At some point, philosophers came up with a general formula for knowledge, called Justified True Belief. K = JTB. In essence, they said that one has knowledge IFF (If and only if) one has a belief that is justified and true. Then Edmund Gettier came along and showed that it was possible to have a justified true belief that was not, in fact knowledge. I didn't care much for his own examples, although I guess they worked well enough for his purpose. Instead, let us consider this story/joke:
Two college students were passing through a campus building when they spotted their philosophy professor in an office. They stopped to talk to him. Noticing all the shelves in the office lined with books, one student says, "Wow, you sure do have a lot of books."
The professor replied, "Yes, I do have a lot of books, but these aren't my books. This is Professor Jones' office, not mine, and I'm just waiting for him to return so I can talk to him."
Gettier's point was that the students had good justification for thinking that their professor had a lot of books, and the professor confirmed for them that he did indeed have a lot of books. However, since the books they saw really belonged to Professor Jones, and not their professor, they didn't really "know" that their professor had a lot of books.
Gettier has a point, but it seems to hinge on what one means by "justified", and could be modified to repair the fault. If, for example, the students had verified if the office was their professor's, or that the books were his, then they would be properly justified in their belief that he has a lot of books. In fact, they are properly justified in their belief when he tells them that he does have a lot of books, for how else would they have known the truth of their belief?
And this brings me to my own point. Gettier's problem presents difficulties about the justification for a belief. However, a more formidable objection presents itself to me about the Truth component of JTB. Suppose we have a justification for a belief. JTB requires us to have a belief that is both justified and true in order to have knowledge. Okay, how is it possible to know the truth of a belief independently of our justification for the belief?
As far as I can tell, it's impossible. Any information we have about a belief is always part of our justification for the belief, and more importantly, we have no way of knowing anything about a belief except for what justification we have for the belief. There is no mystical insight into truth, nor can we peek at the answers in the back of the book. We only think we know something through our justification for it, and for no other reasons.
In our example above, the students found out that their belief was true because the professor told them. Yet his telling them becomes part of their justification for their belief, along with the general idea that professors tend to have a lot of books and that professors tend to be truthful and not tell lies. However, if they wanted more justification, they could go to his office and verify how many books he has.
Since the truth of a belief is unknowable independent of our justification for it, the Truth component of JTB becomes either useless or redundant to the justification component.
Instead, we are reduced to saying that knowledge is merely a justified belief, and in order to get around Gettier's problems, we could require it to be a sufficiently justified belief, or SJB. Of course, how much justification is sufficient is a much more difficult question, and I don't really have a good answer for that. All I know for sure is that JTB = K is a flawed formula, and must be scrapped or modified.