Unknown, your argument amounts to this: Assume we have a countable set of hypotheses. Assume we have a complexity measure such that, for any given level of complexity, there are a finite number of hypotheses that are below the given level of complexity. Take any ordering of the set of hypotheses. As we go through the hypotheses according to the ordering, the complexity of the hypotheses must increase. This is true, but not very interesting, and not relevant to Occam’s Razor.
In this framework, a natural way to state Occam’s Razor is, if one of the hypotheses is true and the others are false, then you should rank the hypotheses in order of monotonically increasing complexity and test them in that order; you will find the true hypothesis earlier in such a ranking than in other rankings in which more complex hypotheses are frequently tested before simpler hypotheses. When you state it this way, it is clear that Occam’s Razor is contingent on the environment; it is not necessarily true.
If you define Occam’s Razor in such a way that all orderings of the hypotheses are Occamian, then the “razor” is not “cutting” anything. If you don’t narrow down to a particular ordering or set of orderings, then you are not making a decision; given two hypotheses, you have no way of choosing between them.
In fact, an anti-Occam prior is impossible.
Unknown, your argument amounts to this: Assume we have a countable set of hypotheses. Assume we have a complexity measure such that, for any given level of complexity, there are a finite number of hypotheses that are below the given level of complexity. Take any ordering of the set of hypotheses. As we go through the hypotheses according to the ordering, the complexity of the hypotheses must increase. This is true, but not very interesting, and not relevant to Occam’s Razor.
In this framework, a natural way to state Occam’s Razor is, if one of the hypotheses is true and the others are false, then you should rank the hypotheses in order of monotonically increasing complexity and test them in that order; you will find the true hypothesis earlier in such a ranking than in other rankings in which more complex hypotheses are frequently tested before simpler hypotheses. When you state it this way, it is clear that Occam’s Razor is contingent on the environment; it is not necessarily true.
If you define Occam’s Razor in such a way that all orderings of the hypotheses are Occamian, then the “razor” is not “cutting” anything. If you don’t narrow down to a particular ordering or set of orderings, then you are not making a decision; given two hypotheses, you have no way of choosing between them.