Alice, while still in the dense wood, comes upon a very small house which she uses her mushroom to shrink to the proportions of. From behind some brush she watches as a fish, dressed as a footman, delivers an invitation to a frog dressed as a footman. The business is transacted at the door of the small house. The invitation is from the Queen to the Duchess, and it invites the Duchess to a game of croquet.
Alice approaches the door where the frog footman still stands and looks to get in, so she knock. But the frog, who is apparently in charge of that door, merely mocks her attempt at knocking because he is, after all, on the same side of the door as she. They engage in this paradoxical word play for a few lines until the door flies open and a dish shoots out toward the frog'' head. A raucous disturbance is going inside the house of the Duchess. Irritated, Alice walks into the house.
Inside Alice finds the Duchess in the kitchen with a cook cooking soup and a crying baby. A grinning cat was at the Duchess' feet. The air is so full of pepper that everyone save the cat is sneezing, and the baby is crying loudly between sneezes. Alice asks why the cat is grinning and the Duchess says it is a Cheshire Cat, and then the Duchess calls the baby a Pig.
In short, the Duchess is very rude to everyone.
The cook then began to throw everything she could find at the Duchess and the baby. Alice is worried for the baby and says so. The Duchess calls for Alice's head to be chopped off. Nothing comes of that demand and so the Duchess returns to nursing the baby. She sings to it a sort of Anti-Lullaby where, at the end of each line, she shakes the baby violently. Then the Duchess flung the baby at Alice to nurse because she had to go and get ready to play croquet with the Queen. Alice decided that she must take the baby away, for to leave it would be murder. Then she discovered that it was, indeed, a pig. So, she let the pig go.
Alice then decided that while that baby had been an awful baby, it turned out to be quite a handsome pig. She then began to ponder whether other awful children she knew would be better as pigs.
Once the pig is gone Alice comes upon the Cheshire Cat in a tree and she asks him directions. The Cat says that anyway is a good as another and that no matter where Alice goes she will be among the mad. Wonderland is for mad people, and therefore Alice must be mad too, says the Cat.
The Cat says: "A dog growls when it's angry, and wags its tale when it's pleased. Now I growl when I'm pleased and wag my tale when I'm angry. Therefore, I'm mad." The Cheshire Cat is here pointing out the odd paradox of being polite. That is, a sophisticated mind must act contrary to what is felt, or people will be getting offended. But, by the same token, politeness and civility is a kind of madness, or at least self-deception.
Alice then marched off to the house of the March Hare. As she approached, she practiced her own form of polite self-deception by using her magic mushroom to transform herself into the appropriate size.
This chapter is most importantly, again, about civil society. Alice is slowly internalizing her own judgment, able now to act as an adult when the matter is thrust upon her. That is, the clearly unfit condition of the baby's home prompts her to respond appropriately and remove the baby from harm's way. Now that Alice seems to have learned to act appropriately, and to tailor her size and demeanor to her surroundings, Alice has to deal with the complexity of adulthood. The Cheshire Cat has stepped in to point out that from now on, adulthood will be madness. That is, just because she can control herself and behave in a civil manner, that doesn't mean that all of the other adults will. Furthermore, the fact that they are behaving in a mad manner may not always be inappropriate. Things grow more complex as we move on, so don't get lost.