[FOM] Falsify Platonism?

Monroe Eskew meskew at math.uci.edu
Sun May 2 01:33:44 EDT 2010

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

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


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