A different perspective: Godel doesn’t say that there is any particular question about reality that we cannot answer, only that however far into the model-building enterprise we get, there will always be some undecidable propositions, which can be translated into questions about reality with the TM-enumerating-sentences experiment. So if we have a model of reality M and it fails to answer a question about reality Q then there’s always hope that we could discover further regularities in reality to amend M so that it answers Q, but there is no hope that we would ever be free of any open questions. Am I correct in thinking that this rules out the possibility of a GUT, at least if a GUT is defined as a model that answers all questions.
Godel doesn’t say that there is any particular question about reality that we cannot answer
Of course! It’s a theorem about math. There are no theorems about reality.
Am I correct in thinking that this rules out the possibility of a GUT, at least if a GUT is defined as a model that answers all questions.
Yes and no. You can build computers that enumerate proofs even in universes with simple and known physics, like the Game of Life. But to mathematically define something like an infinite Game of Life grid, you need integers, and we don’t have a complete axiomatization of those. So you could have a GUT that’s completely defined “relative to the integers”. I guess most physicists would accept that as a good enough GUT, even though it’s incomplete in the Godelian sense.
A different perspective: Godel doesn’t say that there is any particular question about reality that we cannot answer, only that however far into the model-building enterprise we get, there will always be some undecidable propositions, which can be translated into questions about reality with the TM-enumerating-sentences experiment. So if we have a model of reality M and it fails to answer a question about reality Q then there’s always hope that we could discover further regularities in reality to amend M so that it answers Q, but there is no hope that we would ever be free of any open questions. Am I correct in thinking that this rules out the possibility of a GUT, at least if a GUT is defined as a model that answers all questions.
Of course! It’s a theorem about math. There are no theorems about reality.
Yes and no. You can build computers that enumerate proofs even in universes with simple and known physics, like the Game of Life. But to mathematically define something like an infinite Game of Life grid, you need integers, and we don’t have a complete axiomatization of those. So you could have a GUT that’s completely defined “relative to the integers”. I guess most physicists would accept that as a good enough GUT, even though it’s incomplete in the Godelian sense.