[FOM] John Baez on David Corfield's book

[Neil Tennant]

On Mon, 29 Sep 2003, Jon Williamson wrote:

> For a while now it has become clear that any philosophical
> foundations that arise out of FOM are not going to be very intuitive and are
> likely to satisfy few people. 

Let P be the claim

"Any philosophical foundations that arise out of FOM are not going to be
very intuitive."

It is not clear to me that P is true. I could not hold P by
generalization from philosophical foundations already proposed, because at
least some of them strike me as intuitive (ZFC and the cumulative
hierarchy, for example).  Nor could I hold P on the basis
of an a priori argument, because I have no clear delineation of the
concept "philosophical foundations that arise out of FOM".

I have no argument with the philosopher of mathematics who wishes to
devote philosophical reflection to a wider range of concepts and issues in
mathematics than is customary in FOM. But I strongly believe that FOM's
focus is on the right concepts and issues, because of their centrality and
importance. That's what gives us the F in FOM.

It remains to be seen whether the further philosophizing about what, to
FOM, are more peripheral or less basic issues, might cause the FOM-er to
reassess what counts as central, important, and basic. And there is still
the prospect that whatever neglected notion N is philosophized about in
Corfield's fashion can have its interest explained entirely in terms of
those notions that are currently taken as central, important and basic in
FOM.

To give just one example: Suppose one were to ask why certain mathematical
concepts or results strike mathematicians as elegant. It might turn out
that the notion "E is elegant" can be analyzed in terms of (or the
appearance of elegance explained in terms of, or reduced to) certain local
and global features of logical syntax, trains of definitions, etc.

Neil Tennant