[j2kun]

We don't know that the physical world has infinite precision. In particular, time doesn't even seem to be continuous as far as we can tell (cf. Planck constant). And we think there's a finite amount of mass in the universe, so how could we encode arbitrarily large natural numbers (as is required to model Peano arithmetic)?

[yohanatan]

We don't have to encode arbitrarily large natural numbers. Rather we have to encode the rules that allow us to construct them (which is quite simple actually). And, I think 'digital physics' is more compatible with Incompleteness implications than the alternatives; not less.

[j2kun]

How can you construct something which is larger than the amount of mass in the universe?