In this article, and in epistemology in general, the kind of knowledge usually discussed is propositional knowledge, also known as "knowledge that." This is distinct from "knowledge how" and "acquaintance-knowledge". For example: in mathematics, it is known that 2 + 2 = 4, but there is also knowing how to add two numbers and knowing a person (e.g., oneself), place (e.g., one's hometown), thing (e.g., cars), or activity (e.g., addition). Some (though not all) philosophers think there is an important distinction between "knowing that", "knowing how", and "acquaintance-knowledge", with epistemology primarily interested in the first.
Bertrand Russell is famous for distinguishing "knowledge by description" (a form of knowledge that) and "knowledge by acquaintance" in Problems of Philosophy. Gilbert Ryle is often credited with emphasizing the distinction between knowing how and knowing that in The Concept of Mind. In Personal Knowledge, Michael Polanyi argues for the epistemological relevance of knowledge how and knowledge that; using the example of the act of balance involved in riding a bicycle, he suggests that the theoretical knowledge of the physics involved in maintaining a state of balance cannot substitute for the practical knowledge of how to ride, and that it is important to understand how both are established and grounded. This position is essentially Ryle's, who argued that a failure to acknowledge the distinction between knowledge that and knowledge how leads to vicious regresses.
In recent times, some epistemologists (Sosa, Greco, Kvanvig, Zagzebski) have argued that epistemology should evaluate people's properties (i.e., intellectual virtues) and not just the properties of propositions or propositional mental attitudes. One reason is that higher forms of cognitive success (i.e., understanding) are said to involve features that can't be evaluated from a justified true belief view of knowledge.
Statements of "belief" sometimes mean the speaker predicts something that would prove to be useful or successful in some sense—perhaps the speaker might "believe in" his or her favorite football team. This is not the kind of belief usually addressed within epistemology. The kind dealt with is when "to believe something" simply means any cognitive content held as true. For example, to believe that the sky is blue is to think that the proposition "The sky is blue" is true.
Knowledge entails belief, so the statement, "I know the sky is blue, but I don't believe it," is self-contradictory.
Belief is a subjective personal basis for individual behavior, while truth is an objective state independent of the individual, i.e., a fact.
Whether someone's belief is true is not a prerequisite for its belief. On the other hand, if something is actually known, then it categorically cannot be false. For example, a person believes that a particular bridge is safe enough to support him, and attempts to cross it; unfortunately, the bridge collapses under his weight. It could be said that he believed that the bridge was safe, but that this belief was mistaken. It would not be accurate to say that he knew that the bridge was safe, because plainly it was not. By contrast, if the bridge actually supported his weight then he might be justified in subsequently holding that he knew the bridge had been safe enough for his passage, at least at that particular time.
In Plato's dialogue Theaetetus, Socrates considers a number of theories as to what knowledge is, the last being that knowledge is true belief that has been "given an account of" — meaning explained or defined in some way. According to the theory that knowledge is justified true belief, in order to know that a given proposition is true, one must not only believe the relevant true proposition, but one must also have a good reason for doing so. One implication of this would be that no one would gain knowledge just by believing something that happened to be true. For example, an ill person with no medical training, but with a generally optimistic attitude, might believe that he will recover from his illness quickly. Nevertheless, even if this belief turned out to be true, the patient would not have known that he would get well since his belief lacked justification. The definition of knowledge as justified true belief was widely accepted until the 1960s. At this time, a paper written by the American philosopher Edmund Gettier provoked major widespread discussion. See theories of justification for other views on the idea.
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