The quote you link to (here's a link for those in the US since google books links are sometimes country-specific) doesn't seem to be basing this on any other writings of Hawkings besides the one they quote on p. 121, rather they seem to be inferring that Hawking thought the laws of physics were needed to protect the laws of logic based on his argument about time travel (or treating it as an unexamined presupposition of his argument, perhaps). I think they are simply misreading his argument though. If anyone isn't able to see the google books preview, here's Hawking's quote:
By traveling in a space ship on one of these closed timelike curves, one could travel into one's past. This would seem to give rise to all sorts of logical problems, if you were able to change history. For example, what would happen if you killed your parents before you were born. It might be that one could avoid such paradoxes by some modification of the concept of free will. But this will not be necessary if what I call the chronology protjection conjecture is correct: The laws of physics prevent closed timelike curves from appearing
The authors comment:
The problem with Hawking's argument is that it presupposes that the laws of physics are required to "protect" the laws of logic. But this gets things the wrong way round. The laws of logic (in particular, the law that there can be no true contradictions) are more fundamental than the laws of physics, and so the laws of logic will be respected whatever the laws of physics are. To say that the laws of physics must be such as to rule out any possibility of a time travel paradox is like saying that the laws of physics must be such as to prevent any manufacturing process that produces circular squares.
But I think Hawking's idea is not that he thinks there's a possible world where the laws of logic are violated, rather he's just saying that if one fact about the laws of physics might seem to lead to a logical paradox (namely, the fact that the laws of general relativity in principle allow for backwards time travel, with time travel often seen as being impossible since it would lead to logical contradictions like the grandfather paradox), since obviously any real universe's laws can't lead to logical paradoxes (taking the rules of logic as basic), there must be some other aspect of the laws of physics that prevents the seemingly-paradoxical scenario from occurring (this is part of the reason that he postulates the chronology protection conjecture, though there are other possible ways of having time travel without paradox like the Novikov self-consistency principle, which is probably what he was referring to when he commented 'It might be that one could avoid such paradoxes by some modification of the concept of free will').
Consider the analogous case of a proof by contradiction in some branch of mathematics like arithmetic. One might for example start by assuming there is a largest prime number, and then using that assumption in common with other basic assumptions about arithmetic, show it leads to the conclusion that one can construct an even larger prime number, contradicting the original assumption. From this, one concludes that in fact there must be no largest prime number. But is this sort of argument saying the assumptions of arithmetic are more basic than those of logic, and that the conclusion "there is no largest prime number" is being used to "protect" the laws of logic? Clearly not, and similarly Hawking's conjecture that it is not actually possible to go back and interact with your grandfather before he conceived any children (since in combination with some notion of 'free will' that assumption could lead to a paradox) is not intended to "protect" logic, just to infer something about what laws are possible based on presupposing that there can be no genuine logical paradoxes.