OK, we *know* that there are unsolvable problems in math. We *know* there is information about the universe we can never have.
At one point, Hawking thought we might be near the end of physics because of the nature of Planck lengths and times. Now, he suspects we may never get to the end because of self-referentiality.
I am truthfully less than convinced by either argument. Godel's results have hypotheses that simply are not met by most physical theories. They are important results *for mathematics*, but I also disagree with Hawking that ever unsolvable problem in math leads to an unsolvable problem in physics. So his link between the math and the physics seems to me, in this case, to be very weak.
So what would the impact of not having a TOE be? Well, research would continue. We would continue to extend our knowledge incrementally (like we have always done) and we won't reach an endpoint. But we would continue to learn.
I fail to see the problem with that, except for those who have a philosophical bias concerning how much we should be able to know.
At one point, Hawking thought we might be near the end of physics because of the nature of Planck lengths and times. Now, he suspects we may never get to the end because of self-referentiality.
I am truthfully less than convinced by either argument. Godel's results have hypotheses that simply are not met by most physical theories. They are important results *for mathematics*, but I also disagree with Hawking that ever unsolvable problem in math leads to an unsolvable problem in physics. So his link between the math and the physics seems to me, in this case, to be very weak.
So what would the impact of not having a TOE be? Well, research would continue. We would continue to extend our knowledge incrementally (like we have always done) and we won't reach an endpoint. But we would continue to learn.
I fail to see the problem with that, except for those who have a philosophical bias concerning how much we should be able to know.