Distinguishing knowing that from knowing how
Is knowledge a subset of that which is both true and believed? (See below)
In this article, and in epistemology in general, the kind of knowledge usually discussed is propositional knowledge, also known as "knowledge-that" as opposed to "knowledge-how." For example: in mathematics, it is known that 2 + 2 = 4, but there is also knowing how to add two numbers. Many (but not all) philosophers therefore think there is an important distinction between "knowing that" and "knowing how", with epistemology primarily interested in the former. This distinction is recognized linguistically in many languages, though not in modern Standard English (N.B. some languages related to English still do retain these verbs, as in Scots: "wit" and "ken").
In Personal Knowledge, Michael Polanyi articulates a case for the epistemological relevance of both forms of knowledge; 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.
In recent times, some epistemologists (Sosa, Greco, Kvanvig, Zagzebski) have argued that we should not think of knowledge this way. Epistemology should evaluate people's properties (i.e., intellectual virtues) instead of propositions' properties. This is, in short, because higher forms of cognitive success (i.e., understanding) involve features that can't be evaluated from a justified true belief view of knowledge.
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Main article: Belief
Often, statements of "belief" mean that the speaker predicts something that will prove...