FOM: the interface between philosophy and f.o.m.

[Stephen G Simpson]

Right now the FOM list has a lot of interesting issues on its plate.
But later, when we are less preoccupied with other matters, I'd like
to discuss an important topic that came up recently: the interface
between philosophy and f.o.m.  I find this interface intriguing.
Furthermore, I have always felt that philosophers ought to find it
intriguing, because in f.o.m. one can see how various epistemological
doctrines play out in a scientific setting.

This was behind my posting of 3 Mar 1998 22:38:09 where I said:

 > I feel that it's difficult in principle to separate f.o.m. research
 > from philosophical motivation.  If Dummett's philosophical position
 > is truly different from Brouwer's, then this should be reflected in
 > the mathematics.

Somewhat to my surprise, Adriano Palma and Neil Tennant objected to
this.  Adriano Palma 04 Mar 1998 05:59:45 said:

 > It is a thorny issue whether this should be reflected in the
 > mathematical results one wants to found, ground or otherwise
 > discuss.  The two appear to me independent.

and Neil Tennant 4 Mar 1998 17:34:58 said:

 > My first reaction is: why? Why should it not be possible for a
 > recommended practice, initiated by someone with a certain set of
 > quirky inspirations, to be amenable to a better rationalization later
 > on from wholly different, and more appealing, principles? 

I guess my question about this would be: If philosophical doctrines
have no bearing on f.o.m., then what is philosophy of mathematics all
about?

-- Steve