Very interesting, and the kind of technical aspect I tried to avoid by not refuting "face-on" since I don't feel qualified to answer this without looking into i

Very interesting, and the kind of technical aspect I tried to avoid by not refuting "face-on" since I don't feel qualified to answer this without looking into it further :) Still, if there are reasons to allow uncomputable numbers as elements of a quantum theory, that still doesn't invalidate the larger point that any predictions of those theories are computable; it's just a constraint on which axiom scheme we follow when manipulating our equations. Again, even if a theory involves uncountable sets, it may still have countable models (following either Skolem's "paradox", or a similar argument; since QM operates at much higher level than formal systems, I'm not sure if it's first-order, second-order, higher-order, etc.).