White Daisy Chains & Red Falling Leaves

In his Categories, Aristotle uses white and red as his examples of passive qualities, and says, “All colors, like white and black, are qualities as well and passive…  We give them that name from the fact that they spring from affections or passions.  There are numerous changes of color that clearly arise from affections.  When men are ashamed, then they blush; when alarmed, they turn pale and so on.  So much is this really the case that, I think, when a man is by nature disposed towards shame or alarm as arising from a certain concomitance of bodily elements in him, we may not unfairly conclude that he takes on the corresponding color.” (9b 10-20)  Aristotle says that there are temporary passing states of character, which are different from enduring dispositions.  He uses the example of anger as a temporary passionate state and anger as an enduring condition of madness, like the enduring rudeness and foolishness of the Mad Tea Party, who are unchanging in time.

In his On Interpretation, Aristotle uses white as his example of a quality that can be affirmed or denied with the four forms of proposition, and to illustrate what he means by contradiction, a central topic: “When the subject of two propositions is one and the same but the affirmative proposition clearly indicates that the subject is taken universally, then negative proposition, that the subject is not taken universally, I call contradictorily opposed.  Examples are, ‘Every man is white,’ ‘Not every man is white’ and the like, or, again, we have, ‘Some men are white,’ to which,  ‘No man is white’ is opposed in the manner of which I am speaking.” (17b 15-20)

Boole and Carroll, like many today, use the word white to mean European in ethnicity, a more permanent condition of complexion and color than Aristotle’s passive, temporary states of health, just as Hindu upper-caste Brahmins have identified the color white with their higher caste and complexion, the color black to refer to those of lower caste, and the British have referred to Indians as blacks in general, as they and Americans do Africans.  When Aristotle says Socrates was a white man as a central example of logic, he likely means that Socrates is old or sick, and certainly didn’t mean that Socrates was white in ethnicity, as are Germanic tribes, as ancient Greeks did not use the word this way.

Boole follows Aristotle’s example and uses white as a basic example of a class of things that are similar, saying, “Thus, if x alone stands for ‘white things,’ and y for ‘sheep,’ let xy stand for ‘white sheep…’”  but Boole proceeds to use white in the way of enduring complexion and ethnicity, which isn’t Aristotle but overlaps with his more temporary use of this color as character, when Boole, attempting to ground Aristotelian logic in algebraic mathematical expressions, expresses, “European men and European women,” as z(x + y), with z as European, x as men, and y as women, “All men except Asiatics,” as x – y, with x as men and y as Asiatics, and “White men, except white Asiatics,” as z(x – y), possibly referring to the Brahmins of India. (II.11)

Carroll uses the colors white and red several times in Wonderland and the Looking Glass as Aristotle does, to signify affections and passions as states of character, the extremes of too weak, pale and white, and the extreme of too brash, flush and red.  Carroll also pairs these affections with the positions of childhood and adulthood, passionate subject and reasoning ruler, several times in both books.  In the beginning of Wonderland, Alice thinks of making a white daisy chain, falls asleep and follows the White Rabbit, and in the end of Wonderland Alice disrupts the King of Heart’s trial, wakes up and sweeps falling red leaves from her face that she mistook for the playing cards rising up against her.  When she reaches the overly general in the garden of the Queen of Hearts, the first thing she sees is white roses painted red, and the Queen grows red in the face as she demands Alice’s execution.  Many of Carroll’s favorite poets spoke of the purity of childhood, and in the Looking Glass the White Queen is characterized as a carefree child, with Alice pinning her shawl for her, and the Red Queen is characterized as a strict governess.

Alice’s Adventures

White Red

Wonderland

Daisy Chain

Timid White Rabbit

White Roses Painted

Falling Leaves

Brash Queen of Hearts

Roses Painted Red

Looking Glass White Kitten

White Childlike Queen

White Knight protects Alice

Black Kitten – Red Queen

Red Governess Queen

Red King ignores Alice

Logicians who follow Aristotle, like Boole and Carroll, have taught that the propositions All A is B and No A is B contradict each other, and can’t both be true at the same time in the same way, just as Some A is B and No A is B contradict each other.  The two universal propositions at the top of the Square of Opposition contradict each other, such that, as Boole and Carroll both explain, the propositions All men are white and No men are white can’t both be true at the same time.  The positive universal proposition also contradicts the negative particular, and the negative universal contradicts the positive particular, from corner to diagonally opposite corner, such that if All men are white then it is contradictory to assert Some men are not white, and if No men are white it is contradictory to assert Some men are.

All of this was central and basic to the work of Boole, Carroll, and then Venn, who drew his famous circular diagrams to teach these Aristotelean lessons visually to students of all majors in an introductory logic course.  If Circle A is entirely inside Circle B, such that we can say All A is B, then it can’t be that Circle A is entirely or partly outside of B, so we can’t say without contradicting ourselves that No A is B, nor that Some A is not B, unless something changes.  Similarly, if Circle A is entirely outside Circle B, such that we can say No A is B, then it can’t be that Circle A is entirely or partly inside of B, so we can’t say without contradiction that All A is B nor that Some A is B.  In this way Venn visually presented the system of Aristotle’s four forms of proposition and syllogistic argumentation.

In The Laws of Thought, Boole speculates that if we were a species that split things into threes rather than twos, with trichotomies rather than dichotomies, the laws of human thought would be completely different.  When I was a small child, I listened to a Schoolhouse Rock record about multiplication tables, and the song about multiples of twelve told me as an amazed child that just as these twelve-fingered aliens would have an eleventh and twelfth finger, they would have a tenth and eleventh digit, much as a finger is a digit used for counting, a single symbol for ten and eleven, rather than our two, just as we have a single symbol that stands for the quantities of eight and nine, which aliens with eight fingers might represent with two symbols.  If these two alien species somehow came to the same numeral symbols as much of humanity did in the convergence of Indian, Islamic and European mathematics, the twelve-fingered would represent our “10” and “11” as single symbols we don’t use at all and would represent twelve as “10”, with our two symbols, and likewise the eight fingered aliens, with four on each hand.

If we did not have words intertwined with things, feelings and thoughts, we would not have the thoughts that we have, and if we were not dichotomous beings, we would not have the Square of Opposition, nor words that form pairs of opposites such as all and none, some and some not, without.  As Boole points out, we could be trichotomous beings that feel things are good, bad and zerblat, which is neither good nor bad, and not neutral, as it is opposed to both and its own thing.  Because we are creatures of dichotomy, all things are made up of the classes of men and not men together, and Boole says, “a class whose members are at the same time men and not men does not exist… it is impossible for the same individual to be at the same time a man and not a man,” and follows with the Aristotelian example Animals are either rational or irrational.

Lewis Carroll’s conjunctive White Rabbit is quite human and beast, and so, according to Aristotle, is impossibly a rational and irrational animal in the same individual, overly some and some, too inclusive of opposites to be real, and so is imaginary and fantastic.  Boole says we use the conjunctive words and and or permissively and strictly, equivalent to the combination of classes when permissive and the exclusive choice between classes when strict, and permissive and strict reflect the two colors of complexion Aristotle mentions.  We say x and y and x or y to mean what is both x and y when permissive and mean what is either x, or y, but not both, what is called an exclusive or by later logicians.  We are even told, in the opening of Wonderland, that a White Rabbit with pink eyes runs by, with red and white mixed together as some and some, in the eye of the Rabbit.

The White Rabbit is a strange sort of addition problem, a kind of conjunction, the adding of human reason to beast, which Aristotle argues is what we ourselves essentially are, and so is impossible in the case of a rabbit, who lacks what makes us human.  At the end of Alice’s adventures we find ourselves with Alice between the excessively inclusive and exclusive White and Red Queens, and they test her on whether or not she can do sums.  John Stuart Mill, whose work on logic Carroll owned, and who is said to be the most influential philosopher in Britain as Carroll studied logic and wrote Wonderland, argued that we learn logic and math through everyday practices of gathering and dividing objects, not from internal rules of logic.  The Queen of Hearts’ game of croquet similarly lacks rules and turns, like logic in real life, and Alice is tested in gathering and dividing things in everyday life, which she considers odd to call sums.

After praising Aristotle and laying out his examples of white sheep, men and Asiatics, Boole says that his work is designed to prove two positions: “First, That the operations of the mind… are subject to general laws.  Secondly, That those laws are mathematical in their form, and that they are actually developed in the essential laws of human language.” (III.11)  Whether or not Carroll believed this, Wonderland seems to supply counterexamples that contradict Aristotle, as well as Boole, as the characters who rule Wonderland, and later the Looking Glass, contradict Alice continuously, and hardly rule a coherent empire based on common purpose and form.  The Queen of Hearts’ croquet game, which doesn’t seem to have regular rules or turns to Alice, portrays the human world, British politics and history as a highly illogical affair, and Carroll mocks the insanity of politics and history throughout his fictions and works on logic.

Carroll owned several works by John Stuart Mill about logic and several other subjects, including the subjection of women, and Mill wrote: “Now I cannot wonder that so much stress should be laid on the circumstances of inconceivableness, when there is such ample experience to show that our capacity or incapacity of conceiving a thing has very little to do with the possibility of the thing in itself, but is in truth very much an affair of accident, and depends on the past history and habits of our minds.”  Whether or not we live in a regal, logical, law-abiding universe with Boole or a chaotic world of bloody, unruly politics like Wonderland, Carroll presents human logic, rules and authority as good and bad, as enabling but abusive, absurd authority figures who are logically operative, explaining their positions to Alice with their own logics and purposes, but in ways that are fantastic and absurd to Alice and us, embodying ideal, impossible extremes which may not be able to exist but Carroll can create with his imagination, imagining and then creating the impossible, as Mill suggests we do.  Carroll hopes that Alice and all of us keep the light of childhood alive in our adult selves, remaining creative and imaginative, as absurd examples can be highly instructive, as well as memorable.

Aristotle’s Categories & The Hunting of the Snark

I have been developing my theory that Aristotle’s categories fits the order of characters and events of Wonderland and The Looking-Glass.  In the process, I realized that The Hunting of the Snark has ten characters with no individual names but whose jobs start with B, and that each could fit with Aristotle’s ten categories, types of being, as well.  If Carroll used Aristotle’s categories to plot out Alice’s adventures, it is not unlikely that the Snark works like a logic puzzle.  In his Game of Logic, Carroll similarly listed buns, babies, beetles and battledores (an early badminton racket) as examples of things, also known as beings.  In Carroll’s introduction he says his work shows he is incapable of nonsense, and this brief but instructive poem includes precise arithmetic truth and natural history, both which apply to Aristotle’s categories.

Edward Guiliano pointed out that the Bellman looks like Father Time and carries a school bell for lessons.  The best candidates for each  of Aristotle’s categories are: 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 brides cake, doesn’t lie, forgets his specific name and fades away, vanishing without a trace in the end is substance.

The Overall Shape of My Theory About Aristotle & Alice

My theory is that Lewis Carroll possibly used the major lessons of Aristotle’s logic to structure his Wonderland and Through the Looking Glass, including the ten categories, the ten sorts of things that can be said about anything in Aristotle’s Categories, and four statements, the four ways something can be said about anything in Aristotle’s On Interpretation, which correspond to the four “perfect” forms of the syllogism in Aristotle’s Prior Analytics and are also known as the four corners of the Square of Opposition.  The overall lesson of both books about Alice is patience over time and tolerance between positions to balance between extremes, the overall lesson of Aristotle’s ethics.

Here is the overall shape of my theory regarding the ten categories and four statements, with more evidence for each and more about balance and ethics to follow.  I am in the process of working out the evidence and details, but Carroll knew Aristotle’s work on logic well and there is much that corresponds well with both books about Alice.

If we take Aristotle’s order of the ten categories from the beginning of Aristotle’s Categories, and we reverse their order, as if seen in a mirror, starting with passion, the last, and ending with substance, the first, they correspond remarkably with the order of events of both books, chapter by chapter, together.  The first chapter of each work is about passion, with the White Rabbit of Wonderland and the Black Kitten of the Looking Glass.  The second chapter is about action, with the swimming Mouse and the running Red Queen.  The third chapter is about state, with the Dodo’s caucus race and the Gnat on the Train.  The fourth chapter is about position, with Alice taking a position in the White Rabbit’s house and between Tweedle Dum and Dee.

The fifth and sixth chapters of each work are about time, space and relations interwoven together, with the Caterpillar, Cheshire Cat and Duchess of Wonderland and the White Queen, Sheep and Humpty Dumpty of the Looking Glass.  In each book, time comes first, the Caterpillar and White Queen, followed by relations, the Duchess and Humpty Dumpty.  In Wonderland, space appears as the Cheshire Cat, who is in the house of the Duchess, though he speaks about space and position to Alice after she experiences the Duchess’ poor relations with others.  In the Looking Glass, space appears as the Sheep, who is also time, the White Queen, before Alice meets Humpty Dumpty and his poor relations with her.

The seventh chapter of each work is about quality, with the Tea Party and the Lion & Unicorn, and the Mad Hatter and Hare appear in both.  The eighth chapter is about quantity, with the playing cards of the Queen of Hearts and inventions of the White Knight.  The remaining chapters of each work are about substance, with the insubstantial lies of the Mock Turtle leading to the King of Heart’s Trial over tarts, and the test about sums leading to the Queens’ Banquet.

The four royal court figures of both books, the White Rabbit, Duchess, Queen of Hearts and King of Hearts of Wonderland and the Red Queen, Red King, White Queen and White King of the Looking Glass, correspond with Aristotle’s four types of statements and four “perfect” forms of the syllogism, found in Aristotle’s On Interpretation and Prior Analytics: In Wonderland, the White Rabbit is particular and positive, accepting some and some, worried about being late for others and accepting Alice into his house as a servant, the Duchess is particular and negative, rejecting some and some-not with punishments and morals in her house, the Queen of Hearts is absolute and negative, subtracting and excluding anyone entirely for any mistake in her garden, and the King of Hearts is absolute and positive, accepting any and all testimony as equally and entirely valid for consideration in his court.

In the Looking Glass, the Red Queen is absolute and negative, like the Queen of Hearts of Wonderland, who tells Alice all ways are hers, thus none are Alice’s in her garden.  The Red King is particular and negative, who dreams of Alice but in his own dream, out in the woods.  The White Queen is absolute and positive, who believes impossible things before breakfast, and the White King is particular and positive, accepting the somewhat steady agreement of the battling Lion and Unicorn.  In Wonderland, the royalty all rule indoor spaces, but in the Looking Glass, they are all outside in the open.

There is much that makes sense with this interpretation, and I believe it makes much sense of details that have puzzled many  in the books. I got the idea by studying the text for many years in the light of Wittgenstein, Poe and others, and then a recent strong feeling that the Caterpillar stands for time led to another feeling that the Cheshire Cat stands for space, which led to looking up Aristotle’s list of the ten categories and seeing that relations, space and time are much like the Duchess, Cat and Caterpillar of Wonderland, such that Aristotle’s order seems inverted by Carroll, as if seen in a looking glass.

Chapter Wonderland Looking Glass
1: Passion  White Rabbit & Golden Key Black Kitten & Looking Glass
2: Action Mouse & Pool of Tears Flowers, Red Queen
3: State Dodo, Caucus Race Train, Gnat, Fawn
4: Position White Rabbit’s House, Puppy Tweedle Dum & Dee, Crow
5: Time/Space Caterpillar (Time) White Queen (Time) & Sheep (Space)
6: Relations Duchess (Relations) Cheshire Cat (Space) Humpty Dumpty (Relations)
7: Quality March Hare, Mad Hatter Haigha, Hatta, Lion & Unicorn
8: Quantity Queen of Hearts, Croquet Red Knight, White Knight
9: Substance Kind Duchess, Gryphon, Mock Turtle Red & White Queens, Frog & Banquet
10: Substance Lobster Quadrangle Red Queen
11: Substance King of Hearts, Trial Black Kitten
12: End Alice & Ending Alice & Ending

 

A Theory About Aristotle’s Logical Categories & Lewis Carroll’s Alice

Lewis Carroll’s Wonderland and Through the Looking Glass are many things to many people, and they serve well as a series of amusements for children and allegories for adults, but they also serve as memorable illustrations of the basic lessons of Aristotle’s logic and ethics, as a set of absurd characters that children can remember and adults can enjoy that verbally and visually display playful engagement with serious lessons and forms, including both ancient Aristotelian and modern Boolean forms of logic that Carroll, mathematics professor and logician, knew well.  Carroll owned and wrestled with the work of Aristotle, Boole, De Morgan and others as a logician in the years before and after telling Alice and her sisters his stories, and he developed a system for visually teaching forms of logic in the years after publishing his books about Alice.

If Carroll included forms of ancient and modern logic in his books about Alice, then he possibly used Aristotle’s ten categories, which Carroll knew well from the first book of Aristotle’s works on logic, to order the events and characters of Wonderland and the Looking Glass, in the order Aristotle himself listed them in the Categories, but backwards, in reverse order, as if in a looking glass or from the perspective of a child looking up to an adult, from lowest to highest, up from child of passion to adult of substance, in Wonderland from worried rabbit to king with tarts and then in Looking Glass from taunted pawn to queen of a banquet.

If we interpret the books as illustrations of Aristotle’s ten categories, along with many other forms of ancient and modern logic, politics, ethics, philosophy, history, and mathematics that Carroll interwove throughout the books, many things in the stories correspond and make many sorts of sense.  If Carroll included forms of logic in his published Wonderland and again in his Looking Glass, Aristotle’s ten categories could be the most important and central example of this, as their order can be found throughout both books and is possibly central to their structure and plot.  

If so, in Wonderland the White Rabbit is passion, the Mouse is action, the Dodo and his Caucus Race are state, the White Rabbit’s House is position, the Caterpillar is time, the Cheshire Cat is place, the Duchess is relations, the Mad Hatter’s Tea Party is quality, the Queen of Hearts is quantity, and and the King of Hearts is substance.  In the following sequel, Through the Looking Glass, corresponding chapter by chapter numerically with Wonderland, the Black Kitten is passion, the Red Queen is action, the Train is state, Tweedle Dum and Dee are position, the White Queen is time, the Sheep is place, Humpty Dumpty is relations, the Lion and Unicorn are quality, the White Knight is quantity, and the Queens’ banquet is substance.  Consider how the text makes sense in light of the reverser order of Aristotle’s ten categories, first through the course of Wonderland and what this could teach Alice, and then mirrored and balanced in the sequel.

In the first chapter of Wonderland, Alice is bored, falls asleep, and dreams of the first character, the White Rabbit, who is passionate, upset and late to meet his superiors, and Alice follows him down the Rabbit Hole without a thought of how to get out, blindly following her passion.  She falls down into a banquet hall, and sees a golden key on a glass table with three legs that fits a door to a beautiful garden, but she is either too big to get through the door or to small to reach the key.  As a child, Alice is too passionate and extreme one way and then the other to grasp the golden key, the balance between extremes Aristotle teaches as central to his ethics, what some call the Golden Mean, which includes balance between ourselves and others, taking the smaller individual perspective of ourselves and the larger social perspective of others.

Alice does not solve this problem now, but returns and solves it after she has spoken to Time, which the Hatter thinks Alice hasn’t.  Time, the Caterpillar, teaches Alice patience, to tolerate time and change in ourselves and others, and gives Alice the mushroom after she shows him she can be patient which allows her to change and balance between the smaller and larger positions, which gets her the key, out the door and into the garden.  Unfortunately, before conversing with the Caterpillar, Alice is a child who hasn’t yet learned the lesson of patience and tolerance over the course of time through discourse with others, much like the Hare and Hatter are rude and don’t plan well for the future, as Time refuses to move for them.

In the hall, following the passion of the White Rabbit, Alice cries and creates a Pool of Tears that sweeps her out of the enclosed hall and into an open ocean of emotion, which ends the first chapter.  The Mouse, swimming in the pool and then away from Alice, is action, reacting to Alice’s passion for her cat, which shows she still lacks the perspective of others and balance.  Alice also acts and reacts, swimming after the Mouse, blindly acting without knowing where either is going.  Then she leads a multitude of animals ashore, a result of her action and leadership in a steady but stupid state, which ends the second chapter and introduces us to the Dodo.

Lewis Carroll, Inverted White Knight

Some have said that the White Knight of Lewis Carroll’s Through The Looking Glass is Carroll himself.  If the order and characters of Wonderland and the Looking Glass fit the order of Aristotle’s ten categories, backwards, as I believe, this makes the White Knight, like the Queen of Hearts in Wonderland, quantity, and Carroll was, in his real life, a mathematics professor.

In the same way Carroll inverted several of the characters between the two books about Alice, as if in a mirror, the Queen of Hearts of Wonderland is quantity as too negative, exclusive and cruel, and the White Knight is quantity as too positive, inclusive and kind.  Alice can us the overly negative and overly positive example of both to steer a middle way between them, as Aristotle (as well as Buddha, Confucius, and many others) advises in ethics.  The White Knight guides Alice to the final square, where she is immediately given a test on sums, quantities, but as substances, Aristotle’s first and thus for Carroll final, category, which confuses Alice, who sits between the two positive and negative extremes.

The White Knight has a great quantity of ideas he produces, but he is a bit backwards and often upside down, much like the categories backwards.  Alice has to help him turn himself around, just as Carroll likely hoped the reader would see the inverted, mirror-image forms of logic he set in both books about Alice.  Aristotle would say, from the White Rabbit onward, Alice has been committing categorical errors (a fallacy found in Aristotle’s Sophistical Refutations) throughout her dreams.  She confused and dreamed her desire to be like her sister, her passion, to be an absurdly formal conjunction, the White Rabbit at the beginning of Wonderland, and at the end of the Looking Glass she dreams that quantity is a Knight, and then substance is a queen’s banquet, where the people turn out to be food and the food turns out to be people.

Aristotle, Lewis Carroll & The Order of Alice’s Adventures

I believe Lewis Carroll used the categories of Aristotle backwards, as if seen in a mirror, to plot out and order the events of Alice’s Adventures In Wonderland and Through The Looking Glass.  In Aristotle’s Categories, which Carroll knew well as the first of Aristotle’s works on logic, Aristotle lists the ten types of things we can say about things as substance, quantity, quality, relations, place, time, position, state, action and passion.  In Carroll’s mirror-image order, these are passion, action, state, position, time, place, relations, quality, quantity, and substance.

In Wonderland, the White Rabbit is passion, the Mouse is action, the Dodo and his Caucus Race are the state, the White Rabbit’s House is position, the Caterpillar is time, the Cheshire Cat is place, the Duchess is relations, the Mad Hatter’s Tea Party is quality, the Queen of Hearts is quantity, and the King of Hearts is substanceThrough the Looking Glass, corresponding exactly chapter by chapter with Wonderland, as if in a mirror, the Black Kitten is passion, the Red Queen is action, the Train is the state, Tweedle Dum and Dee are position, the White Queen is time, the Sheep is place, Humpty Dumpty is relations, the Lion and Unicorn are quality, the White Knight is quantity, and the Queens’ banquet is substance.

Some have said Wonderland and Through the Looking Glass are works of nonsense, meant to amuse more than educate.  Carroll designed both books to illustrate forms of logic with emotional and unreasonable characters, memorable illustrations and bad examples for Alice to learn and remember well.  I have used these to teach students Aristotle and logic, and they work for well. Carroll inverts many things between the two books, but he kept the order of the categories consistent.  The lesson of both books is also the overall lesson of Aristotle’s Ethics, balance, avoiding extremes on either side and learning with patience over time and by position between places to make good choices for ourselves and others.

There are many more lessons of Aristotle and others hidden in the works, but these are the overall structure and purpose.  As Carroll told Alice, we should not go anywhere or do anything without a proper porpoise.

The next logic lesson from Aristotle which can be found that is hidden but central to both of Alice’s adventures is royal characters of the court, the greater pieces of the game and plot, serve as Aristotle’s four types of assertions and corresponding perfect forms of the syllogism, fundamental to Aristotle’s Prior Analytics, well known by Carroll as the second book of Aristotle’s logic, and to many as the four corners of the Square of Opposition.

In Wonderland, the White Rabbit is positive and particular, Some A is B, the Duchess is negative and particular, Some A isn’t B, the Queen of Hearts is negative and universal, No A is B, and the King of Hearts is positive and universal, All A is BIn the Looking Glass, the Red Queen is negative and universal, No A is B, like the Queen of Hearts of Wonderland, the Red King is negative and particular, the White Queen is positive and universal, and the White King is positive and particular, like the White Knight, and like the White Rabbit, in the beginning of Wonderland.

The Looking Glass shows what Aristotle calls sub-alternation twice, with each particular king following his universal queen.  If we know No A is B, then we also know and later meet Some A isn’t B, the Red Queen leading to the Red King, and if we know All A is B, then we also know and later meet Some A is B, the White Queen leading to the White King, and later White Knight.

Syllogistically, in the Looking Glass, the White Queen, inclusively open like a child, is the universal positive (All, All, All), the Red Queen is the universal negative (All, None, None), the White King is the particular positive (Some, All, Some) and the Red King is the particular negative (Some, None, Some-Not).

In the end, Alice sits as an inclusive-exclusive OR between All and None, as the one who must decide for herself, with her powers of logic and reason, some and some not like an adult between the extremes, as Aristotle advises us in ethics. There are countless examples of syllogistic reasoning in both texts, but here are central examples that show each royal chess piece as an Aristotelian corner.  Aristotle starts with the Positive Universal, so Carroll starts with the opposite, not Negative Particular, but Negative Universal, the Red Queen, continuing much as if at the end of Wonderland, with the Queen of Hearts screaming for executions.

CELARENT, the Negative Universal Syllogism: If All A is B, and No B is C, then No A is C.  If All ways are mine, as the Red Queen says, and None of what’s mine is yours, as the Duchess moralizes, then none of these ways are yours, is what the Red Queen means but doesn’t say, which we understand and infer quite syllogistically from what is given in her words.  As a Venn diagram, if A is entirely B, and no B is C, then no A can be C.

FERIO, the Negative Particular Syllogism: If Some A is B, and No B is C, then Some A is not C.  If all things are dreams, as Tweedle Dum and Tweedle Dee tell Alice, and some dreams are untrue or not ours alone, then all things are somewhat untrue, and somewhat aren’t ours alone, which is what Tweedle Dum, Dee and the Red King dreaming silently imply, but don’t say.  As a Venn diagram, if some A is B and no B is C then some of A is C. As Aristotle says, if we have only some and no all or none, we can’t draw syllogistic judgements completely, leaving us with only a relative, somewhat satisfying conclusion, just as the Red King silently dreams and says nothing to Alice after she happily dances around hand in hand with both twin brothers.

BARBARA, the Positive Universal Syllogism:  If All A is B, and All B is C, then All A is C.  If all things are possible to think if you Shut your eyes and try very hard, as the White Queen suggests to Alice, and if all impossible things are things indeed, even if they, unicorns and we are all quite mental, then Alice can think six or more impossible things before breakfast if she shuts her eyes, imagines, and tries very hard, as the White Queen implies but doesn’t say directly, meaning what she doesn’t say syllogistically.  In Venn diagram form, if A is entirely B, and B is similarly C, then A must also be C.

DARII, the Positive Particular Syllogism:  If Some A is B, and All B is C, then Some A is C.  If the White King says he sent almost all his horses along with his men, but not two of them who are needed in the game later, and if Alice has met all the thousands that were sent, 4,207 precisely who pass Alice on her way, then Alice has met some but not all of the horses, namely the Red and White Knights who stand between Alice and the final square where she becomes a queen.  As a Venn diagram, if some A is B and all B is C then some A must be C.

Wonderland, the Looking Glass & Aristotle’s Logical Categories

I have been developing the theory that Lewis Carroll used the logical forms of Aristotle, Boole and De Morgan throughout his Alice’s Adventures in Wonderland and Through the Looking Glass, and both books follow Aristotle’s logical categories in reverse order as the basis for the order of events in the plots of both books, more than any other form I’ve found, and more than any form anyone else seems to have found by far, which means the books are instructional illustrations of forms of logic that are memorable and teachable to both children and adults alike.

In his Categories, Aristotle starts with what he says is the highest category, substance, and ends with the lowest, passion, but Carroll starts both books with the lowest, passion, and works upwards to substance, opposite the order Aristotle discusses them in his Categories.  In Carroll’s mirror-image order, Aristotle’s ten categories are passion, action, state, position, time, place, relatives, quality, quantity, and substance.

1) Passion: In Wonderland, Alice follows the White Rabbit out of passion and delight, with no thought as to how she would get out of the rabbit hole.  In the Looking Glass, Alice scolds the Black Kitten out of passion and anger, threatening to leave it out in the snow which would surely kill it.  Summer outside becomes winter indoors, the White Rabbit becomes a black Kitten, and the passion of delight turns to anger, all mirrored inversions, like the inverted order of Aristotle’s categories in both books.

2) Action: In Wonderland, Alice upsets the Mouse by telling him about her cat, which causes him to act and swim away from her.  In the Looking Glass, Alice confuses the Flowers, which cause them to act and mock her, and the Red Queen drags Alice with her instead of fleeing from her like the Mouse, acting on her.  The illustration of the Mouse swimming from Alice and the Queen dragging Alice are remarkably similar, and Carroll was exacting about the images, asking for several to be painstakingly redone.  Acting away from Alice turns to acting towards Alice, the single Mouse becomes the many Flowers, and Alice forgetting the small size of the Mouse turns to Alice intimidated by the Flowers that tower over her, all inversions.

3) State: In Wonderland, Alice finds herself in a useless caucus race that goes round and round in circles which mocks politics.  In the Looking Glass, Alice finds herself on a train with people who read mass printed papers and repeat popular hasty conceptions, mocking the public escalation and industrialization of culture like a train gaining speed on a track, and Alice is told she is going the wrong way by the conductor, not merely her static inverted position, but her state in motion over time.  The race round and round going nowhere becomes a train gaining speed down the line of a track, and Alice goes from uselessly going nowhere to wrongly heading down the quickening public track.

I am posting a longer post today that clarifies both lists.

Wonderland & Looking Glass As Illustrations Of Aristotle

Some have claimed Lewis Carroll’s Alice in Wonderland and Through the Looking Glass are both works of nonsense, meant to amuse but not educate, but this is wrong.  Carroll designed both books to illustrate forms from the history of logic with memorable, emotional and unreasonable characters.  While Carroll mocked the work of Boole, De Morgan and others throughout the two tales, both also primarily serve to illustrate and teach central concepts of Aristotle’s work on Logic, specifically his categories and syllogisms, the forms of Logic that Carroll taught and studied for a living.

I actually had the chance to use Wonderland this morning to teach Aristotle’s categories to my Greek philosophy students, and one said that it served well to help her visualize and remember each category, as the examples draw on classic memories and are emotively meaningful.  This demonstrates the texts are not useless nonsense or mere entertainment, but lesson plans in logic.  My theory is that Carroll believed others would find this list of Aristotle’s categories reversed, but when no one noticed he began the sequel Through the Looking Glass with the idea of mirror-images, reversals and putting a text up to the mirror to show that he was inverting Aristotle’s classic text on logic, and going to use inversions and reversals with logic even more in the second story.

Alice’s first adventure in Wonderland illustrates Aristotle’s Categories, presenting the ten categories in the order Aristotle discussed them but in reverse: passion, action, state, position, time, place, relatives, quality, quantity, and substanceFirst, the White Rabbit is passion, who acts on AliceSecond, the mouse is action, acted-upon by Alice.  Third, the bird’s caucus race is stateFourth, Alice takes the position of the White Rabbit’s servant and fills his entire house.  Fifth, the Caterpillar is time, who accepts change and uncertainty.  Sixth, the Cheshire cat is space, who shows Alice exclusive and opposed positions.  Seventh, the Duchess and baby are relatives or relations.

Eighth, the Mad Tea Party is quality, with the unsound Hatter and Hare who used the best butter.  Ninth, the Queen of Heart’s garden is quantity, with the two, five and seven cards forming an addition problem and the Queen threatening everyone with subtraction.  Tenth and finally, the King of Heart’s trial of who stole the tarts is substance, as the tarts are still there substantially but the trial and evidence are insubstantial.

Alice’s second adventure Through the Looking Glass illustrates the syllogistic forms found in Aristotle’s Prior Analytics in an order that shows subalternation twice. The four royal pieces, the Red Queen, Red King, White Queen and White King, are the four corners of Aristotle’s Square of Opposition, a visual presentation of logic popular in Europe for centuries.  The White Queen, inclusively open like a child, is the universal positive (All, All, All), the Red Queen is the universal negative (All, None, None), the White King is the particular positive (Some, All, Some) and the Red King is the particular negative (Some, None, Some-Not).  In the end, Alice sits as an inclusive-exclusive OR between All and None, as the one who must decide for herself, with her powers of logic and reason, some and some not like an adult between the extremes, as Aristotle advises us in ethics.  There are countless examples of syllogistic reasoning in both texts, but here are central examples that show each royal chess piece as an Aristotelian corner.

BARBARA, the Positive Universal Syllogism:  If All A is B, and All B is C, then All A is C.  If all things are possible to think if you Shut your eyes and try very hard, as the White Queen suggests to Alice, and if all impossible things are things indeed, even if they, unicorns and we are all quite mental, then Alice can think six or more impossible things before breakfast if she shuts her eyes, imagines, and tries very hard, as the White Queen implies but doesn’t say directly, meaning what she doesn’t say syllogistically.  In Venn diagram form, if A is entirely B, and B is similarly C, then A must also be C.

CELARENT, the Negative Universal Syllogism: If All A is B, and No B is C, then No A is C.  If All ways are mine, as the Red Queen says, and None of what’s mine is yours, as the Duchess moralizes, then none of these ways are yours, is what the Red Queen means but doesn’t say, which we understand and infer quite syllogistically from what is given in her words.  As a Venn diagram, if A is entirely B, and no B is C, then no A can be C.

DARII, the Positive Particular Syllogism:  If Some A is B, and All B is C, then Some A is C.  If the White King says he sent almost all his horses along with his men, but not two of them who are needed in the game later, and if Alice has met all the thousands that were sent, 4,207 precisely who pass Alice on her way, then Alice has met some but not all of the horses, namely the Red and White Knights who stand between Alice and the final square where she becomes a queen.  As a Venn diagram, if some A is B and all B is C then some A must be C.

FERIO, the Negative Particular Syllogism: If Some A is B, and No B is C, then Some A is not C.  If all things are dreams, as Tweedle Dum and Tweedle Dee tell Alice, and some dreams are untrue or not ours alone, then all things are somewhat untrue, and somewhat aren’t ours alone, which is what Tweedle Dum, Dee and the Red King dreaming silently imply, but don’t say.  As a Venn diagram, if some A is B and no B is C then some of A is C. As Aristotle says, if we have only some and no all or none, we can’t draw syllogistic judgements completely, leaving us with only a relative, somewhat satisfying conclusion, just as the Red King silently dreams and says nothing to Alice after she happily dances around hand in hand with both twin brothers.

Aristotle’s Categories & The Order Of Carroll’s Wonderland

Aristotle argued in his Categories that there are ten sorts of things, substance, quantity, quality, relatives, place, time, position, state, action and passion.  In reverse order, this charts the order of events and characters in Lewis Carroll’s Wonderland.  I have often wondered if the Caterpillar and Cheshire Cat stand for inclusive and exclusive OR, but also as time and space.  Time includes many things together all at once, while space is exclusive, such that nothing can be exactly in the same space as anything else, much like the dueling perspectives the Cat mocks as oppositely insane.  Now I see that Carroll was working from inclusive passion, being acted-upon, to exclusive substance, things that are identical to themselves and nothing else.

In reverse order, Aristotle’s ten categories are passion, action, state, position, time, place, relatives, quality, quantity, and substance.

First, the White Rabbit is passion, who acts on Alice, moved by her passion without thinking into chasing after the rabbit.

Second, the mouse is action, after the banquet hall, where Alice can’t act but is moved by her tears, where Alice acts on the mouse who flees her passionate talk of her cat, acted-upon by Alice, but negatively, opposite the way the White Rabbit acted-upon her.

Third, there is the bird’s caucus race, which mocks politics, also known as the state.

Fourth, the White Rabbit mistakes Alice for his servant, and Alice takes on the servant’s position, ultimately finding herself in quite the imposition, filling the White Rabbit’s entire house.

Fifth, the Caterpillar is time, who takes away the certainty of all things, and includes all changes and possibilities as indeterminate.

Sixth, the Cheshire cat is space, who shows Alice conflicting positions, each exclusive and opposed to the other.

Seventh, the Duchess and baby are relatives or relations, and Alice moves from taking the position outside the pigeon defending the egg in her next, to the cat who watches the Duchess beat her baby, to Alice dropping the baby when it turns into a pig, as the cat thought it would.

Eighth, the Mad Tea Party is quality, with the Hatter and Hare insane, of bad mind, and the Hare insisting he used the best butter to fix the pocket watch, which is terrible.

Ninth, the Queen of Heart’s garden is quantity, with the two, five and seven cards forming an addition problem and the Queen threatening everyone with subtraction.

Tenth and finally, the King of Heart’s trial is substance, or lack thereof, just as the Tea Party lacked quality, with the tarts as a substance stolen and returned, the jury and king incapable of coming to substantive, proof-worthy judgements, and Alice declaring everything to be an empty pack of cards, devoid of substance and meaning.