(a) S knows P if and only if
(i) P is true,
(ii) S believes P, and
(iii) S is justified in believing P
(b) It is possible for a person to be justified in believing a proposition that is in fact false.
example : A fire has just been lit to roast some meat. The fire hasn’t started sending up any smoke, but the smell of the meat has attracted a cloud of insects. From a distance, an observer sees the dark swarm above the horizon and mistakes it for smoke. “There’s a fire burning at that spot,” the distant observer says. Does the observer know that there is a fire burning in the distance?
(c) It is possible for a person to be justified in believing a proposition is indeed true, but true for the wrong reasons.
Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following conjunctive proposition: (d) Jones is the man who will get the job, and Jones has ten coins in his pocket.
Smith’s evidence for (d) might be that the president of the company assured him that Jones would, in the end, be selected and that he, Smith, had counted the coins in Jones’s pocket ten minutes ago. Proposition (d) entails: (e) The man who will get the job has ten coins in his pocket.
Let us suppose that Smith sees the entailment from (d) to (e), and accepts (e) on the grounds of (d), for which he has strong evidence. In this case, Smith is clearly justified in believing that (e) is true. But imagine, further, that unknown to Smith, he himself, not Jones, will get the job. And, also, unknown to Smith, he himself has ten coins in his pocket. Proposition (e) is true, though proposition (d), from which Smith inferred (e), is false. In our example, then, all of the following are true: (i) (e) is true, (ii) Smith believes that (e) is true, and (iii) Smith is justified in believing that (e) is true. But it is equally clear that Smith does not know that (e) is true; for (e) is true in virtue of the number of coins in Smith’s pocket, while Smith does not know how many coins are in his pocket, and bases his belief in (e) on a count of the coins in Jones’s pocket, whom he falsely believes to be the man who will get the job.
https://en.wikipedia.org/wiki/Gettier_problem
Thus, (a) is an insufficient definition of knowing.
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