What is it to forget that p? A simple analysis is that S forgets that p iff at one time S knows that p, and at a later time, S does not know that p. But this can’t be right, for the following four reasons.
If at t1, S knows that p, and at t2, S is dead, so knows nothing, S has not forgotten that p.
At t1, George knows that he has hands. At t2, he reads the Meditations, and starts to doubt that he has hands. That is, he no longer believes he has hands. He doesn’t any more know that he has hands, but nor has he forgotten that he has hands.
At t1, John knows that the New Deal substantially lowered unemployment. At t2, John reads a newspaper column, in a usually reliable newspaper, saying that this was not true. With his new evidence, he now (quite reasonably) doubts that the New Deal substantially lowered unemployment. So he does not know this. But nor has he forgotten it.
At t1, Paul knows that his meeting is scheduled for 2pm. At t2, he gets an email (falsely) saying that the meeting has been moved to 3pm. Paul glances at the email, but doesn’t take in what it says. So he still believes that the meeting is at 2pm. Nevertheless, he doesn’t know this, for the email is a defeater for his knowledge. But nor has he forgotten the time of the meeting.
That seems to dispose of the simple theory fairly conclusively. But is there anything we can put in its place?