I don’t think there’s a consensus on whether physics is continuous or discrete, but I expect that what matters ethically is describable in discrete terms. Things like wavefunctions (or the motions of physical objects) could depend continuously on time or space. I don’t think we know that there are finitely many configurations of a finite set of atoms, but maybe there are only finitely many functionally distinct ones, and the rest are effectively equivalent.
I think we’ve also probed scales smaller than Planck by observing gamma ray bursts, but I might be misinterpreting, and these were specific claims about specific theories of quantum gravity.
Also, a good Bayesian should grant the hypothesis of continuity nonzero credence.
FWIW, though, I don’t think dealing with infinitely many possibilities is much of a problem as made out to be here. We can use (mixed-)continuous measures, and we can decide what resolutions are relevant and useful as a practical matter.
I agree that a good Bayesian should grant the hypothesis of continuity nonzero credence, as well as other ways the universe can be infinite. I think the critique will be more compelling if it was framed as “there’s a small chance the universe is infinite, Bayesian consequentialism by default will incorporate small probability of infinity, the decision theory can potentially blow up under those constraints “
Then we see that this is a special unresolved case of infinity (which is likely an issue with many other decision theories) rather than a claim that the universe is by its very nature infinitely non-measurable and thus not subject to evaluation, which is quite an intuitively extreme stance!
(The specialness of this critique makes it clearer where the burden of proof is, akin to “our modest epistemology forces us to believe that the stars do not exist).
I don’t think there’s a consensus on whether physics is continuous or discrete, but I expect that what matters ethically is describable in discrete terms. Things like wavefunctions (or the motions of physical objects) could depend continuously on time or space. I don’t think we know that there are finitely many configurations of a finite set of atoms, but maybe there are only finitely many functionally distinct ones, and the rest are effectively equivalent.
I think we’ve also probed scales smaller than Planck by observing gamma ray bursts, but I might be misinterpreting, and these were specific claims about specific theories of quantum gravity.
Also, a good Bayesian should grant the hypothesis of continuity nonzero credence.
FWIW, though, I don’t think dealing with infinitely many possibilities is much of a problem as made out to be here. We can use (mixed-)continuous measures, and we can decide what resolutions are relevant and useful as a practical matter.
I agree that a good Bayesian should grant the hypothesis of continuity nonzero credence, as well as other ways the universe can be infinite. I think the critique will be more compelling if it was framed as “there’s a small chance the universe is infinite, Bayesian consequentialism by default will incorporate small probability of infinity, the decision theory can potentially blow up under those constraints “
Then we see that this is a special unresolved case of infinity (which is likely an issue with many other decision theories) rather than a claim that the universe is by its very nature infinitely non-measurable and thus not subject to evaluation, which is quite an intuitively extreme stance!
(The specialness of this critique makes it clearer where the burden of proof is, akin to “our modest epistemology forces us to believe that the stars do not exist).