final theory explaining everything, and we will find if and only if:

   
   

   i) We are clever enough to find such a theory. ii) We make good and sophisticated enough mathematics. iii) We guess the right axioms/principles/ideas. iv) We interpretate data correctly and test the putative final theory with suitable instruments/experiments. "

   
   

Supposing 3) is the right approach...

Question: How could we prove the mere mathematical existence of such a theory? Wouldn't it evade the Gödel's incompleteness theorem somehow since, as a Theory of Everything, it would be explain "all" and though it should be mathematically self-consistent? How could a Theory of Everything be a counterexample of Gödel's theorem if it is so, or not?

Note: The alledged unification of couplings in supersymmetric theories is a hint of "unification" of forces, but I am not sure if it counts as sufficient condition to the existence of a final theory.

Complementary: Is it true that Hawking has changed his view about this question?

SUMMARY:

1') Does a final theory of physics exist? The issue of existence should be tied to some of its remarkable properties (likely).

2') How could we prove its existence or disproof it and hence prove that the only path in Physics is an infinite sequence of more and more precise theories or that the Polyverse is random and/or chaotic at the most fundamental level?

3') How 1') and 2') affect to Gödel's theorems?

I have always believed, since Physmatics=Physics+Mathematics (E.Zaslow, Clay Institute) is larger than the mere sum that the challenge of the final theory should likely offer so hint about how to "evade" some of the Gödel's theorems. Of course, this last idea is highly controversial and speculative at this point.