Inside Baptista's home, Katharina has bound her sister's hands. She demands that Bianca say which of her suitors she prefers, and when Bianca does not, Katharina slaps her. Baptista enters and rescues his younger daughter, reprimanding Katharina. Katharina rails against him as well before leaving Baptista alone to greet the arrival of Gremio, Lucentio (disguised as Cambio), Petruchio, Hortensio (disguised as Litio), Tranio (disguised as Lucentio), and Biondello.
Shocking Baptista, Petruchio explains that he has come to Padua from Verona to verify reports of Katharina's modesty and meekness, and has brought with him musician to instruct Katharina. Baptista is skeptical until Petruchio remarks that he is the son of Antonio, whereupon Baptista, who knows the man well, welcomes the suitor to his house. Gremio, in turn, presents Lucentio as a Latin teacher. Appropriately, Gremio introduces the disguised Lucentio as Cambio (Italian for "change").
Tranio next explains that he is a suitor to Bianca, alludes to his wealthy parentage and requests to be granted as much access as her other suitors; as a token of appreciation, he presents a lute and a packet of Greek and Latin books. As soon as Tranio notes that he is "son to Vincentio" of Pisa (2.1: 103), Baptista grants him the access he seeks. Baptista then calls for a servant to escort the tutors to his daughters.
Petruchio then abruptly demands of Baptista what dowry he will receive when he marries Katharina, upon which Baptista replies: "After my death the one half of my lands,/And in possession twenty thousand crowns." (2.1: 121-122) Petruchio is satisfied, and reassures Baptista that he will successfully woo the feisty Katharina. Just then, Hortensio reenters with a broken lute on his head, explaining that, when he tried to correct Katharina's fingering on the instrument, she promptly attacked him with it. Petruchio, far from disturbed, declares that he is all the more eager to "chat with her."
Soon Katharina appears and the others leave Petruchio to woo her. A battle of wits ensues, filled with sexual puns and insults. Petruchio indicates that, whether she wants to or not, he will take her for his wife. Baptista, Gremio, and Tranio join them and Petruchio happily informs the men that he has won Katharina's heart and that the two will be married on Sunday. Katharina snaps back: "I'll see thee hanged on Sunday first." (2.1: 296) Petruchio reassures his companions that Kate and he have agreed that while in public she will remain "curst" though they will be affectionate in private.
He takes Katharina by his arm and exits, leaving Baptista, Gremio, and Tranio to marvel at the speed of his conquest. Now that Katharina seems to be taken care of, Baptista moves on to the subject of his younger daughter, promising her to whomever procures the "greatest dower." It is soon clear that it Tranio's (that is, Lucentio's) wealth is greater. However, Baptista notes that he requires Tranio's father's "assurance" (2.1: 385) that Tranio has the wealth available. If this assurance is procured, Bianca belongs to Tranio; if not, she goes to Gremio. Tranio determines to find someone to play the part of Vincentio, in order to allow him to win Bianca.
Paradox is central to the comedy of Shrew. While preparing himself for Katharina's entrance, Petruchio proclaims his intention to believe the opposite of whatever Kate tries to say about herself: "Say that she rail, why then I'll tell her plain/She sings as sweetly as a nightingale." (2.1: 170-171) This strategy dominates the following interaction, in which language itself comes under close scrutiny. Although Petruchio stubbornly refuses to accept the things Kate says - and, vice versa, she is unable to accept the things he says - there is a clear affinity in the way they say them. Their connection is through rather than content; through rhetoric rather than meaning. They share little more than a style of delivery. But that alone seems to be the basis of a genuine compatability. Consider these lines:
KATHARINA: "Asses are made to bear, and so are you."
PETRUCHIO: "Women are made to bear, and so are you."
KATHARINA: "No such jade as you, if me you mean."
PETRUCHIO: "Alas, good Kate, I will not burden thee,/For knowing thee to be but young and light."
KATHARINA: "Too light for such a swain as you to catch,/And yet as heavy as my weight should be."
PETRUCHIO: "Should be? Should-buzz!"
KATHARINA: "Well ta'en, and like a buzzard." (2.1: 199-206)
Read the above lines aloud. Get a sense of their rhythm and punch. Sure, they are disagreeing on the surface, but Kate and Petruchio share one another's language, spinning puns out of insults and insults out of puns. The first two lines quoted above echo one another syllable for syllable, with a play on the word "bear" (used here to signify both "carry" and "give birth"). After an interjection by Katharina, Petruchio launches into a couplet which is swiftly answered by the woman.
This pattern of call and response, of rhyme and repetition gives way, in line 206, to a single line stretched between two speakers, so that the meter suggested by "Should be? Should-buzz!" is completed by "Well ta'en, and like a buzzard." Thus Kate and Petruchio have subtly merged in a single verse. Though they don't seem to get along at all, this cooperative insulting foreshadows their coming marital union. This paradoxical combination of combat and compatibility makes The Taming of the Shrew one of Shakespeare's most influential plays. Shrew is perhaps the first of a host of romantic comedies, ranging from the theatrical works of Shaw to Hollywood's screwball comedies and beyond, that use this strategy.
Katharina finally becomes Petruchio's because he is the only man around who can match her in a battle of wits. The game of love is a game of poetic one-upmanship. Grumio recognizes this when he assures Hortensio back in Act One that Petruchio will conquer the feisty Katharina, no matter how sharp-tongued she may be: "I'll tell you what, sir: an she stand him but a little, he will throw a figure in her face and so disfigure her with it that she shall have no more eyes to see withal than a cat." (1.2: 111-114) In describing his master, Grumio seems to adopt some of his facility: the noun "figure" becomes the verb "disfigure," leaving no doubt that Petruchio's language is a decidedly violent weapon. Indeed, words replace blows when it comes to Petruchio and Katharina. Whereas Katharina physically smashes a lute over Hortensio's head, she relies on her tongue when it comes to Petruchio.
Tranio, too, demonstrates the power of language in the play. He plays Lucentio's part well, convincing Baptista and the others. Tranio's ability to pull of the trick is based in part in his costume, but more so in his language. The imagery of riches he conjures up in his contest with Gremio easily beats that of his old and foolish rival. Words, therefore, break down social barriers. That said, words are not enough for the time being in Tranio's case. Baptista demands that Tranio obtain his father's "assurance," declining to trust Tranio's words alone. Yet Tranio will prove able to provide assurance through yet more theater - yet more masquerade and trickery. So far in the play, there is little that a successful manipulation of illusion, whether of words or appearances, can not accomplish.