One who balks at intentional objects on the ground of their queerness will presumably also balk at dispositional objects. But there is reason to speak of dispositional objects. And there is the outside chance that the foes of intentional objects might be 'softened up' by a discussion of dispositions and their objects. But I am not particularly sanguine about bringing the Londonistas out from under their fog and into the Phoenician sunshine.
We can sensibly speak of object-directedness both in the case of thoughts (acts of thinking) and in the case of dispositions (powers, potencies, capacities, and the like). I cannot think without thinking of something. That of which I am thinking is reasonably called the object of my thought. Said object may or may not exist. So we speak of intentional objects. The intentional object of a mental act is the object precisely as intended in the act.
But dispositions have objects too. Call them 'dispositional objects.' Dispositions are directed to these objects which may or may not occur. Thus dispositions to dissolve, shatter, or swell under certain circumstances are directed to dissolvings, shatterings, and swellings which may or may not occur, and indeed without prejudice to object-directedness.
A sugar cube, for example, is disposed to dissolve if immersed in water or some other fluid. Distinguish the following four: the sugar cube, its disposition to dissolve, the causal factors needed to trigger the disposition, and the manifestation of the disposition, i.e., its actual dissolving. The last-mentioned is the object of the disposition, the dispositional object. It is an event that may or may not occur depending on circumstances. A disposition can exist without ever occurring. Suppose a sugar cube is manufactured, exists for a year, and then is destroyed by being pulverized with a hammer. It never dissolves. But at each time during its career it harbors the disposition to dissolve. It is liable to dissolve whether or not it ever does dissolve. It follows that one must not confuse a disposition with its manifestation. Dispositions are what they are whether or not they are manifested, whether or not their dispositional objects occur.
Similarly, acts of thinking are what they are and have the specific aboutness that they have whether or not their intentional objects exist in reality. In an earlier post I drew out the parallel between intentionality and dispositionality more fully. There is no need to repeat myself here. The point I want to make in this post is as follows.
If you admit that there are dispositions, then you must admit that there are dispositional objects. Thus if you admit that a sugar cube, say, has the disposition to dissolve in certain circumstances, then you must admit that this disposition points beyond itself to an event -- the manifestation of the disposition -- that may or may not occur. Why then balk at intentional objects?
Note that the following is apparently contradictory: X is disposed to do something (e.g., shatter) but nothing is such that X is disposed to it. That parallels: I am thinking of something but nothing is such that I am thinking of it. Clearly, both statement-forms have some true substitution-instances. So the statement forms are not contradictory.
How do we show that the apparent contradictions are not real? By distinguishing between intentional and dispositional objects on the one hand and real objects (objects-as-entities) on the other.
How will the Londonistas respond? Will they deny that there are dispositions? They might. But if they accept dispositions, then they must accept dispositional objects and a fortiori intentional objects. I write 'a fortiori' because, while dispositionality can be doubted, intentionality cannot be doubted, it being phenomenologically evident. It is certain that I think and just as certain that I cannot think without thinking of something.