When you hear the name Lewis Carroll, the first thought that probably comes to mind is the fun and nonsense associated with his children's books and not the rigor of logic and mathematics. And yet, when you look at such books as Alice in Wonderland and Through the Looking Glass more closely, you begin to notice that they are filled with puzzles, riddles, and brainteasers that refer to logical and mathematical concepts. Some characters, such as the Duchess and the Mad Hatter in Alice in Wonderland, employ words and phrases that evoke syllogisms or logical arguments. A syllogism is a pair of propositions that, when put together, yield a new conclusion. The simplest form a syllogism can have is the following: All A is C; All B is A; Therefore, all B is C.

Logic and mathematics were topics that fascinated Lewis Carroll throughout his life. Carroll, whose real name was Charles Dodgson, was born in England in 1832 and studied mathematics in high school and college. After receiving his degree in 1854 from Christ Church College in Oxford, he became a teacher of mathematics, logic, and writing. He also published a number of treatises and pamphlets on such topics as Euclidean and algebraic geometry. Later in life, Carroll became especially interested in logic and studied the works of such important figures as George Boole and John Venn, whose approaches to logic are still used today. Carroll published two books on logic, The Game of Logic in 1886 and Symbolic Logic in 1895, which are both geared toward teaching children.

In order to make logic more appealing to a young audience, Carroll used two strategies. First, he tried to make his syllogisms fun and interesting by using animals and food in his examples. He presented them as riddles to be solved, and some of his resulting syllogisms are quite silly, such as the example below.

No bald creature needs a hairbrush;
No lizards have hair.
Answer: ??.

Carroll's second strategy was to invent a board game to teach children how to diagram the syllogisms. The Game of Logic actually came with a board and game pieces so that students could practice diagramming syllogisms as they used his book. In the diagram below, you can see how this game can be used to get the answer to the syllogism above. The regions on the board stand for the different properties of things contained in the syllogism: bald creatures, things that need hairbrushes, and lizards. The red piece shows that the property is present. The gray piece shows that it is not present.

Knowing that Lewis Carroll loved math and logic helps to explain some of the language he used in his books, but it doesn't make them any easier to understand. It sometimes seems as if he uses such syllogistic phrasing to both confuse and delight the reader. In the words of Tweedledee, one of the many characters Alice encounters on her adventures: "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."