FOM: categorical non-foundations; three challenges for McLarty

Vaughan Pratt pratt at cs.Stanford.EDU
Sun Jan 25 00:33:57 EST 1998

From: Stephen G Simpson <simpson at>
>Challenge 3. McLarty needs to forthrightly concede that, as Harvey put it,
>> there is no coherent conception of the mathematical universe that
>> underlies categorical foundations in your sense.

(Sorry about the nesting, Sol, my usual technique didn't quite work here.)

While I believe there is such a conception, namely the geometric
conception of morphism as a line segment, it troubles me that this isn't
Colin's conception.  On the one hand Colin is an experienced category
theorist while I'm barely an amateur.  On the other, if my elementary
picture of morphism is wrong then I have *no* idea what other elementary
concept, one that a 3-year-old could relate to, would improve on it.

Vaughan Pratt

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