These are constraints from computational complexity.
My point is the question "is it deterministic" is wrong without considering the level of detail you're looking at. Even in deterministic universe, a roll of dice is considered to be undeterministic, and this is good enough for casinos.
If you're asking "in principle", then it might as well be unknowable because, as I pointed out, how we might observe the system to be (our model of it is deterministic or not) doesn't have to correspond at all whether it is actually deterministic or not at the lower level. So there always can be another level which can behave differently.
My point is the question "is it deterministic" is wrong without considering the level of detail you're looking at. Even in deterministic universe, a roll of dice is considered to be undeterministic, and this is good enough for casinos.
If you're asking "in principle", then it might as well be unknowable because, as I pointed out, how we might observe the system to be (our model of it is deterministic or not) doesn't have to correspond at all whether it is actually deterministic or not at the lower level. So there always can be another level which can behave differently.