FOM: the interface between philosophy and f.o.m.
Stephen G Simpson
simpson at math.psu.edu
Wed Mar 4 22:38:36 EST 1998
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
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