In Hamlet's "To be or not to be" speech, he is contemplating death by comparing it to sleep. He says that by dying, "heart-ache" and the "thousand natural shocks" end, indicating that from his point of view, death ends hard times. However, he also states that he is scared of the "dreams that may come" or nightmares. The afterlife may be worse than the suffering that is currently happening.
When he speaks of "to be or not to be" he is talking about life itself. He ponders where it is better to just take on the hardship and let the mind "suffer" or to commit suicide. These words are important to Hamlet as he has truly gone mad due to his tragic flaw. Even after so much time has passed, he still has not completed the task in murdering Claudius. Hamlet keeps saying that he will kill Claudius, but there always seems to be an excuse or reason that stops him from doing so. For example, later in the play when Claudius is praying, that is the perfect chance for Hamlet to kill Claudius. Hamlet over thinks the situation and ends up putting the murder off once again. His inaction is ultimately causing him to suffer as Claudius is still king, his mother is still married to Claudius, and his father is still dead. Hamlet is getting nothing done but is still suffering emotionally by his situation. Thus, he wonders if he should just endure the suffering (since he clearly has no courage to act) or just kill himself so he doesn't have to think about this anymore.
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