TITLE: On critical reviews of Hawking's lecture "Gödel and the end of the universe"
QUESTION [38 upvotes]: 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.

REPLY [7 votes]: Based on some of the comments I have seen, some commentators are finding Hawking's arguments vague or unconvincing. These are legitimate criticisms. But I think he has been partially, if not completely vindicated, by two recent advances that were not fully developed at the time the paper was published.

The undecidability of the spectral gap problem.

Hawking states: if there are mathematical results that can not be proved, there are physical problems that can not be predicted.
Since Hawking wrote this article, Cubitt, Perez-Garcia and Wolf showed that the spectral gap is undecidable by proving that the spectral gap decision problem is equivalent to the halting problem. And the halting problem is the theoretical computational equivalent of Godel's first theorem. This result does indeed suggest that some problems regarding the in quantum physics cannot be predicted, and many of the most challenging and long-standing open problems in theoretical physics concern the spectral gap,

David Wolpert's inference engine proof

Hawking states: "But we are not angels, who view the universe from the outside. Instead, we and our models are both part of the universe we are describing. Thus a physical theory is self referencing, like in Godel’s theorem."
The Wolpert "inference engine" proof is , similar to the results of Gödel’s incompleteness theorem and Turing’s halting problem, and, indeed, even the the Spectral Gap problem. It relies on a variant of the liar’s paradox—ask Laplace’s demon to predict the following yes/no fact about the future state of the universe: “Will the universe not be one in which your answer to this question is yes?” For the demon, seeking a true yes/no answer is like trying to determine the truth of “This statement is false.” Knowing the exact current state of the entire universe, knowing all the laws governing the universe and having unlimited computing power is no help to the demon in saying truthfully what its answer will be.
Philippe M. Binder, a physicist at the University of Hawaii at Hilo, suggests that Wolpert's theory implies researchers seeking unified laws cannot hope for anything better than a “theory of ALMOST everything.”