Logic – Wittgenstein
For this lecture, read pages 1-21 of Wittgenstein’s Philosophical Investigations.
Turtles All The Way Down And Around
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.
Wittgenstein’s Vienna & Russell’s Trinity
Ludwig Wittgenstein (1889-1951 CE) Wittgenstein had two periods of this thinking. His early work is found in his Tractatus Logico Philosophicus, the only book published in his lifetime. In this book, Wittgenstein presented the world with his truth table method of logic, which is still taught today in logic classes, thoroughly replacing Aristotle’s syllogisms. This early work was foundational for Logical Positivism and the Vienna Circle, dominating Analytic thought until the 1960s. Wittgenstein spent the twenty years between returning to Cambridge in 1929 and his death in 1951 writing, revising and reordering notebooks that would become his Philosophical Investigations and other posthumous works, arranged and published by those he trusted most after his death. He considered publishing his Investigations alongside his Tractatus to show his later thinking in contrast against the “grave mistakes” of his earlier work.
In an end of the century poll in the year 2000, philosophy professors from America and Canada were asked to list the five most important books that influenced their own work. When the results were tallied, the Philosophical Investigations was first, and the Tractatus was fourth. The Philosophical Investigations was cited far more frequently than any other book, was listed first on far more ballots, and crossed over more into many different disciplines and areas of study than any other book.
In 1911 Wittgenstein was supposed to study in Manchester after experimenting with weather-monitoring kites and dreaming of creating a better propellor than the Wright Brothers just had a few years earlier in America, but after visiting Frege he instead he went to Cambridge to hear Bertrand Russell’s lectures on logic and mathematics, and didn’t register as a student there until the following year. Wittgenstein read and adopted the idealist philosophy of Schopenhauer during his teenage years, as had Nietzsche, until he read and followed the conceptual realism of Frege. Throughout his life Wittgenstein held a Schopenhauerian belief that true freedom can only be found in renouncing will, often through the experience of art.
Wittgenstein, an eccentric and difficult personality, was never fully comfortable at Cambridge and often got into disagreements with Russell, threatening to leave many times before fleeing to Norway where he finished his Tractatus. He tried to get it published, but no one would take it, so Russell intervened back in Cambridge, wrote an introduction to it and had it published. Wittgenstein read the introduction and realized Russell had greatly misunderstood his work. Believing that his Tractatus had solved all the problems of Logic, Wittgenstein left Russell and Cambridge again and went to be a school teacher in Austria. He gave away his portion of the family fortune, anonymously to writers but also to his rich family saying, “They won’t be corrupted by it”. He left the school after a short while, became a gardener’s assistant, and then his sister had him design her a house.
Wittgenstein’s Tractatus & The Single Truth
Wittgenstein says that the fundamental idea of his Tractatus is that the logical constants of connectives such as AND and OR are not representatives of particular things or practices, siding with Frege against Mill. For early Wittgenstein, logic is not a practice of gathering and dividing things, but tracing out the structure of the single general propositional form. Logic is prior to experience, the is of things being itself in its structure, and we do not experience it, rather experience different arrangements of it. Hegel argued in his Logic that being itself does not have particular qualities or quantities, such that being isn’t always green or thirteen of anything, and so cannot be differentiated from anything else. For early Wittgenstein, all questions that can be solved by logic can be completely solved by understanding the structure of logic, and everything else is quite undetermined and contingent in our experiences.
For example, we can say that I have an apple and I don’t have an apple is a contradiction, necessarily false regardless of what is the case, and we can say Either I do have an apple or I don’t have an apple is a tautology, necessarily true regardless of what is the case, but between these two we can’t say whether or not we have an apple, or what makes it so I must have an apple, as having an apple is not essential to the structure of our experiences and is contingent on changing circumstances. We don’t always have an apple, but contradictions are always false and tautologies are always true according to Boolean algebra and Fregean logic.
Wittgenstein famously says in the Tractatus that anyone who understands it and what he means sees that the text and what it states is nonsensical, and we can toss the ladder away after we climb up and above it, much as Sextus Empiricus said of the ladder of skeptical inquiry and Buddha said of the raft of his teachings. If the Tractatus is nonsensical, why would Wittgenstein need to write it, or we need to read it or climb above it?
If logic is the necessary structure of experience, and not something possible or dependent on other things, then we do it whether or not we know it and cannot do otherwise, but we get tangled up in useless questions if we start mixing the certainties with the possibilities, the necessary structure with the contingent. If I try to understand what is necessary about having an apple, I would chase this idea and possibly not see that there is nothing there, so Wittgenstein feels the need to show us what is necessary to us and that everything else is simply dealing with the chaos of life.
This is why his Tractatus, which introduced formal truth tables as a model for logical certainty to the world, ends with the mystical and open-ended, much as Alice’s adventures end with a blank page as the final chapter, much as Locke said we are a blank page waiting to be filled. Other than the structure, nothing is necessary at all. Once we see this, and work through the basics of truth tables and how we perform operations of logic, we can see what questions are unanswerable, as well as answer all the questions that can be with complete tautological certainty, such that we are aware of what we must do whether or not we want to or know that we are, and not confused that anything else must be.
One of the fundamental problems for Wittgenstein is what he called the mystery of negation. In the Looking Glass, the White King says he wishes he had eyes like Alice’s, strong enough to see no one on the road, a negative fact that isn’t. Wittgenstein wanted to account for negation and how we can say things aren’t without dualistically separating the single, coherent, general form of the proposition, saying dualism can’t exist. When Alice says she sees no one, she is saying she sees an empty road, which is one possibility compared to and included with others, such as one, two, many or all people on the road. All the king’s men just streamed past Alice as a single army, an all compared to the none she then sees, compared to one, the king’s expected messenger, which is Carroll exhausting all the logical possibilities.
Following Frege, Wittgenstein argued that A and ~A have the same propositional structure, meaning and sense, regardless if they refer to anything, so what differs between them is not the structure but the possible truth values, which change as the structure remains the same, the underlying idea that produced the truth tables. ~A is simply another way of saying A, but when it is false, not true, inverting the same structure for an opposite use, declaring something isn’t rather than is.
The separate symbols create the illusion we are dealing with different forms rather than the single form. The truth values change, but the form remains the same, much as Aristotle said I am standing is true when it is, and then isn’t when it isn’t with the passage of time, much as Hegel said old utterances grow stale, and much as Boole places OR between exclusive NOT and inclusive AND. Wittgenstein was trying to describe the single shape of Kant’s categorical glasses.
The reason logic and tautological structures are nonsense is not because they are homicidal like the Queen of Hearts, but that quite unlike her they don’t say or judge anything to be the case. Saying I may or may not have an apple or I can’t possibly have an apple and not have one doesn’t tell us anything, but I have an apple or If I have an apple, its a Tuesday does tell us something that could be the case or not, such that anything that is meaningful, that tells us something about our world that is or isn’t the case right now, must be possible, not necessary, nor impossible.
This opens the issue that anything meaningful is also fallible, possibly wrong, because it is dependent on other things. If I tell you I’ll have an apple for you Tuesday this tells you something meaningful and also something that could possibly be wrong, which is the only way it could also, structurally speaking, possibly be true, not necessarily true or false. All of this is based, as it was for Kant, Frege and Russell, on the Principle of Non-Contradiction. While the form itself can’t be divided via dualisms, Wittgenstein polarizes the truth values.
All of the logical operations, what Wittgenstein calls the whole of logical space, are given in each and every proposition. This means that the affirmation and inclusion involved in AND, the negation and exclusion of NOT, the contingency of the OR in between, and the way IF-THEN works in all cases except where it doesn’t follow are structurally dependent on each other, with the possibilities of the others in and against the way each connective is used, whether or not we trace this out along with Wittgenstein’s Tractatus. Tautologies and contradictions are only about themselves, saying nothing about things, but meaningful, possible propositions are always about other things outside of themselves and the structure, creating not a dualism in the structure but between the structure and content, the necessary container, like the empty jars Alice falls past, and the possible contents.
Let us imagine a game played with pieces on a board, a logistical space for moving the pieces. What is on the board is true and certainly the present case. The pieces on the board and in the box beside the board contain all the pieces that can possibly be used, all the possibles and possibilities, such that if we see the pieces on the board and beside the board, we don’t know what pieces will be played but know all the pieces that could be played. A piece beside the board is false and dead, unless it gets onto the board, and then it is true and live in the game, and a piece on the board is false and dead if it is taken off the board. There are also things that are not in the game, the logical universe of discourse, the subject under discussion or consideration, and these are neither true nor false, as the are not in the cards, are not possibilities or pieces that can possibly enter the game or be negated to the side.
With this structure alone, we can exhaust all the connectives we use in formal Sentential Logic the way Wittgenstein envisioned it in his Tractatus and set it with truth tables. First, AND puts pieces on the board, including them together, but it could also, in combination with NOT, take sets of pieces off the board, adding them to the possibilities currently false rather than those currently true. NOT takes pieces off the board, or adds them if it is tied up with other NOTs. OR considers pieces, involved with whether or not pieces are moved on or off the board, completely indeterminate by itself, but determinate in combination with pieces added to or dropped from the board with ANDs and NOTs.
IF-THEN connects pieces possibly on the board together, such that one should lead to the other. Sluga argues that there are connections between things in the moment, such as speciation, with all men being mortal all at once or always, and connections between things over time, such as causation, with one thing leading to another. If the game changes with the possibilities over time, the first would be statements about the relationships between pieces at the same time, and the second different times. Bivalence, IF-AND-ONLY-IF, would simply state the relationship is reciprocal, working both ways, which would work with speciation and causation in a chicken-and-egg situation, where two things lead to each other circularly over time, again and again.
Wittgenstein’s Oven & Thinking Between Tangles
While finishing the house, he was contacted by members of the Vienna Circle, Positivists who hoped that Wittgenstein’s Tractatus could give a solid foundation for science and logic. Realizing that they had misunderstood his work much like Russell, Wittgenstein became increasingly disgusted. He began to realize that there were fundamental problems with his Tractatus and truth tables, and got into intense arguments with the Vienna Circle members, at one point turning his back on his guests and reading Tagore, an Indian transcendental poet, out loud until they left. For the rest of his life, Wittgenstein thought the Logical Positivists misunderstood his Tractatus.
In 1929, he decided to return to Cambridge to correct his thinking and teach. To his horror, when he arrived at the train station he was greeted by a vast crowd of intellectuals as the author of the Tractatus, the work he now thought was wrong. The famous economist John Maynard Keynes wrote to his wife, “Well, God has arrived. I met him on the 5:15 train“. Wittgenstein continued to lecture at Cambridge, developing his ideas. In 1934, he visited Soviet Russia and considered defecting, saying that he wanted to be a plumber and work with his hands. When he was told that the Soviets would put him to work as a philosophy professor in Moscow or elsewhere, he returned to Britain.
In one passage from Lectures and Conversations, notes of his seminar students, Wittgenstein attacked the reductionist approach of Freud, boiling all of human behavior down into the drives towards sex and violence. Wittgenstein proposes a thought experiment: If we cook a human being down to carbon ash in an oven, are we left with the essence of the human being? A human being is a carbon-based life form, so carbon is a dominant element. Consider that we could cook a human down to water in the same oven, and claim that because humans are 3/5ths water we have the essence of the person. Would it be correct to say that humans are essentially ash, or essentially wet? Why not?
A human being is a complex situation that is not reducible to a single element. The properties of carbon or water do not in themselves explain how humans behave or what they mean to us. If we cooked people down to ashes or water, we have destroyed the complex situation and can no longer investigate how they work. In the same way, a person is not merely their DNA. While carbon, water and DNA have very important, even necessary roles to play in any person, they are not exclusively the essence or meaning of the complex that is a human individual.
In the same way, Freud boils human thought and behavior down to sex as if it alone explains anything. Wittgenstein asks, what would Freud say is the secret meaning of an openly sexual dream? More sex? Wittgenstein says in the Lectures and Conversations that we have to avoid the “lure of the secret cellar”, the urge to boil situations down to a single element like Freud tried to boil human relations, meaning and the mind down to sex or Wittgenstein himself had tried to boil logic down to its simple and essential structure. Life is unfortunately not like an episode of Scooby-Doo, where problems are finally resolved after we pull the mask off the single villain, who would have gotten away with it were it not for meddling teenagers, revealing everything important and tying up all loose ends.
In the book Wittgenstein’s Poker, there is an interesting account of Popper’s infamous argument with Wittgenstein. In 1946 at Cambridge, Karl Popper gave a visiting lecture about the nature of philosophical problems to the Moral Science Club, of which Wittgenstein was the president. Popper, Russell and Wittgenstein began heatedly arguing about the nature of truth, and Wittgenstein, pacing the aisles in frustration, grabbed a poker from the fireplace and began to gesture with it wildly as he spoke. Russell asked Wittgenstein to put the poker down, but he refused.
Wittgenstein demanded that Popper give him one example of a universal moral principle, to which Popper replied, “Not to threaten visiting lecturers with pokers”. Wittgenstein, furious that Popper had made a joke rather than offer a serious universal example, dropped the poker and left the room in disgust. Clearly, Popper thought he had bested Wittgenstein, though Popper did not in fact answer the question with a universal underlying law.
Wittgenstein’s Investigations & Uncertain Situations
Wittgenstein wrote in the preface to his Investigations, which he penned before he died and was subsequently published posthumously, that he never found a satisfying order for his later thoughts because they were interconnected in complex ways, like many sketches of landscapes from different perspectives composed over long wandering journeys. The following is my attempt to weave Wittgenstein’s thoughts together to put the ideas in a more teachable sequence.
The ancient Greek philosopher Heraclitus said that all is in flux and thus we cannot step in the same river twice. Wittgenstein quoted these two thoughts in different notes, and wrote that if we want to understand life we must learn to feel at home in primeval chaos. Our world and ways of life in it continuously change, and so our lives are full of doubts and uncertainties. The bustle of life is not exactly regular, repeating itself often but never entirely, and neither are the ways we speak and think about it. Uncertainty is in the roots of life and every deep philosophical question. Wittgenstein said that this difficult point is perhaps the best place to begin our philosophical investigations, even though this is not the way the Philosophical Investigations begins, focusing rather on children learning language.
Would we want to exchange our unpredictable lives of uncertainty for predictable lives of certainty? Would we want to know what will happen to us in the future, or what exactly we will do next week? Would we want to know what others feel and think, eliminating the possibility of lies, games and mysteries? It is not clear that we would trade our lives in for certainty, as living in certainty would be quite unfamiliar and possibly unpleasant. It is quite clear that we would not trade our lives in for complete chaos. Thankfully, there are things that remain somewhat the same that we grow to trust as familiar, familiar people such as parents, family, friends, teachers and authorities, familiar objects such as food, toys, tools, and furniture, and familiar places such as home, school, parks, stores, streets, roads and trails.
We absorb the ways of each of these things as we familiarize with them growing up, learning what things are included and excluded, gathered and divided, added and subtracted, as we watch many things getting done and many mistakes being made all around us. We watch things get broken into smaller, simpler parts or included in larger, complex groups depending on how they are used. When we ask for a broom, we are not asking for the broom’s handle or for a broom-shaped collection of atoms. The basic, simple, elemental parts of a chair are pieces of wood or the atoms in them depending on how we are using what parts, just as a chair can be used as a chair, as a door stop or as a philosophical example of a general, familiar object.
Just as we are not taught to play chess in our minds without a board and pieces, meaning is not privately inside our minds but rather public, shared practices in familiar circumstances where we have learned how to do things. Meaning isn’t a mental activity anymore than a rise in butter prices is an independent act of butter. Most of the time, in familiar everyday cases, we easily understand and use words, but the stranger the case the less clear it is what to say or how what is said should be used. If all cases were abnormal the ways we use words would not work, just as if lumps of cheese unpredictably changed size weighing and pricing cheese would be useless and thus meaningless. As the Red Queen tells Alice, there is a game of chess being played all over the world, a both predictable and unpredictable arrangement.
We come to feel familiar with many ways of doing things, just as we feel with old friends, but ways that are different feel unfamiliar, strange and odd, as we feel with complete strangers who approach us with unknown purposes. Most everyday ways feel neither familiar nor strange and we pay them little attention, as we do with random people we pass on the street. We learn to trust ourselves and others, and even objects and places, but not completely. We misunderstand and are misunderstood, creating problems that require interaction and negotiation. Much of the time we trust the familiar without thinking, sitting in a chair that happens to collapse, and other times we trust with too much thinking, reasoning away what we hope isn’t true. Regardless, trusting as we do in situations that are always somewhat unknown and unfamiliar is the background and backdrop of all the ways we speak and think about what is and isn’t.
Wittgenstein remarked that if he looked out his window and saw a strange unfamiliar world that he would suppose he’d gone mad. Trust is so central to truth and meaning, to grounding the ways of our lives, that if we found ourselves in an unfamiliar world, we would doubt our own senses and reasoning, the most trustworthy and reliable sources of experience and evidence in our lives. This is why Zhuangzi the Daoist can wonder if he is a butterfly dreaming he is a man and Descartes the Rationalist can imagine that this world is the work of a deceiving demon.
Much of Wittgenstein’s thought is focused on the many ways we use language, which is why the Investigations opens with a quote from Augustine rather than Heraclitus. Wittgenstein says we can imagine a language that works like a chest of drawers, with each word and concept used with a particular type of thing much as a drawer holds either socks or pants. Naming a thing or group of things is like attaching a name tag or label to them, and using a name to call for a thing is like using a name tag to identify and open a drawer. While we can use such a simple drawer-like language to do things, such as ordering several pillars, slabs and beams to build a house, the languages we use to live our lives have many types of words other than nouns because we use language in many more ways than we use a chest of drawers. Wittgenstein says that Augustine describes hearing language as a child the way that adults already familiar with language hear an unfamiliar foreign one.
We teach young children language by directing their attention to things and saying words to help them form associations, and things which have been associated together increasingly feel as if they fit and belong. As we learn language we may or may not have images in mind when using words because of these associations, but words are not simply used to bring images into our heads. We do not need to imagine an apple whenever we use the word ‘apple’, and the word can be used to identify actual apples just as much as invoke imaginary ones.
Consider that children learn to use words such as ‘this’ and ‘that’, but we cannot point to what ‘this’ or ‘that’ are in themselves as they are used to refer to many different things, but children learn to use these words by watching others use them, associating the act of pointing to or talking about things with the words. Just as a brake lever in a train cabin is only a break in conjunction with the rest of the machine, words are useful because they are situated in the familiar background of our lives.
In Wonderland, a duck is asked if he knows what the word ‘it’ means, and he replies that for him ‘it’ typically is a rock or a worm, and the question is what did the archbishop find. We do not need to think of complete descriptions of what we mean in words as we mean things with words, just as we do not need to be conscious of whether we use four words or five to mean something with certainty. The meaning of what we say is not found in words alone, but in the entire situation of using them. Because language works in familiar living situations, we can still use names of people and objects long after they are dead and gone.
The meaning of a word is overall the way it is used. Just as a toolbox holds many different tools, such as a hammer, pliers, saw, screwdriver, ruler, glue, nails, screws and other useful things for putting things together and taking things apart, languages have many types of words that are used in many ways. Similarly, a train cabin has a crank which is moved in circles, a switch that can be on or off, a brake which is intensified with greater pressure and other mechanisms.
Because words such as ‘apple’ and ‘pear’ are very much the same every time we hear or see them, we mistakenly think that words are used in one way rather than many, like a simple set of drawers. When we think and talk about speaking and thinking philosophically, abstracting language and logic from particular complex situations, misunderstandings can arise. Wittgenstein thought that Logical Positivism, Russell and his earlier work, misunderstood the foundations of things in just this way. Rather than define ‘and’ in a single, exclusive and rigid way, we can see people using ‘and’ successfully in loose ways and do not need to prevent this from happening by fully solving logic. We can see language best in the situations where it lives and works, not when it it is on abstract vacation.
Just as the meaning of words depends on how we use them, the ways we classify words in groups depends on how we use the classification. We could group tools together by the type of job they do, by the combination in which we use them, by when they are available, by weight, by color, or countless other ways depending on whatever purposes we have and situations we find ourselves in. In a game of chess, we might group pieces into ours and theirs, pieces that are more or less valuable, pieces that can move more space or less, or pieces that can jump over others, using these classifications in various combinations depending on the game we are in, which moves we want to make and which moves we want to avoid, which can change in unpredictable ways in a single game.
While we could say that a language simpler than ours is incomplete if it does not suit all our purposes, we could say that the languages we use are all incomplete, as they do not yet contain all of the words and ways to use them that we need for all our possible and future purposes. Our languages, like old cities, are mazes of large and small buildings, streets and spaces that grew over many years and in many stages, and they are just as “complete” now as they were before the suburbs of modern chemistry and infinitesimal calculus grew around them.
The forms of life we live, including the language games we play, are not set in permanent stone. There is no fixed number of ways of using language or thought, with new ways being added and others forgotten, just as we see in the history of mathematics and the sciences. We can use a picture of a boxer to do many things, such as show someone how to stand, how not to stand, how someone once stood, and countless other things. Language and thought give us innumerable tools to use, and each tool can be used in innumerable ways. This is entirely opposite the idea that there are a fixed number of forms that complete logic as a set, with each used in a single, universal way, what Wittgenstein argued in his Tractatus and what many philosophers and logicians still wrongly cling to according to Wittgenstein himself.
The way we use words to directly refer to particular things, the most simple and drawer-like way we do language, can be variously interpreted as it can be used in various ways. If we point to two apples and use the word ‘zorp’, this could mean apple, or apples, two, red, round, on the table, ready to eat, or any number of things. If we say, “By ‘zorp’, I mean the number,” we would then have to define ‘number’ by pointing at other things, and there is no final definition in this chain anymore than there is a final house on a street where we can build a new one. Just as children can learn chess by watching, without ever hearing about rules in words, children learn language by watching, listening and then participating, without ever hearing about the rules of grammar or the rules of when to apply a particular word. Thus, if a child is familiar with chess, they could learn what the queen piece is and what it does before learning to call it “the queen”.
While we can use words in many different ways and invent new ways to use them, we typically use them in ways we share with others because language would not work as it does without familiar practices and routines. We cannot say “Bu bu bu,” out of the blue and mean “If it doesn’t rain I’ll go for a walk”. We could get familiar with saying “Bu bu bu” as a regular practice, but saying only once lacks significance as no meaningful association forms. Humpty Dumpty tells Alice in Through the Looking Glass that when HE uses a word, it means just what he wants it to, but Humpty is an immature egg who doesn’t seem aware that language is a shared practice in which neither the sender nor receiver has complete control or the final word on how the situation is interpreted.
Rather than search for the essential and universal form of all language, putting faith in a final authority that will settle all disputes in this or that area of our lives, we should investigate the interrelated variety of ways language works between participants. Wittgenstein repeatedly used the terms ‘language games’ and ‘forms of life’ to describe what he later found fundamental, as opposed to the ideal Kantian logic he sought in his earlier work. Games do not all share one common thing, but board games and card games and ball games are interrelated in many overlapping ways. Sometimes there are multiple players or winners and losers, but not always.
Games do not need to be perfect to be playable. Our ways and practices rest on unspoken assumptions and expectations. We only try to describe what our presuppositions and expectations are when we suppose that someone else doesn’t share them and needs to. The use of a word, like a move in a game, is not entirely bounded by rules, just as there are no rules about how high or hard one can throw the ball when serving in tennis. We draw boundaries and use rules for specific purposes, such as when there are problems. Because we do not often have problems recognizing the family resemblances shared by games or plants, we do not need to completely define what games, plants or our concepts of these are with rules or words.
Descriptions and rules are not complete explanations, but tools we use for particular problems. Just as we can tell someone to hang out in a general area rather than stand in a precisely defined spot, we do not always need to replace blurred pictures with sharper ones or general loose conceptions of apples with absolutely complete ones. What would a complete understanding of apples be, and why would we need it? When we speak about apples in general as apples, we aren’t tracking all of their individual movements. We often need concepts and practices that are open to variation, which is how we learn and teach others through general examples that roughly apply but allow for innumerable exceptions. We can make our understandings and expressions more exact in ways, but this can mislead us into thinking that complete exactness is our actual and achievable goal.
Just as a sign is placed where it will prevent many from going the wrong way but cannot completely prevent anyone from going the wrong way, rules can prevent misunderstandings but not entirely. Rules, like signs, can be doubted or interpreted differently. Descriptions, reasons and rules are useful, and can rest on other descriptions, reasons and rules, but because there can always be further disputes about descriptions, further descriptions could always be useful, such that no final description makes further descriptions impossible.
Because reasons can remove doubts and misunderstandings, we wrongly think they can remove them all even though further doubts and misunderstandings are always conceivable. Wittgenstein uses the example of the child at the blackboard, who learns to do math as they see it done without having everything in math entirely explained. Wittgenstein knows this because his earlier truth table logic was supposed to be the final grounding set of rules for mathematics as well as logical human thought, the foundation for Positivism sought by Russell.
The strength of a thread is not found in a single fiber that runs the whole length, but in the interweaving of many fibers. Just as the members of a family resemble each other in many overlapping ways rather than sharing one thing all together in common, the ways we use language, games and other things form families that do not have universal underlying forms. While it seems that red itself can’t be destroyed as red objects can, we can imagine red ceasing to occur in our world and our culture forgetting the color entirely, along with the use of the word and our ability to imagine it. ‘Red’ does not exist in itself or in a particular location, does not exist truly in the mind or truly in reality without our eyes to see it, but rather in the ways and places we use the color, word and concept, sometimes in the mind and sometimes in the world. Red is an interweaving of us seeing it separated from other colors as a child by adults who use a word around it while pointing, and it is us having the image of it often coupled with the word, and all of the associations and dissociations we have in our lives with it.
Thinking is a similar interweaving. To fully describe our everyday thinking in words would be like trying to repair a spider’s web with our fingers. Like red, thinking is an interweaving of different elements such as feelings, images and words, and it need not be grounded in one more than another in any particular thought. When we ask ourselves what reason we have to fear that fire will hurt our hand or expect a table will resist our touch, innumerable reasons drown each other out as we’ve had innumerable experiences.
The more we seek an ideal universal logic or set of rules in how we speak, think and act, the farther we are from finding good footing in our world, as if trying to walk on slippery ice without a hint of friction. In order to take significant steps forward in understanding the forms of life we live, we must turn away from the crystal clear ideal world of timeless ghosts that view things from nowhere in particular and return to the rough ground of actual existence, where things can always be slightly more complicated and we can always be quite misinformed in this or that space and at this or that time.
Jastrow’s duck-rabbit, a popular optical illusion, can be seen as either a rabbit’s head looking to the right or duck’s head looking to the left. It was an image that Wittgenstein was pondering as he wrote his final notes. We could look at it surrounded by rabbits on one page of a book, look at it surrounded by ducks on another page and not notice they are one and the same figure because we see the same thing but see it in two different ways.
In the middle of Wonderland, the Cheshire Cat tells Alice that everyone in Wonderland is mad, and illustrates this by comparing cats and dogs, with dogs thinking cats are backwards for wagging their tales when angry and growling when happy. Alice says she calls it purring, not growling, and the cat says she can call it whatever she likes. Everyone is crazy because people do things in particular ways against other people, making everyone backwards and insane to someone opposed to them.
Wittgenstein similarly said that in debates between realists and idealists, those who say truth and meaning are facts found in the world and those who say they are ideals constructed in the mind, each attack the other’s statements as if they are uncompromising universal declarations and defend their own statements as if they are reasonable common sense that allow for exceptions. Philosophy should not be about defending an abstract position in thought, but rather unlocking genius, enabling imagination to see new possibilities in all the interconnected things around us. Truth and meaning are in the world, in the mind, and our minds are in the world along with countless other meaningful, useful things. As Wittgenstein said, the point of philosophy is not to spare others the trouble of thinking, but to help others stimulate new thoughts of their own by showing them all the situations they’re in.