Ludwig Wittgenstein (1889 – 1951) is my favorite of the latest, greatest philosophers, and I learned his work from Hans Sluga and Barry Stroud at Berkeley, who taught me that Wittgenstein’s later thought experiments can lead to much more than he or we have worked out about truth and meaning. Wittgenstein’s thinking can answer many questions about thinking, not completely but more fruitfully, as Wittgenstein says, than other thinkers can.
The turn between Wittgenstein’s earlier and later thought is much like the Indian metaphor of turtles supporting the world and the question that arises from such an arrangement. Locke, Hume, Russell and other European philosophers have brought up the Indian debate about what the world sits on such that it is stable and continues. Some say that it sits on a turtle, an animal that symbolizes the cosmos in India and China, as it is flat on the bottom like the earth, and round on the top like the sky. Others ask what the turtle sits on if the world sits on it, and someone once said it’s turtles all the way down. Some have called this an infinite regress, an endless series that vanishes over the horizon, Buddha called it an unsolvable problem, Plato called it the greatest difficulty for philosophy, and today some call it the foundationalism debate, arguing whether or not knowledge or certainty sit on anything known or certain.
Philosophy is the love and study of wisdom, truth, meaning and thought. Thought interweaves several elements in our world. We sense, see, hear, touch, smell and taste things in our world. We also feel, feeling good, bad, tense and calm about the things we sense. We also remember, sense and feel things that are not in our world, but were. We also reason, building what we remember from sense and feeling into thoughts. In the middle of all this are words, things we hear and see from others that are interwoven with what we sense, feel, remember, and think.
Is sensing a thing without words, feelings or memories a thought? Is looking at an apple thinking? Is looking at it and feeling a feeling thinking? If I look at an apple and feel happy, is that a thought without words or images in mind? Some say yes, and others say no. Once we have several things interwoven, including the words we use to mean things, many call that thought. Some say thought is logical and rational, such that it follows rules, or follows rules when it is right and correct in judgement. Others say that this is the turtle problem yet again.
If things need thoughts to make sense of them, and if thoughts need thoughts, such as rules, or plans to make sense of them, is there thought that makes logical, self-aware, rational sense of thought itself? Are there words that make sense out of how we use words to mean things and know things? Some say yes, and it terminates in the rules and forms of logic, and others say no, and we simply continue to gather and divide things without an underlying logic that brings all of our wants and plans into common, coherent systems, visions or words. As Zhuangzi the Daoist asks, What do our ways or words rely on such that our words mean things?
What do turtles sit on? Some say other turtles. The Buddha in India and Wittgenstein in Britain answered the question with similar, simple metaphors that show us more than any system or logic in images or words can completely in itself. Thought and our world are interwoven, such that it isn’t turtles all the way down, but turtles all the way around. Much as Nicholas of Cusa and Hegel said about a circle, it is an infinite regress, but it is also complete in itself, and continues right in front of us. It isn’t that truth or rules rely or rest on any specific thing, but rather situations of sense, feeling, memory, reason and words mean things all together.
Situations shift, and these shifts show us how things mean things to us better than any specific words can. As Wittgenstein said, there is what can be said, but what can be said is only a part of what can be shown, which is best done not with complete, enclosed systems of words or images but by leading people through many open-ended situations of mind, stagings of thought, what Wittgenstein called thought experiments that involve many and any elements.
Much as Alice is frustrated with her sister’s text without pictures in the opening of Wonderland, words and rules without many interrelated examples of rich situations and the infinite variety found in them confuse us and lead us into considering words outside of actual, useful meaning. Carroll wrestled with Boole’s algebra much as Wittgenstein wrestled with Frege’s logic, and both came to the conclusion that words and systems can trap us like a fly in a bottle.
As Zhuangzi said, once we have the rabbit, we can forget the trap, and then we can involve the trap or not as we like, such that we can have words with others who have forgotten words, remembering and forgetting words and understandings freely as we please rather than sitting on particular words or systems as final, fixed foundations. Wittgenstein enjoyed reading Alice’s adventures to two sisters in Wales where he worked on his final thoughts, and he likely heard and felt Carroll’s deeper meaning, that it is good to use thought, rules and logic to show others how open-ended thought can be, beyond anyone’s particular logic, words, thought or feelings.
Buddha called the interweaving of everything codependent-arising, life as a tangle of many forms of life, as we see in Klimt’s painting Death and Life, which he began in Vienna 1908 and finished in 1915, the time Wittgenstein left Vienna to study logic, mathematics and philosophy with Russell at Cambridge. Klimt was not only one of the most influential painters of Wittgenstein’s Vienna, he painted a portrait of Wittgenstein’s sister, who was also psycho-analyzed by Sigmund Freud. As we might suspect, Wittgenstein’s family had some pull in Vienna, which in Klimt’s day was the city with the latest, greatest culture, replaced in the 1920s by Paris, the 40s by New York and the 60s by San Francisco. Wittgenstein said that life and thought are like an old city, with many forms of life inter-tangled for centuries.
Much as Buddha taught there is no essence or nature that completely defines or causes a thing because it arises out of the relationships it shares with other things outside of itself, Wittgenstein argued that life is like a thread without a single strand running through the entire length, and so we should always beware of the lure of the secret cellar, the proud idea that we have hit bedrock and completely revealed the truth rather than revealed yet another strong connection between different interwoven things. The cure for this proud ignorance, what Heraclitus called the human disease, is a rich variety of interwoven examples and elements that continue to show us more and more about the greater whole, endlessly.
I have been working on Lewis Carroll’s Alice in Wonderland and Through the Looking Glass for many years now to find the logical and philosophical forms hiding inside it, and as I have been teaching logic this semester I have used the class as an excuse to go over Aristotle, Boole and Carroll’s work carefully. In the process, I have found many Aristotelian and Boolean forms that are structural to both works that I have never seen before.
Aristotle’s four “perfect” syllogisms and Boole’s inclusive and exclusive operations of AND, OR and NOT, gathering and dividing as John Stuart Mill would say, form the positions and plot of both Alice books. Carroll was studying the logic of Aristotle, Mill and Boole as he wrote both of Alice’s adventures, visually presenting logic as characters, but also as emotions, as inclusive and exclusive feelings that operate in our thoughts and our world together. Carroll was trying to show us that syllogisms and logical operations are series of emotions, of feelings that gather and divide things in sequences as the underlying structure of thought with the underlying structure of his stories about Alice.
In the first book of Wonderland, Alice works her way from an inclusive AND, the White Rabbit, past the inclusive OR of the caterpillar, the exclusive OR of the Cheshire Cat, to the NOT of the Queen of Hearts, who chops off heads. The various symbols for NOT Boole and other logicians use look a bit like an ax next to a capital letter, a symbol for a group much like a regal head who stands for the common people. Alice says it is all a pack of cards, meaningless manipulation of symbols and pieces regardless of meaning, and disrupts her imaginary dream.
The White Rabbit is like an addition problem, an AND, Alice and her older sister, inclusive of different elements, the two sisters, and exclusive, specialized and late to a specific event at a precise time. This makes the White Rabbit an absurdly rational animal, as Aristotle would say, both man and beast. Alice, bored with her sister reading to herself, charges after the White Rabbit down the rabbit hole, with no thought as to how she would get out again, like a wildly inclusive child, mirroring the absurdly inclusive combination of a rabbit with a waistcoat, and unlike her sister, who is carefully considering a specialized text. Alice dreams she follows the absurdly complex White Rabbit as she can’t follow her sister in reading a boring specialized text that gathers a very narrow sort of element. A child needs emotions, pictures, words and many things to stay interested in a story.
In the second book of the Looking Glass, Alice works her way from the Red Queen, another NOT like the red Queen of Hearts, past the White Queen, a childlike inclusive AND, timid like the White Rabbit, to the end of the board where Alice is the OR, who must inclusively and exclusively choose between inclusive AND, the White Queen on her right, and exclusive NOT, the Red Queen on her left. The Queens test Alice and find she can’t inclusively add or exclusively subtract things the ways they ask her to, they take her to a banquet where food turns into people and people into food, and Alice hates it and turns the table over, upsetting her second dream. Wonderland works from childlike AND past OR to adult NOT, from inclusion to exclusion, and the Looking Glass works from adult NOT past childlike AND to bring the childlike-adult balance of OR, both inclusive and exclusive.
The four royal pieces of the Looking Glass world, the Red Queen, Red King, White Queen and White King, are the four corners of Aristotle’s Square of Opposition, a visual presentation of logic popular in Europe for centuries. The White Queen, inclusively open like a child, is the universal positive (All, All, All), the Red Queen is the universal negative (All, None, None), the White King is the particular positive (Some, All, Some) and the Red King is the particular negative (Some, None, Some-Not). In the end, Alice sits as an inclusive-exclusive OR between All and None, as the one who must decide for herself, with her powers of logic and reason, some and some not like an adult between the extremes, as Aristotle advises us in ethics. There are countless examples of syllogistic reasoning in both texts, but here are central examples that show each royal chess piece as an Aristotelean corner.
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.
If you are interested in more, please read my lecture on Logic, Lewis Carroll and Alice’s Adventures, which is very much under development and in progress at the moment, as can hopefully be understood. It may turn out that all negativity is merely a playful, innocent kitten after all.
Gottfried Wilhelm Leibniz (1646 – 1716 CE) was a German philosopher and mathematician who invented calculus around the same time as Isaac Newton. Newton tried to confusingly name everything after himself, with many types of newtons, so science kept one kind, the newton as unit of force, and used Leibniz less self-serving system of notation for the rest of Calculus and physics instead. Leibniz’s first job was alchemist’s assistant, and then he became a lawyer’s assistant, perhaps with more worldly success. Leibniz published little during his lifetime, and to this day no definitive collection exists of his various and disparate writings. His most famous writings are his Monadology and his Discourse on Metaphysics.
Leibniz invented the binary system still used by computers today, which may or may not give way to something else like quantum computers in the future, which do not rely on two separate values such as 1 and 0. Leibniz was a sinophile, who loved Chinese culture, studied Chinese thought that was available to him, and invented his binary system inspired by the Yi Jing (I Ching), the ancient Chinese binary divination system that represents all possible situations with solid and broken lines just as Leibniz’s binary system represents all numbers with ones and zeros. Leibniz was communicating with Christian missionaries in China, and he, like some of the missionaries, believed that Europeans could learn much from Confucianism that was in line with Christianity. An admirer of the Chinese abacus, Leibniz was one of the most important innovators of the mechanical calculator, an early computer which employed his binary system.
Like Descartes and Spinoza, Leibniz believed that God created the world as a rational, mechanical apparatus. Because of this, Leibniz famously argued that this is the best of all possible worlds. As God is omniscient, God was aware of all possible worlds before creation, and chose this to be the created world, so it must therefore be the best. Of course, many who ponder the problem of evil, the theological problem debated for centuries about how suffering in a rational world is possible, would question this assertion. Leibniz came up with a pure deductive understanding of the world, which was quite unlike how we experience it. The infinite, the eternal, is for the mathematician Leibniz an infinite series of distinct points, the elementary particles of the universe, eternal and indivisible, like the atoms (“without cut”) of the ancient Indian and Greek atomists. This infinite plurality is entirely made of mind, and each is its entire universe, what Leibniz calls a pre-established harmony.
Leibniz is a strange, outlying philosopher, one I mention but don’t cover extensively for Modern European Philosophy, but he is very important to the history of logic, not only because he helped invent the binary computer, which is where many modern logics live, but he is also one of the first to articulate something Aristotle argues for but doesn’t draw into an explicit principle, what some logicians still call the Law of Non-Contradiction, but most others refer to as the Principle of Non-Contradiction, as it is more understood by secular scholars today as something psychological, but was, for Aristotle, Avicenna, Aquinas and others a law of the universe, one that Nagarjuna of India, Heraclitus of Greece and Hui Shi of China would certainly deny.
The Principle of Non-Contradiction, or PNC for short, can be stated as: If a statement is true, then its negation is false, and if a statement is false, then its negation is true. For example, if the statement Leibniz is a logician is true, then the statement Leibniz is not a logician is false, and vice-versa. Kant and Russell, advocates of logic and the Principle of Non-Contradiction, studied the work of Leibniz intensely, advocating this principle. Russell, who founded Logical Positivism, the basis of Analytic Philosophy, the dominant school of philosophy in the Anglophonic world, argued that we can base all logic, mathematics and certain, objective science on the single truth of the Principle of Non-Contradiction. In formal logic, Graham Priest at CUNY is one of the most famous critics of the principle, arguing, like Hui Shi and Heraclitus, that at least some contradictions are possible, such that Leibniz could be a logician but also not in different ways for different purposes which are both valid.
What is a contradiction? It is an argument, between sides, in its most visible and audible form. We can contradict ourselves, and argue with ourselves, which isn’t the same thing, but similar. A simple contradiction in speech, between two sides, whether or not there are one or two people, or more, is I turned the lights off and No, you didn’t, which is a difference of opinion. If we assume there isn’t a relative dimmer switch, and the lights could go more on or more off, then one side is right and the other side is wrong. Switches are designed as bifurcating devices, as a serious dilemma that could go one way or the other, like the contradiction over the switch. Checking to see if the lights are on or off can resolve the dilemma, debate and contradiction, unless there is a twist, and it turns out, given further evidence and experience, that the switch doesn’t work, or the lights were turned off by someone else later, or its the wrong switch, or the wrong set of lights that should never be turned off, unlike all the others. Even given the simple, bifurcating device of the switch there is a complex human situation that can easily involve contradiction between differently interested parties.
If this is what a contradiction is, then what is the principle of non-contradiction saying? That people can’t get into debates? Aristotle, like Kant long after him, and like Russell long after Kant, argued that not all questions can be solved correctly, but some can, and it is the task of the human mind to use reason to solve what can be solved completely. As for favorite flavor of ice-cream, there are some flavors that would turn heads in many cultures, but it is a matter of subjective taste and opinion. However, insofar as math and logic are supposed to ideally work, in these matters and questions there are true, objective and singular answers that are not relatively true, but absolutely true, much as many would say that two and three together making five is universally, objectively, absolutely and even ideally true, beyond practices or culture.
The principle of non-contradiction applies to these truths, such that if someone contradicts what is absolutely true, they are necessarily wrong. If two and three make five, in all possible ways, then anyone who says two and three make four or six is simply and completely wrong, regardless of their upbringing, practices, cultures, or success, as it is not about what pragmatically works, but what is positively true. Much as Kant argues about morality, it isn’t what keeps the ship sailing, but what is true that we should believe, even if it means disaster and we all go down with the ship, because right is what is overall important, not results. This is the major issue we will talk through again in many ways between positivism and pragmatism.
Aristotle, Farabi, Avicenna, Aquinas, Leibniz, Kant and Russell are some of the central thinkers who made the principle of non-contradiction what it is today. Aristotle said that skeptics like Heraclitus are no better than plants, understanding nothing. Avicenna said those who say fire and beatings are and are not good, only relative evils, should be burned and beaten until they stop saying such things, which is hopefully a joke at the expense of skeptics like al-Ghazali, the Sufi mystic, who criticized Avicenna and was criticized by Averroes. Russell argues that Mill, Dewey and all other instrumentalists, utilitarians and pragmatists, who argue truth is not ideal but relative cannot say anything with certainty, and have to investigate all possibilities continuously to absurdity, such as wondering if we truly did have coffee with breakfast.
I suggest Wittgenstein was right, as a pragmatic person myself, when he said the trick is to see we can stop and start doing philosophy when we want to, as we may never hit bedrock and have the final understandings or answers to anything. Like Priest, Wittgenstein wrote that contradictions need not be false. Logic which excludes all contradictions as nonsense is only a small part of the ways we use language. Lewis Carroll certainly thought so. Aristotelian logic is not the genuine basis of all reasoning any more than trigonometry is the genuine basis of all geometry. (LWPP1 525) The logic of language is more complicated than it looks. (LWPP2 44)
Wittgenstein wrote that some believe in the excluded middle, that a statement cannot be both true and false, but it is rather that true and false divide the field of possibilities, but not always into exclusive parts. Wittgenstein gives the sad example, “Have you stopped beating your wife?” which is not simply a yes or no question, as if someone has never beaten their wife, it is true in one sense, as I am not currently engaging in domestic violence, and false in another, as saying yes implies that I used to, in a way that resembles subalternation. (RPP1 274) The comedian Mitch Hedberg joked, I used to do a lot of drugs… I still do, but I used to, also. Wittgenstein said contradictions are not catastrophes to be feared and avoided, but problems that require engagement with contrary judgements. (Z 685-9) This is likely why Wittgenstein had a deep appreciation of the nonsensical problems found in the arguments of Wonderland.
I I tell you A is true and false, am I telling you nothing, or am I telling you a great deal? If I say nothing I say nothing, even if the silence implies something significant, but if I say something contradictory, that Steve is good and Steve is not good, that the girl with the curl in the middle of her forehead is sometimes very, very good, but when she’s bad she’s horrid, I’m saying at least two things, if not implying more. An argument tells us a lot about both sides, and often shows us things both sides can’t fully see about each other. Humor and nonsense are directly contradictory, just as fantasy contradicts reality by degree, and they teach us much about us.
Leibniz has two other principles which are important in the history of formal logic, and which Kant and Russell both support. The second is the Principle of Identity of Indiscernibles: If two things are without any discernible difference, then they must be not two things, but identical, the same single thing. Of course, if two things are in different locations or exist at different times, this is a discernible difference, one that would shoot any instance of the principle down. Many illustrate this today with the example of two types of minerals labeled equally as jade in ancient China, before humanity had the technology to tell the difference.
The third is the Principle of Sufficient Reason: If something exists, there must be a reason why it exists the way it does. Leibniz believes that the world was teleologically created by God, who controls all in this best and most rational of all possible worlds, and so he assumes that each thing can be rationally explained because each thing was rationally created by an intellect superior but similar to our own. Many secular modern people hold this principle, but without teleology it is difficult to argue that humanity can come up with intelligible reasons that explain apples entirely, or anything else. Are there sufficient reasons apples exist and behave as they do? What is sufficient enough for this? Is it to our satisfaction, or are there objective reasons, in number, that exist independently?
There is one last principle that should be mentioned and strangely isn’t as much, the Principle of Bivalence: A statement must be true or false, not neither true nor false. This is somewhat the inverse of the Principle of Non-Contradiction, that a statement must not be both true and false together, which is the third of Nagarjuna’s four things, and the Principle of Bivalence is the fourth. Leibniz, Kant, Russell and others are focused on non-contradiction, not bivalence. This could be because Aristotle himself wanders in his answer whether neither good nor bad is both or neither, and concludes it is more-so, relatively speaking, neither, which means Aristotle allows for Nagarjuna’s fourth but not third thing. It seems those who argue for non-contradiction think both sides can’t be right, but both sides could be wrong, as if correct is exclusive, but incorrect is inclusive, regardless of how much we all have common sense.
This is the first in a series of my distillations of the Long Discourses of the Buddha (the Digha Nikaya), the Buddha’s original teachings shortened for easy reading.
In the first of the Long Discourses, the Brahmajala Sutta (The Supreme Net), the Buddha is traveling with 500 monks from town to town, and unwittingly followed by Suppiya, a teacher who criticizes the Buddha, and Brahmadatta, Suppiya’s student who praises the Buddha. It seems that positive and negative opinions and arguments about the Buddha follow him and his followers wherever they go. They all stop for a night at a park with shade and water provided by royalty and guarded with a wall for travelers to rest along their way. In the morning, followers of the Buddha were talking about how wonderful it is for the Buddha to be aware of the varied opinions that follow him.
The Buddha hears them and says that they should not be angry with anyone who criticizes him, his teachings or his followers, as this will hold them back and prevent them from seeing if the criticism is right or wrong. Rather, they should explain what is wrong with the criticism. Similarly, they should not be pleased by those who give praise, as that will also hold them back. Rather, they should explain what is right with the praise. The Buddha says that only foolish, worldly people praise him for abandoning violence, sex, lies, entertainment, luxury, property, and servants, for doing the right thing and saying the right thing at the right time and to the right extent. Only foolish, worldly people criticize his opponents, such as the Hindu Brahmins, for acting in ways that lead to addiction and destruction, speaking about useless things, claiming to know what others do not in debate, running errands for those in power or misleading others with expert advice and fortune telling.
Rather, there are other things that are hard to see and beyond ordinary thought that the wise can know that do deserve praise. Neither discipline nor reason can reveal these things. The particular knowledge that these practices reveal leads to further birth and death, but being unattached to this itself is to know true peace and freedom. Each time the world is reborn, God (Brahma) becomes lonely and creates the other gods and beings. Later, those who seek wisdom beyond the home discover that things are impermanent, pleasure is addictive and logical reasoning gives stability to the ideas of the mind, and they split into those who believe that the self and world are permanent and those who do not (“Eternalists and Non-Eternalists”, also the “Infinitists and Finitists”).
Some argue that things are permanent, others that things are impermanent, others that things are both permanent one way but impermanent another, and others that things are neither in any particular way. (These are the Catuskoti of Nagarjuna.) Similarly there are those who debate whether we know what is good or bad, those who debate whether or not there is life after death in another world beyond this one, those who debate whether things happen by chance or necessity, and those who debate whether enlightenment and freedom are here now or somewhere else.
These “wriggly eels” on each side evade questions in debate that they can’t answer. Those who take one side against the other do not see the fear and chaos that makes them and the other cling to one side, nor do they see that clinging to one side will not bring them peace or safety, but merely trap them in a vast, intricate net, like a fish too large to swim between the knots. When anyone sees what is beyond all these sides, they see what only the wise can see, the supreme net of all possibly viewpoints and the superior victory over all battles.
Zen Speaks is a modern collection of Zen stories and koans by the author and artist Tsai Chih Chung that I highly recommend which contains wonderful cartoon renderings of many of the koans and stories we’ve already covered. I just found out that you can watch the entire work as a cartoon in Cantonese with English subtitles on YouTube.
In Zen Buddhism, the 77th case of the Blue Cliff Record is cake. A monk asked Yunmen, “What is talk that goes beyond buddhas and patriarchs?” Yunmen said, “Cake.” He makes us think of cake, imagining it’s sweetness, texture and satisfaction, a strange ghost that can be raised with a single word, somewhat like the ghosts of ancestors. The thought of a cake is both a cake and not a cake, much as a rock is sometimes a rock and sometimes the thought of a rock, and thus not a rock. Whether or not this has anything to do with the buddhas and patriarchs, it certainly has to do with cake.