Was Hamlet Mad or Mad?

Hamlet's state of mind is very debatable thoughout the play. His sanity has been questioned for hundreds of years, and my belief is that Hamlet was sane. The play begins with Hamlet grieving over his dead father. He is also troubled by his mother's quick and incestuous remarriage to his uncle, and the appearance of a ghost that looks like his deceased father.
In ACT I, Scene V, Hamlet returns from talking to the ghost. Horatio and Marcellus question him hysterically about the ghost, but Hamlet refuses to talk. Instead he makes them "swear by his sword" not to mention anything about the gho…