Contrast two competing models of belief:
(A) [Full-blown existence.] Beliefs are something like sentences in the head, written in the language of thought, and physically located in one's "belief box" -- a special area of the brain, perhaps.
(B) Beliefs are more like useful fictions, patterns (Dennett compares them to centers of gravity), or projections that track certain dispositions. So they do not have any independent existence. Rather, S's believing that P is reducible to its being correct to ascribe or attribute this belief to S -- where the correctness conditions for this ascription make no further appeal to beliefs as such.
One may initially be tempted toward the first view on the grounds that it better captures the distinction between explicit and implicit beliefs. Explicit beliefs are literally there in your belief box, whereas one implicitly believes whatever can be easily inferred from one's explicit beliefs (for some appropriate standard of 'ease').
But this doesn't work at all, as Stalnaker points out in 'The Problem of Logical Omniscience, I'. What we want is a distinction between accessible and inaccessible information, but this is independent of the explicit/implicit distinction given to us by the belief box view. After all, just because some information is etched in our brains doesn't necessarily mean (given our search and computational limitations) that we will be able to find this information when we need it.
Imagine the phonebook man (I forget whose example this is), who has memorized the entire phonebook, ordered alphabetically. This way of storing the information means that, given a name as input, he can easily find the number that goes with it. But the reverse is not true: given a random phone number, Phonebook Man has little chance of finding the corresponding name in any reasonable period of time. So it would be misleading to say that he knows (or believes) that #555-5555 belongs to John Smith, even though this information is explicitly stored in his belief box.
On the other hand, he clearly does know the equivalent proposition that John Smith has phone number 555-5555. (He can look up John Smith and get the answer, no trouble.) The dispositions which underlie "belief" are thus relative to a question or probe. This seems to contradict our common-sense notion of belief.
How are we to resolve this puzzle?