The existence of determinism could very well be an undecidable problem.
In essence, in my opinion, it is impossible to determine whether a system is deterministic or not from within the system itself.
With a good night’s sleep and a clear(er) morning head, I feel better able to think about this problem. Surface thoughts:
I think I agree at the moment that you probably cannot prove that you live in a non-deterministic system. There is always the lingering doubt that any randomness you find is, as credited to Hooft, an emergent effect of some underlying system you simply don’t (can’t?) understand yet.
If the system is deterministic, you may be able to unravel all of its mysteries. If your system of Physics is sufficient to describe predict everything that you can observe, then there is no reason left to doubt the system’s determinism. Make no mistake, though: that is an extremely high bar.
With a good night’s sleep and a clear(er) morning head, I feel better able to think about this problem. Surface thoughts:
I think I agree at the moment that you probably cannot prove that you live in a non-deterministic system. There is always the lingering doubt that any randomness you find is, as credited to Hooft, an emergent effect of some underlying system you simply don’t (can’t?) understand yet.
If the system is deterministic, you may be able to unravel all of its mysteries. If your system of Physics is sufficient to
describepredict everything that you can observe, then there is no reason left to doubt the system’s determinism. Make no mistake, though: that is an extremely high bar.