A Common Skeptical Argument:

[Bork]

1. If S knows that p, then necessarily S is not mistaken in believing that p.

2. S is mistaken in believing that p = df {[S believes that p] but not-p}.

3. If p is not incorrigible for S, then it is possible that {[S believes that p] but not-p}.

4. Therefore, if p is not incorrigible for S, then S does not know that p.

Does this argument succeed? Does it contain any fallacies or defects?