Alice & Aristotle: A Theory About Lewis Carroll & Logic

Hi.  My name is Eric Gerlach.  I teach philosophy, logic and ethics at Berkeley City College, and I have a theory I published in the Knight’s Letter, the journal of the Lewis Carroll Society of North America, that I want to share with you, and hope you enjoy and share with others.

I have been searching Wonderland and the Looking Glass for forms of ancient and modern logic to study Carroll and how he is like Wittgenstein for many years.  I was offered an Intro Philosophy class after I gave a talk about the Mad Tea Party and logic at the Dominican School of Philosophy and Theology, and there’s a bit of that in everything I’ve taught since.

I think that there are many ancient and modern forms of logic, Aristotle, Mill, Boole, DeMorgan and others, hidden in the fiction of Carroll, and his puzzles are often simple enough that a child could solve them, but let’s ignore everything other than what I shared with the Carroll Society, the most significant form I have found.  I cannot prove that Carroll meant what he did not say, but Carroll loved puzzles, and he would leave things unsaid for others to find.

Historically, the first form of Aristotle’s logic, a form ignored by Boole and formal logicians who followed, the central idea of Aristotle’s first work on logic, The Categories, is the ten categories, a list of ten types of being, ten sorts of things we can say about things and argue anything about anything at all.  Aristotle’s ancient forms of logic were strategies for debate, but in Carroll’s day Boole, De Morgan and others Carroll studied were turning Aristotle’s arguments into abstract algebraic mathematics, rigid forms which do not care in the slightest, like gears, pistons and other surly mechanics, about time, space, individuals or emotions.

If Carroll used fiction to teach form, and followed Alice and forms of Aristotle through a dream about time and space that mocks universal forms of Boolean logic at an eternal, timeless Mad Tea Party, then the Caterpillar himself is time, a him to the Hatter, the Cheshire Cat, as a character, is space, somewhat visible, and the order of events of Wonderland, the cast of characters, follows the list of Aristotle’s ten categories, in the order Aristotle first lists them, but in reverse, as if seen through a looking-glass, like the mind, which mirrors the world.

Aristotle lists his ten categories, the ten types of things we can say about things as: substance, the material of a thing, quantity, the number or amount of a thing, quality, an aspect of a thing like good or green, relations, the interaction of a thing with others, space, the place of a thing, time, the duration of a thing, position, the situation of a thing with others, state, the status of a thing in itself, action, what a thing does to itself or others, and passion, that moves a thing to this or that action.  If we turn Aristotle’s own list of ten categories backwards, starting from the lowest rather than the highest, like a text backwards in a looking-glass mirror, we have: passion, action, state, position, time, space, relations, quality, quantity, and substance.  This inverted list fits the order of events and characters of Wonderland.

ChapterWonderlandLooking Glass
1: Passion – MotiveWhite Rabbit & Golden KeyBlack Kitten & Looking Glass
2: Action – ActivityMouse & Pool of TearsFlowers, Red Queen
3: State – StatusDodo, Caucus RaceTrain, Gnat, Fawn
4: Position – SituationWhite Rabbit’s House, PuppyTweedle Dum & Dee, Crow
5: Time/Space – DurationCaterpillar (Time)White Queen (Time) & Sheep (Space)
6: Relations – InteractionDuchess (Relations) Cheshire Cat (Space)Humpty Dumpty (Relations)
7: Quality – AspectMarch Hare, Mad HatterHaigha, Hatta, Lion & Unicorn
8: Quantity – AmountQueen of Hearts, CroquetRed Knight, White Knight
9: Substance – MaterialKind Duchess, Gryphon, Mock TurtleRed & White Queens & Banquet
10: SubstanceLobster QuadrangleRed Queen
11: SubstanceKing of Hearts & TrialBlack Kitten
12: EndAlice & EndingAlice & Ending

If so, in Wonderland, the worried White Rabbit is passion, the swimming Mouse is action, the presiding Dodo is state, the Rabbit’s House and task is position, the slow Caterpillar is time, the Cheshire Cat with perspective is space, the tyrannical Duchess is relations, the rude Mad Tea Party is quality, the Queen’s garden with cards is quantity, and the Mock Turtle who sings of soup and the King’s trial of tarts is substance.  Space shares space and a chapter with relations in the middle, which is deliberately confusing, like the wig of the fish and the wig of the frog entangled, there in the text, with the Cheshire Cat in the House of the Duchess, and the last few chapters are about substance, or lack thereof, from the Mock Turtle to the Trial of Tarts.

If so, Carroll repeated this order, character by character, theme by theme, numerical chapter by chapter, almost identically, with little change, in the order of events and characters of the Looking Glass, regardless of what Alice found there, such that the playful Black Kitten is passion, the running Red Queen is action, the Train with passengers is state, dueling Tweedle Dum and Dee are position, the backwards White Queen is time, sharing space with herself as the Sheep in a shop, who is space, narcissistic Humpty Dumpty is relations, the noble Lion and Unicorn are quality, the creative White Knight is quantity and the Queens’ banquet is substance.

The first chapters of both books are about passion without the satisfaction of action, the second about action without a state of destination, the third about state with confused positions, and the fourth about positions that lack relations wisened by perspective.  The fifth and sixth chapters are about time, space and relations interwoven, space mixed with relations in Wonderland, the Cheshire Cat in the house of the Duchess, and space mixed with time in the Looking Glass, the White Queen turning into the Sheep.

The seventh chapters are about quality of relations, the eighth about quantity and relations, with the executive fury of the Queen of Hearts mirrored by the gentle, inventiveness of the White Knight, and the remaining chapters are about substance, or lack thereof.  I believe that the confusions in the middle of each book, like the multiple sets of knitting needles of the Sheep, question how separate formal categories or mathematics are in the emotional, embodied and individually lived world.  Categories and mathematics can be abstract, like a dream, but individuals are always many things interwoven, together.

If any of this is so, Lewis Carroll wrote Alice’s Adventures and The Hunting of the Snark to teach children of all ages the basic forms of Aristotle’s logic with memorable characters, while mocking the ancient logic of Aristotle, material with time and space, and the modern logic of Boole, ideal, universal forms with no relations to particular individuals, time or space.  Carroll, mathematician and logician, taught the logical forms of Aristotle to men, women and children, and after he wrote Alice and the Snark Hunt, he wrote amusing books on logic for children.

Aristotle starts with substance, the most true form of being itself, and descends to passion, which we share with lowly beasts and uneducated children.  Carroll starts with lowly, untamed passion, the White Rabbit and Black Kitten, with Alice’s childlike curiosity, and ends in a royal court and banquet that are confusing forms without much stable substance, mere playing cards and formal roles, as Carroll seems to think of Boolean disembodied, dispassionate logic.  Perhaps Aristotle was too much the Hare and Boole too much the Hatter to Carroll.

If Aristotle’s list fits the plotting of Alice’s adventures, it is not impossible that the Snark works like a logic puzzle, to be solved by process of elimination, and each of the ten with jobs starting with B could stand for an Aristotelian type of be-ing.  In his Game of Logic, Carroll listed buns, babies, beetles and battledores (an early badminton racket) as examples of things.  The Bellman looks like Father Time, and carries a school bell for lessons.  In Carroll’s introduction he says his Snark shows he is incapable of nonsense, and that this brief but instructive poem includes precise arithmetic truth and natural history, both which apply to Aristotle’s categories.

If so, then the best fit is: the Bellman is time, the Boots is place, the Maker of Bonnets and Hoods is position, birth and death, the Barrister who dreams of the pig’s trial is relations, the Broker who values the goods is quality, the Billiard-Maker who chalks his own nose is action, the Banker is state, the Beaver who knits lace is passion, the Butcher who carves things up, dresses formally for the fight and teaches the Beaver addition is quantity, and the Baker who leaves everything on the beach, wears many layers, bakes wedding-cakes, doesn’t lie, forgets his specific name and fades away, vanishing without a trace in the end, is substance, fleeting mortal being to a Christian like Carroll.

I will follow soon with a video about each chapter, chapter by chapter, starting with the passionate White Rabbit of Wonderland, both rational and animal, then the Looking Glass, and Snark, in order.  My theory has some problems, and we are not infallible, formal beings, neither in thought, nor in mind, nor neither in deed, because all these categories are confusingly interwoven in our minds and lives, but please let me know what you think of the theory, kindly if you can, and I will further argue that the royal court characters of Alice’s adventures, the White Rabbit, Duchess, Kings and Queens, stand for Aristotle’s four forms of proposition, all, none, some and some-not, the central idea of the second and third books of Aristotle’s ancient, argumentative logic, and the central idea of Aristotle that Boole’s modern, formal logic.

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