"The continuing appeal of Hamlet is that the audience cares about Hamlet's dilemma" What is Hamlet's dilemma? 

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The long-term permanent dilemma for Hamlet is to determine the "right action" for him in the face of the Ghost's appearance, an appearance that could be a false temptation of "the devil," his own subconscious wishes and fears, etc., or a legitimate message from his dead father to avenge his murder; Hamlet must "act" in the real world, without anything but his own strength of character to guide him.  If the alleged murderer had been just anyone -- a stranger or a political enemy -- it would have been difficult enough, but when the "suspects" are his uncle and his own mother, the decision is a real dilemma. Two subtle effects of the detail of Yorick's death and the convoluted romance with Ophelia are their emphasis on Hamlet's aloneness.  In the early soliloquy, in which Hamlet debates with himself "whether 'tis nobler in the mind/To suffer the slings and arrows of outrageous fortune" his main dilemma is foreshadowed. The play's lasting quality is that his dilemma is our own: whether the real world is "all there is" or whether we should believe, and act on, the possibility of another reality.