Petruchio’s monologue in Act IV, scene i explains most of what transpires in this scene, as he tells the audience of his scheme to bend Kate to his will. He will tame her as the falconer trains his bird, by holding lures out in front of it, just out of reach. All has been planned in his mind in advance: “Thus have I politicly begun my reign,” he says, where “politicly” means “with careful calculation” (IV.i.169). Petruchio wishes to bend Kate’s hostile temperament into benevolence by turning everything against her—ironically, under the guise of heightened concern for her well-being. He means to “kill [his] wife with kindness” (IV.i.189). Though Petruchio’s treatment of Kate is undoubtedly condescending and chauvinistic, it is nevertheless significant that Petruchio decides to “kill” her with kindness rather than with force. By couching his attempts to smooth out Kate’s rough temper in language of love and affection, Petruchio both makes himself more sympathetic in the eyes of the audience and opens the way for an actual loving relationship with Kate once she decides to accept her new role as his wife. Had Petruchio simply attempted to dominate his wife forcibly, he would have appeared monstrous to the audience, making a pleasant union impossible.
Though Shakespeare loves to use disguise as a means of transgressing social boundaries, in The Taming of the Shrew social roles and social positions are ultimately too binding to escape. This is one reason why the stakes are so high in Petruchio’s “game” with Katherine. Petruchio’s monologue indicates the importance of his plan. He understands that despite Kate’s independence, her only hope for achieving happiness lies in her ability to adapt to her role as a wife. Otherwise, she will be forced to continue the socially alienated misery of her life as a maiden, out of sync with her role in society. For Petruchio and Katherine, this negotiation is well under way, and, despite their frequent quarreling, it is aided by their obvious attraction to one another. But for the parties involved in the subplot, who continue to deceive themselves and those around them, uncharted waters lie ahead.
In Act IV, scene ii, the subplot nearly reaches complete success. Through the duping of Hortensio and the acquisition of the services of the naïve pedant, all obstacles between Lucentio and Bianca seem to be removed—except, of course, for the fact that the man Baptista knows as Lucentio is really Tranio. This was the fundamental flaw in the plan, which is why Biondello, perhaps the most sensible character in the play, later arranges for the two lovers to elope while Baptista speaks with the pedant. All in all, the whole scheme amounted to little more than an entertaining distraction, since the disguises cannot be maintained forever if Bianca and Lucentio ever wish to fulfill their desires.
From Biondello’s news, we see that the ploy has begun to unravel quickly, now that they have finally reached their goal. Once Lucentio and Bianca have married, they must either flee Padua or reveal their ruse, since Baptista soon expects to marry Bianca to the disguised Tranio. It would be no great matter for Lucentio to return to Pisa, or to go elsewhere, since he is wealthy and educated, but for Bianca it would mean abruptly leaving her family, friends, and inheritance. In fact, the young lovers don’t have the faintest idea what their married life will be like, since Lucentio has been acting a role from the beginning, and they have had to court each other in secret. They may represent the ideal of young love at first sight, but their love does not seem to be developing in a way that facilitates future growth.