FOM: quasi-empiricism and anti-foundationalism

[Stephen G Simpson]

Stephen Ferguson 16 Sep 1998 15:18:36 writes:

 > if what Lakatos calls the "Euclidean" view is taken of mathematics,
 > there would be no point in all this rigour, because we would be
 > certain, right from the start that we were correct.

I truly don't understand what you are driving at.  Euclideanism as
*anti*-rigor?  I think it's pretty conventional to view Euclid as the
father of mathematical rigor: definition-theorem-proof.  I agree with
this conventional view.  Mathematical rigor is our means of attaining
mathematical certainty.

 > can we finally on this list begin to see what was
 > so odious about ninteenth century foundationalism?

No.  At least I can't see it.  Tell me, what was so odious about 19th
century foundationalism?  

In your posting of 12 Sep 1998 00:43:56 you referred to

 > ... the discredited philosophical doctrine of foundationalism ...

When was it discredited?  Who discredited it?  How?

 > The 'mathematical' discipline of F.O.M. is in one sense the heir of
 > ninteenth century foundationalism: it grows out of the work of
 > mathematicians come philosophers such as Frege, Hilbert, Brouwer,
 > Cantor, etc. but carries on the formal side of their work, without
 > regard (or without primary/ substantial regard) for the
 > philosophical motivations behind that earlier work.  If you
 > understand that, then you can see why Hersh did not include
 > Friedman et al in his sweeping condemnation of foundationalists.

No, this is flatly wrong.  A lot of Harvey Friedman's f.o.m. research
stems from the same kinds of philosophical motivations as Frege,
Hilbert, Brouwer, et al.  Don't let Harvey's talk of whoring confuse
you.  But perhaps I should let Harvey speak for himself on this.

In any case, you said "Friedman et al".  Well, I myself should
probably be counted as one of the "et al", and I certainly aspire to
this kind of philosophical significance in my own f.o.m. research.

 > Giving such a Stratoan account ...

I don't understand much of what you said about Stratoism.  But I'm
certainly in favor of greater collaboration between f.o.m. researchers
and philosophers of mathematics.  If you also want collaboration, then
why are you quasi-empiricists so hostile, even openly hostile, to what
you call "foundationalism".  Is this an artifact of postmodernism,
continental philosophy, etc.?

 > But to do that, there will need to be a much greater awareness to
 > the fact that mathematicians and philosophers use different
 > vocabularies, which have some overlap, but also some 'false
 > friends', words that sound alike but have differnt connotations.

Yes, I agree, we need to be aware of this.  For a start, how about
defining what you mean by "foundationalism"?

-- Steve