FOM: anti-foundationalism

[Stephen G Simpson]

Stewart Shapiro 30 Mar 1999 00:44:47 writes:
 > As far as I know, the FOM discussion is the first time I
 > took some heat for the anti-foundationalist stance itself.

That's interesting.  Evidently the reviewers of your book agreed with,
or at least didn't dispute, your anti-foundational stance.  If I'm not
mistaken, all of the reviewers are academic philosophers.  Are they a
fair sample?

Do you share my impression that many or most academic philosophers
take anti-foundationalism for granted?  I wonder why they do that?

 > >Could you please explain why you yourself ... are so vehemently
 > >opposed to foundationalism?
 > 
 > Foundationalism goes back to the rationalism of, e.g., Descartes,
 > and is a quest to put science (or in this case mathematics) on an
 > absolutely secure foundation (or, failing that, as secure a
 > foundation as is humanly possible).

Do you think the quest for a secure foundation automatically implies
that foundationalism is false?  Does this explain why you yourself are
opposed to foundationalism?

 > I did not mean to be "vehement", as Steve suggested.

It seems to me that the phrases from your book `Foundations Without
Foundationalism' reproduced in 29 Mar 1999 20:17:04 are evidence of
vehement anti-foundationalism.

 > [Weyl] went for an absolutely secure foundation and was willing to
 > cripple mathematics in order to achieve it.

Dramatic metaphors such as this one -- `crippling mathematics' and the
like -- are sometimes adduced rashly, in disregard of relevant
evidence.  Have you taken account of modern work exploring which parts
of standard mathematics can and cannot be developed in the system of
Weyl's `Das Kontinuum' and similar systems?

 > do people think that the modern progress contributes to
 > the original *epistemological* goals of the Hilbert program?

Yes, some people think that.

Earlier you indicated that you have been too busy to read the relevant
discussions here on FOM.  I suggest you have a look at 3 Mar 1999
19:23:38 and the references there, so that we can base this discussion
on relevant evidence.

 > A more modest way to put the thesis of this aspect of my book is
 > that there is value to foundational studies independent of the
 > epistemological goals of the Hilbert program.

This version of your anti-foundationalist thesis is very modest
indeed.  I'm sure everyone can agree with this version of your thesis.
For example, foundational studies may prove their value by keeping
some children off the streets (like midnight basketball).

-- Steve