Ludwig Wittgenstein (1889-1951) is one of the most important thinkers in academics today. His first book, the Tractatus Logico-Philosophicus, and the later book, the Philosophical Investigations, are considered two of the most important influences for the American and British Analytic school of philosophy, the dominant school of philosophy in America.
In an end of the century poll in 2000, philosophy professors from America and Canada were asked to list the five most important books that influenced their own work. When all of the results were tallied up, the Philosophical Investigations was #1, and the Tractatus was #4. 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. In 2014, the New Republic named Wittgenstein the top philosopher of the past century, and mentioned first and foremost his Philosophical Investigations.
Wittgenstein’s thought can be divided into his early, middle and later work. His early work is the book the Tractatus, the book which gave the world truth table logic. This tool, as Wittgenstein later came to see it, remains the mathematical system taught as logic today. Just as Wittgenstein became famous for his truth tables, he switched positions in his thinking and came to reject much in his earlier work. He continued to write in many notebooks that were only published after his death, and the Philosophical Investigations is the most celebrated of these.
Wittgenstein’s Father was the Austrian Carnegie, making a fortune in Steel. Though his father was Protestant, and his mother Jewish, Ludwig was baptized Catholic because of antisemitism at the time. In his early years, Ludwig was a proud atheist but by the time he was working on his Tractatus he had a mystical transcendental outlook which he kept for the rest of his life. Though never religious, and though he had to bribe Nazis later to smuggle his “Jewish” family from Austria, he was buried as a Catholic. The Wittgenstein family was known for intense criticism, musical talent, depression, and suicide. Three of Wittgenstein’s four brothers committed suicide, and he himself considered suicide for awhile before launching into his late period. Unfortunately, suicide was considered romantic for Austrian elites at the time.
Wittgenstein was in Hitler’s elementary school, 2 days younger, but because he was put forward a grade and Hitler was held back a grade he was 2 years ahead. Both he and Hitler hated the school and the lessons.
He began studying at university in Berlin to become an engineer with an interest in flight. The Wright Brothers had recently invented the motorized glider, but flew it in France and Germany until 1907 as the US Army did not believe them. After failing in his attempt to build a better propeller, he began studying mathematical theory and philosophy of mathematics, becoming entranced with two thinkers who are along with Wittgenstein foundational for Analytical philosophy and logic: Russell from Britain, and Frege from Germany.
Wittgenstein went to see Frege, who did not fully understand his questions and advised him to go see Russell, which he did in 1911. He showed up unannounced to Russell’s room at Trinity College, impressed him with his intense and brilliant arguments. Russell became convinced that the young Austrian was going to carry his work forward and be his successor, solving the remaining problems of logic that Russell’s work on the foundations of mathematics had left open. As mentioned last lecture, Russell had shown there were contradictions unresolved in Frege’s work with set theory, but Russell had become frustrated trying to solve these contradiction with his theory of types.
Wittgenstein, an eccentric and difficult personality, was never fully comfortable at Cambridge, and often got into disagreements with Russell and threatened to leave many times before fleeing to Norway where he believed he could finish his work on Logic. While some still disagree, it is generally accepted that Wittgenstein was gay, developed a relationship with Pinsent, a young graduate student, and some believe that Russell encouraged the relationship if he did not introduce the two with the purpose of keeping the emotional and unstable genius with him at Cambridge.
When WWI broke out, he served for Austria, at the same time as he was developing the material for the Tractatus Logico-Philosophicus. Learning of Pinsent’s death in the war in Italy, he became suicidal, moved in with his uncle and finished the Tractatus which he dedicated to his ‘friend’ Pinsent. He tried to get it published, but no one would take it. Remember: this book went on to be the #4 influence in the US and Canada according to the poll, the book that gave modern logic truth tables, the method that replaced Aristotle’s syllogisms.
Russell intervened back in Cambridge, and had it published and wrote and introduction for it. This was the start of the end. Though Russell saw the work as genius, he did not completely understand much of it and his introduction reflected this. Wittgenstein read the introduction and realized Russell had great misunderstandings of his work. Believing that his Tractatus had solved all the problems of philosophy, 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 family. Since his family was already wealthy, he wrote in a letter, “they won’t be corrupted by it”. He left the school after a short while (not a good fit, as the parents thought he was crazy). He became a gardener’s assistant, and then his sister had him design her a house.
While finishing the house, he was contacted by members of the Vienna Circle, positivists using Hegel’s logic and Wittgenstein’s Tractatus to give a solid foundation for science and mathematics. This was what Russell had hoped for, minus the Hegel who Russell hated. While Wittgenstein had been away, the Tractatus had become famous, and central to many already inspired by Frege and Russell. Many came to visit and discus and progressively Witt became 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. For the rest of his life, Wittgenstein thought logical positivism (the analytic school of philosophy) misunderstood his Tractatus.
In his early period, Wittgenstein believed he had fully solved the problems of a complete system of logic. He saw it like Schopenhauer, a big early influence: logic is a perfect crystal tool of analysis, life is a messy chaotic ocean, and so logic is perfect but unfortunately never fits perfectly with life. This is like having the perfect tool for an impossible and continuous job. In conversations with positivists he started to change his thinking around and continued to write until he died. These writings were published after his death as the Philosophical Investigations and other books. In his later thought, Wittgenstein saw logic not as a perfect crystal castle in the sky but as rules and games that are imperfectly lived in the real world imperfectly and without complete definition. He no longer believed that logic could provide a foundation for mathematics, science or philosophy. He denied that contradictions are necessarily false, or disprove a mathematical-logical system.
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 new hero, the author of the Tractatus, the work he now thought was exactly wrong. The famous economist 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 defected to Soviet Russia, wanting to be a plumber or work with his hands. When he was told that according to the Soviet system he would be put to work as a philosophy professor in Moscow, he defected back to Britain.
In 1937, Hitler annexed Austria. Wittgenstein had to bribe Nazis to get his Jewish family passage out and spend the equivalent today of $50 million in gold and foreign currency. Since he had given away his own portion of the family fortune, he had to get much of this from his colleagues at Cambridge and other admirers of his work.
In his early thought, expressed in the pages of the Tractatus, reality consists of atomic facts, states of affairs that are true. Thought, expressed grammatically in language, ‘pictures’ the world with these atomic facts. The world does not perfectly fit this atomic language, but because it is the way the head makes sense of the world we cannot understand things otherwise.
Wittgenstein said that it is the part of the book that is unwritten that is important, the part where life itself goes beyond this logic and makes the world what it is. Of the world beyond logic, he wrote “Of what one cannot speak, one must remain silent”, which is in fact a quote from Confucius, whether or not Wittgenstein himself knew this. Our logic and the world are two things that do not fit, yet mysteriously the two are one.
If we boil logic with truth tables down to its tautologies, the necessary and basic workings, and leave the rest open as the world which always is beyond our thoughts, we can have the perfect system of logic and grammar that we use to understand things spelled out even if it cannot perfectly predict the world or tell us how the world works. Think of logic as a set of reading glasses, and the world as something one looks at through the glasses. Wittgenstein believed that with the Tractatus he had spelled out the perfect crystal form of the glasses, and beyond this nothing can be said for certain.
When it comes to facts in the world, however, everything is contingent on something else and is neither simply necessary or simply impossible. Logic is the necessary and impossible book-ends with which we interpret the world and its facts, but the world is always between the necessary and the impossible, is always somewhat necessary and somewhat impossible, which creates a gulf between our pure and necessary logic and the unpredictable world. For Wittgenstein, only logic and math can be sets of necessary truths, and this is because (as Avicenna and Mill believe) they are concepts and are ideal, unlike situations of real things in the world. Once we nail down the perfect tool of logic, we can use it to examine the world and all of its messy situations. Our examinations will never be perfect because of the gap between logic and the world, but at least the logic will be necessary and perfect. The reason’s Wittgenstein’s truth tables were such a success is that they proved, for the first time, that many of the axioms logicians had discovered were necessarily true (tautologies) in a way that is simple to do and easy to see.
THE LATER THOUGHT OF WITTGENSTEIN
At first Wittgenstein thought that he had solved all the problems of philosophy with the Tractatus truth table system (we do still use it today to teach formal logic), so he left philosophy and Cambridge behind, fought for Austria in WWI, had many experiences, and came to see that his earlier thinking contained horrible problems. He no longer believed that logic could be crystallized in the head as a truth table matrix, but rather it existed as a complex out in the world, as arrangements of people, thoughts, symbols, and objects. He continued to work on notebooks, progressing in his thought until his death, after which his notebooks were published.
There is an excellent passage from Lectures and Conversations that illustrates the turn nicely. This work was taken not from Wittgenstein’s notebooks but from the notes of his seminar students in the years leading up to his work on the notebooks which would be published after his death as the Philosophical Investigations. At this time Freud’s ideas had stormed onto the academic scene, infuriating Wittgenstein who now had come to hate the idea that things in the world, even logical operators and systems, can be boiled down to a single essential element or factor like sex, power or truth. It is this skepticism, which can be called the “problem of essences”, which marks the turn from his earlier thinking to his more influential later thought.
Wittgenstein attacked Freud’s psychoanalysis and dream interpretation for boiling everything down to sex. In the Lectures and Conversations (20-21), Wittgenstein proposes a thought experiment for consideration which I like to call Wittgenstein’s Oven. He asks, 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 ashy, or essentially wet? Why not? We would not say that a human is essentially carbon or water, nor would we say ashy or wet, because the 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 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, Wittgenstein had come to believe that neither facts in the world nor logic in the head can be reduced to a single element or necessary structure. Facts and logic are not true in themselves, but true in real situations of the world which are irreducibly complex. 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 structure.
The task of philosophy, logic and science is not to fully or completely explain anything, but to investigate things. Thought never fully defines things but rather describes and re-describes things. If science is thinking about the world, then science has endless work to do describing and re-describing things. Consider whether we fully understand apples, or whether we ever need to entirely understand them in order to continue to understand them and use them a great deal. Likewise, if philosophy and logic are ‘thinking about thinking’, and if thinking is merely a possible description of things, philosophy and logic have endless work to do describing our descriptions, describing and re-describing the ways that we describe things. Much insight can be gained even if no subject is entirely explained or exhausted.
One good way to approach this is to describe how cultures of thought, perspectives, facts and models are gathered together and lived in institutions. Thought ceases to be completely abstract, but is rather a culture and situation in the real world that involves people, buildings and money. The cryptanalysis of algebra worked so well as a modeling language that we came to believe that the mathematics was not in our practices and text books but rather sewn into the fabric of the world itself. As we look over the history of thought in the wake of Wittgenstein’s later work, it becomes evident that mathematics and logic are tools and lenses, not the hidden structures of things operating at secret levels out of our immediate sight.
In scholarship today, particularly the history of religion, philosophy and science, it has become popular to consider a system of thought as a real lived situation rather than an abstract set of beliefs and ideas. A religion or science is in fact a situation of human beings who never have to have entirely the same set of beliefs as long as they can generally and relatively cohere as a culture.
THE PHILOSOPHICAL INVESTIGATIONS
In his Philosophical Investigations, one of my favorites of modern European thought, Wittgenstein argues for a middle way between two extreme positions, between the scientific positivism (objective truth is facts in the world) and psychological skepticism (subjective truth is meanings in the mind). He presents each position in quotes again and again, and then argues against both in a three stage process. First he states a position, then shows situations in which the position works, then shows situations in which the position does not work. He shows us that taking either position to extremes would be understandable given particular ways we think and act, but neither position explains all the ways in which we think and act. We live in complex ways that depend both on there being a coherent world and there being human perspectives. Wittgenstein argues that we can take both positions rather than determine one to be the actual and the other to be the illusion.
In his earlier thought, the world and the head are separated by a Kantian gulf between objectivity and subjectivity. In his later thinking, the world and our heads work together seamlessly as a complex situation. This is very similar to Hegel, who thought that Kant’s gap between our experience and the thing-in-itself had to be overcome. One cannot remove either the head or the world to get the bedrock or anchor of meaning and truth without resulting in absurdities. The clean and ideal side of logic, math and grammar mislead us into thinking that meaning must be anchored entirely on one side, either exclusively in the head or exclusively in the world, but we gain much more ability to think and describe our heads and our world if we stop looking for meaning and truth to be entirely in one place rather than the other. In the same way, rather than determine which facts are absolute truths to the exclusion of their opposites, or refuse to identify coherence of belief as it is all ‘mere theory’, we can better understand the facts and theories we can share by recognizing that they are one and the same viewed from opposite sides. If we can continue to determine relative fact from relative fiction, there is no need to entirely separate the two. To use the tool analogy, as long as we have decent tools we do not need perfect or eternal ones.
Games and rules gather people together, but individuals can also variously interpret rules and meanings. Rules can always be variously interpreted is a central idea of the Philosophical Investigations. This is not to say that they always are or they should be, but a window remains open. Both are only what they are together as a form of life. Notice that this thinking has much in common with Laozi’s thinking on the wheel as both empty and solid at the same time, and much like the Zen koans of a rock being not a rock and a rock and the sound of one hand clapping.
Consider the child at the blackboard thought experiment used in the text. It is always possible for a child to misunderstand rules and demonstrate this misunderstanding by making mistakes, even after you show the child and explain. Let us say that you then write a new ‘inner’ set of rules to further explain the rules when the child fails. What if the child does not understand those? Is there a bedrock set of rules that the child can not possibly misunderstand? If the child can misunderstand rules, then no set of rules about rules about rules is ever perfectly airtight. We have an infinite regress unless we can find a set of rules that can never be misinterpreted.
Just like Wittgenstein had been seeking the fundamental inner workings of logic and mathematics, as Frege and Russell had tried to do before him, if people do math decently there need not be any inner rules aside from the explanation and demonstration that, if repeated, children can often follow. Notice we are considering mathematics as a culture, practice and behavior, learned by children and taught by adults, not as an abstract set of necessary or immutable rules. It turns out that there are no inner workings to mathematics. Mathematics works as it does openly, on the board in front of one’s face, without the need of a ‘secret cellar’. If mathematics on a board is not entirely secure in itself as a practice, then no inner set of rules could or must be either for it to function.
When we try to explain anything, it is not being simplified, being stripped down to its core, at all. It is the opposite: we are making it more complex as we try to simplify and explain it. The rules are not being discovered in the thing, but being added to the thing with our conceptions. When we explain things, we are not whittling away the unnecessary but adding our descriptions. In the same way, when we do science to explain apples or human beings, we are adding our descriptions and the situations of our descriptions, not uncovering the simple truth of the thing. The simple truth of a thing is the simple thing itself, very Zen. The simplest truth of an apple is the single apple. An explanation of where apples come from is very useful, but it puts the apple in a complex with many other things (such as trees, farms, stores, trucks). An apple is not merely its DNA, but is in a infinitely complex situation with its DNA and ourselves attempting to isolate components with the tools and technology we bring into the situation.
We are always essentializing, as we are when we generalize in saying, “We are always essentializing”. Meaning, grammar and logic do separate things into parts, focusing our attention on basic elements. They are useful for doing so. However, Wittgenstein is arguing something quite revealing: There are no final explanations, only complex descriptions. Any explanation is a partial human description, which can then itself be described and explained. The task of philosophy, science and mathematics is not to reduce things to simple truth, but to generate more meaning and situations.
In the preface to the Philosophical Investigations, Wittgenstein says that he now sees grave mistakes in his Tractatus. He says that this new book is not to spare thinking, but to stimulate thinking. The Tractatus had the opposite goal: to put an end to the problems of logic and philosophy. In his later thinking, Wittgenstein does not believe that anything can or need be fully solved or closed, but should rather be opened up and made complex.
In section 7, Wittgenstein says that language games are actions and language interwoven as forms of life. He considers that words such as ‘this’ and ‘there’ are learned interwoven with gestures such as pointing. ‘This’, ‘now’, and other simple words get their meaning from their use by gesturing human beings. They can not be described fully in language alone, nor do they represent specific objects consistently. Rather, they are demonstrated to children and translated into other languages of cultures that share similar gestures.
We know from neuroscience that in the brain the centers of language and control of the hands are next to each other, likely because language developed in apes along with gestures. There are also similarities in the basic gestures of humanity, including extending the arm to indicate the direction of sight and attention. Infants only months old will read eye direction to try to see what others are seeing, and if they can not see what is being looked at they will check the eyes again. The arm, whether a culture uses the index finger or not, provides an extension of the line of sight so that it can be easily recognized and followed by others. Notice that ‘this’ is as simple as it gets in itself, and to further explain it we need to bring arms and neuroscience into the picture.
In section 11, he says language is like toolbox, a complex set of tools that have no absolute necessity but are useful as a set. Consider that a hammer, a screwdriver and glue are a decent set of tools. Are they absolutely right or necessary tools? We could invent others, but they work decently well for putting things together and taking things apart. We do not need an absolute screwdriver any more than we need to completely understand the relationship between the hammer and screwdriver. We need only use them.
In the same way, we do not need to understand the word ‘and’ such that it is always used exactly the same way, nor do we need to completely understand its relationship to ‘or’. When we use them relatively, not exclusively, they are interchangeable. At a buffet, I could equally say, “You can have eggs or salad or steak” or “You can have eggs and salad and steak”. The two can sometimes be used differently and sometimes similarly, as long as we are decently consistent in all of our interconnected uses. Indeed, the words, like tools such as hammers and screwdrivers, are more useful being often but not always used in particular and exclusive ways (ex: one can use a screwdriver to open paint cans). ‘And’ and ‘or’ are more useful when we can use them oppositely, but also identically. In his earlier thinking, with the truth tables, Wittgenstein was trying to secure them merely opposite and different meanings, which does not give us their full usage and meaning.
In section 12, Wittgenstein uses the metaphor of a locomotive cabin to further illustrate the same point. There are many levers and switches that function in various ways. Words and language function in various ways that form a complex with their environment. We could always redesign the train cabin, but it works well enough as it is.
In section 15, he uses another simple tool-oriented metaphor to make language and meaning physical rather than ideal: naming is compared to attaching a label (or sticker, with “Hello My Name Is”). The association of a word with a particular thing is like attaching a label for ease of use and identification.
In section 17, he says that we can classify words as we do things, but our classifications will depend on our situation and purposes. He uses the metaphor of chess pieces. If you want to move a great distance, you would classify chess pieces one way, but if you want to break through or jump over the enemy lines (with a knight or a bishop) you would classify them another way. The pieces, like words and other things, do not have classifications and meanings in themselves, but in how they can be used in concrete situations. This is again much like Mill.
In section 18, he says that a language is like an old city, with side streets and squares. It is interesting to compare San Francisco to Salt Lake City here. San Francisco can be a nightmare to drive, while Salt Lake City is almost entirely a perfect grid surrounding the Mormon Temple. In San Francisco, you never know which way a street might turn due to hills or other intersecting streets. European cities are similarly often much older than the automobile, and do not lend themselves to outsiders’ easy navigation. A language, like an old city or old growth forest, is the result of a long process of many layers of evolution and development. We can understand meanings just as we can navigate streets, but things are not always clear cut as Salt Lake City.
In section 57 and 58, he asks about where red exists. He suggests that ‘red’ as a color does not exist in itself, but as an association of many red things having been experienced, the word ‘red’ being said by others and oneself associated with these things, as well as the imagination/projection of the color red in the mind. None of these things needs to be exclusively present for there to be red. We could even say the word without any red things or thinking of red, and it still means the color in our language and culture. We could likewise see a red thing, and it is red without using the word or seeing red in the imagination. Thus, the color red is not essentially any red thing, or the word, or the color in the mind, but the complex of all these. The color red is not simply a subjective concept, nor it is an objective fact, but it is a conception and association of many things and words, both in the head and the world together.
In section 65, Wittgenstein argues that there is no form common to language games or forms of life, such as the color red or the use of a tool. The common element is rather a family resemblance or association. In the same way that Hegel argues that Being itself can not be qualified (green, good, necessary) or quantified (much, fourteen, half), Wittgenstein argues that there is no common form to meaning. It is a complex association that can take any possible form. This is similar to the organic forms of fractal geometry: No two trees are identical, but they share what Wittgenstein calls a ‘family resemblance’. In the next section (66), he uses the example of games. There is no rule common to all games, but they resemble each other as a family.
In the next section (67), he uses the metaphor of a thread (one could also use a rope). The thread is strong not because there is one underlying strand that runs through its entire length, but because many stands overlap each other. Mathematics and the meaning/use of a word do not need a single inner rule to make them entirely consistent. Rather they are complex networks that are continuously reinforced by our re-inscription as we use them daily.
Derrida, the French deconstructionist, argues that there is no language set in stone. Old English, like Old French, drift slowly like tectonic plates. When we use language, we are not using something already set. Rather, we are resetting it, re-associating it, re-gluing it together with the only glue it was ever fashioned from, each and every time we speak or write. Likewise, mathematics such as algebra is not true in itself. We continue to use it consistently, and this rebinds its consistent use. When dividing by zero creates problems, we add additional rules and then continue to lash them together with the system.
In section 83, Wittgenstein gives another metaphor to describe the emergence (a chaos-theory, fractal geometry term) of forms of life. Imagine people in a field, playing with a ball. The ball is tossed about, another person joins and kicks it back to another, who chases it, then pegs the kicker with the ball, and then it is tossed about again. A game has arisen, but it does yet does not seem to have consistent rules. It is being made up as it goes along. Human beings are rule making, association generating beings, who know how to follow and bend rules as they see fit. This means that the only complete consistency is both consistency and inconsistency, the only consistent rule is there are yet there are not consistent rules.
In section 85, he gives another metaphor to back up this conception. A rule is like a signpost, such as a sign that points to the right and reads, ‘San Jose’. Does the sign force you to go to San Jose? No. If you go to the right, will you surely reach San Jose without getting lost or running out of gas? No. We can even imagine that if you go to the left, because you are afraid of San Jose, you could get turned around and end up there anyway. In spite of these loose ends, we find signs quite useful.
In section 99, Wittgenstein considers that if we lock someone in a room, but leave a way for them to get out, have we locked them in or not? What if we lock someone in a room, but leave the window open? You can not lock someone in a room such that they can never get out. There are no simply solid substances. There are no things without cracks of any kind. Similarly we can not secure meanings such that they will always stay exactly the same, but we can secure them by locking them down repeatedly through use and association. To give an entire account of how a meaning is secured would be like “repairing a torn spider’s web with one’s fingers” (106). Just like an old city, we can use things without ever being able to fully describe them.
Wittgenstein writes, “We must do away with all explanation, and description alone must take its place” (109)…”What we do is to bring words back from their metaphysical to their everyday use” (116)…”What we are destroying is nothing but houses of cards and we are clearing up the ground of language on which they stand” (118).
Do we base our own behavior, let alone the culture of mathematics, on simple rules? He gives the example of being certain that a table will resist one’s finger, that a fire will hurt one’s hand.
It is not that there is a simple rule set in an atomic language that reads, ‘Table is solid’ or ‘Fire hurts hands’. Rather, “a hundred reasons present themselves, each drowning out the voice of the others” (478). Like the thread woven of many strands, our belief and certainty that objects are solid and flame hurts us are woven out of many experiences that are then woven together with the table and flame before us.
Wittgenstein writes, “To say, ‘This combination of words makes no sense’ excludes it from the sphere of language and thereby bounds the domain of language. But when one draws a boundary it may be for various kinds of reason. If I surround an area with a fence or a line or otherwise, the purpose may be to prevent someone from getting in or out, but it may also be part of a game and the players be supposed, say, to jump over the boundary” (499). Wittgenstein seems to be thinking specifically of humor and comedy, though it could also apply to modern and conceptual art, forms of culture that break rules on purpose. Comedy and modern art are games where the rule is to break the rules without breaking anyone’s neck. Wittgenstein had an appreciation both for the Alice books of Lewis Carroll as well as American slap-stick comedy which he preferred to opera. At the end of the course, we will study the Alice books, humor and modern art in light of the later work of Wittgenstein.
The last image to examine, near the end of the book, is Jastrow’s duck-rabbit, often called Wittgenstein’s duck-rabbit because the psychologist Jastrow is far less famous. One can look at the figure from the left, and it is a duck, and one can look at the figure from the right, and it is a rabbit. Which is the single correct face? Wittgenstein says we may have seen only the rabbit face our entire life, and that does not prevent us or others from seeing the duck when it is pointed out. This is much like the duel between objectivism (truth is in the world) and subjectivism (meaning is in the head).