[FOM] John Baez on David Corfield's book

Stephen G Simpson simpson at math.psu.edu
Fri Oct 24 16:41:46 EDT 2003

Alasdair Urquhart Mon, 13 Oct 2003 10:26:22 -0400 writes:

 > I was surprised by the fact that a few people engaged in heated
 > discussions on FOM of David Corfield's recent book "Towards a
 > Philosophy of Real Mathematics" without having read it.

Alasdair, who are you referring to?  I haven't read the book (nor do I
plan to), so I didn't comment on it.  My comments were based solely on
the material available at Corfield's web site.

What puts me off about Corfield is, first of all, his obvious
hostility toward f.o.m.  Why is he so hostile?  And, why has he been
venting his hostility here on the FOM list, of all places?

>From one of his remarks (1 Oct 2003), he seems to think philosophers
interested in f.o.m. (what he calls "the neo-Fregean program") are
getting way too much money (a "huge chunk").  But, if he wants piles
of money, philosophy of mathematics is the wrong profession anyway, so
what is his real problem?

You tried to explain it as follows:

 > There are quite a lot of passages in the book that could be read as
 > showing hostility to logic and formal research in the foundations
 > of mathematics, but I believe that they are rather to be
 > interpreted as directed against what Corfield takes to be a
 > narrowness in the current philosophy of mathematics community.

I don't know what is in the book.  What I do know is that, here on the
FOM list, Corfield's comments have been shrilly and obtusely hostile
to f.o.m.  As just one example, Corfield said

   As for foundations, it may just be the case that they have
   naturally evolved to become completely divorced from the question
   of the proper organisation of mathematical concepts.  

   (Corfield Sep 25 2003)

thus disgarding the obvious fact that mathematicians choose to
organize their concepts in a thoroughly foundationalist manner
(definition-theorem-proof).  This goes far beyond a call for
philosphers to broaden their horizons.

Another irritating aspect of Corfield's postings is that he keeps
insisting there is lots of non-f.o.m. mathematics that is
philosophically interesting, but he refuses to give even one example.
Instead, he answers the challenge with airy, patronizing nonsense:

   When philosophers treat a knowledge-acquiring discipline, a large
   part of what they do is to study the means by which this knowledges
   grows.  In this case, there's no need to point to a particular
   concept or theorem, except by way of a case study to illustrate
   some of the forms this growth takes. A large part of philosophy of
   science concerns this task, e.g., at the moment the role of
   modelling in science is very prominent. Scientists have of course
   been using models for centuries, [...]  

   (Corfield, 1 Oct 2003)

At any rate, it seems Corfield can't name any "real mathematics" that
is of philosophical interest.

Peter Smith (FOM, 18 Oct 2003) concurs: "We are repeatedly told that
it would be salutary for philosophers of mathematics to take a hard
look at some contemporary real mathematics.  And various examples are
mentioned, but never in enough detail to get much clue as to what
philosophical lessons are there to be drawn."  And John Steel (FOM, 4
Oct 2003) said: "At various points, it is hard to distinguish the
activity Corfield advocates from popular science writing."

In other words, philosophically speaking:

                Where Is The Beef ????

Of course I am not saying there is no beef, i.e., "real mathematics"
that is of philosophical interest.  I am only saying that Corfield
hasn't come up with any beef, at least not here on FOM.

A few FOM subscribers sympathetic to Corfield have been more
forthcoming with alleged beef.  I hope to take up their comments
later, if I get time.

-- Steve

Stephen G. Simpson
Professor of Mathematics
Pennsylvania State University

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