The main function of paradox in the book is to show how Wonderland inverts reality. Nothing is quite as Alice expects it to be. For instance, the Dodo's caucus "race" consists of many animals running in a circle and stopping all at once. In Chapter 3:
They began running when they liked, and left off when they liked, so that it was not easy to know when the race was over [...] at last the Dodo said, "Everybody has won, and all must have prizes."
This obviously isn't a race at all; the Dodo suggests running to dry off the animals. However, calling it a race makes it a race, and consequently, someone must have a prize. In fact, in another inversion of expectation, all the animals must have prizes.
Another example of paradoxical inversion is that Alice, a polite and kind young girl, rather terrifies the Mouse and the Pigeon. She strives to communicate with them, but her words only intensify their fear.
In a sense, Alice's Adventures in Wonderland is a fictional expression of Carroll's Paradox. This idea, first published in Mind in 1985, stated that the most perfect axioms are not sufficient for determining the truth. Throughout the book, Alice runs into characters who make ridiculous statements about the truths of Wonderland. These truths, of course, come true, but they seem ridiculous. So Wonderland represents the impossibility of a world in which mere words (axioms) create truth.
