On intentionality and causal theories

Lewis wrote this in his essay De Futilitate:
We are compelled to admit between the thoughts of a terrestrial astronomer and the behaviour of matter several light-years away that particular relation which we call truth. But this relation has no meaning at all if we try to make it exist between the matter of the star and the astronomer's brain, considered as a lump of matter. The brain may be in all sorts of relations to the star no doubt: it is in a spatial relation, and a time relation, and a quantitative relation. But to talk of one bit of matter as being true about another bit of matter seems to me to be nonsense.
Of course materialists are going to say that it is not a bit of matter that is about another bit of matter, it is a state of the brain (along, perhaps, with a set of causally related items outside the brain) that is about something else.
In virtue of what is some physical state about some other physical state? This is the familiar worry about intentionality, a worry made more difficult by my claim that the kind of intentional states involved in rational inference are states in which the content is understood by the agent and put into a propositional format. Is there a set of necessary and sufficient conditions which are physical in the sense in which we are understanding it here, and which jointly entail the conclusion that agent A is in the state of believing, or doubting, or desiring, or fearing, the proposition P is true?
When we consider material entities that exhibit intentionality, we see that they do not have their intentional content inherently, but have it relative to human interests. The marks on paper that you are reading now are just marks, unless they are related to a set of users who interpret it as such. In other words, it possesses a “derived intentionality” as opposed on “original intentionality.” As Feser points out
More to the point, brain processes, composed as they are of meaningless chemical componenets, seem as inherently devoid of intentionality as soundwaves or ink marks. Any intentionality they would also have to be derived from something else. But if anything physical would be devoid of intrinsic intentionality, whatever does have intrinsic intentionality whatever does have intrinsic intentionality would thereby have to be non-physical. Sine the mind is the source of the intentionality of physical entities like sentences and pictures, and doesn’t get its intentionality from anything else (there’s no one “using” our minds to convey meaning) it seems to follow that the mind has intrinsic intentionality, and thus is non-physical.
For example, clearly the relationship between brain states and states of affairs
cannot be a matter of resemblance. If what I perceive is a pine tree, then what I see is green, but there is nothing green in the gray matter of the brain that corresponds to the green tree in the world. So there must be something that connects the brain states to the mental states. But what could that be?
Some naturalistic theories have been developed to provide a physicalist account of intentionality. Feser delineates four types of theories of this nature: conceptual role theories, causal theories, biological theories, and instrumentalist theories.
Conceptual role theories explicate intentional states in terms of their conceptual roles, that is, in relation to other intentional states. Of course, this does not explain why there is a network of intentional states in the first place.
A more popular approach to coming up with a naturalistic account of intentionality are causal theories of intentionality. These appeal to the causal relations that intentional states stand to items in the external world. Thus if I believe that there is a computer monitor in front of me as I type these words, there is a causal connection between the monitor and my visual cortex, which causes states of my brain to be affected by it.
However there are some fairly obvious difficulties which must be confronted by any causal theories. First of all, how would we explain our relationship to non-existent objects? How could we meaningfully refer to Superman if Superman does not exist? How could a cat cause us to form the belief that a dog is on the mat? This is frequently called the misrepresentation problem. These are problems that causal theorist have been frequently discussed in the literature, and various responses have been proposed.