Alice & Wonderland

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 substance. First, the White Rabbit is passion, who acts on Alice. Second, the mouse is action, acted-upon by Alice. Third, the bird’s caucus race is state. Fourth, 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.

November 26, 2019 4

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.

November 21, 2019 0

Turtles All The Way Down & Around

Ludwig Wittgenstein (1889 – 1951) is my favorite of the latest, greatest philosophers, and I learned his work from Hans Sluga and Barry Stroud at Berkeley, who taught me that Wittgenstein’s later thought experiments can lead to much more than he or we have worked out about truth and meaning. Wittgenstein’s thinking can answer many questions about thinking, not completely but more fruitfully, as Wittgenstein says, than other thinkers can.

The turn between Wittgenstein’s earlier and later thought is much like the Indian metaphor of turtles supporting the world and the question that arises from such an arrangement. Locke, Hume, Russell and other European philosophers have brought up the Indian debate about what the world sits on such that it is stable and continues. Some say that it sits on a turtle, an animal that symbolizes the cosmos in India and China, as it is flat on the bottom like the earth, and round on the top like the sky. Others ask what the turtle sits on if the world sits on it, and someone once said it’s turtles all the way down. Some have called this an infinite regress, an endless series that vanishes over the horizon, Buddha called it an unsolvable problem, Plato called it the greatest difficulty for philosophy, and today some call it the foundationalism debate, arguing whether or not knowledge or certainty sit on anything known or certain.

Philosophy is the love and study of wisdom, truth, meaning and thought. Thought interweaves several elements in our world. We sense, see, hear, touch, smell and taste things in our world. We also feel, feeling good, bad, tense and calm about the things we sense. We also remember, sense and feel things that are not in our world, but were. We also reason, building what we remember from sense and feeling into thoughts. In the middle of all this are words, things we hear and see from others that are interwoven with what we sense, feel, remember, and think.

Is sensing a thing without words, feelings or memories a thought? Is looking at an apple thinking? Is looking at it and feeling a feeling thinking? If I look at an apple and feel happy, is that a thought without words or images in mind? Some say yes, and others say no. Once we have several things interwoven, including the words we use to mean things, many call that thought. Some say thought is logical and rational, such that it follows rules, or follows rules when it is right and correct in judgement. Others say that this is the turtle problem yet again.

If things need thoughts to make sense of them, and if thoughts need thoughts, such as rules, or plans to make sense of them, is there thought that makes logical, self-aware, rational sense of thought itself? Are there words that make sense out of how we use words to mean things and know things? Some say yes, and it terminates in the rules and forms of logic, and others say no, and we simply continue to gather and divide things without an underlying logic that brings all of our wants and plans into common, coherent systems, visions or words. As Zhuangzi the Daoist asks, What do our ways or words rely on such that our words mean things?

What do turtles sit on? Some say other turtles. The Buddha in India and Wittgenstein in Britain answered the question with similar, simple metaphors that show us more than any system or logic in images or words can completely in itself. Thought and our world are interwoven, such that it isn’t turtles all the way down, but turtles all the way around. Much as Nicholas of Cusa and Hegel said about a circle, it is an infinite regress, but it is also complete in itself, and continues right in front of us. It isn’t that truth or rules rely or rest on any specific thing, but rather situations of sense, feeling, memory, reason and words mean things all together.

Situations shift, and these shifts show us how things mean things to us better than any specific words can. As Wittgenstein said, there is what can be said, but what can be said is only a part of what can be shown, which is best done not with complete, enclosed systems of words or images but by leading people through many open-ended situations of mind, stagings of thought, what Wittgenstein called thought experiments that involve many and any elements.

Much as Alice is frustrated with her sister’s text without pictures in the opening of Wonderland, words and rules without many interrelated examples of rich situations and the infinite variety found in them confuse us and lead us into considering words outside of actual, useful meaning. Carroll wrestled with Boole’s algebra much as Wittgenstein wrestled with Frege’s logic, and both came to the conclusion that words and systems can trap us like a fly in a bottle.

As Zhuangzi said, once we have the rabbit, we can forget the trap, and then we can involve the trap or not as we like, such that we can have words with others who have forgotten words, remembering and forgetting words and understandings freely as we please rather than sitting on particular words or systems as final, fixed foundations. Wittgenstein enjoyed reading Alice’s adventures to two sisters in Wales where he worked on his final thoughts, and he likely heard and felt Carroll’s deeper meaning, that it is good to use thought, rules and logic to show others how open-ended thought can be, beyond anyone’s particular logic, words, thought or feelings.

Buddha called the interweaving of everything codependent-arising, life as a tangle of many forms of life, as we see in Klimt’s painting Death and Life, which he began in Vienna 1908 and finished in 1915, the time Wittgenstein left Vienna to study logic, mathematics and philosophy with Russell at Cambridge. Klimt was not only one of the most influential painters of Wittgenstein’s Vienna, he painted a portrait of Wittgenstein’s sister, who was also psycho-analyzed by Sigmund Freud. As we might suspect, Wittgenstein’s family had some pull in Vienna, which in Klimt’s day was the city with the latest, greatest culture, replaced in the 1920s by Paris, the 40s by New York and the 60s by San Francisco. Wittgenstein said that life and thought are like an old city, with many forms of life inter-tangled for centuries.

Much as Buddha taught there is no essence or nature that completely defines or causes a thing because it arises out of the relationships it shares with other things outside of itself, Wittgenstein argued that life is like a thread without a single strand running through the entire length, and so we should always beware of the lure of the secret cellar, the proud idea that we have hit bedrock and completely revealed the truth rather than revealed yet another strong connection between different interwoven things. The cure for this proud ignorance, what Heraclitus called the human disease, is a rich variety of interwoven examples and elements that continue to show us more and more about the greater whole, endlessly.

November 19, 2019 0

Lewis Carroll’s De Morgan Fireplace

In the 1860s, Carroll had his most troubled and inspired years, producing both Alice books as he struggled with how to be a good person and great mathematician and logician, as well as his father’s death and the social isolation he felt at Oxford. Just after completing Alice in Wonderland, Carroll moved into a suite of rooms in 1868 with the money from his popular book and he lived there the rest of his life.

An excellent piece of evidence that Carroll was staging logical connectives as animal characters can be found in his personal fireplace. Carroll had the logician Augustus De Morgan’s son, William De Morgan, design tiles for his fireplace, most with animals, several with animals attacking each other, and several pairs of tiles with the same animals in opposite emotional states. When Carroll was later in charge of the common room in the building, he hired De Morgan’s son yet again to put similar tiles in the fireplace and other furnishings.

In Wonderland, many of the characters act as logical connectives, the sorts of nots, ands, and ors that Boole, De Morgan and Carroll worked on as logicians. There are many puns about oars, like ors, that involve choices, and Alice in the end of her adventures sits between the White and Red Queens much as Boole’s or sits between his inclusive and and exclusive not. The Caterpillar acts as a more inclusive but reclusive or, who gives Alice the power to change size and perspective.

The Cheshire Cat acts as an exclusive or, who sees and travels between exclusive perspectives opposed to each other, with dogs insane to cats and cats insane to dogs as he explains to Alice, which is why everyone is crazy to someone in Wonderland. This is why we don’t see him entirely, most of the time, because just like the elephant to the blind men from India, each perspective, such as Alice’s, only sees part, not the whole. This is how his head watches others argue about whether or not he can be beheaded, each side of the argument seeing a part of the truth, but not the whole situation, as he grins on them from above, seeing both sides fight.

The Caterpillar is like time, which includes more in our lives as it continues in series, but the Cat is like space, moves through it freely, and grins at the divisions it inevitably puts between people, even after the passage of time and experience. Carroll is himself from Cheshire, and missed his family there at Oxford. We can see De Morgan’s theorems at work in the plot and characters, and particularly in the moves from the Caterpillar to the Cheshire Cat to the Mad Tea Party, with De Morgan’s second law working one way and then the other back again.

November 19, 2019 0

Aristotle, Boole, Carroll & De Morgan

Lewis Carroll, the pen name and popular title of Charles Dodgson, mathematician and logician at Oxford, author of Alice and Wonderland and Through the Looking Glass, was well versed in the logical forms of Aristotle, Boole and De Morgan, and was working on his own understanding of how logical connectives, thoughts and emotions include and exclude members of sets before Frege, Russell and Wittgenstein set formal logic in its current form and founded analytic philosophy. Carroll was engaged with problems of German idealism and British empiricism found in the work of Locke, Hume, Mill, Boole and De Morgan in the late 1850s and early 1860s, the years that he planned and wrote both of Alice’s adventures.

A careful historical, social and psychological reading of both Wonderland and the Looking Glass show that Carroll used his fantastic characters to lead Alice through the forms of the central figures in the history of logic as he knew it, including Aristotle, De Morgan, Boole and Mill, using both stories to explore how inclusion and exclusion structure our thoughts, feelings, relationships and politics. The characters of both fantasy worlds engage Alice in gathering and dividing, such that through her experiences she assumes the roles and positions she wanders through, engaging with forms and the problems of philosophy and society that involve them.

The forms of Aristotle, Boole, and particularly De Morgan are structural to the characters and plots of both of Alice’s adventures. In Wonderland, Alice works her way from inclusive child to exclusive adult, from the White Rabbit, an absurdly inclusive conjunction, to the Queen of Hearts, who threatens others with total exclusion and negation. In the Looking Glass, Alice works her way from the exclusive Red Queen, much like the Queen of Hearts, and says all ways are hers and not one else’s, to the inclusive White Queen, who accepts impossible and absurd things many times before breakfast, to finally balance in the middle, with the White and Red Queens sitting on either side of her. Alice is a developed OR, having taken all sides, who must gather and divide empirically as she moves through the adult world between total inclusion and total exclusion.

Aristotle’s syllogisms, Boole’s logical connectives, and De Morgan’s theorems and notation are structural to the absurd humor of the work and reveal much of Carroll’s process as he invented the entertaining tales that are also instructive, both false and true, possibilities, fantasies and dreams, half-truths between non-being and being, between 0 and 1 for Boole. In the opening poem before the story, Carroll says, The dream-child (like the fantastic hybrid White Rabbit) moving through a land of wonders wild and new, In friendly chat with bird or beast- and half believe it true.” Aristotle’s syllogisms and the corresponding four corners of the square of opposition can be found in Wonderland in the glass table with the golden key, the reasoning of the pigeon,the Mad Tea Party and several key characters, and in the Looking Glass it is displayed in the Red and White queens and kings, with the queens standing for ALL, the kings for SOME, the white for inclusive positive and the red for exclusive negative. The syllogisms apply to the characters in complex and interesting ways, but simple enough to identify.

De Morgan’s theorems can be found in the structures of the stories as well. After Alice meets the Caterpillar, a very inclusive but reclusive Or who tells her little, questions her much and gives her the ability to grow or shrink in perspective and size, introducing Alice to transformations, she argues with a pigeon who fears for her egg, and then goes to the Duchess’ house, where the Duchess is beating her baby and the cook is hurling everything he can at her. The pigeon is negative to alice but conjoined with her egg, and then Alice wanders into an abusive exclusive OR from a conjunction that is also a mother-child relationship, moving along De Morgan’s first law, from ~(A ^ B), pigeon protecting Alice from egg, to ~A v ~B, with dueling Duchess and baby, as well as Duchess and cook, as Alice has moved into the house and inside the brackets, finding division within.

Immediately after this, the Cheshire Cat, who sits as a grinning exclusive OR inside the divided house, wise to how every position is opposed to another, tells Alice everyone is exclusively in their own dream and mad, opposed to anyone against them, so everyone is insane. The Cat tells Alice he takes the shortcut, just as De Morgan’s theorems are shortcuts for logic, and says you can go one way to the March Hare or the other way to the Mad Hatter, ~A v ~B, but when Alice goes one way she ends up going both ways and finds the two at a table, and they protest there is no room for her, excluding her, which reverses the course of De Morgan’s first law immediately after going the first direction, from ~A v ~B, the choice of one crazy person or another, opposed to Alice’s perspective either way, to ~(A ^ B), where the two are opposed to Alice at the table together, and say there is no room inside for her. The Tea Party resembles the absurdity of Boolean abstract logical algebra, where time doesn’t move unless you ask it to, and the Mad Hatter schools Alice on how IF-THEN works in syllogistic exercises.

November 18, 2019 3

Alice, Aristotle’s Syllogisms & Boole’s AND, OR & NOT

I have been working on Lewis Carroll’s Alice in Wonderland and Through the Looking Glass for many years now to find the logical and philosophical forms hiding inside it, and as I have been teaching logic this semester I have used the class as an excuse to go over Aristotle, Boole and Carroll’s work carefully. In the process, I have found many Aristotelian and Boolean forms that are structural to both works that I have never seen before.

Aristotle’s four “perfect” syllogisms and Boole’s inclusive and exclusive operations of AND, OR and NOT, gathering and dividing as John Stuart Mill would say, form the positions and plot of both Alice books. Carroll was studying the logic of Aristotle, Mill and Boole as he wrote both of Alice’s adventures, visually presenting logic as characters, but also as emotions, as inclusive and exclusive feelings that operate in our thoughts and our world together. Carroll was trying to show us that syllogisms and logical operations are series of emotions, of feelings that gather and divide things in sequences as the underlying structure of thought with the underlying structure of his stories about Alice.

In the first book of Wonderland, Alice works her way from an inclusive AND, the White Rabbit, past the inclusive OR of the caterpillar, the exclusive OR of the Cheshire Cat, to the NOT of the Queen of Hearts, who chops off heads. The various symbols for NOT Boole and other logicians use look a bit like an ax next to a capital letter, a symbol for a group much like a regal head who stands for the common people. Alice says it is all a pack of cards, meaningless manipulation of symbols and pieces regardless of meaning, and disrupts her imaginary dream.

The White Rabbit is like an addition problem, an AND, Alice and her older sister, inclusive of different elements, the two sisters, and exclusive, specialized and late to a specific event at a precise time. This makes the White Rabbit an absurdly rational animal, as Aristotle would say, both man and beast. Alice, bored with her sister reading to herself, charges after the White Rabbit down the rabbit hole, with no thought as to how she would get out again, like a wildly inclusive child, mirroring the absurdly inclusive combination of a rabbit with a waistcoat, and unlike her sister, who is carefully considering a specialized text. Alice dreams she follows the absurdly complex White Rabbit as she can’t follow her sister in reading a boring specialized text that gathers a very narrow sort of element. A child needs emotions, pictures, words and many things to stay interested in a story.

In the second book of the Looking Glass, Alice works her way from the Red Queen, another NOT like the red Queen of Hearts, past the White Queen, a childlike inclusive AND, timid like the White Rabbit, to the end of the board where Alice is the OR, who must inclusively and exclusively choose between inclusive AND, the White Queen on her right, and exclusive NOT, the Red Queen on her left. The Queens test Alice and find she can’t inclusively add or exclusively subtract things the ways they ask her to, they take her to a banquet where food turns into people and people into food, and Alice hates it and turns the table over, upsetting her second dream. Wonderland works from childlike AND past OR to adult NOT, from inclusion to exclusion, and the Looking Glass works from adult NOT past childlike AND to bring the childlike-adult balance of OR, both inclusive and exclusive.

The four royal pieces of the Looking Glass world, 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 Aristotelean corner.

If you are interested in more, please read my lecture on Logic, Lewis Carroll and Alice’s Adventures, which is very much under development and in progress at the moment, as can hopefully be understood. It may turn out that all negativity is merely a playful, innocent kitten after all.

November 7, 2019 0

Is a catnap literal or metaphorical?

Let’s say that something is merely metaphorical if it is simply similar to something but not identical, as the Nyaya logicians of ancient India would say. That means that if I act like a cat, but I am not a cat, it can be said, metaphorically, “Eric is a cat,” as I act like one, but it can’t be said literally AND truthfully that I am a cat, as said. As Saussure the Swiss linguist could say, in French or German, the word “cat” doesn’t look like a cat or sound like a cat, nor does the word nap sound like a nap or look like one, but a catnap, a nap taken by a cat or me later, does look like a napping cat, whether or not I am a cat. This means that when I, a human, take a catnap, I am literally taking a nap, but I am metaphorically taking a catnap. Does this mean when I nap, “Eric is taking a catnap,” is both literally AND metaphorically true in different ways? Can the two be complimentary, or are they exclusive?

If I am a cat, a catnap looks entirely like a cat taking a nap, and if I am not a cat, then it looks like a nap, which I am literally taking, but I am only like a cat, not actually or literally one, as said. So: If I take a catnap with my cat, and you say, “They are taking a catnap together,” did you say something that was metaphorically true for me, but literally true for the cat, or is it both literal and metaphorical for both of us? Does it feel metaphorical to say it about me, and feel literal to say it about the cat? Does it feel or apply to me and the cat differently? Does it depend how it feels to say it, or does it depend on how it is said, and to whom? Nothing seems clear here, no matter how literally or carefully we speak.

October 19, 2019 0