Hamlet appears to be insane, after Polonius’s death, in act IV scene II. There are indications, though, that persuade me to think other wise. Certainly, Hamlet has plenty of reasons to be insane at this point. His day has been hectic—he finally determined Claudius had killed his father, the chance to kill Claudius confronted him, he comes very close to convincing Gertrude that Claudius killed his father, he accidentally kills Polonius, and finally
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showed last 75 words of 463 total
random up until the time of (and after) the duel. Hamlet, though, was not—he even reasoned what death for him was, finishing his question of whether life was worth living for. Hamlet can truley be seen to be sane, and not. The facts that Hamlet was smart and swift thinking, and in such a reversal of emotions (from after Polonius died) in the end, leads strongly to the opinion that Hamlet was not insane.