what if i don't hate model theoretic semantics as much as i once thought?
categorial grammar, as i shakily understand it, goes a little something like this: sentences can be broken down into sytactic constituents, and those pieces can be broken down (into words, say). Each constituent, though, say 'to the store' has meaning that is constant over most of that constituent's appearances in other sentences. Thus, meaning (semantics) and structure (syntax) should go together. if 'the store' has a meaning, it should be some kind of unified structure. ditto 'to the store,' and 'ran to the store.'
already we've made a lot of assumptions i'm not comfortable with: that sentences are the largest semantic unit (and that they express truth conditions), that meanings of constituents are consistent over multiple sentences/discourses, that meaning is compositional (built up from smaller units in a systematic way). yuck.
but, on the other hand, it's a pretty elegant solution once you accept all that.
categorial grammar treats each constituent as a function that operates on sets: input a noun into a verb, and you get a truth value (true if the noun is a member of the set of things that does the verb, false if it isn't). and these functions are identical to the structural categories that build the sentence up syntactically.
i'd love it if i were a math person, but i feel obligated to hate it, since it's a lifeless, bloodsucking way to look at language. i think.