We have the word “see” but also the phrase “seeming to see”. The former implies veridicality, but the latter does not. You can seem to see what isn’t there. The locution is useful in stating certain philosophical doctrines about perception, to the effect that seeing is a composite of an inner sense impression and an outer fact suitably related to that impression. The inner impression is described as a “seeming to see”, which cancels the entailment to veridicality. Similarly, we have “remember” and “seem to remember”: the former implies the fact in question, but the latter does not. The idea is that we can be, as we say, under the impression that we see or remember without actually seeing or remembering, because we might be suffering from an illusion or misremembering. The brain in a vat seems to see but doesn’t really see, and the man born five minutes ago seems to remember his life thirty years earlier but doesn’t really remember it. It is subjectively as if these subjects see or remember but in fact they don’t—it only seems to them to be so. This seeming is not the same as belief: it is not that they believe they see and remember but don’t really, since they may not have this belief—they may be well aware of their odd situation. They may actively deny that they believe they see and remember, citing the fact that they are a brain in a vat or were born five minutes ago. But it still seems to them that they see and remember: their experience gives them the impression that this is so—they simply reject that impression. The brain in a vat will say, “It seems to me that I am seeing things, but I don’t believe that I really am”; and similarly for the man born five minutes ago, mutatis mutandis. What they mean, roughly, is that they have an experience internally indistinguishable from seeing or remembering but which isn’t genuine seeing or remembering. Philosophers have invented names for this experience—“sense-datum”, “sensory impression”, “idea”—but ordinary language already contains a phrase capturing the intended meaning. Thus genuine seeing and genuine remembering consist of seeming to see and seeming to remember plus something else—such as a causal relation to an external fact.
But the case of knowledge is different: here we don’t have the locution “seem to know”. We don’t contrast really knowing with merely seeming to know; indeed, the phrase strikes us as strange—and is never used in ordinary contexts. What would it even be to seem to know something? The concept is empty, possibly nonsensical. It is not that a person who lacks knowledge has seeming knowledge, as a person who fails to see can have seeming seeing: there is no such thing as seeming to know. There is no experience internally indistinguishable from knowing which is the impression of knowing. There is no “knowledge-datum”. It might be thought that belief is this missing element: to have a belief is to seem to know something. But this is wrong: a belief is a commitment to the truth of a proposition, but seeming to know would not be such a commitment. A person who merely seems to know would be able to say, “It seems to me that I know, but I don’t because the proposition I seem to know is one that I believe to be false”. This is the analogue of seeming to see but not believing that one sees. The impression of knowledge should be able to exist even when the subject disavows it; but that is not possible with belief—here the mental state is a commitment to truth. In belief one takes oneself to know, but seeming knowledge would not be like that; so we can’t identify seeming knowledge with belief. Thus the belief component of knowledge is not analogous to the sensory component of perception: the latter is a seeming perception but the former is not a seeming knowing. A belief is not an impression of knowledge in the way a sense experience is an impression of sensing. The proper conclusion is that the phrase “seeming to know” is empty and devoid of sense, which is why it does not occur in ordinary language (or in philosophical language).
I take it this point is obvious, but it has an interesting consequence, namely that it is wrong to model knowledge on perception. In particular, it is wrong to model knowledge on seeing: to know a fact is not to see it in some way (with the eyes or intellectually). For that would imply that there is such a thing as an impression of knowing—a type of seeming that falls short of the fact. It would imply that someone could be in that state of seeming and yet not know; but there is no such type of state, no state of seeming to know. So knowledge is not something that can be analyzed as an inner impression of knowing combined with some outer facts. To know that p is not to see that p, since such seeing would have to allow for mere seeming to see, which would be tantamount to seeming to know. Just as belief can’t be analyzed as seeming to know, so knowledge can’t be analyzed as any kind of seeing. Even perceptual knowledge is not a type of seeing (or otherwise sensing) because no one can seem to know about observable things. Nor can moral or mathematical intuition be modeled in this way, on pain of the mythology of seeming to know. It is true enough that one can know things by seeing them, but knowing itself isn’t a type of seeing: for if it were, one could fail to know by merely being in a state of seeming to know—but there is no such state to be in. Knowing is not a combination of a fact and an impression of a fact, as perception is (also memory). Knowing doesn’t have this kind of structure.
 It has the structure of an internal state (belief) that is combined with other facts, but this internal state is not a type of inner seeming. In belief the world is not presented in a certain way.