I'm very happy to see others writing about Lacan's use of mathematics, e.g. his use of knot theory in Encore XX, something that I've always meant to return to and make an honest and careful study of, "when I have time." About categories in Aristotle--this summer I read Aristotle's work "Categories" and for a little while was very excited about the category-theoretic possibilities in it. Part of what he does in "Categories" is this: regard all "things" (leaving aside for the moment the question of defining a "thing"!) as having a partial-ordering in which x \leq y iff y is predicated of x. Again, Aristotle doesn't define "predicated," but from context he seems to only want to include propositions which are true or meaningful or something like this in his notion of predication, so that this partial-ordering tells you some useful things. At first read, this seems very exciting--since there are many possible ways in which y can be predicated of x, this should be a category in which all those propositions which predicate y of x are the hom-sets. But reading further in the Organon and then looking at a bit of other people's commentaries on "Categories," it seems that Aristotle only wants to consider the copula, "y is x," as his only form of predication. So his category really indeed is just a partially-ordered set. (And he can say some interesting things about it--e.g. existents, really-existing material things in the world, are just minimal elements in this partially-ordered set.) So my sense of it is that Aristotle did not use the word "kategoria" in a way like how we use it, which is a bit disappointing. But there is probably a good opportunity here for someone to come along and give a properly categorical generalization of what Aristotle does in "Categories" and see what you can do with it. Sorry if it's too off-topic, Andrew S. On Thu, 14 Feb 2013, Johannes Huebschmann wrote:
I guess these observations should be interpreted with circumspection, in the light of Lacan's usage of topological notions in psychoanalysis, see e.g. Sokal-Bricmont, Impostures intellectuelles p. 55.
The term category goes back to Aristotle; the word (kategoria) in inself is older but it seems Aristotle attributed to it the kind of meaning we are talking about here.
The term functor derives from the latin verb fungi (deponens). It seems Eilenberg-Mac Lane learnt the term functor from Carnap.
Best
Johannes
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