Logic – Lewis Carroll & Alice
Lewis Carroll’s Life & Passions
Lewis Carroll wrote logic puzzles and stories with hidden meanings much like Edgar Allan Poe, and many have wondered if the mystery of Carroll’s life may or may not hide exciting secrets of sex and drugs over a century before rock and roll invaded the British. Alice in Wonderland was published in 1865, a hundred years before the 60s celebrated the book with blacklight posters full of white rabbits, mushrooms and hookah smoking caterpillars. Unfortunately for the hippies, Carroll certainly used medications that gave him strange dreams, but unlike Poe he probably never did drugs for fun or had sex at all.
Carroll loved children, particularly girls, which doesn’t sound right no matter how you say it, and this hurt his reputation decades after his death in the 1930s and 40s when panic about pornography and pedophilia was on the rise, Freud was popular, and psychoanalysts were over-reading Alice’s adventures down the rabbit hole, warning concerned parents not to give a book with dangerous secret messages to their impressionable children. Carroll took nude photographs of children and shared the pictures with their parents, which is unsettling but nude child models were normal in European painting and Carroll was one of the first amateur photographers as the camera became available.
Carroll had nine brothers and sisters growing up in a large family, mostly younger sisters, and he entertained them with imaginary games, magic shows, a family magazine, and puppet plays. At boarding school he defended younger boys from bullies, and each summer he gave lessons to the boys and girls of his father’s school in Croft. In 1851 he moved to Oxford for college, the oldest in England, and when he became a fellow he was entitled to teach for the rest of his life if he remained unmarried and celibate, which he did until he died. This kept him from having a family of his own, so he played with the children of his colleagues as he had his sisters and brothers, and many of his child friends wrote him loving letters for years after they were grown. Alice was one of these friends, as were her two sisters, the daughters of Carroll’s boss, Henry Liddell, a Greek scholar appointed dean of Christ Church College, Oxford by Queen Victoria.
There is little if any sex in Alice, nor are there jokes about religion, both subjects Carroll thought beyond children and good taste in humor, but there is much fun made of rules, politics, madness, and violence. Neither of the Alice books end well, and while both are about Alice growing up, she doesn’t make sense of why everyone is mad or why the Queen of Hearts rules an ever-changing croquet game by chopping heads off, but children grow up and into a mad, mad world whether we like it or not, and they may read British history at some point. Carroll’s favorite uncle was an inspector of insane asylums, who took his nephew on tours, entertained him with telescopes, microscopes and cameras and was sadly killed by an inmate after both Alice books were complete.
Carroll’s mother and father, like his uncle, were into imagination and absurdity. When he was a boy his mother wrote him a letter sending him exactly one billion kisses, and his father wrote from Leeds that he’ll scream out for ironmongers in the street and, “Six hundred men will rush out of their shops in a moment, fly, fly in all directions, ring the bells, call the constables, set the town on fire. I WILL have a file and a screwdriver, and a ring, and if they are not brought directly, in forty seconds, I will leave nothing but one small cat alive in the whole town of Leeds, and I shall only leave that, because I am afraid I shall not have time to kill it.” His father adds that to escape his wrath old women will rush up the chimneys, followed by cows, ducks will hide themselves in coffee cups and geese in pencil cases, surreal humor worthy of Monty Python. When Carroll got first place in a math exam, he wrote to his sister, “I feel at present very like a child with a new toy, but I dare say I shall be tired of it soon, and wish to be Pope of Rome next.”
Carroll often prayed that his sinful and rebellious heart be reigned in, and he loved and hated breaking rules and expectations. He once called Alice a fabulous monster, and in the beginning of the Looking Glass, after Wonderland ends with a murderous queen and useless court trial, Alice threatens to leave a kitten out in the cold and she frightens her maid pretending she is a hyena and her maid a bone. Carroll sent a penknife to another girl as a present and said she could use it to eat meat or punish her many brothers by stabbing them in the nose. Victorians were afraid of sex but quite open with violence, as beating animals, children and servants was commonly accepted, but Carroll’s passions raised more than one set of eyebrows and still causes talk today.
Carroll was complex, but clearly cared about others, including animals, children and women, though he disliked adults and men. As a boy he made friends with frogs, toads and snails, and as an adult he publicly supported animal cruelty laws. There is a puzzling theme of fish in the second Alice book, along with the consumption of innocent oysters, that suggests the Christian symbol of fish as the lowliest and humblest of creatures and that we should care for them and how they’re consumed. Plato argued that man is the highest and fish the lowliest of creatures. As a logician schooled in the classics, including Plato and Aristotle, Carroll told a friend that the proper definition of man is an animal that writes letters, rather than political. He had several books on animal intelligence, evolution, Darwin, and even wrote to Darwin a few years after his Looking Glass, asking him about emotions in animals and offering a photo as an illustration if Darwin needed it. Perhaps it was a photo of Alice or other emotional children.
When asked if children ever bored him, Carroll said that they were three-fourths of his life, which is considerable for a mathematician, and that playing with children was, “very restful as a contrast to the society of books, or of men.” Blake, a favorite poet of Carroll’s, said that Jesus wants us to be like a little child to enter heaven on earth, and Carroll’s own poetry is filled with child-like innocence. In his poem Beatrice, an angelic child with eyes of living light is joined by a beast from jungles in the east, a tiger with death in his eyes who forgets his dream of feasting and lies as a slave at the child’s feet. In Wonderland, Alice and a fawn forget who they are in the nameless woods and walk to the edge together, where the deer remembers Alice is a human child and bolts in fear for her life. Coleridge, whom Poe contrasted with Hegel in his Philosophy of Furniture and Carroll quoted frequently, said children have an intuitive spark and imagination we must protect as we mature. Wordsworth, another favorite poet, wrote The child is the father of the man, Shades of the prison-house begin to close upon the growing boy, and Heaven lies about us in our infancy. Ambrose Bierce joked in his Devil’s Dictionary (1906) that the world begins lying about us pretty soon afterwards.
Carroll had double-standards of personal freedom and self-control. He loved to surprise others and be free as a child, but also kept strict control over his life, brewed tea for ten minutes precisely, weighed packages and brought exact change for postage and each leg of train fares. He didn’t want to be known as an author or have photos taken, collected but gave no autographs, and showed up unannounced but hated when others dropped by. Some said he only gave unbirthday gifts, like the tea party talks about, free for him to do with no conventional obligation to others. He was both harshly judgmental and incredibly compassionate. After forgetting an appointment with a 10 year old, he wrote to her that he realized his terrible mistake while out walking with his dear friend Bibkins, asked Bibkins the hour, then the day, then the year, crying, weeping, and screaming after each, and was brought home in several pieces by cart.
Like children, Victorian men claimed in print that women have no sexual thoughts and, like children, are pure unless corrupted by men, which Carroll believed even as he saw the violent hyena in Alice, and he was haunted for years after hearing young girls sing the curse word damn in a production of Gilbert & Sullivan’s HMS Pinafore. In a college poem he wrote: The man that smokes, that reads the Times, that goes to Christmas pantomimes, is capable of any crimes! He spoke out for charity for “fallen women” but also worried that campaigns against child prostitution would attract the improper attentions of improper men, and hoped that women would be educated in segregated women’s colleges free of co-eds.
Morals, Mustn’t & A Sittin’ On A Gate
Carroll had many conflicting feelings about control, as well as structure and instruction. On the one hand, he loved to teach people logic and mathematics, and on the other he loved the freedom of emotional expression, both a poet and mathematician as Poe’s detective Dupin would say. Like Dupin, Carroll loved contradiction, one of the central issues of logic and truth. Many want to find or build a form that fits everyone, and others want to see or use forms as they fit but not universally, and Carroll was on both sides, which his White Knight calls a-sitting on a gate and Carroll says our American cousins call sitting on the fence. This both some and some-not position is the third of the Buddhist Nagarjuna’s four things (catuskoti), but denied by Leibniz and Kant’s Principle of Non-Contradiction (PNC). In many ways there are rules that can’t or shouldn’t be contradicted, and in many ways there are not, much as there are and aren’t rules in chaotic croquet under the uneven rule of the Queen of Hearts.
Whether or not there is a moral or rules to life is the deeper contradictory moral of Wonderland and the Looking Glass world. Carroll loved contradictions and double-meanings, and he gave the Liddell sisters Holiday House (1839) as a Christmas present, which broke from tradition as a children’s book by encouraging imagination rather than merely moralizing. In the story, a brother and sister full of energy and plans are overseen by a prickly governess and amused by a humorous uncle who likes to tell stories. The book was a model for Carroll’s own, and Wonderland was loved by children and adults as it mocks moralizing authorities talking down to subordinates, much as a governess does to children. Carroll would marvel at high-born children lecturing servants as if the servants were the children, which is how the lower class were treated. In a letter to a child sent with a different book, Carroll said the book has a moral, so it need not be mentioned that it is not a book by himself. Like Poe, Carroll doesn’t say all he means, nor does he say we ever can.
Morals are mocked often in Alice’s adventures, but they are a part of growing up, even if adults remain absurd. Several times Alice is asked to recite nursery rhymes, not because they are useful information to adults but because they teach children to obey and repeat adults and themselves, and Alice mis-recites the rhymes, creating more entertaining and dangerous versions in spite of herself. Carroll wrote silly poetry as a child for his sisters and brothers with mock Victorian morals such as Don’t dream and Never stew your sister. One poem mocks Christian hypocrisy, saying, If you are able, don’t have a stable, with any mangers; Be rude to strangers, followed with the overall moral Behave. Another is worth quoting in full:
I have a fairy by my side, which says I must not sleep, When once in pain I loudly cried; It said, “You must not weep.” If, full of mirth, I smile and grin; It says, “You must not laugh”; When once I wished to drink some gin; It said, “You must not quaff.” When once a meal I wished to taste; It said, “You must not bite”; When to the wars I went in haste; It said, “You must not fight.” “What may I do?” at length I cried; Tired of the painful task. The fairy quietly replied, and said, “You must not ask.” Moral: “You mustn’t.”
When he first tutored in college at Oxford he wrote to his younger sister and brother mocking his position of authority as if it was a nonsensical child’s game of telephone. The most important point, Carroll assures them, is that the tutor should be dignified, at a distance from the student, and the student should be degraded as much as possible, otherwise they are not humble enough, so he sits at the furthest end of the room, and outside the door, which is shut, sits the scout, outside the outer door, also shut, sits the sub-scout, half-way down the stairs sits the sub-sub-scout, and down in the yard sits the student, outside. In lecture the tutor shouts, What is twice three?, the scout, What’s a rice tree?, the sub-scout, When is ice free?, the sub-sub-scout, What’s a nice fee?, and the student timidly suggests, Half a guinea?, the sub-sub-scout shouts, Can’t forge any!, the sub-scout, Ho for Jinny!, the scout shouts, Don’t be a ninny!, and the tutor looks offended, but tries again with another question.
Carroll’s father was quite conservative and fond of traditional authority, unlike his son who was socially and politically on the fence. In some causes Carroll supported conservative authority, and in others progressive acceptance, what was known as the Hight Church and the Broad Church to Anglicans at the time and widely debated. Carroll’s father argued in several High Church sermons that traditional dogma is necessary for salvation and grace, while Carroll sought out liberals such as Maurice, leader of Broad Church liberalism and founder of Christian Socialism, and shared his beliefs that eternal damnation was superstition and that salvation is not for those faithful to doctrine or denomination but for those who love others as Jesus did. Maurice was accused of heresy and expelled from his post as professor of divinity at King’s College, London for his rejection of eternal punishment in his sermons.
Carroll wrote in letters to friends that beliefs are unnecessary for salvation, that many non-believers would be surprised when they were saved by Jesus at the end of time, and that if he thought the Bible taught eternal torment he would give up the Bible. If he had publicly stated these positions, he would have lost his teaching position like his friend Maurice. On a trip to Russia he enjoyed visiting Catholic and Orthodox churches, Jewish temples, and Islamic mosques. Carroll described himself as both High and Broad Church at different times, and in one letter he wrote to a Mrs. Rix, “I myself belong to the ‘High Church’ school,” but six months later he wrote to Rix’s daughter Edith, “I hope you won’t be very shocked at me as an ultra ‘Broad’ Churchman,” possibly hoping the mother and daughter would talk and find out he was telling the elder he was conservative and the younger he was liberal.
Mean What You Say & Say What You Mean
At Oxford, Carroll would have learned ancient Greek classics such as Plato and Aristotle but not modern philosophers such as Leibniz, Kant or Mill, whether or not they were German idealists or British empiricists. Philosophy and history were not Carroll’s strong subjects, and even though he dedicated his Symbolic Logic to Aristotle’s memory, he also wrote that Aristotle, “scarcely deserved being called a philosopher,” “wanted concord and unity in all things so much, that he erected a lofty structure upon feeble foundations,” and criticized his syllogistic logic as “an almost useless machine, for practical purposes, many of the conclusions being incomplete, and many quite legitimate forms being ignored.” Carroll created a counting board method of placing tokens on a square somewhat like Aristotle’s square of opposition and similar to Venn’s circular diagrams to make greater sense of Boole’s algebraic formulations. Wittgenstein’s truth tables later filled this role after Frege and Russell.
Studying Islamic, Christian and European logic, we can see that logic becomes algebraic, abstract and symbolic but also retains its objective force in the mind, such that De Morgan, Boole and other logicians in Carroll’s day joked that a syllogism can be completely valid but the conclusion false if the structure follows but the starting premises are false. Carroll wrote in the preface to his Game of Logic that, “It isn’t of the slightest consequence to us, as Logicians, whether our Premises are true or false: all we have to make out is whether they lead logically to the Conclusion, so that, if they were true, it would be true also.” The example I use to teach the difference between truth and validity is, If puppies are green and green things are involved in evil, then puppies are evil, as the premises and conclusion are false, but the logic follows and structure is valid. When the pigeon of Wonderland reasons that she doesn’t know what little girls are, but if they eat eggs then they must be some kind of serpent, she is reasoning validly and in accord with her interests, whether or not we think she is right.
Carroll was interested in cases when mathematics looks like it would work according to the formula but does not apply to actual situations, much like syllogisms being valid whether or not they are true in the slightest. For example, he would pose what he called The Wall Problem to his students: If it takes 10 men so many days to build a wall, how long would it take 300,000 men? As the students began to calculate in their heads, Carroll would comment, disrupting their process, “You don’t seem to have observed that that wall would go up like a flash of lightning, and that most of those men could not have got within a mile of it.”
Carrol argues in his work on logic that a form doesn’t have one necessary meaning, but neither does a meaning have one necessary form that expresses it, asking, “Is it better to say ‘John is-not in-the-house’ or ‘John is not-in-the-house’?… This is no question of Logical Right or Wrong: it is merely a matter of taste, since the two forms mean exactly the same thing… The fact is, ‘The Logicians’ have somehow acquired a perfectly morbid dread of negative Attributes, which makes them shut their eyes, like frightened children, when they come across such terrible Propositions as ‘All not-x are y’; and thus they exclude from their system many very useful forms of Syllogisms.” Logicians are frightened of types of non-being, so they insist that there are single forms of expression and single meanings of expressions because they are afraid of change, variety and the unknown. Forms can have various meanings, and meanings can be expressed with various forms.
Carroll wrote to Alice and her sisters that their saying his fictional Sea Dirge is ‘Not true’, was, “rather a sweeping condemnation.” It is sweeping, whether or not it is justified. Carroll considers the mathematical problem of determining the value of examiners when no examinations are held. Much like later Wittgenstein, who asks what a train station means on Mars and quotes Carroll in his work, this suggests logic is a matter of taste and practice, not absolute, exclusive, singular forms or meanings. Carroll argued that Christian beliefs are axioms, like those in mathematics and science, “quite incapable of being proved, simply because proof must rest on something already granted”, and that if one accepts an axiom but another does not, then no useful discussion can be had. Much like De Morgan, he wrote:
The writers, and editors, of the Logical textbooks, which run in the ordinary grooves… speak of the Copula of a Proposition ‘with bated breath,’ almost as if it were a living, conscious Entity, capable of declaring for itself what it chose to mean, and that we, poor human creatures, had nothing to do but to ascertain what was its sovereign will and pleasure, and submit to it. In opposition to this view, I maintain that any writer of a book is fully authorized in attaching any meaning he likes to any word or phrase he intends to use. If I find an author saying, at the beginning of his book, ‘Let it be understood that by the word black I shall always mean white, and that by the word white I shall always mean black,’ I meekly accept his ruling, however injudicious I may think of it. And so, with regard to the question whether a Proposition is or is not to be understood as asserting the existence of its Subject, I maintain that every writer may adopt his own rule, provided of course that it is consistent with itself and with the accepted facts of Logic.
At Cambridge, Carroll’s friend Maurice openly fought the Utilitarian Benthamites, the dominant philosophical party at Oxford who argued that there is a collective form that should be best for everyone, and Carroll wrote to a student who told him she liked figure drawing more than he did that a unit of pleasure could be standardized as, “the pleasure felt in eating one penny-bun in one minute”, and that she should calculate how many units of pleasure she derived from figure drawing and compare it to his own self calculation of 235, which is mocking Mill’s utilitarianism as well as Bentham’s idea of a felicitous calculous, a form we can use to calculate what pleases everyone the most.
Maurice attacked those who “pull down other men’s truth because it is not the same position as their own,” and that evil exists in “the inclination of every man to set up himself, to become his own law and his own center, and so to throw all society into discord and disorder.” Carroll argued that utilitarian justifications for animal experiments was “worship of the self,” and in an editorial letter to the Pall Mall Gazette entitled Vivisection as a Sign of the Times, signed Lewis Carroll, he wrote: “The enslavement of his weaker brethren – the labour of those who do not enjoy, for the enjoyment of those who do not labour – the degradation of women – the torture of the animal world – these are the steps of the ladder by which man is ascending to his higher civilization.” He argued that harming animals results in the degradation of humanity, and speculated that experimentation on criminals and the incurably insane was possible in the future, predicting Mengele, the Tuskegee study and many other atrocities.
Carroll studied and taught Euclid’s Elements, central to his education and used in Victorian England to train the mind for rational thought, but there were many versions that differed in style and content, and Carroll was critical of those that mangled the original. Euclid listed five postulates, what Carroll described as “something to be done, for which no proof is given”. The first three are, 1) Let it be granted, that a line may be drawn from any point to any other point, 2) That a line may be produced (lengthened) to any extent, and 3) That a circle may be drawn about any point, and at any distance from that point. In The Dynamics of a Parti-cle, Carroll satirized the party politics of a parliamentary election for the representatives of Oxford University with postulates that parody Euclid’s, writing,1) Let it be granted, that a speaker may digress from any one point to any other point, 2) That a finite argument (i.e. one finished and disposed of) may be produced to any extent in subsequent debates, and 3) That a controversy may be raised about any question, and at any distance from that question.
As Carroll wrote the Alice books there were growing calls for examinations to be based on more than just Euclid, and an Anti-Euclid Association formed. Carroll wrote his Euclid and his Modern Rivals (1879) in protest, pitting Euclid against a German professor who argues for any thesis, true or untrue, mocking Hegel’s dialectics, no doubt, and who argues for each of the positions of the modern rivals. A procession, which mocks the Anti-Euclid Association, includes Nero carrying his unfinished Scheme for Lighting and Warming Rome and Guy Fawkes, president of the Association for Raising the Position of Members of Parliament. It is said Nero allowed Rome to burn, and Fawkes tried to blow up the parliament building with dynamite, with the members of parliament inside, which would raise their position considerably, but only for several seconds. Carroll rejected non-Euclidean geometries as irrelevant to our geometrical world, which is ironic given one of the three primary non-Euclidean geometries is spherical, and Euclid likely thought the Earth was flat, like his geometry.
When Carroll died in 1898 he was famous as the author of the Alice books, but both he and Oxford were embarrassed by the association with popular children’s literature, so even though he was widely famous and had lived at Oxford for almost half a century, they made no effort to preserve his papers or library, destroying his papers and selling off his books as quickly as possible. Carroll had many books on many subjects, including two books on Poe, a few on narcotics, and many on women, which the introduction to his published library says, “suggest that at least he kept himself informed about the theory even if he avoided the practice.”
The only ancient philosophy is Aristotle’s Poetics and Cicero, and the only modern philosophy is Locke’s Philosophical Works, though he also had Hume’s History of England, as well as much of Mill’s work on logic and society. He had many books on culture and folklore of the world, including esoteric Buddhism, the psychology of Shakespeare, Chinese drama, Swahili tales, African American experiences, Indian poetry, Japanese fairy tales, Kipling’s Jungle Book, popular German stories, the Arabian Nights, the conquest of Peru and realities of Irish life.
Many of his books, not as many as about folklore but many more than philosophy, were about logic, including Mill, Sidgwick, Venn, Boole, Mansel, De Morgan, and others. In the Alice books, there are continuous problems involving gathering and dividing by sameness and difference in the world, the central problem of Mill’s inductive logic. Boole’s work dominated logic in the later 1800s, except at Carroll’s Oxford where it got little attention, but Carroll was privately working on his own Logical Algebra to get, in his words, “a simpler notation that Boole’s.”
At the end of Alice’s adventures she sits between the Red and White Queens, like a Boolean OR between NOT and AND. The Red Queen is negative, judgmental and limiting, like a close-minded, bossy adult, the White Queen is positive, forgetful and inclusive, like an open-minded impressionable child, and neither are simply good nor bad, as Alice needs to grow into the OR, to choose between judgement and forgiveness, between being the adult or the child as needed in her world, as Carroll did with children and adults. Carroll said resolving a contradiction is sometimes simply asking which overrules the other.
William Bartley argues Boole and Carroll worked on logic just before it was formally codified by Frege and Russell into the basis of formal logic today, and that most textbooks don’t teach logic as a useful exercise in situational thought, such as that found in the twists of detective stories, mysteries and comedies. Rather, formal logic sets up exercises to prove the formal foundations of mathematics can lead validly from premises to conclusions, but unlike any other form of mathematics we are given the answer and told to solve for it, and unlike life it is irrelevant whether the premises are true, merely that they can lead to the prescribed conclusion. This is useful for the committed formal logician but not for anyone else who wants to better exercise reason, and so Bartley lends his name to the movement for practical, informal logic, and argues we should go back to Carroll to teach logic in ways that actually benefit the public in daily life.
Some of the more interesting answers to the syllogistic puzzles Carroll invented as exercises, answers that are only given in the answer key, are, No lobsters are unreasonable and so they don’t expect impossibilities, Some things meant to amuse are not Acts of Parliament, Babies cannot manage crocodiles, Guinea pigs don’t really appreciate Beethoven, Some mischievous creatures are not soldiers, No banker fails to shun hyaenas, Some fierce creatures don’t drink coffee, Opium-eaters do not wear white kid-skin gloves, No hedgehogs take in the Times, Rainbows can’t bear the weight of wheel-barrows and thus cannot be used as bridges, No Member of Parliament should ride in a donkey-race unless he has perfect self-command, Logic puzzles me and so it isn’t intelligible, and All these riddles that can’t be solved interest me.
I am working on an interpretation of Alice in Wonderland and Through The Looking Glass which centers on the major logical and ethical ideas of Aristotle. I believe that the ten categories of Aristotle, one of the first major lessons of the Organon, Aristotle’s collected works on logic, plot out chapter by chapter much of what happens in both books, and the two books mirror each other with each categorical theme chapter by chapter. I am posting day by day with my serious findings and silly suspicions.
Lewis Carroll in Numberland by Robin Wilson, Norton 2008
The Hunting of the Snark (1876) Definitive Annotated by Gardner, Norton 2006
Beyond Wonderland by S.I.B. Gray, Math Horizons vol. 6 No. 4 April 1999, pp. 18-23
Lewis Carroll: A Biography by Michael Bakewell, Heinemann, London 1996
Lewis Carroll: A Biography by Morton N. Cohen, Alfred A. Knopf 1995
Lewis Carroll’s Symbolic Logic, ed. by William Warren Bartley III, Potter, NY 1977
To Catch A Bandersnatch, by Mark Burstein, 1970
There is no assignment for this week. Work on completing the assignments so far.