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Charlie-Boo wrote:
> lugita15@xxxxxxxxx wrote:
> > It is very easy to formalize arithmetic of finite numbers, i.e.
> > First-order Peano Arithmetic.
>
> It's much easier (better by Occam's Razor) to see that Peano's Axioms
> amount to the assertion that the set of natural numbers is recursively
> enuerable. Do you agree to this equivalence?
Eh? What can that possibly mean, given that taken literally it is quite
plainly false? (For a start: Any finite set is trivially r.e.. So the
assertion that the set of natural numbers is r.e. is compatible with
there only being a finite number of naturals, while any model of PA
must have an infinite domain. So PA can't can't "amount to amount to
the assertion that the set of natural numbers is recursively
enumerable".)
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