Thought Itself

The History of Philosophy, Logic & The Mind with Eric Gerlach


Lewis Carroll

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.

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.

Wittgenstein & the Mad Tea Party of Wonderland

Alice Mad Tea PartyThe Journal of the Philosophical Society of England just posted an article I wrote for them about Wittgenstein and the work of Lewis Carroll, one of my favorite subjects. Here is the link:

Euclid, Carroll & Political Satire

lewis-carroll-in-numberlandI have been researching the work of Lewis Carroll, and just now found a remarkable piece of Carroll’s wit in Robin Wilson’s book Lewis Carroll in Numberland (2008).  Carroll, a professor of mathematics and logic at Oxford, was very familiar with Euclid’s Elements, the classic Greek text on geometry which was used to sharpen the minds of students in Victorian England.

Euclid’s first three postulates are:

Euclid1) Let it be granted, that a line may be drawn from any point to any other point.

2) That a line may be lengthened to any extent.

3) That a circle may be drawn about any point, and at any distance from that point.

Carroll, mocking the politics of parliamentary elections, produced these three:

Lewis Carroll1) Let it be granted, that a speaker may digress from any point to any other point.

2) That a finite argument may be lengthened to any extent.

3) That a controversy may be raised about any question, and at any distance from that question.

“Pigs may fly, but it’s not likely.” – Old Scottish Proverb

I found this proverb going through the Alice books in a note (p. 93) to Martin Gardner’s Annotated Alice.  Then, in Wikimedia Commons, I found this picture:

first pig to fly

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