From “Is Justified True Belief Knowledge?” by Edmund L. Gettier
Attempts to state necessary conditions for someone’s knowing a given proposition:
S knows that P IFF (i) P is true;
(ii) S believes that P;
(iii) S is justified in believing that P.
Gettier provides two more examples of similar logic and sets out to show that they do not constitute a sufficient condition for the truth of the proposition that S knows P.
First of all, it is possible for a person to be justified in believing a proposition that is in fact false.
” … for any proposition P, if S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q as a result of this deduction, then S is justified in believing Q.”
Which means that secondly, propositions can be justified based on false premises, if the foundational P is in fact false.
A summary of Case 1:
Smith and Jones both go for a job …
Smith has strong evidence for the following conjunctive proposition:
(1) Jones is the man who will get the job, and Jones has 10 coins in his pocket.
(2) This proposition entails that the man who will get the job also has 10 coins in his pocket.
Smith has in this case deduced the second proposition from the first and is justified in believing this to be true.
Unknown to Smith, it is in fact he himself who will get the job. Also, unknown to Smith, he himself has 10 coins in his pocket. The second proposition is still true, though the first is now false. Smith is therefore justified in believing proposition 2, but does not know that proposition is true, given that he does not know that proposition 2 is true in virtue of proposition 1.