Blogs, Fun and Games, Mathematical Reasoning

Alice in Logicland.

Today, I begin my logic section in my introduction to proofs class.  It is true that students learn more if they are having more fun.  While logic is always fun, it is more fun if the ideas presented are connected to written quotes.  While there are many written quotes to choose from, none are more fun than the ones written by Lewis Carroll in his many books.  Therefore, if my goal is to get my students to learn as much as possible, I should …

I’ll let you finish that thought as a warm-up for today’s blog.  While, I often try to be much more concise in my writing (and therefore wouldn’t usually include a paragraph written like the one above) there is something wonderful about the way Carroll, author of Alice’s Adventures in Wonderland, can present a very precise logically-sound idea in the most perplexing of ways.  Trying to take his words, and then convert them into something resembling normal spoken language is an exercise in logic itself.

For example we have the following interaction between Alice and the Chesire Cat

“Would you tell me, please, which way I ought to go from here?’
‘That depends a good deal on where you want to get to,’ said the Cat.
‘I don’t much care where -‘ said Alice.
‘Then it doesn’t matter which way you go,’ said the Cat.
‘- so long as I get SOMEWHERE,’ Alice added as an explanation.
‘Oh, you’re sure to do that,’ said the Cat, ‘if you only walk long enough.”
― Lewis Carroll, Alice in Wonderland

Here, the Chesire Cat takes what Alice says literally and gives her very appropriate answers to the questions posed.  However, the interaction gives students to use the imagination and picture a girl and a cat talking, while also trying to discern the logical meanings of the words used by Alice and therefore if they statements given by the Cat are true.  Note that instead of reading the book this morning and searching for quotes I found this, along with many more, on, choosing this because I personally like it.  If you haven’t read the book in a while, I highly suggest you do so.

While there is sufficient material in Alice’s Adventures in Wonderland to get you through an entire course, Carroll also has an entire book, The Game of Logic, explaining and providing examples in logic in ways that only he could.  While it would be worth rephrasing his works so that you can use the notation you are following in your own book, the goal of reducing statements to more concise statements can really help decipher what other people are saying and further a student’s understanding of logic.  According to Carroll himself,

Once master the machinery of Symbolic Logic, and you have a mental occupation always at hand, of absorbing interest, and one that will be of real use to you in any subject you may take up. It will give you clearness of thought – the ability to see your way through a puzzle – the habit of arranging your ideas in an orderly and get-at-able form – and, more valuable than all, the power to detect fallacies, and to tear to pieces the flimsy illogical arguments, which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art.

I found this quote at Lecture Notes for Math 100 which also provides even more Carroll Puzzles to work.  The first example the site goes through is,

(a)  All babies are illogical.

(b)  Nobody is despised who can manage a crocodile.

(c)  Illogical persons are despised.

What, then, can we infer through transitivity?  Well, firstly, babies are despised, and, secondly, that babies cannot manage crocodiles.  While I don’t believe that babies are truly despised (in fact I love my son, my son is a baby, therefore not all babies are despised) it provides a great way for student to follow through the logical implications of statements made.  I highly suggest looking at the rest of the exercises provided by G.N. Hile for the math department in Hawaii.

While I started the day planning on giving my personal experiences on using Carroll in my logic class, I found that this is a topic that has been richly explored by many people.  Instead of providing my anecdotal evidence, I decided instead to refer to you legitimate research that has been done on the subject.  In particular, please look at the article Logic in Wonderland.  Here, the authors run a study teaching children logic while using Alice in Wonderland.  They provide the method of instruction used, the activities they implemented.  They further go on to discuss the results they had within their study.  While there was no significant difference in grades, the authors still felt it was a worthwhile endeavor.


Hile, G.N.  Lewis Carroll Puzzles.

Lewis Carroll Quotes.

Movshovitz-Hadar, Nitsa & Shriki, Atara. (2009). Logic in Wonderland: Alice’s Adventures in Wonderland as the Context of a Course in Logic for Future Elementary Teachers. 4. 85-103. 10.1007/978-0-387-09669-8_7.

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