It is really important to revisit this common theme here. Hamlet, himself, participates in this theme when he says, "As I perchance hereafter shall think meet / To put an antic disposition on." What does this mean? Hamlet is going to pretend to act crazy for the rest of the play. How does he plan to do this? Sometimes, says Hamlet, it will be through his appearance through "arms encumb'red thus, or this headshake." Sometimes, says Hamlet, it will be because he speaks irrationally "by pronouncing of some doubtful phrase." Now, why is this appearance vs. reality? Well, according to Hamlet, he will "appear" crazy, but he will be sane in "reality." That is one way to look at it. However, there is another interpretation that should be considered. Does Hamlet simply appear crazy, or might he actually be crazy? Does the method of acting crazy for days and days (months?) suddenly make mental illness a reality? When something appears real, does that make it real in its reality? Is Hamlet crazy now, or does he become crazy throughout his act? Is it possible that Hamlet never becomes crazy and always remains sane? Such is the fodder for scholar fits and fights.