As the other answer to this question suggests, postcolonial theory in Othello has much to do with the central race relations of the play. One way of approaching a postcolonial critique of the play is to consider how the European perception of Othello forces him into fulfilling racial stereotypes.
For instance, throughout the play there is the subtle suggestion that Othello, despite his high status, is considered dangerous by his European counterparts. Brabantio is scandalized when he learns of Othello's relationship with Desdemona, and this revelation almost leads to Othello's arrest and accusations that Othello has kidnapped or stolen his future wife. It's as if the citizens of Venice can't imagine a white woman would have a consensual relationship with a black man, or as if Othello's race poses a threat to the European familial order. Othello continuously subverts this perception, comporting himself with dignity despite European mistrust.
However, in being manipulated by Iago into...
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