FOM: set/cat "foundations"

Colin Mclarty cxm7 at
Thu Feb 26 21:41:08 EST 1998

	When I have more time I'll comment on which kinds of music
are most comparable to SET/TOP. Here I point out a confusion by
Mossakowski which surprizingly escaped Friedman in his Thu, 26 Feb

>Mossakowski 1:53PM 2/26/98 wrote.

>Perhaps a problem of categorical foundations is that the meta-theory
>of first-order logic is naive set theory.

	Mossakowski suggested categorical foundations could use
sketches instead of first order logic, and Friedman said he might
be onto something. But oviously a formal metatheory of first order 
logic is easy to give in a weak intuitionistic third order 
arithmetic--thus in any topos with natural numbers, and in many 
weaker categories. 

	If you think first order logical foundations require
metatheory, and the categorical metatheories are "merely formal" 
and not foundational; then why would you say anything different
about categorical metatheory for sketch foundations?

	As to strength, there are various kinds of sketches, 
some weaker than first order logic and some stronger.


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