What? Is Hawking speaking of something other than physics?
Godel and the End of Physics
From the article:
" I mean a set of rules that in principle at least enable us to predict the future to an arbitrary accuracy, knowing the state of the universe at one time. "
This was the goal of classical physics, which was a deterministic system that , in theory, could do exactly that.
But, for the last 100 years or so, we *know* that the real world is not deterministic. So, with the advent of quantum mechanics we simply do not *expect* to be able to predict the future state of the universe to arbitrary accuracy given the state at one time.
What Hawking is talking about is that the classical goal is not possible to achieve. His argument goes further to say there may not be an 'ultimate' theory, even if we allow the types of quantum indeteminacy we know exist.
Again, I don't find this too surprising. I expect to see a sequence of better and better approximations and not ever a fully encompassing theory.