The Logic of Alice: Clear Thinking in Wonderland

The Logic of Alice: Clear Thinking in Wonderland

by Bernard M. Patten

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Many commentaries have been devoted to Lewis Carroll’s masterpiece, Alice’s Adventures in Wonderland. The interpretations range from Freudian analysis to speculations about the real-life people who may have inspired the animal characters.

In this unique approach to interpreting Alice, the fruit of ten years of research, Dr. Bernard M.

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Many commentaries have been devoted to Lewis Carroll’s masterpiece, Alice’s Adventures in Wonderland. The interpretations range from Freudian analysis to speculations about the real-life people who may have inspired the animal characters.

In this unique approach to interpreting Alice, the fruit of ten years of research, Dr. Bernard M. Patten shows that Charles Lutwidge Dodgson, aka Lewis Carroll, fused his passion for logic, mathematics, and games with his love of words and nonsense stories to produce a multifaceted, intricately structured work of literature. Patten provides a chapter-by-chapter skeleton key to Alice, which meticulously demonstrates how its various episodes reveal Dodgson’s profound knowledge of the rules of clear thinking, informal and formal logic, symbolic logic, and human nature.

As Patten makes clear, Alice’s Adventures in Wonderland, far from being just an entertaining children’s book, is more complex and deeply reflective of Dodgson’s character than it may seem. By making an effort to understand its deeper layers, both children and adults may profit from this masterful tale by learning to think better and, along the way, having fun.

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Prometheus Books
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Clear Thinking in Wonderland

By Bernard M. Patten
Prometheus Books
Copyright © 2009

Bernard M. Patten
All right reserved.

ISBN: 978-1-59102-675-4

Chapter One Down the Rabbit Hole

The phrase "down the rabbit hole" has become the symbol for adventure into the unknown. That is why Neo in the movie The Matrix is told to follow the White Rabbit, which he soon sees is a tattoo on a woman's arm.

Neo's curiosity, like that of Alice, leads him to follow the signaling woman (her arm has a White Rabbit tattoo) to the disco. From thence he goes on to meet Trinity. Thus begins Neo's journey of enlightenment and adventure.

Which pill would you choose, the red or the blue? Is ignorance bliss? Or is the truth worth knowing, no matter what? The blue pill contains nothing and will not change Neo's situation. The red pill has neurotrophins and lysins that will liberate Neo from the pink goop in the pink pod. The red pill will take Neo out of the (pleasant) unreal world of the Matrix and release him into the (harsh) real world of the non-Matrix.

Those of you who saw the movie may recall that Neo took the red pill. His reason: he wanted to "see how far down the rabbit hole goes."

What? What are we talking about here? What have a rabbit hole and The Matrix to do with anything?

On the anagorical level-well, I'll leave that to you to work out. Mystical interpretations are not my forte. And Carroll repeatedly denied that any exist in AAW. He wrote to Edith Rix, "I have a deep dread of argument on religious topics. My vew [sic] of life is, that it's next to impossible to convince anybody of anything because one of the hardest things in the world is to convey a meaning accurately from one mind to another."


O.K. Alice followed the rabbit down the hole for the same reason that Neo followed the rabbit tattoo, for the same reason that you are probably reading this book-(no special reason at all) just CURIOSITY and a certain bursting youthful spirit avid for mischief, adventure, and new knowledge. Recall how Alice plunged right in: "never once considering how in the world she was to get out again."

Humans are by nature a curious lot. Our expansive sense of time and space stimulates us to ponder our place in the scheme of things. That's what we do.

But what is curiosity? Who has it? And why? And what good is it?

The fact that you are reading this book is evidence that you are curious. In general, our species remains curious about anything and everything. Aristotle held that certain basic drives were part of human nature, among these he reckoned drives toward food, drink, sex, and knowledge. Yes, knowledge. "All men," said Aristotle, "desire to know." Aristotle was therefore asserting that all men are curious; they want to experience and understand. They want to know.

That's good. I like the idea. And wouldn't it be nice if it were true?

In a sense, curiosity is the seeking of the truth and knowledge. Truth seeking is good and normal. Most of us are curious. Most of us normally seek the truth. That's what Aristotle implied when he said in book I of The Metaphysics: "All men by nature seek to know."

But was he right?


Strictly speaking, Aristotle was wrong. He was wrong because the all-inclusive word "all" makes his claim overly general, simple and simplistic, and easily refuted by finding just one counterexample.

If just one man does not seek to have knowledge, then the statement "All men by nature seek to know" cannot be true. If the statement cannot be true, then it is false.

The reason that the statement would be false is that the word all means all. In the parlance of logic school and logicians, the statement "All men seek the truth" is a statement in the Universal Categorical Affirmative form (what the medieval scholastics called mood A) that entails several subaltern claims including multiple particular claims like "some men seek to know," "many men seek to know," "this man currently drinking his can of Bud seeks to know," and so on, as well as the bigger and more general claim "No man seeks not to know."

Here's the nub and the rub: If we find one man who doesn't seek to know, then Aristotle's statement is proven false.

Personally I know quite a few men who don't want to know (much about anything) and prove it every day. Whether or not most men seek to know is also debatable. If that were true, then how come most men don't know the names of the bushes, flowers, and trees in their front yard? How come most men don't have the foggiest idea of how their TV works or what mathematical algorithms let their computer fetch the e-mail?

Neo and Alice are different. They are not like all men. They are not like most men. They are like us, you and me. They are curious. They are curious in both senses of the word. They are curious (inquisitive and prying) to explore, learn, find out, and know. And they are curious (strange, unusual, and odd-set off from the group and the ordinary), arousing our attention and interest.

It so happens that "curious" is also the favorite word of Mr. Spock, an emotionless Vulcan, an almost purely intellectual personality on the television series Star Trek. Spock is never excited, amazed, or dreadfully afraid. He is detached, sometimes amused, and (like Alice) always curious (interested in finding out stuff) and also he is always curious (strange and unusual), especially with those long ears (or are those ears just pointy, simply appearing long?). But unlike Alice, characters like Spock and the others in Star Trek are as unbelievable as the rest of television.

What I did just then by using a word like "curious" in a single context while implying different meanings is an equivocation, something Carroll is fond of demonstrating and that is of course a classic error in thinking. For in a given context the meaning of a word must remain constant else we are likely to reach an erroneous conclusion. Here's the classic example of this error:

All men are rational. Women are not men. Therefore, women are not rational.

Women not rational? That can't be true. So where is the error?

The error is in the equivocation or double meaning of the word "men." In the first sentence (the major premise) "men" means all humans. In the second sentence (the minor premise) "men" means the male sex. Hence, the meaning of the word "men" has changed. Therefore the conclusion cannot follow. This error was known to our ancient ancestors as the error of the fourth term because the argument contained four terms (men1, men2, women, rational) and not three. Cool!


One famous example concerns the oracle at Delphi, the supreme court of the ancient world to which important political and military questions were often referred: "Croesus, king of Lydia and other countries, believing that these are the only real oracles in all the world, has sent you such presents as your discoveries deserved, and now inquires of you whether he shall go to war with the Persians, and if so, whether he shall strengthen himself by the forces of a confederate."

Both the oracle at Delphi and the oracle at the shrine of Amphiaraus agreed in the tenor of their reply, which was, in each case, a prophecy that if Croesus attacked the Persians, he would destroy a mighty empire. There was also a recommendation to look and see who were the most powerful of the Greeks and to make alliance with them.

At the receipt of these oracular replies, Croesus was overjoyed. Feeling sure now that he would destroy the empire of the Persians, he attacked, leading his forces into Cappadocia, fully expecting to defeat Cyrus and destroy the empire of the Persians. In so doing, the ancients believed he had interpreted the oracles in the wrong sense. An empire was in fact destroyed. However, it was not the Persian Empire. It was his, his own empire.

The Delphic oracle was great at equivocation. Take for instance the prediction given to expectant parents. The question was, "Will it be a boy or a girl?" The answer was, "Boy not girl."

This statement equivocates because "Boy, not girl" means a boy is predicted and "Boy not, girl" means a girl. Irate parents who complained that the prediction was wrong were told, next time around, to listen more carefully.


When Neo and Alice don't know something, they want to know or at least they want to try to find out. In fact, Neo and Alice both made an existential choice to find the truth. That they were able to make that choice indicated that free will exists: that choice, their choice, was an exercise of their free will.

Neo chose the red pill, proving he could choose what to take. Neo chose not to choose the blue pill, thereby proving he was free not to choose the blue. If he was free to choose and if he was free not to choose, he was free because "free to choose or free not to choose" is logically equivalent to "free." In the same way, if I tell you never speculate if you don't have money and never speculate if you do have money, I am actually saying never speculate, as that is the logical equivalence of what I said. And, by the way, it's good advice.


f = false

t = true

Let F = free, C = choose, then (F&C)V(F&~C) = F where "=" means "is logically equivalent" and "V" equals the logical operator "or." This "or" is the inclusive "or" meaning either one or the other or both.

F C ~C (F&C)(F&~C) [(F&C)V(F&~C)] 1. t t f t f t 2. t f t f t t 3. f t f f f f 4. f f t f f f

Note that in every case the truth values of F are the same as for (F&C)V(F&~C), which in symbols says free to choose or not choose, proving that the complex expression is logically equivalent to "free."

By the same token and the same reasoning and demonstration, it can be proved that Alice was free. She was free to choose to make a daisy-chain and free to choose not to make a daisy-chain:

So she was considering, in her own mind (as well as she could, for the hot day made her feel very sleepy and stupid), whether the pleasure of making a daisy-chain would be worth the trouble of getting up and picking the daisies.

And Alice is free to choose not to follow or to choose to follow the rabbit down the rabbit hole.


Epicurus (341-279 BCE) thought that if every event is caused by other events, there can be no free will. That idea is obviously nutty. So he postulated that the atoms (following Democritus, he believed that these small units constituted the material universe) randomly "swerve" as they move through space. The random swerve, according to him, knocks out complete determinism and permits a degree of indeterminism that in turn permits free will.

The problem with indeterminism so conceived is that it seems to undermine the notion of causal responsibility. Think about this: "Alice chose to go down the rabbit hole" compared to "Alice happened to go down the rabbit hole." The second version clearly does not involve a causal claim about choice and seems to make going down the rabbit hole more a matter of happenstance, if not chance. Well, which is it? Did she choose or did she not choose to go down the hole? Read the AAW text for the answer or read on and I will give you the answer.

Modern physics backs up Epicurus with evidence that certain events-like radioactive decay-are purely random. The concept is important because if there were no free will, there would be no responsibility for action because nothing humans do would be up to them.

This faith in human freedom despite our deterministic sciences is the first postulate of moral experience and is a key point in AAW where Alice makes so many choices. Her first choice is not to make a daisy chain and her second choice is to follow the White Rabbit down the hole. Yes, that is the answer to the aforementioned question: Alice actually chose to go down the rabbit hole.

By the by, the demonstration of Alice's freedom also curries favor with children. If Alice is free, then the children reading AAW might also be free. If Alice has enough freedom to make choices, the kids who are reading the book, and the kids who are having the book read to them, might also have the freedom to make choices. If Alice can sit on the riverbank and "consider, in her own mind (as well as she could, for the hot day made her feel very sleepy and stupid), whether the pleasure of making a daisy-chain would be worth the trouble of getting up and picking the daisies," so can the kids reading the book consider what they might or might not want to do.

We adults, too.

This stuff might apply to us. We might be free. If we are free to choose or free not to choose, we are free.


But of course we all know that we don't need atomic physics to prove that we have free will. We prove that we have free will every goddamn day by making the multiple choices that we make. Just the way Alice proves her freedom by making the multiple choices that she makes.

It's true, of course, that we are not entirely free to do entirely what we want, which is to say that our choices are limited-often severely limited-by constraining reality: I can't flap my arms and fly to the moon. To go to the moon, I need a rocket ship. There have been many days that I would have liked it to rain Irish whiskey. But alas, there was a disappointment ahead. To get a good stiff drink, I would have to go to a package store or a bar. The reality is that I would stand outside with my tongue out forever and it would never rain whiskey, neither Irish whiskey nor any other type of whiskey. Water is just about all that I can reasonably expect from rain, no more and no less.

Thus my will is not entirely free. My will is constrained by the external realities of this wide world. Immanuel Kant (1724-1804), the philosopher of the 1700s who ranks with Aristotle and Plato of ancient times (the guy we took down a peg above), said the things of the world are real, but it is the job of the human mind to form and shape those realities and to give meaning to the relationships between them. And then (and this is the kicker) in so doing to alter them as much as possible for human benefit.

So ...

We have free will all right: Not a whole lot of it. Not that much. Just enough-just enough of it to make life interesting. And just enough for us to change the world or get it into trouble.

Once a choice is made, it becomes a thing of the past, a past that is closed and fixed, indestructible really. Yes, the past is beyond change and fixed and indestructible such that we can't change it. We can't change what's happened, as this quote from Omar the tent maker says:

LI (verse 51) The Moving Finger writes; and, having writ, Moves on: Nor all thy Piety nor Wit Shall lure it back to cancel half a Line, Nor all thy Tears wash out a Word of it.

Rubàiyàt of Omar Khayyàm (1048-1022) -trans. Edward FitzGerald


Once Neo takes the red pill, he can't go back into the Matrix. Once Neo takes the red pill, he must emerge from that pink goop in that pink pod, never to return again. Once Alice heads down that rabbit hole, she can't return again until her adventure is over.

So please remember this: The past is closed. You can't change it. But because of free will, the future is open. The future can unfold in multiple ways. Some of those ways depend on your choices-the good, the bad, and the ugly.


Free will allows us to direct the future. In a sense, make the future. Think about that! Making the future is a big deal-a major responsibility. Isn't that fantastic? Are you up to it?

About free will and (no excuses) existential philosophy, more later. Meanwhile, let's consider that Alice's opting for adventure is human enough. It has advantages and disadvantages.


The quest for adventure led humans out of Africa to inhabit (eventually) most regions of this planet. The quest for knowledge, especially new knowledge, led to our fictive downfall in the Adam and Eve story, wherein that primal couple suffered exile from the Garden of Eden for eating (I am not making this up, as fantastical as it may sound) some kind of fruit (an apple) from the tree of knowledge. Weird, right?

Lots of stories in the Bible are weird. But they have a message behind them. Take for instance the tale of Adam and Eve. They ate the fruit of the forbidden tree, learned in the process the difference between good and evil, and suffered a big penalty. Weird, right?


Excerpted from THE LOGIC OF Alice by Bernard M. Patten Copyright © 2009 by Bernard M. Patten. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

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