Gettier problem
A type of counter example to the definition of knowledge as justified true belief.

From Theory of Knowledge Course at UC Davis:
The first examples of the Gettier problem were published in 1963 by Edmund Gettier. As an example of the problem, consider:
A teacher has two students, Mr. Nogot and Mr. Havit, in her class. Mr. Nogot seems to be the proud owner of a Ferrari (a rare and expensive car). He says he owns one, drives one around, and has papers which state that the car he drives is his - but he does not actually own a Ferrari.
The teacher, on the basis of this evidence, concludes that someone in her class owns a Ferrari. This is true enough, but only because Mr. Havit, who shows no signs of Ferrari ownership, secretly owns one. So, it seems that the three conditions (truth, justification, and belief) of knowledge have been met, but that there is no knowledge.
Another example of a Gettier case can be developed from an example concerning whether an executive's secretary is in his office. Suppose that she looked into the office and saw, sitting behind the desk, a figure who looked to her exactly like her secretary. We may suppose that she would be completely justified in accepting that her secretary is in his office. However, it may be that the person sitting at the desk is her secretary's identical twin brother. The real secretary is hiding behind the desk, waiting to leap up and surprise her. So it is true that the secretary is in the office, the executive accepts that it is true, and she is completely justified in so accepting that he is.
Chris Eliasmith