I suggest we approach the problem, or one of the problems, of intentionality via the following aporetic triad:
1. We sometimes intend the nonexistent.
2. Intentionality is a relation.
3. Every relation R is such that, if R obtains,then all its relata exist.
This is a nice neat way of formulating the problem because, on the one hand, each limb is extremely plausible while, on the other hand, the limbs appear collectively inconsistent. To solve the problem, one must either reject one of the limbs or show that the inconsistency is merely apparent.
Enter Peter Lupu's solution. He described it to me last night after Christmas dinner. He thinks we can uphold all three propositions. Thus his claim is that the triad is only apparently inconsistent.
Suppose Shaky Jake seeks the Lost Dutchman Gold Mine (LDM). Now seeking things like lost gold mines typically involves all sorts of physical actions; but at the root of, and animating, these actions are various mental states many of which are intentional or objected-directed. Believing, hoping, desiring, fearing, planning -- these are all intentional states. Among them is the state of wanting. To want is to want something. Thus Jake wants, or wants to find, the LDM. But a subject's wanting of x does not entail the existence of x in the way that a subject's owning of x does entail the existence of x. You can't own, beat, eat, etc. what does not exist; but you can desire, imagine, think about, etc. what does not exist. This is a crucial fact about intentionality. Peter of course is well aware of it.
Now either the LDM exists or it does not. If it exists, then Jake's wanting relates him (or his mind) to the LDM in a way that is consistent with the truth of both (2) and (3). If the LDM does not exist, then Jake's wanting relates him (or his mind) to the CONTENT of Jake's mental act. But this too is consistent with the truth of both (2) and (3). For the content exists whether or not the object exists.
In this way, Peter thinks he can uphold each of (1)-(3). Supposing, as is overwhelmingly likely, that the LDM does not exist, (1) is true: Jake intends (in the mode of wanting) something nonexistent. This instance of intentionality is relational: it connects Jake's mind to a content. (2) is thus maintained. But so is (3): Jake's mind and the content both exist.
I will call this a 'surrogate object' solution. It works by substituting the content for the external object when the external object does not exist. This guarantees that there will always be an existent object, either the external object, or the surrogate object to serve as the object relatum of the intentional relation.
But isn't there an obvious objection to the 'surrogate object' solution? Jake wants a gold mine. He doesn't want a content. A gold mine is a physical thing. But whatever a content is, it is not a physical thing. A content is either mental as a part of the intentional mental state, or it is an abstract item of some sort. To appreciate this, let us consider more carefully what a content is. A content is an intermediary entity, roughly analogous to a Fregean sense (Sinn), which mediates between mind and external concrete reality. And like Fregean senses, contents do not reside in external concrete reality. They are either immanent to consciousness like Twardowski's contents, or abstracta like Frege's senses. And just as linguistic reference to the planet Venus is achieved via the sense of 'morning star' or via the sense of 'evening star,' mental reference to an object is achieved via a content. To employ the old Brentano terminology of presentations (Vorstellungen), the object is that which is presented in a presentation whereas the content is that through which it is presented.
Now my point against Peter is that when I want something that doesn't exist, my wanting cannot be said to relate me to a content. My wanting involves a content no doubt, but the content is not the object. Why not? Well, if I want a flying horse, I want a physical thing, an animal; but no content is a physical thing, let alone an animal. When Bobby Darin pined after his Dream Lover, it was something lusciously concrete and physical that he was pining after.
Suppose I am imagining Pegasus and thinking: Pegasus does not exist. The imagining is an intentional state that involves a content, the mental image. But this mental image exists. So it cannot be the mental image that I am thinking does not exist. It is Pegasus himself that I am thinking does not exist. And therein lies the puzzle.
Suppose Peter responds as follows. "I grant you that it is not the mental image that I am thinking does not exist. For, as you point out, the image does exist. What I am doing is thinking that the mental image is not a mental image of anything. So when I imagine Pegasus and think: Pegasus does not exist, the object relatum is an existent item, the Pegasus image, and what I am thinking about it is that it is not an image of anything."
But this too is problematic. For the nonexistence of Pegasus cannot be identified with the Pegasus-images's not being an image of anything. And this for the simple reason that an objective fact such as the nonexistence of Pegasus cannot depend on the existence of mental images. There are times and possible worlds in which there are no mental images and yet at those times and worlds Pegasus does not exist.
But Peter persists: "Well, I can say that when I am thinking about Pegasus I am thinking about a necessarily existent conjunctive property the conjuncts of which are being a horse, having wings, etc., and when I think that Pegasus does not exist I am thinking that this conjunctive property is not instantiated. And when I think that Pegasus is winged, I am thinking that the conjunctive property has being winged as one of its conjuncts."
This is better, but still problematic. If Peter wants Pegasus, then presumably what he wants on his analysis is not the conjunctive property in question, but the being instantiated of this property. Being instantiated, however, is relational not monadic: if the conjunctive property is instantiated it is instantiated by an individual. And which individual must it be? Why, Pegasus! The analysis, it appears, is viciously circular. Let's review.
Peter wants to say that intentionality is a relation and that the holding of a relation entails the existence of all its relata. But Pegasus does not exist. To want Pegasus, then, cannot be to stand in relation to Pegasus, but to a surrogate object. If you say that the surrogate object is a necessarily existent property, then the problem is that wanting Peagsus, an animal, is not wanting a causally inert abstract object. If. on the other hand, you say that to want Pegasus is to want the being instantiated of that abstract object, then you want the being instantiated of that abstract object by existing Pegasus -- in which case we have made no progress since Pegasus does not exist!