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Hi all; Darcy here. I’m a philosophy major at Yale, where I think mostly about signification at the limits of formal semantics (and otherwise air my dissatisfaction with the state of the analytic program). I first found my way to category theory in high school, when I stumbled across Goldblatt’s book on topoi and categorical logic, and got a feel, albeit preliminary, for its vast powers of description. Though it was more flirtation than study, cat theory nevertheless struck me twice: one, for the possibility it wagered of a purely algebraic or relational ontology, and the philosophical stakes associated; and two, more practically, for the line of communication it seemed to outfit between disparate conceptual frameworks.
These days, I’m interested in category theory, mostly, for the ways it can make possible and make elegant certain conceptual (or meta-conceptual) reconciliations. In particular, category theory seems a fruitful way to describe the “attitudes” systems and theories encode towards their objects; i.e., whether they place them in a local ontology or instead identify them, intratheoretically, as theoretical categories ( — call it doing theory from within the theory; cat theory seems like the way to meaningfully superpose this perspective over the aerial one.) This question bears weight, I think, on understanding the limitations and perhaps even non-closures of formalisms ranging from the empirical to the ideological, from physics to Marxism.
More concretely, I’m also interested in category theory as a model for the accretive procedures behind lexical semiosis — typically, the bane of compositional semantics! — and the coherence of allegedly “irreducible” linguistic units. Category theory seems, too, like it could contribute profitably to current descriptive theories of metaphor (half-way between cognitive science and philosophy of language) that attempt to systemise the faculties of over-lay and isomorphism that, at once, constrain and enable “sound” analogical thinking.
Oh, and finally, on an exegetical note: I’d like to know what on earth is up with Alain Badiou :P
So, all in all, I come with many questions and few answers, and am looking forward to making my highly impressionistic sense of what categories can do a bit more rigorous — in the direction of other kinds of philosophical and empirical inquiry.