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Peter_Smith wrote:
> 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,
Also with there being an infinite number, if it is r.e. Don't you
think the set of natural numbers is r.e.?
C-B
> 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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