[FOM] Falsify Platonism?

[Monroe Eskew]

On Thu, Apr 29, 2010 at 3:02 PM, Andrej Bauer <andrej.bauer at andrej.com> wrote:
> I would like to remind the participants of this discussion of an
> alternative definition of natural numbers which is algebraic and
> categoric in the sense that it defines the natural numbers up to
> isomorphism as an initial algebra. This definition is expressed in
> first-order logic.

Of course in set theory you can just define the natural numbers as
omega, which is unique.  I don't think the reason for interest in PA
lies in an intuition that it "defines" the natural numbers, but
rather:

(1) The second order version is categorical.
(2) The first order version is reasonably powerful, but
(3) Goedel's incompleteness theorems.


Monroe