Knowledge and Belief
According to the tradition stemming from Plato, knowledge is a special type of belief. In order to know that p one has to believe that p and meet various further conditions on that belief—that the belief be true, that it be justified, that it not be accidentally true, etc. The object of knowledge is a proposition of a certain sort, and one stands in the relation of belief to that proposition; in the jargon, knowing that p is a “propositional attitude” with belief as its foundation. We can call this the “doxastic theory of knowledge”: knowledge is belief restricted and qualified.
But let us review some linguistic facts that cast doubt on this venerable theory. Consider the sentence “John knows that London is the capital of England”. We can paraphrase that sentence by “John knows the fact that London is the capital of England”, but we can’t paraphrase it by “John knows the proposition that London is the capital of England”. The latter sentence sounds like it means that John is acquainted with a certain proposition, if it means anything, but this isn’t what the original sentence means. On the other hand, the sentence “John believes that London is the capital of England” can be paraphrased by the sentence “John believes the proposition that London is the capital of England”, but not by the sentence “John believes the fact that London is the capital of England”. The latter sentence sounds like it means that John believes a certain fact, if it means anything, but that is not what the original sentence means. One believes propositions not facts (though one may believe in facts): propositions, not facts, are the proper objects of belief. But in the case of knowledge this is inverted: one doesn’t know propositions (except perhaps in the sense of being acquainted with them), but one does know facts. Thus we may conclude that belief and knowledge have different objects—propositions and facts, respectively. One believes propositions and one knows facts, and facts and propositions are different kinds of thing (we needn’t here go into exactly what kinds of thing they are).
Then we can formulate a different theory of knowledge—call it the “factive theory”.  Knowledge is a relation to facts not propositions, while belief is a relation to propositions not facts. Knowledge is not a propositional attitude but a factive attitude; hence it is not a form or type of belief. This doesn’t mean that belief is not a necessary condition for knowledge; it just means that knowledge itself is not logically a type of belief—as it might be, meritorious belief. To know something is not to believe a proposition of a special type (a true and justified proposition), but to stand in a relation to another type of entity altogether, viz. a fact. The knowledge relation is a sui generis relation not a special case of the belief relation. There are propositions and there are facts: belief maps onto the former, while knowledge maps onto the latter. The believing relation relates the subject to a proposition, while the knowing relation relates the subject to a fact.
It is the same with perception and memory: these too are better handled by the factive theory than the doxastic theory. You can give “John perceives the fact that p” but not “John perceives the proposition that p” as a paraphrase of “John perceives that p” (if John perceives propositions at all, that is not the meaning of “John perceives that p”). And you can paraphrase “John remembers that p” by “John remembers the fact that p” but not by “John remembers the proposition that p”. So perceiving and remembering are not type of belief either, though there may be suitable beliefs in the offing. If I remember the fact that I went shopping yesterday, I presumably also believe the proposition that I went shopping yesterday: but these are not the same thing. The verbs “remember” and “believe” have a different grammar, a different logic. If we came to the view that perception, memory, and knowledge do not require an underlying belief after all—being psychologically more primitive than belief—that would not surprise the factive theorist, since he never thought they were special types of belief to begin with. There may not be beliefs and propositions in the picture at all, just facts and knowledge of them. Animals incapable of belief may still be able to stand in the relation of knowledge to facts–as when an animal knows it is about to be attacked but has no beliefs about the matter (it doesn’t form an opinion about its parlous condition).
And then there is the matter of referential transparency and opacity. Suppose the sentence “John knows the fact that Hesperus is a planet” is true: is “John knows the fact that Phosphorus is a planet” also true? I submit that the second sentence will also be true: John knows the fact underlying this kind of re-description (renaming). It is the same with “John perceives the fact that Hesperus is twinkling”: we can substitute “Phosphorus” here too. But notoriously we cannot make this kind of substitution inside belief contexts. We preserve the same fact under such substitutions, but not the same proposition. Therefore knowledge is not a type of belief: knowledge is referentially transparent, but belief is not. The context generated by “the fact that” does not have the logical properties of the context generated by “the proposition that”—because, intuitively, facts concern objects and properties in the world while propositions concern modes of presentation of objects and properties in the world. Mode of presentation (representation) doesn’t matter to facts, but it does matter to propositions—because propositions exist at the level of representation not at the level of things represented (sense not reference). Ascriptions of knowledge relate individuals to objective mind-independent facts, while ascriptions of belief relate individuals to representational entities. Hence the former ascriptions are transparent and the latter opaque.
The sentence types “x knows that p” and “x believes that p” are superficially similar in form, which may fuel the doxastic conception of knowledge, but they differ in logical form and in the ontology presupposed. One expresses a relation between an individual and a fact, as revealed in the paraphrase containing “the fact that”; while the other expresses a relation between an individual and a proposition, as revealed in the paraphrase containing “the proposition that”. Different relations, different objects: so the former is not a special case of the latter.
 I am using “factive” in a new sense—not the familiar idea that “knows” is a factive verb, i.e. implies the truth of what is known, but the idea that knowledge is to be understood as a relation to facts as part of its analysis.