Hamlet Act I

I find it extremely perceptive of Hamlet that even though he is in a state of grief he focuses more on the suspicion he has as to what causes his fathers death, not to dwell on it but to make sure he isn't taking things laying down like everyone else after this tragedy. It is not known for sure if Gertrude has any suspicions and is simply turning the other cheek to appear happily married for the sake of Denmark or if she really is ignorant and blinded by Claudius' love. Either way she wants Hamlet to put out any doubts in his mind that might hurt Claudius.

The ghost wouldn't come back to Hamlet without some sort of motive. At first Hamlet isn't convinced if it is the Devil in the shape of his deceased father who's trying to make Hamlet into some sort of murderer to sabotage his chance at ruling Denmark, or if it is really his father.

 Even if this apparition wasn't real, so to speak, and only in Hamlet's mind, it still didn't mean he was crazy. His mind was making him see the truth and he knew that even if he was going insane he had to test the ghost's words on Claudius.

Sometimes the minds perception of something isn't fully comprehendible to all, but for few, it can help insure justice and punish wrongdoing.