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MagnetoHydroDynamics comments on Logical Pinpointing - Less Wrong
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We don't know whether the universe is finite or not. If it is finite, then there is nothing in it that fully models the natural numbers. Would we then have to say that the numbers did not exist? If the system that we're referring to isn't some physical thing, what is it?
Finite subsets of the naturals still behave like naturals.
Not precisely. In many ways, yes, but for example they don't model the axiom of PA that says that every number has a successor.
True, but the axiom of induction holds, and that is the most useful one.