Lately I've been working on the problem of phenomenal properties, but (owing to covering Chapters 10 and 11 on Davidson and Dennett in John Heil's Philosophy of Mind in my class this week) I am today thinking about intentional properties. All of this talk about properties is sloppy, I don't think that there are any such things as phenomenal "properties" for example. If there are such things as formal properties or relational properties then maybe there are intentional properties, which would be some kind of those former.
Posing the problem, suppose that you were a physiologist studying the various organs of the body. You work with the stomach for a while, figuring it out, see the digestive system and how it functions. Moving along you'll eventually come to the nervous system, and it too will be described as a physical system with physical processes going on. But psychology has a way of talking about persons that does not seamlessly mesh with the way we talk about bodies and brains. (A crucial point to understanding mind-body relations is that intentional ("belief-desire") psychological ascriptions are made of whole people, with all of their fingers and toes and dogs and cars, and not of brains or parts of brains. Keeping that in mind clarifies the brain process/consciousness relation a lot.)
The problem is that ordinary intentional psychology ascribes mental states to persons, and these mental states have content. This involves us in the idea that something functions as a symbol with meaning. But when we as physiologists learn and describe the physical processes in organs, we (sense of "one," no I'm not a physiologist) don't (seem to) describe these processes in terms of information processing or intentional content etc. The semantic properties of mind and language don't seem to map on to any physical properties. Davidson gives us some arguments that take the problem beyond the basic issue of whether or not correlative relations are constitutive of causal relations (I think maybe yes at this point): He points out that the way we're going to have to interpret any little bit of a person's mental content (literally, the meaning that is symbolized by their mental representations) is in terms of that content's interactions with a larger system of content, inference, implication, value, memory, etc. The "web of belief" Quine called it, my coinage is to speak of the "intentional economy" of a person. We will also have to ascribe to the person a minimum level of "rational" behavior, guessing that they will follow out the "rules" of the intentional economy more or less as some model "rational" person would. These two features of psychological interpretation, the "holistic" character of meaning and the rationality assumption, had no correlary in physical description, Davidson argued, and thus "psychophysical" laws were not possible.
I'm not so sure about the propositional nature of the "attitudes" as Davidson is, or even if I think a representational model of mind is correct (although it seems to be enjoying a vogue at the moment). But I do agree that intentional explanation may not be "translatable" or "analyzable" into physical explanation: that reductive materialism fails to account for the metaphysics of intentionality, because the properties that intentional descriptions pick out (that of believing that "x" and desiring that "y," say) are multiply realizable (or "supervenient") properties and thus may characterize some indefinitely wide set of physical systems. Thus it looks to me that intentional properties are some sort of formal or relational properties, like the intailments of geometry proofs. The benefit of this view is that the metaphysical problem turns out not to be specific to the mind-body relation. Rather there is a universal problem for materialism. It looks like it may also, by locating content in a "wide" way (that is, as an emergent property of the system's relationship with its environment), be useful as an eliminativist approach to representation. Just stir in a little Plato and everything's fine!