Hawking theorizes that it may well be gravitational waves alone that might have started our universe off, so his use of the term "nothing" essentially means nothing besides the gravitational waves themselves. Taking his words out of their context is not helpful in understanding what he was actually saying.
Since you did not specify who your post was meant for I will assume it was for me since I mentioned Hawking's pathetic attempt at philosophy. If you want some tips concerning addressing a post to someone please let me know. Ok, so now to your statements above.
1. I did not quote his statement in any context at all. So it is impossible I took what he said out of context. To claim a statement was out of context is the last shriek a person makes in defense of a doomed argument in many cases.
2. Also in this case his statement's meaning is obvious without mentioning any context.
3. Hawking has arrogantly proclaimed the entire field of philosophy was no longer viable. However he hypocritically then spent most of his latest book making statements of philosophy which he has no competency with instead of science for which he is supposed to be competent.
4. Now then lets see that even if what you stated was actually what he meant concerning gravity waves. (however since he did not actually say waves I would like you to explain how it is you know he meant waves instead of what he actually said, but I will simply assume you are right and evaluate whether claiming his claim was about waves makes what he said less absurd).
5. As even the physics learned by freshmen in college (and I have far more than that) is enough to see that gravity or gravity waves cannot bring anything into being.
6. Gravity or gravity waves (whatever you think the difference is) are a property of mass. However Hawking posits the insane claim that gravity (waves?) brought mass into existence. This is ridiculous.
7. Additionally Hawking states that gravity (waves?) is the explanation for the universe coming into existence out of nothing. What the heck is he talking about. He has equated gravity (waves?) with nothing. Yet gravity is something and not nothing. So in effect Hawking is saying that something is the explanation for how something created everything out of something. This sounds like teenagers smoking pot discussing the nature of reality.
8. As all philosophers do or should know nothing has no causal relationship with any and all effects. And nothing (not something, even gravitational waves) is what actually existed prior to the big bang in the sense of matter, space, and time which includes gravity waves.
9. If someone was drinking the Kool-Aid that the theoretical physics are handing out so that they wanted to resurrect even a still born theory like what Hawking stated they might attempt to suggest that Hawking was talking about the law of gravity. However that is no help either as natural laws do not stand in causal relationships either. 2 + 2 for example has never created 4 of anything.
BTW I have a math degree but forget my qualifications. Everything I have stated above is consistent with mainstream physics, philosophy, cosmology, and applied mathematics. I first heard of Hawking's abortive attempt at philosophy in the non-scientific statement from him that I quoted while listening to a very well credentialed philosopher and a professor in pure mathematics from Princeton or Oxford (I can't remember which ).
