[FOM] Simpson on Tymoczkoism

David Corfield david.corfield at philosophy.oxford.ac.uk
Fri Sep 26 04:07:18 EDT 2003

Stephen G Simpson wrote

>It does not seem reasonable for authors like Tymoczko and Hersh, and
>perhaps Corfield, to ignore or downplay the rigorous
>definition-theorem-proof methodology, yet still claim to be in touch
>with "the pulse of contemporary mathematics."

I can only speak for myself of course. This reaction is very common. When
talk about some features of the life mathematics other than proof, you get
accused of downplaying it. It's as though the world's zoologists were
to deal with the fact that an elephant has a trunk every time they discuss
Someday a young zoologist discusses the role of the elephants ears without
mentioning the trunk, and is pointedly asked "Do you really believe
don't have trunks?"

Conceptions of space are a very important part of contemporary mathematics,
just as they have always been. (a) For a more complete philosophical account
of mathematics should we not look at these conceptions? (b) Must anyone who
does this be required to mention theorem-proof methodology to avoid
accusations of downplaying it, even if it is not relevant to their

What we need is another list. COOM - conceptual organisation of mathematics.
I'm not in a position to run such a thing at present. Any volunteers?

David Corfield

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