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The Gettier problem is a fundamental problem in contemporary epistemology (the philosophy of knowledge), issuing from counterexamples to the definition of knowledge as justified true belief.
The problem owes its name to a remarkable three-page paper published in 1963, by Edmund Gettier, called "Is Justified True Belief Knowledge?". In the paper, Gettier argues that it is not.
Until Gettier's essay was published, most analytic philosophers took it for granted that something we might call the JTB account of knowledge was correct. The JTB account claims that knowledge can be conceptually analyzed as justified true belief--which is to say that the meaning of sentences such as "Smith knows that it rained today" can be given with the following set of necessary and jointly sufficient conditions:
A subject S knows that a proposition P is true if, and only if:
Gettier's paper used counterexamples to argue that there are cases of beliefs which are both true and justified--therefore satisfying all three conditions for knowledge on the JTB account--but which do not appear to be genuine cases of knowledge. Gettier, therefore, argued that his counterexamples show that the JTB account of knowledge is false--and thus, that a different conceptual analysis is needed to correctly track what we mean by "knowledge."
Gettier's case is based on two purported counterexamples to the JTB analysis. Both of them rely on the fact that justification is preserved by entailmentImplication or entailment is used in propositional logic and predicate logic to describe a relationship between two sentences or sets of sentences. Semantic Implication states that the set A of sentences semantically entails the set B of sentences. Formal: that is, that if Smith is justified in believing P, and Smith realizes that the truth of P entails the truth of Q, then Smith would also be justified in believing Q. Gettier calls these counterexamples "Case I" and "Case II":