I am unsure now whether he describes the set of mathematical objects by enumeration and evaluation. He definitely describes the set of universes this way, as be

I am unsure now whether he describes the set of mathematical objects by enumeration and evaluation. He definitely describes the set of universes this way, as being “run”, so it is a computation. But you are right that he never discussed the substrate that they are run on. He assumes the existence of that enumeration to be axiomatic, like an uncaused cause, somewhere in the space of all mathematical objects that simply exist. I guess, if we had a proof that all non-computable formal systems are inconsistent then we could also skip one layer and assume the enumeration of all programs as axiomatic in order to be maximally agnostic.