The Gettier problem

The Gettier problem is that a belief can be justified and true without being knowledge, so that the classical analysis of knowledge as justified true belief fails. Edmund Gettier set it in a three-page paper in 1963. In his first case, Smith has strong evidence that Jones will get a job and that Jones has ten coins in his pocket, and infers that the man who will get the job has ten coins in his pocket. Unknown to Smith, he will get the job himself, and he too has ten coins in his pocket. His belief is justified and true, and he does not know it. Both of Gettier’s cases, the replies to them and the earlier versions are set out in full under the Gettier cases.

Earlier cases of the same shape exist, among them Russell’s stopped clock, which happens to show the right time when someone glances at it. The structure is constant: justification and truth come apart, and meet only by luck.

The responses fill a literature. One may add a fourth condition: no false lemmas, a causal connection between fact and belief (Goldman’s early proposal), indefeasibility, or a modal condition such as safety or sensitivity. One may replace justification with reliability or with apt performance. Or one may follow Williamson and stop analysing knowledge. Zagzebski argued that any analysis on which justification falls short of guaranteeing truth will face Gettier cases.

The problem matters for the epistemology of AI because it isolates the relation that frequency reliability lacks. A user who reads a correct answer from a frequency-reliable source has a true belief, and some justification in the source’s record, yet the source’s asserting it may bear no explanatory relation to its truth. The broken thermometer in a thermostatted room makes the point at the level of the source rather than the believer: its readings are correct for a stable reason, and nothing about the temperature explains them. What Gettier cases teach about belief, that truth and grounds must be connected rather than coincident, the Tracking Minimum applies to the production of assertions.