[FOM] John Baez on David Corfield's book

[Charles A Stewart]

Stephen Simpson wrote:
> I haven't read Corfield's book, but judging from this web page,
> Corfield's "anti-foundationalist" preoccupations sound similar to
> those of Tymoczko and Hersh.

I also haven't read Corfield's work, but I have ordered it.  I recommend that
people who are interested in this debate read at least pages 5-10 from the
chapter available from the publisher that concerns "The Foundationalist Filter":
  http://assets.cambridge.org/0521817226/sample/0521817226WS.pdf

Despite his attachment to Lakatos, I didn't get the impression that Corfield was
anti-foundationalist in the sense of Tymoczko and Hersh (ie. was some some of
empiricist or pragmatist about mathematical entities); rather while I guessed
that Stephen would dislike Corfield's work, I expected him to dislike its
"list-2" mindset.

Here is a quote from the introduction that I think crystallises the
disagreement:  Corfield says that a reason why mathematics is treated
differently by philosophers of science than physics is that philsophers
think:

  The mathematics relevant to foundational questions, which is all that
  is relevant to philosophers, was largely devised before 1930, and that
  which came later did not occur in mainstream branches of mathematics but
  in the foundational branches of set theory, proof theory, model theory
  and recursion theory.  Physics, meanwhile, is still resolving its
  foundational issues: time, space, causality, etc.

and goes on to say that this view imposes a filter that screens off
philosophers of science so that they "fail to detect the pulse of
contemporary mathematics".

It seems to me that Corfield and Simpson can agree to disagree: my
interpretation is not that Corfield is trying to put across a new set of
fundamental mathematical concepts, but rather is saying that philosophers of
mathematics are ignoring philosophically interesting work because it is not
about fundamental concepts.  It would be as if philosophers of physical science
thought biology was not interesting because biology had nothing to say about the
fundamental constitution of the universe.

I think also the inflammatory nature of the book for some FOMers would be
reduced if we were to read "core mathematics" for "real mathematics".

Charles


A few more relevant posts by Stephen from the golden age:
  http://www.cs.nyu.edu/pipermail/fom/1997-November/000178.html
   - Simpson's original attempt to try to separate what is FOM from what is not.

  http://www.cs.nyu.edu/pipermail/fom/1997-November/000233.html
   - Simpson on why he thinks Chow's lemma doesn't cut it.

  http://www.cs.nyu.edu/pipermail/fom/1998-January/000775.html
   - Simpson introduces his "list-2" definition

  http://www.cs.nyu.edu/pipermail/fom/1998-January/000853.html
   - Simpson talks about how we arrive at fundamental mathematical concepts