[FOM] Simpson on Tymoczkoism

Richard Zach rzach at ucalgary.ca
Sun Sep 28 19:37:05 EDT 2003

On Sun, 2003-09-28 at 07:57, Neil Tennant wrote:
> Corfield
> emphasizes the relevance of real/core mathematical practice to the
> philosophy of mathematics, and complains that philosophers pay too little
> attention to it. Perhaps his emphasis here is really on the context of
> discovery---involving the Lakatosian process of conjecture, failed
> attempts at proof, subsequent conceptual tinkering, and eventual success
> with proof---rather than the context of justification.

I think that Corfield  would not see himself as emphasizing discovery
over justification.  The point is that if you are *only* interested in
justification ("What makes this theorem true?"), only in truth and
proof, as it were, you just don't have anything to say about a large
part of mathematical practice.  You don't have anything to say, for
instance, about why some proofs are better (simpler, more explanatory,
more natural) than others.  These questions just can't be answered
without *also* emphasizing the mathematical practice.  But they are not
merely questions about a process of discovery; e.g., when trying to
account for the difference between an explanatory proof and one that's
not, the process of discovery is complete.  

Richard Zach ...... http://www.ucalgary.ca/~rzach/
Assistant  Professor,   Department  of  Philosophy
University of Calgary, Calgary, AB T2N 1N4, Canada

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