I think the hypotheses are assumed to be mutually exclusive. For example you could have a long list of possible sets of laws of physics, at most one is true of this universe.
Right, that’s another way of stating the same assumption. But we usually apply Occam’s razor to statements in languages that admit sets of non-mutually-exclusive hypotheses of infinite size. So you’d need to somehow collapse or deduplicate those in a way that makes them finite.
I find I mostly apply Occam’s razor to mutually exclusive hypotheses, e.g. explanation A of phenomenon X is better than explanation B because it is simpler.
I think the hypotheses are assumed to be mutually exclusive. For example you could have a long list of possible sets of laws of physics, at most one is true of this universe.
Right, that’s another way of stating the same assumption. But we usually apply Occam’s razor to statements in languages that admit sets of non-mutually-exclusive hypotheses of infinite size. So you’d need to somehow collapse or deduplicate those in a way that makes them finite.
I find I mostly apply Occam’s razor to mutually exclusive hypotheses, e.g. explanation A of phenomenon X is better than explanation B because it is simpler.