Final answer:
The literary device used in Shakespeare's 'Hamlet' phrase, 'To be or not to be, that is the question,' is alliteration, characterized by the repetition of the 'b' sound.
Step-by-step explanation:
The literary device used in the phrase from Shakespeare's Hamlet, “To be or not to be, that is the question,” is alliteration. Alliteration is a literary device that involves the repetition of initial consonant sounds in a sequence of words, which is demonstrated with the repetition of the letter ‘b’ in ‘be’ and ‘not to be’ in the given phrase. Though famous for his use of various literary devices such as metaphors, similes, and personification, in this particular example, Shakespeare's choice of repetition emphasizes the existential dilemma Hamlet is expressing.