The History of Thought with Eric Gerlach
In the 1400s and 1500s the story of Phyllis riding Aristotle was popular in art and literature in France and Germany, illustrated by artists and associated with stories from the Bible, Greeks and Romans warning men about the dangers of giving women power over them, known collectively as the Power of Women tales, Weibermacht in German. The story about Aristotle first appears in the early 1200s in the sermon of Jacques de Vitry, who ridiculed Aristotle, and in a court poem Le Lai d’Aristote by Henri d’Andely, praising love as all powerful, superior to reason. Maurice Delbouille argued that there are glaring similarities to the earlier Arabic story of Al-Jahiz of the 800s, The Vizier Saddled & Bridled. The story seems to have nothing to do with the life of Aristotle or ancient times, told centuries after Aristotle was long dead.
The basic story is that the wise elder Aristotle scolds his young student Alexander for ignoring his studies and state for his lover, and then the lover, an unnamed Indian woman or Phyllis, servant of the Greek Queen, takes revenge by seducing Aristotle, demanding he let her ride him like a horse to have her, and then shows this to Alexander. Aristotle admits that love conquers all, or flees in shame to another country where he ponders the evils of women and passion. Either way, Aristotle warns Alexander that his own failure serves as the perfect example of how dangerous women are to all men, particularly the young and the powerful.
The image of Aristotle ridden by Phyllis is found in art, architecture, tapestries, furniture and as a metaphor in sermons of the time. Just as Adam was deceived by Eve as the first man, and Samson was bested by Delilah, even though he was the strongest of men, Aristotle was bested by Phyllis even though he was the wisest of men, warning strong and wise men not to underestimate the dangers of women, passion and seduction. Sometimes the images of Samson and the lion, not Delilah, are paired with Phyllis and Aristotle, comparing seduction to consumption, and sex to death. The popular use of the image in items shared by married couples suggests it was not just a serious warning to men but also a joke between men and women that women can or do have power over men in some ways, particularly in the home, something psychologists and sociologists have argued about.
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.
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.
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.
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.
Fifth, the Caterpillar is time, who takes away the certainty of all things, and includes all changes and possibilities as indeterminate.
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.
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.
Let us imagine a game played with pieces on a board, a logistical space for moving the pieces. What is on the board is true and certainly the present case. The pieces on the board and in the box beside the board contain all the pieces that can possibly be used, all the possibles and possibilities, such that if we see the pieces on the board and beside the board, we don’t know what pieces will be played but know all the pieces that could be played. A piece beside the board is false and dead, unless it gets onto the board, and then it is true and live in the game, and a piece on the board is false and dead if it is taken off the board. There are also things that are not in the game, the logical universe of discourse, the subject under discussion or consideration, and these are neither true nor false, as the are not in the cards, are not possibilities or pieces that can possibly enter the game or be negated to the side.
With this structure alone, we can exhaust all the connectives we use in formal Sentential Logic the way Wittgenstein envisioned it in his Tractatus and set it with truth tables. First, AND puts pieces on the board, including them together, but it could also, in combination with NOT, take sets of pieces off the board, adding them to the possibilities currently false rather than those currently true. NOT takes pieces off the board, or adds them if it is tied up with other NOTs. OR considers pieces, involved with whether or not pieces are moved on or off the board, completely indeterminate by itself, but determinate in combination with pieces added to or dropped from the board with ANDs and NOTs.
IF-THEN connects pieces possibly on the board together, such that one should lead to the other. Sluga argues that there are connections between things in the moment, such as speciation, with all men being mortal all at once or always, and connections between things over time, such as causation, with one thing leading to another. If the game changes with the possibilities over time, the first would be statements about the relationships between pieces at the same time, and the second different times. Bivalence, IF-AND-ONLY-IF, would simply state the relationship is reciprocal, working both ways, which would work with speciation and causation in a chicken-and-egg situation, where two things lead to each other circularly over time, again and again.