Logic – Lewis Carroll

Lewis CarrollBorn 1832, Lewis Carroll taught mathematics and logic at Christ Church College at Oxford from college there (1851) to his death (1898).  Carroll had many brothers and sisters, mostly younger sisters, and he enjoyed entertaining them as a boy. He created and organized imaginary games, magic shows, a family magazine, and puppet plays that involved many of his siblings.  At the boarding school he attended as a boy, he was known for defending younger students from bullies.  Later, after he joined the faculty of Oxford as a professor of mathematics and logic, he loved to entertain the children of his colleagues, telling them stories, making up games, and teaching them math and chess.  He hated them growing up, because they stopped being innocent and started being deceitful and hypocritical like the adults they imitated.  He wrote the Alice books, first Alice in Wonderland and then Through the Looking Glass, for an actual Alice and her two sisters as well as other children who he enjoyed playing with and having conversations.

Lewis Carroll with ChildrenHe was especially fond of children, particularly little girls, which doesn’t come out right no matter how you say it.  This became an issue in the 1930s, when in America during an anti-pornography-by-mail moral craze he was labeled a pedophile.  Freudian readings of the texts had flourished by this time, and Carroll did not help himself with his photography of children or his friendship with the real Alice, Alice Liddell, the daughter of the dean of Christ Church College.  It is possible that Alice’s older sister, also a friend of Carroll’s, was too close to Carroll for their family’s comfort as a teenager, and the family broke off contact with Carroll to avoid scandal.  It is also possible that Carroll craved female companionship, but sought this with prepubescent girls to keep himself free of sexual feelings which filled him with shame.  There is good evidence that Carroll was somewhat the Victorian prude, and felt guilty about his own repressed sexuality.  As a fellow at Oxford, Carroll was entitled to teach for life, provided that he be ordained a minister and remain unmarried.  This prevented him from having a family of his own, though he came from a large family with many children.

Christ Church

alice booksMany have tried to crack the code of his books to uncover the essential meaning underneath.  Some say that his books are centrally about mocking the politics of his day.  Others say they mock theories of mathematics and logic that Carroll disliked.  Others say that there is no meaning at all and the books are simply nonsense play.  Listening to late Wittgenstein, we will likely not find some hidden cellar that solves the text with a single solution.  Carroll made up the tales as he went along, clearly hiding clever jokes throughout them but not necessarily giving the hidden gems an underlying coherence.  Carroll refused to answer questions about the Alice books or be interviewed as their author.  For those who are interested, Gardner’s Annotated Alice is an excellent source for insights and context that easily escape modern readers.

alice father williamThere are repeated themes of nonsense, dream, and parody in the Alice books.  Carroll took logic, nursery rhymes, school lessons and hierarchies and he warped and reversed them in conversations between Alice and her dream companions with hilarious consequences.  Alice is constantly reciting her rhymes she is taught, hands folded, but strange warped versions come out.  Children were taught rhymes to recite, not because they contain value in themselves, but because they train children to imitate and conform.  The Alice books are full of mockery of the way that we are hypocritical and irrational while following rules, standards and ideals in the language games we play with others.  Like Wittgenstein, Carroll was uncomfortable with polite society, and was aware that teaching logic and math is similar to following the formality of politics and tradition.  On the one hand, the rules and behaviors are the most important thing, but on the other, they are arbitrary and often infringe on the lives they are designed to preserve.

wittgenstein grafCarroll was fascinated by reversals, playing music boxes backwards to hear  “music standing on its head”.  Scholars have noted that he was fascinated not by what worked but the puzzle cases, the problems and mysteries.  He noted that children in noble families would sometimes speak to servants as if the servants were themselves the children.  In the beginning of Through the Looking Glass, Alice wonders about the reversed room on the other side of the mirror, and whether or not the smoke she sees from the fireplace is real or is set up to deceive her on purpose.  If someone does something nice for you, you could interpret this as genuine kindness, or as a deceptive attempt to get something in return.  Likely it is both mixed together, interpreted from two different and opposite perspectives, much like Wittgenstein’s duck-rabbit.

AvicennaIn many ways, the imagination is the same as yet the opposite of reality.  For example, consider the horse and unicorn example of Avicenna.  The concept of a unicorn is imaginary in the same way that the concept of a horse is imaginary.  One can have either concept with or without a unicorn or horse.  Plato considered ideas to be more genuine and permanent than the world we see around us, but Hume and Nietzsche argued the opposite, that ideas are copies of the things we perceive.  Which is more meaningful, the ideal or the real?  We can’t eat our conception of a red apple, but we can always have our concept even if we have no apples.  Mental objects are ideal, just what they are, while real objects are always imperfect and temporary.  Remember that in ancient world cosmology, the real world is often the fake and temporary world compared to the hidden world, and in modern science and logic the things themselves are imperfect compared to the rules and patterns of behavior.

alice red queenWe must think, be in the process and mental motion of thinking, to have a conception of an apple, but we need to engage in physical motion to get a real apple.  In both Wonderland and the world of the looking glass, Alice is in a dream, as she discovers at the end of each book.  In Through the Looking Glass, the Red Queen tells Alice, “Here, we have to run as fast as we can just to stay in place”.

lewis-carroll-logicLewis Carroll was, of course, not actually named Lewis Carroll, his pen name for the Alice books.  His real name was Charles Dodgson, and it amused him after his Alice books became famous that he was now better known by his fake name.  For those who still write and speak about him and his books, he is best known by his fake name, not his real name, so it has indeed become his most proper name, his name by habit and custom.  Charles Dodgson also wrote books on logic and mathematics under his real name, in which there are many passages that show a cynical view of humanity and culture as little more than a dream and less than the ideal.

Studying Logic, he wrote, “will give you clearness of thought – the ability to see your way through a puzzle – the habit of arranging your ideas in an orderly and get-at-able form – and, more valuable than all, the power to detect fallacies, and to tear to pieces the flimsy illogical arguments which you will so continually encounter in books, in newspapers, in speeches, and even in sermons, and which so easily delude those who have never taken the trouble to master this fascinating Art”.

“And so you think, do you, that the chief use of Logic in real life is to deduce Conclusions from workable Premises, and to satisfy yourself that the Conclusions deduced by other people are correct?  I only wish it were!  Society would be much less liable to panics and other delusions and political life especially would be a totally different thing, if even a majority of the arguments that are scattered broadcast over the world were correct!  But it is all the other way, I fear.  For one workable pair of premises (I mean a pair that lead to a logical conclusion) that you meet with in reading your newspaper or magazine, you will probably find five that lead to no Conclusion at all; and, even when the Premises are workable, for one instance, where the writer draws a correct conclusion, there are probably ten where he draws an incorrect one.”

“You will find these seven words – proposition, attribute, term, subject, predicate, particular, universal – charmingly useful, if any friend should happen to ask if you have ever studied Logic.  Mind you bring all seven words into your answer, and your friend will go away deeply impressed – ‘a sadder and a wiser man’.”

LobsterCarroll enjoyed constructing syllogism puzzles, which often had amusing and subversive answers, such as, “No riddles that interest me can be solved”, “No lobsters are unreasonable”, ”No Act of Parliament is amusing”, ”Some caterpillars are not eloquent”, ”Generals do not write poetry”, ”Some savage animals do not drink coffee”, and, the only genuine drug reference I have found in Carroll’s work, “Opium eaters do not wear white kid gloves”.

OLYMPUS DIGITAL CAMERAWhile the 60s counterculture embraced the Alice books as trip-friendly, there is no evidence that Carroll tried opium himself, though he was fascinated by delusions and insanity.  Carroll modeled himself on his favorite uncle, who also enjoyed mathematics and was an inspector of insane asylums.  My favorite scene in the Alice books, the Mad Tea Party, was based on actual mock tea parties given to asylum inmates to teach them, much like the rhymes of school children, to follow rules and conform to accepted practices of social behavior.  Again, there is the theme of rule as both imaginary and important, both dream and daily practice.  Just like a little girl’s tea party, the party is indeed a party, but there is no real tea, only the motions of a polite social gathering.

Sylvie and BrunoAfter writing the Alice books, Carroll wrote two books about Sylvie and Bruno, a brother and sister who travel together meeting strange and interesting characters.  The books were never as popular as the Alice books, but they have interesting moments which are considered by some French philosophers.  One of the characters encountered is a gardener, who speaks in limericks.  My favorite is the following:

He thought he saw a rattlesnake that spoke to him in Greek.  He looked again and found it was the middle of next week.  What a pity it is, he sighed and said, that it can hardly speak.

RattlesnakeCarroll’s work, when read closely and carefully, reveals layers of complex play and double meanings.  First, a rattlesnake is both a rattle and a snake, and since rattlesnakes are native to the Americas, so there is little reason for a rattlesnake to speak Greek.  Then again, there is little reason for British people or Western Europeans to speak Greek, though it was part of the mandatory formal education for all scholars in Carroll’s day, and Aristotle was still taught as the master of formal logic before the Tractatus of Wittgenstein gave logicians truth tables.  The middle of next week is something we can talk about, like a Greek-speaking snake, though neither can exist here and now, so Carroll is joking that one could, theoretically, mistake one nonexistent imaginary thing for another, and he then notes that neither a Greek-speaking snake nor the middle of next week can speak, as both are imaginary.  This is a good example of Carroll’s sort of humor to consider before jumping into the Alice books.

Alice in Wonderland

alice coverCarroll enjoyed entertaining children, such as the three Liddell sisters, and he would often take walks and boat rides with them while making up games and stories.  One famous day, Carroll was rowing a boat with the three Liddell sisters one afternoon, and Alice asked him for a story.  Carroll began making up, off the top of his head, what later became Alice in Wonderland.  It was only because Alice loved that particular story and asked him to write it down that Carroll remembered and developed it.  He considered many names for the story, including Alice’s Hour in Elf-land, and Alice’s Adventures Underground.  ‘Wonder-land’ is etymologically related to ‘underground’, both being another hidden world of mystery.  In both of the Alice books, Alice does not notice herself falling asleep, and like Zhuangzi or Descartes, cannot tell the difference between the dreamworld and reality.  Human reason, imagination and mathematics are similarly dreams that we take to be reality.

The White RabbitThe first thing that Alice sees in her dream is the White Rabbit, fascinating because he is both animal and human.  Carroll, a classically trained logician, knows that Aristotle defined humanity as the rational animal, an animal crowned with the third, highest and immortal of the three souls of Plato, Aristotle’s teacher.  Alice is puzzled as to why a rabbit would have a watch, and how he could be late to a social gathering.  She follows the white rabbit out of curiosity, and falls down the rabbit hole into Wonderland, just like she followed her thought of making daisy chains as she fell asleep and fell into the dreamworld.

As Alice falls, she passes all sorts of pictures, maps, and shelves full with empty labeled jars.  Like our concept of marmalade, Alice finds that the jar labelled ‘marmalade’ contains no marmalade.  All of these things are containers and images, the abstractions of reason and memory but not real things that they hold and represent.  Alice worries that she will fall through the earth and meet people called Antipathies who walk on their hands upside-down.

alice drink meFollowing the White Rabbit, Alice finds herself in a hall surrounded by locked doors, and she finds a three-legged glass table, a golden key, and a small door that leads to a beautiful garden outside.  Carroll preferred to play out in the gardens with children, rather than do work indoors.  Alice finds out that if she drinks the liquid in the bottle labeled “Drink Me”, she is small enough to go through the door to the garden, but she can no longer reach the golden key on the glass table.  As a logician, Carroll is well aware that Aristotle’s syllogisms, his three sentence forms of deductive proof, provide universal truth and absolute certainty, but it is difficult in the real world, down below the lunar sphere, to find the universal truths that would open our lives to the perfect and flawless Garden of Eden.  In his Philosophical Investigations, Wittgenstein wrote that he had tried to create a perfect system of logic, but that trying to understand life in terms of universal logic is like trying to walk on frictionless ice.

CroquetAlice is frustrated and begins to cry, then scolds herself and commands herself to stop.  We are told that Alice is fond of pretending to be two people, that she often gives herself advice but fails to follow it, and that she once punished herself for cheating at a game of croquet she was playing against herself.  When we make rules for ourselves and then break them, are we the same person we were when we made the rule?  Insofar as Alice is in a dream, she is each of the characters she encounters, having dialogues with herself.  She does not solve the problem of the key and the door, but is rather swept out of the situation by her tears, failing to follow her own command.  Alice will get to the garden much later in the story, but she will find it is not an ideal place at all, occupied by the Queen of Hearts, who keeps screaming for executions, and a confusing game of lawless croquet being played using flamingos and hedgehogs as disobedient equipment.  This reflects Alice commanding herself out of anger, and disobeying her own orders and rules.

white rabbit trumpetThroughout this, Alice is questioning whether or not she is Mabel because she no longer knows the things she does.  Soon after this she is called ‘Mary Ann’ by the White Rabbit, who thinks that she is his servant.  Mary Ann was a common name for maids in Victorian England, and Alice responds as if she is Mary Ann.  Similar to Sartre and the cafe waiter, we are and are not the social roles we play, just as we are and are not the people we believe ourselves to be and others believe us to be.  Like rules, social roles and positions of authority are both imaginary and real, ordering our reality but made very much of the stuff of mind, not matter.

Alice encounters a mouse while she is swimming in a sea of her own tears.  Forgetting that she is as small as a mouse, and that mice hate cats and dogs, she lovingly describes her cat and the neighbor’s dog to the mouse hoping he will find them agreeable.  Later, when Alice, still tiny in size, encounters an enormous puppy, which frightens her.

alice-duchessThis is the first of many trades in perspective for Alice.  First, she encounters a character who holds a position she finds disagreeable, but then when she is in their position, she agrees with their previous position without recognizing her own hypocrisy.  Later, when Alice meets the Duchess, Alice is horrified to see the baby she is holding crying and sneezing while the Duchess calls it ‘pig’ and beats it.  Then Alice takes the baby and flees with it outside, where it transforms into a pig and Alice says “If you are going to turn into a pig, I will have nothing more to do with you”, sets it down and watches it run off into the woods.  Much later, when both the Duchess and Alice are in the garden of the Queen, the Duchess is nice to Alice, unlike she was before when the Duchess was in her own house.

Alice BirdsThe mouse leads Alice to shore, where they gather with various birds.  The mouse tells a dry tale to dry them all off, but when he says, “the Archbishop found it advisable”, he is interrupted by a duck, who asks him what ‘it’ means.  The mouse replies that the duck should very well know what ‘it’ means, and the duck says that when he finds a thing, ‘it’ is typically a frog or a worm, so what did the archbishop find?  Wittgenstein argued that words like ‘it’ and ‘this’ are not defined by the objects to which they refer, but are used to refer to objects in general, the source of the joke here.  Alice once again lovingly mentions her cat, which frightens the entire gathering away.

Alice CaterpillarSoon after, Alice encounters the caterpillar, who is sitting atop a mushroom, smoking a hookah.  He asks her who she is, and when she says she cannot say, the caterpillar asks her to explain herself.  Alice says that changing so often is confusing, just as the caterpillar will have to change into a butterfly, but the caterpillar replies that this is hardly strange at all.  Like Humpty Dumpty in Through the Looking Glass, the caterpillar disagrees with everything that Alice says, making the insecure Alice question herself.  Alice says she wishes that the creatures she encounters would not be so easily offended, and the caterpillar replies that she will get used to it in time.

After being told that the mushroom will allow her to grow large again, Alice becomes gigantic, and encounters the pigeon, who believes that she must be a serpent after her eggs.  When Alice protests that she is not a serpent, but a little girl (who now happens to be gigantic), the pigeon reasons that if Alice eats eggs, then little girls must be some type of serpent.  While the caterpillar forces Alice to question her individual identity, the pigeon tries to identify Alice as a type of serpent using Aristotelian syllogistic reasoning.  The problem is not all things that eat eggs are serpents, but from the point of view of the pigeon, they may as well be.

Cheshire CatAlice goes to the house of the Duchess, steals her baby, and then releases it into the forest after it turns into a pig.  She then sees the Cheshire Cat, who she first met in the house of the Duchess, who tells her that if she goes right, she will find the Mad Hatter, and if she goes left, she will find the March Hare, and that both of them are insane.  Alice says that she doesn’t want to meet crazy people, but the cat replies that everyone in Wonderland is insane, including her and himself.  To demonstrate, he explains that a dog growls when it is angry and wags its tail when it is happy, while he, as a cat, growls when he is happy and wags his tail when he is angry.  Alice says that she calls it purring, not growling, to which the Cheshire Cat replies, “Call it what you like”.  He asks her about the baby, and when Alice tells him it turned into a pig, he says, “I thought it might”.  If everyone is opposite the position of someone else, then everyone is crazy to someone, regardless of how we change positions.

alice-mad-tea-partyAlice decides to go left, to visit the March Hare, but when she arrives she finds that both ways lead to the same place, as the Mad Hatter and March Hare are having a tea party together.  “Mad as a march hare” and “mad as a hatter” were both common expressions in Carroll’s Victorian England.  Rabbits run wild in the spring, their mating season, and hatters were notorious for going crazy, as they would felt the hats with mercury, stick pins in the hats, hold the pins in their mouths, and slowly become poisoned over the years.

Top hatsLike the White Rabbit, the Hare and Hatter symbolize the passionate animal body and the formulating human mind, the duality of desire and reason.  Top hats were considered proper, formal attire in Carroll’s day, and the Hatter, who plays the role of insane logician at the party, is wearing a hat which he later admits is not his own, but one he sells to others.  Carroll was aware that, as a professor of logic and mathematics, he made his living selling ideas and forms of thought to others.  In the song of the White Knight at the end of Through the Looking Glass, the White Knight, whom many consider to be Carroll himself, says that he plucks butterflies from the air and sells them as mutton pies in the street to feed himself.

Bertrand RussellOne of the most interesting connections between Carroll and Wittgenstein is Bertrand Russell, whom many thought looked and acted much like the Mad Hatter.  Russell’s close circle at Cambridge, consisting of himself, G.E. Moore and J.M.E. Taggart, were dubbed “the Mad Tea Party of Trinity” in fun by many colleagues who considered the logicians to be quite insane and living in a fictional world of mathematics grounded in the ideals of logic.  Russell famously stated: “Mathematics is that science in which we do not know what we are talking about, nor whether what we are saying is true”.  There is no better statement to illustrate the Hatter’s confusion of particular case with abstract form.  The number three can designate three mountains, zebras, or logicians, but it does not refer in itself to any particular three things.

WittgensteinWittgenstein was known to be fond of Alice in Wonderland, but there is a debate as to how much Wittgenstein’s philosophy was indebted to them.  Carroll’s name appears in Wittgenstein’s Philosophical Investigations, related to the nonsense words of the Jabberwocky poem.  Both authors are preoccupied with games and rules and how they can be variously interpreted.  Both illustrate this using chess pieces.  Both use utterances that “sound like English” but do not have a use and thus do not make sense.  Both consider the absurdity of private, individual language and giving gifts to one’s own limbs.  Both consider the absurdity of private language and definitions.

Oak Tree in ClearingWhen Alice approaches the Mad Tea Party, which consists of the March Hare, Mad Hatter, and Dormouse sitting outside at a large table underneath a tree, the Hare and Hatter see her and shout, “No room! No room!”.  Are they telling Alice that she is not welcome, or are they telling her that they are outside, not inside, and so there is “no room”?  In either case, Alice interprets this as an insult, as if they are excluding her, and she declares that there is plenty of room, plenty of empty chairs, and sits down in retaliation.

Corvus corax/Common RavenThe Hare offers her wine, but then admits there isn’t any.  Alice says this is rude, and the Hare replies that she was rude to sit down without being invited.  The Hatter tells Alice that she needs a haircut, which Alice says is also rude.  The Hatter then presents Alice with a riddle, a riddle which we later learn has no answer: “Why is a raven like a writing desk?”.

When Carroll first wrote this riddle, he did not believe that it had any answer.  It does sound as if ‘raven’ and ‘writing desk’ both start with R, but ‘writing’ begins with a silent W, as a meaningless matter of conventional practice.  Years later, at the opera, a fan approached Carroll and told him that both a raven and a writing desk can produce flat notes, and Carroll approved of the solution.  Why are people rude to others that are rude to them?  Again, there is the theme of not recognizing one’s position when it is taken by another.  This may be one of the most unsolvable riddles of humankind.

Writing DeskAlice, forgetting the rude exchange, focuses on the riddle, and says, “I believe I can guess that”, making statements about her ability to make statements, thinking she can think of the answer.  The Hare replies, “Do you mean that you think you can find out the answer to it?”, adding a third layer, asking Alice about what she means.  When Alice says, “Exactly so”, the Hare replies, “Then you should say what you mean”.  The joke, absurd but comprehensible, is that the Hare acts as if Alice is acknowledging that she said the wrong thing, not that the two are equivalent.  “I believe I can guess that”, and “I think I can find the answer”, are not exactly the same, but they are, in this situation, decently equivalent.  One could say they are the same, but one could also say they are not exactly the same, even though Alice says, “Exactly so”, overstating the equivalence as we often do when we say, “exactly”, “precisely” or “perfectly”.

Mad Hatter & DoormouseWhen Alice protests, and says, “at least I mean what I say – that’s the same thing, you know”, the Hatter jumps in, playing logician, and says, “Not the same thing a bit!”.  One of the basic lessons in a logic class is that “If A then B” is not the same thing as “If B then A”.  If A is included in B such that whenever A, also B, this does not mean that B is included in A such that whenever B, also A.  The three Tea Party members each give Alice an example that demonstrates this.  The Hatter says, “I see what I eat” is not the same thing as “I eat what I see”.  The Hare says “I like what I get” is not the same thing as “I get what I like”.  The Dormouse (which is not a door, but is a mouse), talking in its sleep, says “I breathe when I sleep” is not the same thing as “I sleep when I breathe”.  The Hatter then turns on the Dormouse and points out that, because the Dormouse is always sleeping and breathing, in its case the two are equivalent.


The joke here is that Alice did say what she meant and meant what she said, and the two are very much the same thing.  In logic, “A and B” is the same thing as “B and A”, in the same way that 2 + 3 is the same thing as 3 + 2.  When Alice says and means something, she also means and says something.  The Hatter interpreted Alice as saying something universal about the conditional relationship between A and B, when she was only saying something about a particular individual case.  In the Philosophical Investigations, Wittgenstein says that opposing camps of philosophers interpret their own position as general, allowing for exceptions, but interpret the opposing position as universal, failing to allow for exceptions.  The Hatter, in turning on the dormouse, shows that his own position is general, as the dormouse is an exception.  Why did he not allow this for Alice?  Likely because he had Alice already framed as rude and wrong in his head.

Alice and Queen GardenAlice leaves the tea party and finds a door in a tree that leads back to hall of doors from the beginning.  Now that she has the mushroom, she can open the small door with the key and get to the garden, but now she finds that the garden is inhabited by the angry and vengeful Queen of Hearts.  Indeed, British history is full of executions for being out of favor with the monarch, and Carroll is giving an excellent send up of politics as a card game that kills people. Alice angers the Queen, who commands, “Off with her head!”, but Alice, who is not afraid of playing cards, simply says, “Nonsense!”, which leaves the queen silent.  In both of the Alice books, Alice does not grow to make sense of the dream world, nor resolve it with a happy ending.  Rather, she becomes assertive, refusing to allow others to influence her.  Carroll was often sad to see his young friends grow up, as they lost their open curiosity and became, like adults, opinionated and uncompromising.

Alice with FlamingoThe Queen has organized a croquet game, played across the irregular garden with flamingos as mallets and hedgehogs as croquet balls.  Alice’s flamingo and hedgehog are uncooperative.  The lack of consistent terrain and rules, the players refusing to take turns in order or stick to their own hedgehogs, and the Queen wandering about ordering executions makes Alice fear that the game is too difficult and dangerous for her.  There do not appear to be any rules, as everyone is constantly fighting over them while refusing to follow them.  Again, this is clearly Carroll mocking British history and politics, cloaking it in a silly game of flamingos and hedgehogs to make it palatable for young children.

Cheshire Cat ExecutionerThe Cheshire Cat shows up, appearing as a disembodied head, causing a commotion.  The King of Hearts, disturbed, asks the Queen if she can have the cat removed, and the Queen, who seems to have only one solution for every problem, demands that the cat’s head be removed.  Since the Cheshire Cat is only a head at this time, this would indeed remove him entirely.  Then the King and executioner get into an argument about whether the head of the Cheshire cat can be beheaded.  The executioner argues that the cat can’t be beheaded without a body to separate from the head, and the king argues that anything with a head can be beheaded.

Alice, Duchess and FlamingoThe Duchess is now nice to Alice, because she was in her own house before but is not in the garden of the Queen.  Alice is delighted, and decides that it was pepper that made the Duchess angry, again not recognizing the change of positions.  Alice theorizes that all anger is caused by pepper, just as all sourness is caused by vinegar and all sweetness is caused by sugar.  The Duchess, who draws herself close to Alice and rests her sharp chin on Alice’s shoulder, as if she is Alice’s uncomfortable conscience, says that there is a moral to be drawn from Alice thinking rather than talking.  As Alice was trying to draw up a set of rules that govern emotions, the Duchess interrupts and proceeds to draw a lesson from each thing that she and Alice say to each other to the point of absurdity, attempting to show Alice that all things must have an underlying moral.  This is much like Wittgenstein’s child at the blackboard, as if things require rules to structure them, then the rules would require rules, leading to an absurd infinite regress.

Alice Pack of CardsAfter spending some time with the Gryphon and the Mock Turtle, Alice finally attends a trial where the King of Hearts is prosecuting the Jack for stealing tarts, in accord with the nursery rhyme.  Alice begins to grow into a giant at the trial, which no one notices until she is called as a witness.  Alice accidentally knocks over the jury box, and puts a lizard back upside down, reasoning that a lizard is just as good a juror either way up.  Alice tells the king she knows nothing about the case, and the king says this is very important to the jury.  Alice says it is not important at all, and the king repeats ‘important, unimportant’, to himself, as if he is trying to decide which word sounds best.  Deciding what is important to include and what is unimportant and can be ignored is central to interpretation and perspective.  Some of the jury write down important, some unimportant.  Giant Alice declares that the evidence is meaningless, the trial is absurd, and then when they all rise up against her, she famously declares that they are nothing but a pack of cards, destroying the trial and her dream of Wonderland.  In the Philosophical Investigations, Wittgenstein says that moving beyond the idea that there are universal rules and absolute definitions is simply destroying houses of cards.

Alice Through the Looking Glass

Through the Looking Glass

We will only consider a small number of passages from the second Alice book, those that are relevant to Wonderland and Wittgenstein.

alice-and-flowersAlice dreams that she passes through the mirror and into the looking glass world and finds herself in a garden with flowers that see her dress and  interpret her to be a flower with petals, much like the pigeon who though Alice was a serpent because she eats eggs.  The flowers tell Alice about the Red Queen, who they also assume is a flower like themselves.  In Wonderland, the queens and kings were cards, while in Through the Looking Glass, they are chess pieces.  In both Alice books, Carroll frames the world as a game, much as Wittgenstein argued that we participate in language games and forms of life.

Alice Red QueenThe Red Queen now appears.  Alice tells her that she has lost her way, to which the Red Queen replies “All these ways are mine”.  Like the March Hare did in Wonderland and Humpty Dumpty will do later, the Queen presumes that she has complete command of how things go, when communication actually involves the cooperation and co-interpretation of both sender and receiver.  Alice points to a hill, and the Red Queen says, ‘I could show you hills compared to which that is a valley’.  Alice replies that a hill can’t be a valley, no matter how small, for this is nonsense.  The Queen replies, ‘I have heard nonsense compared to which that is as sensible as a dictionary’.  While the Queen does not say this, a hill can be reinterpreted as an upside-down valley of earth between hills of air.  As a logician and mathematician, Carroll is quite aware that what appears formulaic can turn out to be quite wrong.

Alice ChessboardThe Red Queen tells Alice she is a pawn in a chess game being played all over the world.  This is similar to the game of croquet in Wonderland, representing politics, which itself can be nonsensical or even homicidal while proceeding according to the rules.  Alice is a pawn who must reach the end of the board to become a queen herself.  Just like in Wonderland, Alice does not, in the end, find herself in a place that makes sense, nor his she happy with being crowned a queen.

Alice White QueenAlice later meets the White Queen, who lives and remembers backwards and finds this best.  While the Red Queen is overbearing and angry, the White Queen is timid and forgetful, dueling sides of Alice’s own personality within the dream.  The White Queen tells Alice she is 101 years old, and when Alice replies that she can’t believe that, the Queen suggests Alice close her eyes and try very hard.  Alice says this won’t work, as one can’t believe impossible things.  The Queen replies that Alice simply needs practice, and that, “When I was your age…I sometimes believed six impossible things before breakfast”.  The White Queen turns into a sheep knitting with seven pairs of needles, a wooly sheep, knitting wool.  Alice finds that they are in a boat, and then in a shop.  In both places, Alice reaches for things, but what she wants is always just out of her reach.  As Russell noted, logic and mathematics deal with ideal things that are not physical, like the things Alice tries to hold and the impossible things the Queen practiced believing in before breakfast.

humpty-dumptyAlice next encounters Humpty Dumpty, who is unaware of his impending fate, as well as the fact that he is an egg, immature and quite fragile. Humpty Dumpty is proud and arrogant, and, as it is said in Proverbs, “Pride cometh before the fall”.  He treats his conversation with Alice as if it was a game that he intends to win by always interpreting the rules in his favor.  When he uses the word ‘glory’ in a way that Alice does not understand, he replies that she could not known what he meant by the word, as he has not yet told her, and that he meant, “There’s a nice knock-down argument for you!”.  In logic and debate, a “straw man” is when you set up your opponent’s argument as overly simple and easy to knock down, and then respond to it believing you have defeated the position.

Alice Humpty Dumpty YellingWhen Alice objects that this is not what ‘glory’ means, Humpty Dumpty says, “When I use a word…it means just what I choose it to mean”.  This is the perfect illustration of Wittgenstein’s argument that private language and definitions are impossible.  Meaning is not simply what the individual wants it to be.  Humpty Dumpty gives himself the right to mean whatever he wants, but he is critical of Alice and gives himself the right, like the March Hare, to tell her what she should have meant.  There are two privileged positions in communication: sender and receiver.  Which one has the true right to say what something meant?  Both seem to have overlapping rights to interpretation that can eclipse each other.

alice white-knightJust before reaching the end of the chessboard and becoming a queen, Alice meets the White Knight, who many have said is Carroll’s portrayal of himself as a loving, absent minded and clumsy friend and protector. The knight is constantly falling off of his horse forwards, backwards and to both sides, like the human mind overgeneralizing and oversimplifying things.  He is constantly coming up with strange, near useless inventions, the problems of which then lead him to ideas for other inventions.  He invents things when he is upside down, having fallen of his horse, as the blood rushes to his head and helps him to think.

The knight tells Alice that he has, after falling, thought of a way of getting over a fence.  He explains that the trouble is in the feet, as the head is already over the fence, so all one needs to do is stand on one’s head, and then one is already over the fence.  In one of Carroll’s works on logic, he says that “our American cousins” have a saying for when they cannot make up their minds as to which political party to vote for, which is, “sitting on the fence“.  Carroll is well aware that traditionally in logic, according to Leibniz and Kant, judgement cannot be on both sides according to the Principle of the Excluded Middle, the rule that things must either be true or false, but not both inclusively.

Alice Knight GateThe knight decides to sing Alice a song to cheer her up, and the song is “A Sittin’ on a Gate”, the thing Alice most clearly remembers later about her second adventure.  The narrator of the song says he saw a man sitting on a gate, and he asks him who he is and what he does.  The man replies that he turns butterflies into mutton pies, a metaphor for teaching logic, mathematics and philosophy as mentioned earlier, but the narrator says that he was not listening, as he had been thinking of a plan to dye his beard green and then conceal it with a large fan so that it cannot be seen.  The narrator becomes more and more violent with the man on the gate, distracted by his own contradictory and foolish ideas such as boiling a bridge in wine, unable to comprehend how the man on the gate is able to transform one thing into another that is completely different in order to make a living.  Concluding, the narrator says that whenever he gets things backwards or makes mistakes, he is reminded of the man on the gate.

queen-aliceAlice then says goodbye to the knight, and becomes a queen, going beyond sitting on the fence, and becoming a ruler and pronouncer of judgement, the thing Carroll lamented about children growing up, losing the wonder and fascination with the impossible, fantastic, and nonsensical.  Hume said that, regardless of what the facts are, we can always imagine they are different, and that we would all be skeptical and imagine how things may be contrary to appearances, but we must eat, and to eat we must be employed as part of a system of judgements, such that we do not question everything, including accepted appearances.  Carroll is clearly an advocate of childlike imagination, the ability to see things the other way round, to play and imagine beyond set social conventions.

alice queensAs soon as she has her crown, Alice scolds herself, telling her (other?) self that queens do not lay about on the grass, as they are dignified.  Alice finds the Red and White Queens on either side of her.  They contradict and misunderstand everything Alice says, and the Red Queen tells Alice that queens never make bargains and never change their minds once they have said that something is so.

Alice Banquet TableclothAlice and the queens attend a banquet in Alice’s honor, and Alice is introduced to each dish and told that it is impolite to eat those to whom one has been introduced.  Then, in a strange political revolution, the guests begin to turn into dishes, and the tableware become the guests.  Alice, frustrated as she was at the trial in Wonderland, pulls the tablecloth from the table, bringing everything to a crashing halt.  Spotting the Red Queen, who has shrunk in size and is chasing the end of her own dress in circles, Alice picks up the Queen and shakes her until she wakes up, finding herself back on the other side of the looking glass again.  Once again, Carroll ends Alice’s adventure with Alice trashing the place out of frustration, turning the tables on a nonsensical world made out of dreams.  We are left wondering if Carroll finds the real world any less contradictory or made of dreaming than the worlds in Alice’s head.

3 thoughts on “Logic – Lewis Carroll

  1. Thank you for this interesting post. I would love to know which syllogism puzzle had the answer ”No Act of Parliament is amusing”!?

    • Thanks! The puzzle is on page 90 of his Game of Logic, #62, which reads:

      All jokes are meant to amuse.
      No Act of Parliament is a joke.

      I actually made a mistake, and will correct it, as I plan to rewrite it while teaching Logic in the fall. The conclusion that can be drawn is not that no Act of Parliament is amusing, but rather that there are some things meant to amuse that are NOT Acts of Parliament, implying in a cynical way that Acts of Parliament are not intended to be jokes, but could amuse us in spite of this.

      • Thank you so much for your response. I am starting to think through a possible article about the relationship of law and humour – or maybe comedy. This is a great point of germination!

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