I wonder if the diachronic perspective on induction mitigates the grue/bleen paradox. Remember: the predicate "grue" means "green if looked at before future time t, blue after." (Vice versa for bleen.) The paradox is that the usual account of induction doesn't explain why we infer that things are green rather than grue (or any of an infinite number of variants of grue), because all past observations are equally consistent with grue and green.
Now there is a symmetry between grue and green: something is "green" if it's grue before time t and bleen after. This symmetry means that the best one can do is say "all reasonable agents should have consistent relative inductive biases." As Tarun pointed out in comments a long time ago, natural selection could not, in any obvious way, have made us prefer blue/green to grue/bleen because natural selection can't see into the future.
On a synchronic theory of induction this is a serious problem: there is nothing in the past to tell green and grue apart. But suppose one has a diachronic theory: in that case, the relevant question becomes, "is it possible for two inductive agents, starting with (possibly different) simple theories about the world and developing these theories according to a good rule of motion -- good enough to have survived natural selection -- to have inconsistent green/grue preferences?" The answer to this question is not obvious, but it's clearly not obviously yes, which is what you'd need for the paradox; and it seems at least plausible that the answer is no. In particular, in the case where all creatures have a common ancestor, the initial simple theory is the same, and the question is whether isolated populations could have developed different rules of motion that were (a) good and (b) led to discontinuous relative inductive biases. It would be very odd if the answer to this question were yes.