The Question of Hamlet
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But that's only a retrospective justification and it doesn't really explain how Hamlet comes to be so fixed on revenge.
Also, speaking of predators and prey, I love the description of young Fortinabras early on:
Young Fortinbras,
Of unimproved mettle, hot and full,
Hath in the skirts of Norway, here and there,
Shark’d up a list of lawless resolutes,
For food and diet, to some enterprise
That hath a stomach in’tThat's why his last lines are all about his fear that everyone will misinterpret what has happened, and regret that he doesn't have enough time to tell Horatio the truth. "O God, Horatio, what a wounded name,/Things standing thus unknown, shall live behind me!" and "So tell him, with th' occurrents, more and less,/Which have solicited. The rest is silence." and so on. (or, for that matter, his whole speech about "I know not “seems.”")
So I think it's less that we're meant to doubt Hamlet's sanity, and more that Shakespeare deliberately set up a weird scenario so that only the audience can understand that Hamlet is sane.
I should reread it!