FOM: category theory, cohomology, group theory, and f.o.m.

[Todd Wilson]

A couple of minor clarifications in my previous post.

On Mon, 21 Feb 2000, Todd Wilson wrote:
> It is perhaps also worth mentioning another, more modern example of
> intuition lagging strikingly behind results:  the almost universally
> strongly held intuition that P is not equal to NP.

Of course, I meant "results lagging strikingly behind intuition".
Several researchers in complexity theory have expressed the opinion to
me that their confidence in P not equal to NP is only exceeded by
their lack of any idea of how to explain it formally.

> So, without taking up any of the particular matters that Simpson is
> criticizing in Bauer's post (I see that Andrej has just written a
> response), I would propose that we acknowledge that the intuitions of
> category theorists concerning the fundamental nature of their subject,
> even in the absence of tangible results vindicating these intuitions,
> need not be a "mass hallucination", and instead make an honest attempt
> to discover whether there really is anything to them.

I should have said "discover what there is to them".  In other words,
I'm sufficiently confident that there is something to these
intuitions; the only questions are what it is and how to explain it.
Anyone interested in better understanding these intuitions should at
least look at the two book chapters by J. L. Bell mentioned in my
previous post and can continue by looking at the references to the
writings of Lawvere and the Synthese essays of Bell mentioned therein.

-- 
Todd Wilson
Computer Science Department
California State University, Fresno