If we are in a Finite Occamian Multiverse, then the Many Worlds interpretation of quantum mechanics must be false, because if it were true, then any multiverse address would have to contain the complete branching history of the universe, so its length would be proportional to the mass of the universe times the age of the universe.

As one rationalist's modus ponens is another's modus tollens, the quantum nature of our world makes me doubt the Finite Occamian account of the mathematical universe; a Turing machine isn't really the native platform for the evolution of the wavefunction. In fact, the FOM hypothesis should imply that our underlying physics will turn out to be a rather simple finite state automaton or something of the sort, and that doesn't seem likely to me.