FOM: categorical dys-foundations

Vaughan Pratt pratt at cs.Stanford.EDU
Sun Mar 1 01:39:12 EST 1998

From: Stephen G Simpson <simpson at>
>Vaughan, I'm surprised at you.  The FOM list is no place for
>insubstantial attacks based on "technical narrowness" or other alleged
>educational deficiencies.

I'm not sure I understand the complaint.  What I said was neither
insubstantial, an attack, nor intended to reflect on anyone's education.
With regard to the second, all of us are technically narrow with respect
to one or another dimension.  If you feel that category theory is not
worth bothering about, I don't understand why it would upset you to be
perceived as narrow with respect to the set-category axis.

>I've slogged my way through a fair amount of categorical literature,
>including several of the topos books that you mentioned.

I've slogged my way through a fair number of algebraic topology books,
probably at a comparable time of life to your efforts with topos theory.
If your grasp of category theory to date is anything like my grasp of
algebraic topology to date then I can confidently say that you currently
have no basis whatsoever for telling those writing about categorical
foundations that their subject is "a sham, false, misleading, etc etc"
(your words).

>High standards are necessary, in order to protect genuine f.o.m. against
>envious attackers, such as the "list 2" crowd.

No comment needed.

>I'm sure that the books you mentioned are all very serious and
>well-meaning.  I view them as expounding some interesting technical
>relationships between certain aspects of category theory and certain
>aspects of mathematical logic.  The only point about category theory
>that I have tried to make here on the FOM list is that topos theory
>isn't f.o.m.

I imagine they view you in much the same light.

>The challenge has not been met.  The attempts to meet it have dissolved
>into incoherence.

And *you* complain about insubstantial attacks.

Vaughan Pratt

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