Cognitive Closure De Dicto and De Re
De dicto belief does not entail de re belief and vice versa. The two have different conditions of possibility. Someone could believe de dicto that the tallest man in the world is over 8 feet without believing de re of the tallest man that he is over 8 feet: he believes the former on general grounds, but he has never met the tallest man and knows nothing about him. Belief de re requires something stronger than mere descriptive reference. But it is also true that we can’t infer de dicto belief from de re belief: you might meet the tallest man, not realizing that he is, and form the belief that he is unhappy, but you don’t thereby believe that the tallest man is unhappy. Belief de dicto requires something stronger than mere acquaintance; you have to think of the object in a certain way. This familiar distinction has implications for the concept of cognitive closure (and allied concepts). A given conceptual scheme can suffer from two sorts of gap: the concepts it contains and the objects it refers to. It can be limited with respect to ideology or with respect to ontology (to use Quine’s terminology)—the concepts it expresses and the objects it denotes. Take a typical ape conceptual scheme: it might contain reference to the Sun but not contain the concept center of the solar system, and it might contain the concept cause of these footprints without there being any de rebelief about the actual cause of the footprints (the animal responsible has never been seen). We can also suppose that the ape conceptual scheme is empty of both sorts of belief with respect to a given subject matter: no de dictobeliefs about remote galaxies and no de re beliefs about them either; ditto for atoms, the unconscious, and dark matter. The apes don’t have the concept and they don’t have the necessary acquaintance. And it is plausible to suggest that they can’t have either: they can’t have the concepts and they can’t achieve the acquaintance. Thus we can say that they are cognitively closed both de dicto and de re to the entities in question: they are lacking both conceptually and perceptually (assuming de re beliefs to require perception). At any rate, there are two sorts of epistemic limitation to consider: how the organism can think and what it can think about. These can be called de dicto cognitive closure and de re cognitive closure. Since the two types of closure come about by different means, they can come apart, either from a conceptual gap or from a perceptual limitation (or causal contact limitation, if that is your preferred account of the conditions of de re belief).  Another species might invert the position of the apes: they might have no trouble conceptualizing the Sun but have no de re knowledge of it, and they might be acquainted with the cause of those footprints but not have the concept of a footprint.
How does this apply to humans? We might have the concept of something that we can never become acquainted with (and hence have de re beliefs about) and we might also have acquaintance with something that we cannot have certain de dicto beliefs about. Dark matter might be an instance of the former, or the universe before the big bang (do we even have de re beliefs about the big bang itself?); and consciousness would be instance of the latter—we have de re beliefs about consciousness but we may not be able to have de dicto beliefs about all of its properties. Many mysterious things are such that we are in direct cognitive contact with them but are not capable of having de dicto beliefs (knowledge) about all their properties. Knowledge by acquaintance is one thing; knowledge by description is another.  Here is an interesting case: do I have de re knowledge of bat experience that I don’t have de dicto knowledge of it? We can agree that my conceptual scheme has a gap where the concept of bat experience ought to be (an area of local cognitive closure), but am I also precluded from forming de re attitudes towards bat experience? One might suppose that I am, since I am not acquainted with bat experience, but that may be too quick: for I am in causal contact with it—it exists in my immediate environment. I can refer to it demonstratively. Do I have de re beliefs about other human minds? Do I believe of your pain that it deserves a visit to the doctor? That doesn’t sound wrong, so can’t we say that I believe of a bat’s experience that it is something I can’t know about de dicto? That is, I know of what it’s like to be a bat that I can’t know what it’s like to be a bat. If so, I have de re attitudes towards bat experience whose nature I cannot conceptualize de dicto: I am not de recognitively closed, but I am de dicto cognitively closed. Bat experience is not like dark matter or other parallel universes, with which we have no causal contact. The case is like the blind man and sensations of color: he can’t know that I am seeing red (that would require him to have the concept red), but does he know of my red experience that it is something he can’t grasp? The case isn’t straightforward but I am inclined to say that de reknowledge is possible in such cases, in which case we can have de re attitudes towards experiences we cannot conceptualize de dicto. Alien minds can be de re objects of our attitudes even when they cannot be conceptualized in the de dicto form. I can believe of an alien mind that it is irremediably alien to me.
Now there is this question: is there anything in the universe that cannot be either de re cognized or de dictocognized by the human mind? Are there any objects or facts that are in principle inaccessible to human cognition of either kind? The familiar mysteries don’t qualify because they all involve de re cognition combined with de dictoignorance: consciousness, free will, creativity, matter, space, and time—or whatever mysteries you happen to believe in. We would need an example of something that we can’t have de re knowledge of and we can’t adequately describe in the de dicto style. It would have to be something like the origin, or fate, of the universe: we are not acquainted with these things, and arguably we can never come to know what they involve. Still, the concept makes sense: real facts that are not objects of de re cognition and also not conceptually accessible to us (save in unrevealing descriptive phrases such as “the origin of the universe”). Consciousness is a de re object of cognition and also known about in various ways, so it is not completely removed from human cognition; but there could be realities that are neither de re objects of cognition nor susceptible to de dicto beliefs—not even recognized as possibilities in our conceptual scheme. Of course, it is impossible to give an example—but that doesn’t mean the idea is incoherent. There might also be things that we can form adequate theories of but which we can never know de re (say, the ultimate constituents of matter). So there are mixed cases of cognitive closure depending on the scope of de re and de dicto modes of cognition. In the most familiar cases we have de re openness combined with de dicto closure (or partial de dicto closure, because we have some knowledge of the things in question). This is really just a special case of the distinction between de re and de dicto belief: we have de re knowledge of the thing but at best incomplete de dicto knowledge of the properties of the thing. Our limited ability to know de dicto about the properties of something is never sufficient to undermine our de re acquaintance with it.  We could be completely wrong about consciousness, say, and yet still have de re beliefs concerning it. Knowledge of objects is not dependent on knowledge of truths, as Russell puts it; it is more primitive than that. It is knowledge of a different order or type. 
We have two basic sorts of cognitive power: the power of acquaintance (to use Russell’s term of art), and the power of conceptualization. They are largely independent of each other and can therefore come apart. With respect to cognitive limitations we need to recognize both types of limitation and classify cases accordingly. Conceptual schemes can suffer (or benefit) from both sorts of gap—ontological or ideological. They can be limited de re or they can be limited de dicto. The human conceptual scheme, like other conceptual schemes, has certain types of limitation, of varying degrees of severity, and its combination of the de re and dicto is distinctive, depending as it does on our contingent powers of perception and conceptualization. It is hard to see how it could be otherwise.
 There is controversy about the necessary and sufficient conditions of de re attitudes, but some sort of causal contact seems to be required—not necessarily perceptual contact. It might even be possible to acquire de re attitudes by testimony, and certainly by introspection. Russell restricted the objects of such attitudes to sense data and one’s own self, but nowadays we prefer to relax this to include the material objects of perception and things in the past—though not the future. The intuitive test is always whether we can say, “X believes of y that such and such” or “Concerning y, X believes that it is so and so”—which always allow wide scope existential generalization. Thus we can’t say that someone has a belief of something unless that something exists.
 See Russell, The Problems of Philosophy (1912). As an aside, let me say that this book breathes an optimism that could no longer exist after the wars of the twentieth century. Its epistemology is supremely lucid and self-confident.
 We could also consider the question of whether knowing-how is subject to cognitive closure: are there some things we could never know how to do? Clearly there are things our animal brethren will never know how to do (play tennis, tie their shoelaces), and we may suppose that some tasks are beyond human cognitive abilities too (what about create a human being from scratch, or a whole universe?). That is, for each epistemic concept we can inquire into questions of cognitive limitation: it isn’t only about the scope and limits of propositional knowledge. Epistemology meets mysterianism.