FOM: Boolean rings; the quandary of categorical mis-foundations

Vaughan Pratt pratt at cs.Stanford.EDU
Thu Mar 12 19:31:38 EST 1998

From: Stephen G Simpson <simpson at>
>Vaughan Pratt and other proponents of
>categorical mis-foundations have stymied this discussion by
>obstinately denying the underlying mathematical notions, e.g. by
>refusing to admit that there is any distinction whatsoever between
>Boolean rings and Boolean algebras.
>(By categorical mis-foundations I
>mean the absurd attempt to claim that category theory is f.o.m.)  And
>in my opinion this perverse obliteration of technically and
>motivationally significant mathematical distinctions, e.g. signature,
>is a large part of the problem that arises in connection with
>categorical pseudo-foundations.
>Why then do I continue this discussion?  Well, it would be easy and
>not at all inappropriate to dismiss categorical pseudo-foundations as
>total nonsense.  (Indeed, many mathematicians dismiss the entire
>subject of category theory as "abstract nonsense".)
>Vaughan, what do you say?

When you give category theorists the credit for downplaying the importance
of basis, you flatter them at the expense of everyone else who regards
basis as unimportant to the structure of varieties.  As I've said many
times, I'm not a category theorist myself, being entirely neutral on
sets vs. categories (in a neutral environment anyway, clearly not FOM).
Maybe El Nino can take the credit for our weather, but the category
theorists can't take all the credit for clear thinking about bases.

People's foundational preferences are irrelevant to the question at hand.

Vaughan Pratt

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