The search for a neat Theory of Everything (ToE) which unifies the entire set of fundamental forces of the universe (as well as the rules which govern dark energy, dark matter and anti-matter realms) has been the subject of a long-standing all-out effort of physicists since the early 20th century. Some complicated theories such as Quantum Field Theory and M-Theory have been developed along these lines. However, the ultimate theory of everything still seems far out of reach and highly controversial.(A related debate: 1, 2).

The difficulty of the hopeless situation brought some physicists, such as Hawking, on the verge of total disappointment. Their general idea was that maybe such an ultimate theory is not only out of reach (with respect to our current knowledge of the universe) but also *fundamentally non-existent*. In his *Gödel and the End of the Universe* lecture Hawking stated:

Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I'm now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery. Without it, we would stagnate. Gödel’s theorem ensured there would always be a job for mathematicians. I think M-theory will do the same for physicists. I'm sure Dirac would have approved.

A glimpse of Hawking's lecture makes it clear that the argument which he uses for refuting the possibility of achieving the Theory of Everything in his lecture, is loosely (inspired by and) based on Gödel's incompleteness theorems in mathematics. Not to mention that Hawking is not the only person who brought up such an argument against ToE using Gödel's theorems. For a fairly complete list see here and here. Also, some arguments of the same nature (using large cardinal axioms) could be found in this related MathOverflow post.

Hawking's view also shares some points with Lucas-Penrose's argument against AI using Gödel's incompleteness theorems, indicating that human mind is not a Turing machine (computer) and so the Computational Theory of Mind's hope for constructing an ultimate machine that has the same cognitive abilities as humans will fail eventually.

There have been a lot of criticism against Lucas-Penrose's argument as well as the presumptions of Computational Theory of Mind. Here, I would like to ask about the possible critical reviews on Hawking's relatively new idea.

Question:Is there any critical review of Hawking's argument against the Theory of Everything in his "Gödel and the End of the Universe" lecture, illustrating whether it is a valid conclusion of Gödel's incompleteness theorem in theoretical physics or just yet another philosophical abuse of mathematical theorems out of the context?Articles and lectures by researchers of various background including mathematicians, physicists, and philosophers are welcome.

The above argument for refuting the possibility of achieving the Theory of Everything in physics is loosely based on Godel's incompleteness theorems in mathematics.--- To me, Hawking's quote does not say this or even suggest this. It seems to me that he was using Godel's theorems and mathematics as an ANALOGY for a certain situation that he believes may be the case in physics (namely, that M-Theory is sufficiently malleable to keep physicists working indefinitely, or something like this). $\endgroup$ – Dave L Renfro Mar 14 '18 at 11:21(MOMENTS LATER)Having now read the entire essay, I now see that in other parts of the passage Hawking does make a more direct link to Godel's theorems. $\endgroup$ – Dave L Renfro Mar 14 '18 at 11:279more comments