In Chapter 2, Alice begins to discover the rules of the Looking-Glass world by testing a paradox:
A little provoked, she drew back, and, after looking everywhere for the Queen (whom she spied out at last, a long way off), she thought she would try the plan, this time, of walking in the opposite direction.
It succeeded beautifully. She had not been walking a minute before she found herself face to face with the Red Queen, and full in sight of the hill she had been so long aiming at.
Alice has been trying and trying to reach the Red Queen, but every time she walks toward her, she ends up back at Looking-Glass House, where she started. The frustrating experience of trying very hard and getting nowhere finally leads her to try walking toward the house instead. By reversing her target, she ends up exactly where she wanted to go all along.
At first, it seems baffling that Alice would end up at Looking-Glass House when trying to walk away from it and that she would end up next to the Red Queen when trying to walk toward Looking-Glass House. But Alice has also noticed that everything in this world seems to be a mirror image of everything in her world. It makes a certain kind of sense that Alice's efforts to reach a certain goal would have an opposite effect in the Looking-Glass world than she would expect in the real world. Her ability to adapt to the logic of this mirror-image world demonstrates that she is a savvy child who learns new rules quickly. This adaptability helps Alice "grow up" and navigate adult spaces. Still, the longer she stays in the Looking-Glass world, the clearer it becomes that not everything is a perfect mirror image of the real world. Some things truly make no sense at all, even paradoxical sense. Alice's ability to adapt to new rules helps her face many challenges. But it is also important for her to retain a childlike skepticism for rules that are simply silly.
In Chapter 5, the White Queen argues that punishment makes people better, and that this is especially the case if the punishment takes place before a corresponding crime ever occurs. This strange idea is a paradox that makes sense given the rules of the Looking-Glass world, but Alice begins to recognize it as a fallacy as well:
“Were you ever punished?”
“Only for faults,” said Alice.
“And you were all the better for it, I know!” the Queen said triumphantly.
“Yes, but then I had done the things I was punished for,” said Alice: “that makes all the difference.”
“But if you hadn’t done them,” the Queen said, “that would have been better still; better, and better, and better!” Her voice went higher with each “better,” till it got quite to a squeak at last.
Alice was just beginning to say “There’s a mistake somewhere——,”
In the Looking-Glass world, many things are reversed. For instance, the White Queen reacts to things before they happen. This reversal of time means that a messenger is about to be tried and possibly executed "next week" for a crime he will commit "last week." Carroll is playing with verb tense and imagining that "last week" is in the future of "next week." According to the rules of a world where everything is a mirror image of the real world, all of this makes sense. The seemingly outlandish idea of executing someone for a crime they haven't yet committed is exactly how things would work in a mirror image of the English justice system. In this sense, what the Queen says about crimes and punishments is a paradox: it seems contradictory but makes sense on further inspection.
But the idea of a punishment preceding a crime still doesn't sit right with Alice. "There's a mistake somewhere—," she says. Even though the White Queen's justice system makes sense as a mirror image of the justice system with which Alice is familiar, the logic itself seems suspect to her. The Queen claims that punishments for past infractions surely made Alice better and that she would have been made better still if she had endured the punishments without even committing the crimes. This claim is a fallacy. It rests on the presupposition that punishment itself improves a person, regardless of the context. Alice can't quite get to the point of breaking down the Queen's logic in this way, but her discomfort invites the reader to break it down. By isolating this false assumption that punishment improves a person, Carroll also invites the reader to think critically about the justice system outside the Looking-Glass World. He does not straightforwardly condemn the idea of a retributive justice system, but he does raise the question of what it means for a punishment to fit a crime.
