What did Hamlet mean when he said "there's a divinity that shapes our ends" (v.ii)?
In stating that "there's a divinity that shapes our ends," Hamlet means that God is in control of what happens to us, guiding us even as we try to forge our own paths through life.
Hamlet makes this statement to Horatio, who has long been his trusted confidante. He goes on to explain what he means, telling Horatio that he happened to be bold enough while on board the ship to England to open the letters that Rosencrantz and Guildenstern were carrying. He learned that they held a command from Claudius that he be killed as soon as he set foot on shore.
Hamlet believes his discovery of this information was providential, the hand of God at work. He was, he tells Horatio, able to write a new letter to replace the one he found, with orders that Rosencrantz and Guildenstern be killed. When Horatio asks how he could possibly have affixed the royal seal, legitimizing the letter, Hamlet says that God provided the way for that too. He had a copy of the Danish seal on his father's ring, which he was carrying...
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