Seven months ago I posted A Case Against Strong Longtermism on the forum, and it caused a bit of a stir. I promised to respond to all the unaddressed comments, and as a result, have produced a four-part "sequence" of sorts.
The first and last post, A Case Against Strong Longtermism and The Poverty of Longtermism deal with longtermism specifically, while the middle two posts Proving Too Much and The Credence Assumption deal with bayesian epistemology, the iceberg-like structure keeping longtermism afloat.
The subsections are listed below and don't need to be read in any particular order. Special thanks to Max Daniel, Jack Malte, Elliott Hornley, Owen Cotton Barratt, and Mauricio in particular, without whose criticism this sequence would not exist.
Now time to move on to other subjects...
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.