There are several arguments as to why Hamlet was mad. The first occurrence of his madness is found after his encounter with the ghost, his father. Hamlet appears to be act insanely when he speaks to his friends about what he saw. He speaks "wild and whirling words, "(Act 1, Scene V, lines 127-134). Horatio and the others are mystified when Hamlet talks like they have never heard him before. Another argument for his madness can be supported in his treatment towards Ophelia. When he first encounters her after speaking to the ghost, he is courteous at first, but then suddenly turns against her. He completely denies ever having loved her, attacks the womankind, and orders her to go to a nunnery. If this is not mad behavior, what is?
Another point where Hamlet acts madly is when he had Rosencrantz and Guildenstern killed even though they had nothing to do with the plan to murder his father. Granted they were carrying letters to England with orders to kill him, but they were not aware of what was written in them. The argument can be further supported when Hamlet is in his mother's chamber. Hamlet alone sees his father's ghost. Every other time the ghost appeared someone else could see it. During this scene, the argument for Hamlet's madness can be strongly supported because his mother could not see it. Gertrude even says, "Alas, how is't with you-That you do bend your eye on vacancy,"(Act 3, Scene 4, lines 133-134). IN that same scene, Hamlet acts violently to his mother. He tells her that she is a whore and to abandon his uncles' bed. Finally, Hamlet's madness can be seen in his actions after killing Polonius. Hamlet even tells Laertes that he killed Polonius in "a fit of madness." When Hamlet is confronted about the murder, he will not tell anyone where the body is and seems very happy about it. These are all strong arguments for Hamlet being mad.
However, one must look at the other side of the argument before making the decision about whether Hamlet was sane or not throughout the play. For example, Hamlet, after meeting the ghost, tells Horatio that he is going to "feign madness" and that if Horatio notices any strange behavior from Hamlet, it is because he is putting on an act. A pattern also emerges on when Hamlet is "mad" and when he is not. Hamlet's "madness" only manifests itself when he is in the presence of certain characters. When Hamlet is around Polonius, Claudius, Gertrude, Ophelia, Rosencrantz and Guildenstern, he behaves irrationally. However, when Hamlet is around Horatio, Bernardo, Francisco, the Players, and the Gravediggers, he behaves rationally.
Several characters also admit to believing that Hamlet is not mad. Even Claudius confesses that Hamlet's "actions, although strange, do not appear to stem from madness,"(Act III, Scene 1, lines 177-180). Polonius admits that Hamlet's actions and words have a "method" to them, and there appears to be a reason behind them, and they are logical in nature. A powerful example that supports this argument is Ophelia's true madness. Ophelia's insanity and Hamlet's are entirely different from one another. In fact, Hamlet's actions contrast them. Ophelia acts mad no matter who is around, and she acts different than Hamlet. Finally, Hamlet believes in his sanity at all times. He never doubts his control over his psyche. He even tells his mother that he is not mad, "but mad in craft," (Act III. Scene IV. Line 210). Therefore, one can see that this argument is also strong.
It is up to the audience to decide whether or not Hamlet was truly mad or not. However, it seems that the argument for Hamlet being sane is stronger. Hamlet tells his best friend that he is going to pretend to be mad. He never lies to Horatio throughout the entire play, why would he then? Hamlet was a strong actor himself. He even gave excellent advice to Players on acting. Why couldn't he be a good enough actor to convince those around him that he was mad? Yet it is for one to decide for themselves. Was Hamlet an actor or was he truly mad?