A Gettier problem is any one of a category of thought experiments in contemporary epistemology that seem to repudiate a definition of knowledge as justified true belief (JTB). The category of problem owes its name to a three-page paper published in 1963, by Edmund Gettier, called "Is Justified True Belief Knowledge?". In it, Gettier proposed two scenarios where the three criteria (justification, truth, and belief) seemed to be met, but where the majority of readers would not have felt that the result was knowledge due to the element of luck involved.
The responses to Gettier's paper have been numerous. Whilst some rejected Gettier's examples, many sought to adjust the JTB account of knowledge to lessen the impact of both Gettier's own problems and other problems (collectively titled Gettier problems) created in their mould. Since 1963, experiments have also been conducted to determine whether the instinctive reactions of those presented with a Gettier problem are uniform or display language or genetic biases.
Read more about Gettier Problem: History, The Cow in The Field, Knowledge As Justified True Belief, Gettier's Counterexamples, False Premises, More General Gettier-style Problems, Other Responses To Gettier
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“It is part of the educator’s responsibility to see equally to two things: First, that the problem grows out of the conditions of the experience being had in the present, and that it is within the range of the capacity of students; and, secondly, that it is such that it arouses in the learner an active quest for information and for production of new ideas. The new facts and new ideas thus obtained become the ground for further experiences in which new problems are presented.”
—John Dewey (1859–1952)