The Tempest How does Prospero defend the sinking of the ship to Miranda?

Prospero explains his motivations for causing the storm by telling Miranda his history with the nobles aboard the ship; he reveals to Miranda that Antonio is his brother, and that he was once the rightful Duke of Milan, a position Antonio now holds. Antonio usurped Prospero's estate and wealth while Prospero became increasingly "rapt in secret studies" and oblivious to his brother's machinations; and in order to take Prospero's title as well, Antonio arranged to have his brother Prospero and Prospero's daughter Miranda killed secretly. But Prospero is widely known to be a good man, so those charged with his death decide not to kill him, Instead, Prospero and Miranda were set adrift on the open sea in a decayed vessel, and were able to survive off the supplies that the honest councilor Gonzalo arranged for them to have; thus, they landed on the island where they now live.