When we think about intentionality we think of the mental state as being directed at, or about, objects in the world, which implies that intentionality is a relation between mental states and objects. But if intentionality is a relation it is certainly an unusual one, because the intentional relation can also hold between mental states and imagined objects, objects that have no real counterparts. How is this a problem? Well, usually relations hold between one kind of thing and another kind of thing. For example, the mathematical relation “greater than” holds between numbers, and the relation “purchaser-of” holds between agents and things that can be bought. But it is hard to see what one kind of thing imaginary objects and real objects could both be described as. Another problem is determining when the intentional relation should hold. Normally a relation holds based on certain properties of its objects. But imagined objects and real objects have few, if any, properties in common. Real objects have real properties, and imagined objects have imagined properties. If the intentional relation holds because of certain real properties of the object then it can’t hold of imagined objects, and vice versa.
A solution taken by many to this problem is to assume that intentionality is simply relation-like, that it seems like a relation but really isn’t. Certainly this is an elegant solution to the problem, but it is also an extremely uninformative one. If intentionality isn’t a relation then what is it? Of course those who take this approach to intentionality rarely stop to describe exactly what it is, instead they describe what how it works, specifically that you are intentionally related to an object when that object somehow fits your mental picture of it. But this handles only the real world cases, and it even mishandles some of them, for example when you think about the martini drinking man, who, unbeknownst to you, is really drinking water (to pinch an example from Donnellan). And to resolve those problems we must invoke some principle of best fit, where objects that are sufficiently close to those being imagined count as fitting the description. But such fixes make intentionally relating to imaginary objects impossible, since they cannot “fit” the description, as they don’t actually exist*.
My solution to this dilemma is to re-cast intentionality as a relation between mental states and object possibilities (sets of possible objects). Specifically I would say that the mind is intentionally related to the possible object that fits the properties it is being conceived of as having (and this is why it is really a relation to a range of possibilities; since not every last detail is conceived of there are a number of possible objects that can fit the description). Of course I can’t ignore the fact that we often do talk about intentionality as though it related us to actual objects. I account for this as simply a way of talking about intentionality, which means that the possible object that the mind is intentionally related to happens to have a real world counterpart (I’ll leave the nature of the counterpart relation unspecified, although it probably involves some notion of “fit”).
The above theory about intentionality has a number of attractive properties. It makes intentionality depend only on internal factors, intentionality becomes a constructed fact (a description of the world instead of a causal part of it), and it explains the absence of a subjective difference between intending real and imaginary objects. Although, for those very reasons, I suspect externalists won’t like it.
* This is why dealing with reference is much easier than dealing with intentionality, you only have to deal with the actual.