[daoboy]

I always feel like these frameworks rely on a semantic sleight of hand that sounds plausible on the surface, but when you drill down a bit they render words like 'simulation' 'reality' or 'truth' as either unintelligible or trite, depending on how you define them.

[measurablefunc]

They're defined relative to the axioms. In this case he is using the standard arithmetic & set theoretic constructions to define the terms & functions he's talking about. It's logically sound, whether it makes physical sense or not is another matter.