FOM: Picturing categorical set theory, reply to Silver (fwd)

[Charles Silver]

On Thu, 22 Jan 1998, Walter Felscher wrote:

> Not about functions, but about the naive notion of iterative set formation:
> 
>    Dana S.Scott: Axiomatizing Set Theory
>    in: Proceed.Symposia in Pure Math. , vol. 13 , part II , ed.Th.Jech 
>    A.M.S. 1974

	Thank you.  I think I may be familiar with this paper.  I read one
awhile back in which Scott developed an account like the ones I mentioned
by Boolos and Shoenfield.  (I've seen a couple of others too. I just
didn't bother mentioning them.)  Or, is this paper of Scott's something
different?  What I'm looking for is a development of category theory, or
perhaps topos theory, that is based on some underlying *conception*.  It
seems to me that there has to be *some* relationship between an underlying
conception (that arises somewhat naturally and intuitively) and a later
mathematical development, for the later mathematical development to be
claimed to be "foundational."  I realize that my focus may be much too
narrow here and that there are many other reasons for claiming that a
branch of mathematics is "foundational," but I think this should be one
component.  Don't you think so? 

Charlie Silver
Smith College