Arguments for Hamlet's genuine madness
* Hamlet begins the play already mourning the death of his father and is deeply affected by it.
* He sees the ghost of his father, which only he can see, and is deeply troubled by it.
* He speaks in strange and illogical ways, and his behavior is often erratic.
* He does not seem to be in control of his actions, and often seems to be acting on impulse.
Arguments for Hamlet's feigned madness
* Hamlet himself tells Ophelia that he is only pretending to be mad.
* He is able to outwit those who believe he is genuinely mad, such as Polonius and Claudius.
* He does not seem to believe his story after witnessing Ophelia's father killed.
* He is able to act rationally and coherently when it suits his purposes.
Ultimately, it is up to the individual reader to decide whether they believe Hamlet is genuinely mad or only feigning madness. There is evidence to support both of these perspectives, and the play is intentionally ambiguous on this point.