The Gettier problem challenges the notion that knowledge is a justified true belief. In short, the problem is about accidental knowledge (if there is such a thing) and having a belief that is true while your reason for justification is false. For example, I leave my keys in my jacket pocket hanging over the back of the kitchen chair. While I’m away, my wife comes around and picks up my jacket to throw it in the wash. Noticing that my keys are in my jacket pocket she thinks I’ll probably be heading out to soon since I didn’t hang up my jacket and put my keys in their respective places. She then places my keys back in my jacket and my jacket back over the chair where they were before. When I return do I have knowledge that my keys are in my jacket? That’s the issue. Do I believe my keys are in my jacket? Yes. Is it true my keys are in my jacket? Yes. Am I justified in believing this? Well… probably not since the reason why the keys are actually there are not the reason why I believe they’re there. Thus, I have no justification for believing this even though I do believe it and it happens to be true.
So, perhaps there are two alternatives for the Gettier problem: 1) justified true belief requires a fourth criterion for knowledge or 2) justification must be reconceived to make it sufficient for knowledge. (I’m not going to offer a possible solution here.)
Here are general rules for Gettier cases. It does not matter how the particular element of knowledge in addition to true belief is to be analyzed. As long as there is a small degree of independence between this other element and the truth, we can construct Gettier cases with the following procedure: Start with a case of justified or warranted false belief. Make the element of justification (warrant) strong enough for knowledge, but make the belief false. The falsity of the belief must be due to some happenstance of luck. Amend the case by adding another element of luck to serve as a corrective for the belief forming process. The second element of luck must be independent of the element of warrant so that the degree of warrant is without change.
We now have a situation in which the belief is justified or warranted in a sense strong enough for knowledge, the belief is true, but it is not knowledge. As long as the concept of knowledge connects the justification component and the truth component, but permits some degree of independence between them, justified true belief will never be sufficient for knowledge.