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Disguise and Illusion
The Induction that begins The Taming of the Shrew introduces illusion as a principal theme. Shakespeare is not content merely to tell a story: he reminds the audience of theater's inherent constructedness. The Taming of the Shrew is a play within a play - one which is very aware of the complications its status as a fiction entails.
This strange beginning continues to resonate during the subsequent action of the play proper. Indeed, when Tranio rises to the role of Lucentio, this mirrors Sly's own donning of a lord's manner. It becomes at times difficult to keep track of the various multiple identities and counterfeit personas: Hortensio as Litio, Lucentio as Cambio, the Pedant as Vincentio. However, this confusion itself is perhaps the point: the very act of disguising oneself, of playing a role, becomes the thing that matters most.
The Taming of the Shrew may thus be interpreted as a play about playing, theater about theater, in which the central concern is not love but illusion. Is love therefore an illusion? Given that Petruchio and Katharina certainly assume roles themselves, though without wearing costumes or changing their names, one is tempted to wonder what "truth" - if any - may inform performance.