The Two Problems of Intentionality

To understand the metaphysics of the mind/body relationship we have to see that there is not one metaphysical problem, there are several (and this also requires us to recognize that "mind" is a heterogenous concept, referring to several different things at once). The problem of phenomenal "properties" requires, I think, a metaphysical solution that is completely different from how we address the problem of intentional "properties" (ultimately I don't think there are any mental properties, hence the scare quotes). Intentionality itself breaks down further into two distinct metaphysical problems.
The first problem is the problem of meaning, that is, the question of how a physical thing can mean anything, be a symbol, refer to something else. There is a keyboard, a mouse, two pads of paper and a cellphone on the desk in front of me (in class I usually hold up my piece of chalk, Luddite that I am). None of them means anything. Physical objects don't mean anything: that's not a property that they have. Books don't mean anything either: readers of natural languages look at the printed marks (letters, words, sentences) on the pages and attribute meanings to them via conventional rules understood by readers of the language. But it has appeared to many over the centuries that mental states do genuinely have this intentional property of meaning, or referring to, something other than themselves. Think of a rhinocerous, the story goes: now your mental state is about a rhinocerous (the little picture in your mind's eye is a picture of a rhinocerous). But wait: if we opened up your head and poked around in there, we wouldn't find any little picture (or word). We'd just find brains, neurons, biomush of one sort or another, with some electrochemical humming and buzzing going on. Brains (human bodies) are just physical things, like pieces of chalk and notepads, and those sorts of things don't mean anything. But mental states do. That's the first problem of intentionality. (Teaser: yes, I have solutions to propose to these metaphysical problems, but just now I'm just trying to get more clear on sorting them out).
The other problem of intentionality doesn't get as much attention, although it is the main problem according to Plato, and it is key to understanding Descartes, Chomsky and Davidson among others. That is the problem that we often see picked out in our contemporary literature with the phrase "the rationality assumption." When we predicate intentional states to persons we not only attribute mental contents to them (that's the first problem again), but we also (must) make an assumption that they are possessed of some minimal degree of rationality: our attribution of such-and-such beliefs and such-and-such desires is only useful in predicting and explaining behavior if the subject connects these contents through a system of logical relations. He believes that the drinking fountain is down the hall, he desires a drink of water: these two intentional states only link up assuming he has a minimal capacity for reason. And this appears metaphysically puzzling as there do not appear to be any logical relations between (after all, contingent) physical states, including brain states. Thus Davidson argues that there can be no psychophysical laws linking any given brain state to any given intentional state, Plato argues that the capacity for logic possessed by rational beings frees them from the determinations of physical laws, and Chomsky argues that the ability to formalize mathematics and logic represents a radical break between rational beings and non-linguistic beings whose behaviors can be explained using learning models (behaviorism) and adaptationist explanations (evolutionary psychology). In fact all rationalists develop some variation on this theme.
As I said, I do have metaphysical solutions to offer to these problems, but right now I have to go home to play with my three-year-old and to bake a quiche with the chicken left over from last night. Subscribe!