[FOM] Constructivism and physics

[Alasdair Urquhart]

On Thu, 16 Feb 2006, A.J. Franco de Oliveira wrote:

> I dont agree. The predicate "standard" in, say,
> Nelson´s IST is not definable classically, nor
> are other concepts (infinitesimal, etc.) defined
> in terms of "standard". So, if one takes these
> new concepts seriously, say in modelisation of
> phenomena from physics, economy or whatever, or
> even pure mathematics, and gives nonstandard
> proofs of such results, there is no a priori
> reason to suppose that one must always find an
> equivalent classical proof.


Sorry, I should have been more explicit in what
I said.  What I meant to say was that every
theorem expressed in terms of standard mathematical
concepts that is provable with nonstandard
analysis is already provable in standard set theory.

By the way, I did not mean to say anything negative
about nonstandard analysis.  I think it is a great
mathematical discovery of Robinson, and that it
deserves the widest possible use.

Alasdair Urquhart