Why does Shakespeare choose Venice for the opening scenes of Othello?
Ha! Great question!
To call a woman a Venetian was akin to calling a man a senator: both were considered prostitutes of sorts.
In Shakespeare's time, Venice was considered the pleasure capital of Europe, and Venetians were known for their sexual licentiousness. The most talented courtesans were reputed to have lived in Venice. What is more, Venetian courtesans did not dress...
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I agree with both the other answers, that Shakespears chose Venice, it seems to be a synecdoche for vice. But also, Shakespeare often set his plays outside of England, in order to guise the social commentary inherent within them. To make a comment on the social system of England, would be seen as unpatriotic, so he disguised his critiques of Elizabethan and Jacobian societies, by setting his plays in other countries. Many of them are set in Italy, or like Macbeth, nearby countries such as Scotland (granted though, that could have been a result of the original nationality of Elizabeth I's successor).