Bayesianism and the multitude of mathematical structures

It seems that every mathematical structure (there are some technicalities as to how to define it) could in fact be the correct description of fundamental physical structure. This means that making Bayesianism be the whole story about epistemology—even for idealized agents—is a hopeless endeavor. For there is no hope for an epistemologically useful probability measure over the collection of all mathematical structures unless we rule out the vast majority of structures as having zero probability.

A natural law or divine command appendix to Bayesianism can solve this problem by requiring us to assign zero probability to some structures that are metaphysically possible but that our Creator wants us to be able to rule out a priori.