True belief and epistemic luck › The two assumptions doing the work

Gettier first allows that a person can be justified in believing something false. This is a form of fallibilism about justification. Evidence can be good enough to justify belief without making error logically impossible. If justification already guaranteed truth, the false starting beliefs in his examples would not meet the stipulated condition.

His second assumption concerns a person's actual reasoning. If S is justified in believing P, P entails Q, and S deduces Q from P and accepts Q on that basis, then S is justified in believing Q. Here entails means that P cannot be true while Q is false. The principle connects justified belief with a recognized and performed deduction. Gettier, p.121.

This qualification prevents an exaggerated reading. Gettier does not need the claim that every person is automatically justified in believing every remote consequence of everything they believe. A consequence that nobody has noticed, or one reached through confused reasoning, is outside the stated setup. His examples specify that the subject sees the entailment and forms the resulting belief.

The principle also distinguishes preservation of truth from preservation of justification. A valid deduction from a true premise cannot yield a false conclusion. A valid deduction from a false premise can yield either a true or a false conclusion. Gettier uses a false premise for which the subject nevertheless has justification, followed by a conclusion that happens to be true.

This combination creates the problem. The justification travels along the subject's reasoning, while the conclusion's truth is secured by something the subject does not know. Calling that gap "luck" summarizes a feature of the cases. It does not yet provide an account of every kind of luck incompatible with knowledge.