Epistemology is the branch of philosophy concerned with the theory of knowledge.
Epistemology is the study of the nature of knowledge, justification, and the rationality of belief. Much debate in epistemology centers on four areas: the philosophical analysis of the nature of knowledge and how it relates to such concepts as truth, belief, and justification, various problems of skepticism, the sources and scope of knowledge and justified belief, and the criteria for knowledge and justification. Epistemology addresses such questions as: "What makes justified beliefs justified?", "What does it mean to say that we know something?", and fundamentally "How do we know that we know?"
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., knowing other persons, or knowing oneself), place (e.g., one's hometown), thing (e.g., cars), or activity (e.g., addition). Some philosophers think there is an important distinction between "knowing that"(know a concept), "knowing how" (understand an operation), and "acquaintance-knowledge" (know by relation), with epistemology being primarily concerned with the first of these.
While these distinctions are not explicit in English, they are defined explicitly in other languages (N.B. some languages related to English have been said to retain these verbs, e.g. Scots: wit and ken). In French, Portuguese, Spanish, German and Dutch 'to know (a person)' is translated using connaître, conhecer, conocer and kennen (both German and Dutch) respectively, whereas 'to know (how to do something)' is translated using savoir, saber (both Portuguese and Spanish), wissen, and weten. Modern Greek has the verbs γνωρίζω (gnorízo) and ξέρω (kséro). Italian has the verbs conoscere and sapere and the nouns for 'knowledge' are conoscenza and sapienza. German has the verbs wissen and kennen; the former implies knowing a fact, the latter knowing in the sense of being acquainted with and having a working knowledge of; there is also a noun derived from kennen, namely Erkennen, which has been said to imply knowledge in the form of recognition or acknowledgment. The verb itself implies a process: you have to go from one state to another, from a state of "not-erkennen" to a state of true erkennen. This verb seems the most appropriate in terms of describing the "episteme" in one of the modern European languages, hence the German name "Erkenntnistheorie". The theoretical interpretation and significance of these linguistic issues remains controversial.
In his paper On Denoting and his later book Problems of Philosophy Bertrand Russell stressed the distinction between "knowledge by description" and "knowledge by acquaintance". Gilbert Ryle is also credited with stressing 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 infinite regress.