[FOM] Remedial mathematics?

[Monroe Eskew]

Jeremy,

I am curious about your use of the word "essentialism," as it sounds
loaded with philosophical connotations.  To me it seems odd to think
of a first-order axiomatizations as capturing the essence of
something, given:

1) Computable axiomatizations are usually incomplete. (Goedel).
2) First order axiomatizations usually are incapable of uniquely
specifying a structure. (Lowenheim-Skolem)

-Monroe


On Mon, May 23, 2011 at 7:11 PM, Jeremy Shipley
<jeremyrshipley at gmail.com> wrote:
> I would have thought that even if ordinary mathematics is
> existentialist, most fom practitioners would be essentialist.
> Otherwise why care about consistency proofs in the first place, which
> find their relevance, or at least their historical motivation, within
> an essentialist program?