Well of course. In reality every cube has 12 edges. But one could think of a cube without thinking of something that has 12 edges, and indeed without thinking of something that lacks 12 edges. If you know what a cube is, and I ask you, "How many edges does a cube have," you might reply, "I don't know." During this exchange you are most assuredly thinking of a cube, but a cube indeterminate in respect of the property of having 12 edges. What you have before your mind is an incomplete object, one that, because incomplete, cannot exist. Your thought has an intentional object, but it is an object that does not exist.
Another example. Peter shows up at my door. I note that he is wearing a brown leather vest. Now anything made of leather must be made of cow leather or horse leather or alligator leather or . . . . But the leather vest that is before my mind as the object of my visual experience is indeterminate with respect to type of leather. What is before my mind is an intentional object.
Peter's vest is brown, and in reality everything brown is colored. But the intentional object of my visual experiencing is brown but not colored. Extracting the principle, we may erect the following thesis:
Non-Closure Under Property-Entailment: Intentional objects, reflecting as they do the finitude of the human mind, are not closed under property-entailment.
It follows from this principle that no merely intentional object exists. (For everything that exists is complete.) But that is not to say that they are denizens of Meinong's realm of Aussersein. Talk of merely intentional objects does not commit one to Meinongianism. One could take the line that merely intentional objects are "ontically heteronomous" to borrow a phrase from Roman Ingarden: their existence is parasitic upon the existence of the mental acts whose intentional objects they are.
Now there are problems with this sketch of a theory of intentional objects, but it is not an obviously senseless or incoherent theory. So I suspect Edward of London feigns incomprehension when he says he doesn't understand it. Does he have a better theory?