Wittgenstein, the Man Who Ended Philosophy Twice

Chapter 01: A Wonderful Life

In the last days of April, 1951, in a doctor's house on the edge of Cambridge, a man lay dying of cancer. He had been born into one of the wealthiest families in Europe, and he had given the entire fortune away. Three of his brothers had killed themselves. He had fought in one world war and pushed a medicine cart through another. He had spent his life in a torment of thought that he often feared would destroy him. When the doctor's wife told him that his closest friends were coming the next day to see him one last time, he said to her, tell them I've had a wonderful life. Then he lost consciousness, and the following morning, with those friends gathered at his bed, he died.

The man was Ludwig Wittgenstein, and many of the people who knew him believed he was the most remarkable human being they had ever met. By every ordinary accounting, his life had been one of the unhappiest a famous thinker ever lived. He was lonely, severe, restless, and frequently in despair. He drove away admirers, abandoned his profession twice, and judged himself without mercy. That such a man should leave the world calling his life wonderful is a puzzle, and it is the right puzzle to begin with, because the answer to it runs through everything he thought.

He was born in Vienna on April the twenty-sixth, 1889, the youngest of 8 children, into a household that resembled a small principality. His father, Karl Wittgenstein, was a forceful, brilliant, domineering man who had run away to America as a boy, worked as a waiter and a violin teacher, and then come home to build, within two decades, the dominant steel empire of the Austro-Hungarian lands. By the time Ludwig was born, Karl was one of the richest men in the empire, and the family home in Vienna was a vast mansion that the city simply called a palace. It held marble staircases, a famous art collection, and seven grand pianos. Music ran through the house like weather. Johannes Brahms was a guest at its evening concerts, and the children grew up assuming that art was not an ornament to life but one of its serious occupations.

The family's position had been built across generations of assimilation. Three of Ludwig's four grandparents had been born into Jewish families that converted, prospered, and merged into the Austrian upper class. The children were baptized, Ludwig as a Catholic, and the household understood itself as Viennese, cultured, and modern. That ancestry would return upon the family with terrible force half a century later, but in the 1890s it seemed a closed chapter of the past.

What was not closed was the conflict between Karl Wittgenstein and his sons. Karl demanded that the boys follow him into industry, and he treated their artistic gifts as weaknesses to be corrected. The results were catastrophic. The eldest son, Hans, was a musical prodigy of a kind that frightened people, a boy for whom music seemed less a talent than a possession. He fled to America to escape the career his father had chosen for him, and in 1902 he vanished from a boat, almost certainly by his own hand, though his body was never found. 2 years later, in 1904, his brother Rudolf, then a student in Berlin, walked into a bar, asked the musicians to play a sentimental song about being forsaken, and drank a glass laced with cyanide. A third brother, Kurt, survived until the last days of the first world war. In October 1918, an officer on a collapsing front, with his troops melting away and refusing his orders, he shot himself.

Of the 5 brothers, two remained. Paul, a pianist of ferocious will, lost his right arm to a wound on the Russian front, and then rebuilt his career playing with the left hand alone. The concerto for the left hand that Ravel later wrote was composed for him. And there was Ludwig, the youngest child, gentle, stammering, watchful, the one member of the family who seemed at first to have no remarkable gift at all. He was educated at home until he was fourteen, and what he showed was not artistic genius but a quiet, intense mechanical aptitude. At the age of ten he built a working model of a sewing machine out of bits of wood and wire. His sisters remembered him as the sweetest tempered of the children, eager to please, and privately tormented, even as a boy, by the question of whether he was being honest enough.

After the deaths of Hans and Rudolf, his father relented, and the surviving sons were allowed their own paths. Ludwig was sent to a provincial secondary school in Linz, where his record was mediocre and his unhappiness considerable. By a strange accident of history, the same school in those same years enrolled another boy, almost exactly his age, named Adolf Hitler. The two were in different grades, and there is no evidence that they ever exchanged a word. The school years cost Ludwig his childhood faith and gave him little in return, and he left it for the path his aptitudes suggested, engineering.

He studied machines in Berlin, and in 1908 he moved to Manchester, in England, to work in the new science of flight. He flew experimental kites from a bleak moorland weather station, and he designed a propeller driven by small jet engines at the tips of its blades, an idea so far ahead of its materials that a version of it was only built decades later. He took out a patent. He seemed launched on a respectable career. But the design work needed mathematics, and mathematics, for a mind like his, was a trapdoor. He began to ask not how the calculations worked but what mathematics itself was, what made its truths true, and he discovered that this question had recently been given a radical new treatment in a book by an English philosopher, Bertrand Russell. The book seized him and would not let go. In the summer of 1911 he traveled to Germany to visit the elderly logician Gottlob Frege, the deepest mind then working on these questions. By his own account Frege wiped the floor with him in argument, and then gave him the most consequential piece of advice he ever received. Go to Cambridge, Frege said, and study with Russell.

In October 1911, an intense young Austrian appeared without invitation at Russell's rooms in Trinity College, Cambridge, and more or less refused to leave. He followed Russell back to his rooms after lectures, argued with him through dinner, and returned the next day to argue again. Russell found him exhausting, obstinate, and unlike anyone he had ever taught. At the end of the term the young man came to him with a question on which, he said, his whole life depended. Am I a complete idiot? If he was, he would become an aeronaut. If he was not, he would become a philosopher. Russell told him to write something over the vacation and bring it back. He read the first sentence of what Wittgenstein brought him, and told him that he must not become an aeronaut. Within a year, Russell, then at the height of his powers, had come to regard this student as his successor, the man who would take the next step in philosophy that he himself could not take.

Then, in 1913, Karl Wittgenstein died, and Ludwig inherited a share of the fortune that made him, at twenty-four, one of the richest men in Europe. His first act was characteristic. He arranged, anonymously, for a hundred thousand crowns to be distributed among struggling Austrian artists and writers, and among the beneficiaries were the poets Rilke and Trakl. His second act, a few years later, was more radical. When the first world war ended, he signed the whole of his inheritance over to his brother and sisters, keeping nothing. He chose them, he explained, because they were rich already, and more money could not corrupt them. The family notary, drawing up the papers, told him he was committing financial suicide, and did as he was asked. Why a man would do such a thing, what had happened to him in the war years to make property feel like a contamination, belongs to the story of those years, and they were also the years in which he wrote the only philosophy book he would ever publish in his lifetime.

For most of the 1920s he disappeared from philosophy altogether, into village schoolrooms, a monastery garden, and the building of a house, convinced that his work in logic was finished. In 1929 he returned to Cambridge and to philosophy, no longer convinced. The second half of his thinking life was spent dismantling and rebuilding the first, and it made him, by slow degrees and almost entirely without publication, the most influential philosopher of his century.

His personal life remained as austere and as difficult as his thought. He lived in bare rented rooms, owned almost nothing, dressed in the same gray flannel, and found most academic company unbearable. He formed few attachments, and those few were overwhelming. In the early thirties he came close to marriage, for the only time, with Marguerite Respinger, a young Swiss woman from a wealthy family, but the union he proposed was so severe, a shared spiritual life without children, that she drew back and married another man. The deepest bonds of his middle years were with younger men, above all with Francis Skinner. He experienced these loves with great intensity, and he confided them almost nowhere except his coded diaries.

In March 1938, Germany annexed Austria, and Wittgenstein, sitting in Cambridge, became overnight a citizen of the German Reich, and under its race laws a Jew. He applied at once for British citizenship. For his sisters, still in Vienna, the danger was mortal, and the family entered into one of the strangest bargains of the era. His brother Paul, who had escaped abroad, and Ludwig himself took part in negotiations that went all the way to Berlin, in which the family signed over its foreign holdings, more than a ton of gold among them, in exchange for a legal reclassification that protected the sisters. The regime sold them their lives, and the sisters survived the war in Vienna. In 1939, the year his British passport came through, Wittgenstein was elected professor of philosophy at Cambridge, succeeding his old friend G. E. Moore in the most prestigious chair in the English-speaking philosophical world.

He held the chair through the second world war, but he could not bear to teach philosophy while the cities burned. He went to London and took work as a dispensary porter at Guy's Hospital, pushing a cart through the wards and delivering medicines, while asking that no one be told who he was. Later he moved north to Newcastle, to a clinical research unit studying the physiology of wounds, where he worked as a laboratory assistant and devised improvements to the unit's apparatus. The professor of philosophy spent the war, by his own choice, as the most overqualified hospital technician in England.

When the war ended he went back to the lectern, and hated it more than ever. He had come to believe that professional philosophy was very nearly a corruption, a way of turning the most serious activity in life into a career, and at the end of 1947 he resigned the chair in order to do nothing but think. He went to Ireland, first to a farmhouse in County Wicklow, then to a whitewashed cottage standing alone at the end of a rocky inlet on the Connemara coast. There he lived in almost complete solitude, writing through the mornings, walking the shore through the afternoons. The local people remembered him as the man the birds trusted. He fed the robins and chaffinches at his door until they came to his hand.

His body began to fail before his work did. In the summer of 1949 he crossed the Atlantic to visit his former student and closest late friend, Norman Malcolm, in Ithaca, New York, and fell ill there. Back in Cambridge, the doctors found cancer of the prostate. He received the news with unsettling calm, saying that he had no wish to go on living anyway, though treatment held the disease back for a time. He went to Vienna to sit with his eldest sister Hermine as she died. In the autumn of 1950 he made a final journey to Norway, the landscape that had always meant most to him, with Ben Richards, a young medical student who was the last of the few people he allowed himself to love.

By February of 1951 he could no longer live alone, and he dreaded ending in a hospital ward. His Cambridge physician, Edward Bevan, took him into his own home. The doctor's wife, Joan, was frightened of him at first, this gaunt, famous, ferociously exact old man, and then became his friend and final companion. He worked on, lucid and exacting, almost to the last day. He died on the morning of April the twenty-ninth, 1951, a few days past his sixty-second birthday, and he was buried by Catholic rite in a parish burial ground in Cambridge. His friends stood at the grave unsure whether he would have wanted the prayers, and unsure he would have minded. None of them claimed to have understood him completely. But none of them thought his last sentence a delusion. He had spent the one thing he valued, his mind, without reserve, on the one activity he believed he was for, and he had refused every comfort that might have blunted it. On those terms, and perhaps only on those terms, the sentence was simply true.

Chapter 02: The Paradox That Broke Logic

In June of 1902, the German logician Gottlob Frege opened a letter from England that quietly destroyed his life's work. The wound that letter opened in the foundations of human knowledge was the wound Wittgenstein came to Cambridge, 9 years later, to heal.

Frege was a professor of mathematics, obscure, methodical, and very possibly the greatest logician since Aristotle. For more than 20 years he had pursued a single, austere ambition. He wanted to prove that arithmetic is logic in disguise. The numbers, and all the laws that govern them, were not to rest on intuition, or on experience, or on the structure of the human mind. They were to be derived, step by rigorous step, from the bare laws of thought themselves, the principles that any rational being must accept on pain of talking nonsense. If the project succeeded, the most certain knowledge the human race possesses, mathematics, would finally stand on a foundation as hard as certainty itself. By the summer of 1902 the second volume of his masterwork on the basic laws of arithmetic was at the printer. The edifice was all but complete.

The letter came from a thirty year old Englishman named Bertrand Russell. It began with deep admiration. Russell had read Frege as almost no one else in Europe had bothered to, and he shared the great ambition completely. Then, with apologies, Russell pointed out a problem.

The problem concerned classes, which are simply collections of things. The class of all teaspoons is not itself a teaspoon, so it is not a member of itself. But the class of all things that are not teaspoons is itself not a teaspoon, and so it is a member of itself. Some classes, then, contain themselves, and most do not. Now, asked Russell, consider the class of all classes that do not contain themselves. Is it a member of itself? If it is, then by its own definition it should not be. If it is not, then by its own definition it should be. Each answer flatly produces the other. A homely version of the same trap has become famous. Imagine a village barber who shaves all the men in the village who do not shave themselves, and only those men. Who shaves the barber? If he shaves himself, he must not, and if he does not, he must. There is no such barber, and there is no such class. Yet Frege's system, built with the greatest care ever lavished on a logical structure, allowed that class to be formed. A contradiction could be derived inside the very foundation that was supposed to make contradiction impossible.

Frege saw the point at once, and his response became a legend of intellectual honesty. He added a postscript to his book, already in press, confessing that hardly anything worse can befall a scientific writer than to have the foundation of his edifice shaken just as the work is finished, and that this letter had done exactly that. Russell said later that he had never seen anything to equal the integrity of that response. Faced with the collapse of his life's labor, Frege's first feeling appeared to be gratitude that the truth had come out.

Russell then spent the better part of a decade trying to repair what his own letter had broken. With the mathematician Alfred North Whitehead he constructed an immense three volume system of mathematical logic, a forest of symbols in which the proof that one plus one equals two arrives only after hundreds of pages of preparation. To block the paradox, Russell introduced a rule known as the theory of types, a kind of legal hierarchy among classes which decrees that a class may never be a member of itself, so that the fatal question can never be asked. It worked, in the sense that a fence works. But Russell knew, and admitted, that it was a fence and not an explanation. The paradox had been forbidden rather than understood. Logic had been saved by decree, and a foundation that needs a decree to hold it up is not the unshakable ground anyone had been promised.

It is worth pausing on what the word logic meant to these men, because it has a thin, technical sound today and it did not then. Logic was not one academic subject among others. It was supposed to be the skeleton inside all rational thought, the thing that makes inference possible in mathematics, in science, in ordinary speech, in every argument anyone has ever made. If mathematics rested on logic, and the sciences rested on mathematics, then the entire structure of human knowledge stood, in the end, on this one foundation. And the foundation had cracked. Worse, nobody could say with confidence what logic itself actually was. Why do its truths hold? What are they about? Russell could manipulate logical symbols with more power than any man alive, and he confessed that he could not answer the child's question underneath, the question of what these unbreakable laws are and where their authority comes from.

That was the state of the subject in 1911, when the intense young Austrian engineer presented himself in Russell's rooms. The discipline standing guard over human certainty was itself in a state of emergency, patched, anxious, and unexplained. Russell was tired, and he sensed it. His hope, which he expressed without embarrassment, was that this strange new student would take the next step, the step into the nature of logic itself, that he no longer had the strength to take. The young man accepted the assignment with total seriousness. The answer he eventually produced would resemble nothing Russell expected, and it would arrive from the mud of a world war.

Chapter 03: The Book in the Rucksack

The only book of philosophy Wittgenstein ever published in his lifetime was written, in large part, within range of Russian artillery. It is a treatise on logic and language, barely 80 pages long, arranged as a chain of numbered remarks, and it is known to the world by the Latin name its English editors later attached to it, the Tractatus. What the book claims can wait. The book cannot be understood at all without the story of how it came to exist, because the war did not merely interrupt its composition. The war got inside it.

The story begins in the Cambridge years, and it begins with a friendship. In the spring of 1912 Wittgenstein was running experiments in the university's psychology laboratory on rhythm in music, and he recruited as a subject an undergraduate mathematician named David Pinsent. The two discovered an immediate, easy sympathy of a kind Wittgenstein found with almost no one else in his life. They shared a passion for Schubert, and they worked out a way of making music together in which Pinsent played the piano while Wittgenstein whistled the other part, with perfect pitch and complete seriousness. That autumn Wittgenstein took Pinsent on holiday to Iceland, traveling in the lavish style only a steel heir could afford, and the following year they went together to Norway. Pinsent kept a diary, and it is from those pages that we know what Wittgenstein was like as a young man, by turns gentle, hilarious, despairing, and impossibly demanding, a companion who could turn a missed train into a moral crisis and an evening of music into something close to worship.

It was on the Norwegian journey that Wittgenstein made a decision that alarmed everyone who knew him. He had concluded that he could not do his real work in Cambridge. The place was full of clever people being clever, and their talk, he said, served vanity rather than truth. What he needed was solitude of an absolute kind. So in the autumn of 1913, having first dictated to Russell a set of notes on logic that preserved his thinking to date, he moved alone to a tiny farming village at the end of a Norwegian fjord, a place of black water and vertical rock, where he would eventually have a small wooden hut built on a slope above the lake, reachable most easily by rowing across. There he worked on the foundations of logic with a concentration that frightened even him, and wrote to Russell that he felt he was living on the edge of madness. Russell, reading the letters in Cambridge, oscillated between awe and worry. His student was attempting to dig beneath the deepest level Russell had reached, down to the question of what logic itself is, and he was doing it utterly alone, in the dark of a northern winter.

Then, in August 1914, Europe went over the cliff, and Wittgenstein did something that no one who thinks of philosophers as sheltered men should ever forget. He had a double hernia and was exempt from service. He volunteered anyway, as a common soldier in the Austrian army. His motives, as far as his diaries reveal them, had little to do with the empire's cause. He went to war because he believed that standing close to death might make him decent, that it would test him in a way that nothing in his privileged life ever had. He hoped, he wrote, that the nearness of death would bring light into his life. He wanted to be changed.

His first posting was unheroic, a fitter's berth on a patrol boat working the Vistula river, among rough conscripts who despised this polite millionaire volunteer and made his life miserable. It was during these months, in a small bookshop in a shelled Galician town, that he found a shop with almost nothing left in it but one title, Tolstoy's retelling of the Christian gospels, The Gospel in Brief. He bought it because there was nothing else to buy, and it took him over completely. He read it and reread it until he knew passages by heart, and he began recommending it to anyone in trouble. The soldiers around him started calling him the man with the gospels. Tolstoy's stripped, radical Christianity, with its teaching that the things of this world are nothing and the life of the spirit everything, fused in him with the austerity he already possessed by temperament. It is here, in a gunboat on a Polish river, that the act which later bewildered the family notary was really decided. A man who had absorbed that book could not go on owning a fortune.

The strangest part is what this religious turn did to his logic. Before the war, his notebooks contain symbolism, propositions, the machinery of his Cambridge problem. As the war deepens, entries on the nature of the proposition begin to sit beside entries that read like prayers. What do I know about God and the purpose of life, he asks, and answers himself in numbered remarks as rigorous as his logic. The two inquiries were becoming one inquiry. The question of how language hooks onto the world was joining the question of how a human being should live, and the book growing in his rucksack would eventually carry both, one on its surface and one in its silences.

In 1916 he asked for the most dangerous assignment available, the observation post, the forward position from which artillery fire is directed and on which enemy fire concentrates. His request was granted just in time for the great Russian offensive of that summer, one of the most lethal operations of the entire war. He stood his post through bombardments that destroyed the positions around him, and his commanders cited him repeatedly for coolness and courage under fire, decorating him more than once. His diary from those weeks records, side by side, terror, prayer, contempt for his own fear, and logic. He had gone to war to be tested, and the test had arrived. The men who knew him at the front, unlike the men who had known him at Cambridge dinner tables, seem to have regarded him with plain respect.

In the spring of 1918, while Wittgenstein was serving as an artillery officer on the Italian front, David Pinsent was killed in England. He had spent the war doing aeronautical research, and he died when an aircraft he was aboard as an observer broke apart in the air during a test flight, far from any battlefield. The news reached Wittgenstein months later through a letter from Pinsent's mother, and it nearly ended him. He wrote back to her that David had been his first and his only friend, and that he owed to him much of the best in his own life. That summer, on leave at an uncle's house, half destroyed by grief and persuaded that his own death was close, he assembled his wartime notebooks and his prewar logic into a single final text. The book was finished. He was 29.

The end of the war then performed its last service to the history of philosophy. In the general collapse of November 1918, Wittgenstein was captured by the Italians and spent the better part of a year as a prisoner, ending in a camp near Monte Cassino. The manuscript was in his rucksack, and he understood with complete clarity that if he died or the pages were lost, the work existed nowhere else. From the camp he managed to get word to Cambridge, and the machinery of his old world creaked into motion on his behalf. Keynes, who had connections everywhere, helped arrange for communication and eventually for a copy of the manuscript to travel through diplomatic channels to Russell. Another copy went to Frege, and brought one of the bitterest disappointments of Wittgenstein's life, because the old logician, the man whose project had started everything, wrote back with courteous, uncomprehending questions about formatting and terminology. Frege never understood a page of it. Russell at least understood that something extraordinary had arrived, and began working to get his former student home and the book into print.

Wittgenstein was released in August 1919 and returned to a Vienna in ruins, citizen of an empire that no longer existed. Within weeks he had signed away his inheritance and begun looking for ordinary work. Whatever else the war had done, it had welded together in him two convictions that would never afterward come apart, that the problems of logic admit of a definitive solution, and that the most important things in life cannot be said in words at all. Both convictions had gone into the little book that survived the trenches and the prison camp in his rucksack. And when that book finally appeared in print, its first page carried a dedication neither to his teachers nor to his family, but to the memory of David Pinsent, a young man killed in a falling aircraft.

Chapter 04: A Picture of the World

The Tractatus opens with one of the most famous sentences in twentieth century philosophy. The world is all that is the case. Seven words, flat as a hammer blow, and nearly everything the book argues is already folded inside them. Wittgenstein arranged the whole work as a sequence of numbered remarks branching out from seven such cardinal sentences, each remark commenting on the one above it, so that the book reads less like an argument than like a crystal growing according to a strict internal law. There are no examples to speak of, no scholarly references, no padding, and almost no visible reasoning. Its preface promises, in one of his most quoted sentences, that what can be said at all can be said clearly. He believed that anyone who had thought these thoughts would recognize them, and that no one else could be helped.

Begin with that first sentence, because it makes a move so quiet it is easy to miss. The world, it says, is the totality of facts, not of things. We naturally imagine the world as a vast warehouse of objects, stars and stones and chairs and people, and the inventory of all of them as a complete description of reality. Wittgenstein is saying that the inventory would tell you almost nothing. Consider a hammer lying on a table. There is the hammer, a thing, and there is the table, another thing, and then there is something that is neither of them, the fact that the hammer is on the table. Move the hammer to the floor and no object has been created or destroyed, yet the world has changed, because one fact has ceased and another has begun. What the world is made of, in the sense that matters, is not the catalogue of its objects but the way those objects stand toward one another, that this is the case rather than that. A possible arrangement of objects he calls a state of affairs, and the facts are the states of affairs that actually hold. The world is everything that is the case, the sum of what holds, surrounded by the shadow realm of everything that could hold but does not.

The question the book then sets itself is the one Wittgenstein had carried from Cambridge to Norway to the trenches. How does language manage to be about this world at all? How can a sound in the air, a row of marks on paper, reach out and touch a fact, and be right or wrong about it? It is among the strangest abilities we have, and the most invisible, because we exercise it every waking hour without the faintest idea of how it works.

The answer came to him, according to the story he told friends, from a Paris courtroom. During the war he read a magazine account of a lawsuit over a traffic accident, in which the court had used a scale model to reconstruct what happened, toy cars and toy figures arranged on a tabletop to stand for the real cars and the real pedestrians at the real crossing. The model could represent the accident because each piece in it stood for something, this toy for that lorry, this doll for that pedestrian, and because the arrangement of the pieces mirrored an arrangement that the actual things could have had. The model on the table was a possible state of the street corner, made small. And it struck Wittgenstein that this is not a special trick the courtroom invented. It is what every proposition does. A sentence is a model of reality. A sentence is a picture.

At first hearing this sounds wrong, because sentences do not look like pictures. The words the hammer is on the table do not resemble a hammer or a table in any way. But Wittgenstein's notion of a picture is deeper than visual resemblance. Think of a piece of music as it exists in four different forms, the melody in the composer's head, the written score, the grooves cut into a gramophone record, and the sound waves filling a room. None of these resembles the others. Ink on paper looks nothing like a groove in shellac, and neither looks like a vibration in the air. Yet they share something perfectly exact, a common structure, a skeleton of relationships, which is why a musician can read the score into sound and an engineer can cut the sound into the record and back again. There are rules of translation between them because the same form lives in all of them. That shared skeleton is what Wittgenstein means by logical form, and his claim is that a meaningful sentence shares logical form with the situation it describes. The words are not the things, and the grammar is not the geometry, but the sentence and the fact are built to a common plan, the way the score and the symphony are. Language can be about the world because language and the world have the same bones.

Once the picture idea is in place, several ancient puzzles open like locks. Take the puzzle of falsehood, which had troubled philosophers since the Greeks. A true sentence states a fact, but what does a false sentence state? There is no fact for it to state, and yet it plainly means something, since we understand it precisely well enough to call it false. On the picture theory the mystery evaporates. A sentence pictures a possible state of affairs, an arrangement the objects could be in. To understand the sentence is to see which arrangement it shows. To call it true is to add that the arrangement actually holds, and to call it false is to say that it does not. The toy cars can be set out in a configuration the real cars never occupied. The model still models. Meaning is one thing, truth is another, and a sentence carries its meaning the way the courtroom table carries the accident, by arrangement, before any verdict on truth has been reached. This is also why understanding is creative in a way we rarely notice. A sentence you have never heard before, describing a situation that has never existed, is intelligible to you instantly, because you know the parts and you can read the arrangement. With old words, language shows you new worlds.

Beneath this, the book runs the analysis all the way down. Ordinary sentences are rough, compound things, and Wittgenstein held that they must be analyzable into elementary propositions, minimal pictures consisting of names in immediate combination, where a name is a word that simply stands for an object and does nothing else. The names touch the objects, the arrangement of names mirrors the arrangement of objects, and there the contact between language and reality is finally made, like teeth of a zipper meshing. He was driven to this by an austere thought about precision. If the sense of a sentence is to be definite, the analysis must somewhere bottom out in simples, in objects with no parts, for if everything could be divided forever, no sentence would ever finish saying what it says. It is one of the most striking confessions of the book that Wittgenstein could not produce a single example of such a simple object, and declined to try. The theory demanded that they exist. What they were, he said, was not the logician's business. It was an architecture built from the roof downward, and he knew it, and at the time he trusted the roof.

From the elementary propositions, the rest of language is assembled with a small set of tools, the words and, or, not, if. Every meaningful statement, however elaborate, is on this account just a pattern of agreements and disagreements with the elementary pictures, a vast switchboard of yes and no. Say that the window is open and the door is shut, and you have agreed with two pictures at once. Say that either the bell rang or the post is late, and you have spread your agreement across alternatives. However high such constructions are piled, nothing new ever enters except pattern. Here Wittgenstein drew the consequence that answered the question Russell had set him, the question of what logic itself is. Consider the sentence, either it is raining or it is not raining. It has the costume of a statement about the weather, yet a moment's thought shows that it tells you nothing whatever. Whatever the sky is doing, the sentence holds. It is compatible with every possible world, excludes nothing, risks nothing, and therefore says nothing. Wittgenstein called such propositions tautologies, and his claim, breathtaking in its simplicity, is that the truths of logic, all of them, the entire unbreakable canon, are tautologies. They are not deep descriptions of an abstract realm, not the most general laws of nature, not reports on the furniture of a Platonic heaven. They are the points at which our switchboard of combinations spins without gripping the world, the places where language runs on empty. That is why logic cannot be refuted by any experience and needs no evidence. Its certainty is purchased at the price of content. A tautology is certain because it has already agreed with everything, and it is empty for exactly the same reason.

This was the answer carried out of the war in the rucksack. Logic is not a science standing above the other sciences, with mysterious objects of its own. Logic is the scaffolding of language showing itself, the shadow cast by the rules of representation. The unbreakable laws hold not because reality obeys them but because nothing would count as a description of reality, or even as a sentence, without them. They mark the limits of what can be pictured, and so they cannot themselves be pictured, any more than an eye can appear in its own visual field. What had seemed the hardest question in the foundations of knowledge receives an answer of total, dissolving calm. There was never a foundation to inspect. There was only the frame.

It is a beautiful machine, and it is worth standing back to see what the machine has quietly done. If a sentence has sense only as a picture of a possible state of affairs, then the only things that can be said, strictly said, are things of the kind the sciences say, that the objects stand so, that the hammer is on the table, that the acid turned the litmus red. And a description of that kind, however complete, records what is, never what is good, never what anything is worth. A theory that draws the boundary of language with such exactness must face what it has placed on the far side of the boundary, and Wittgenstein had drawn the line knowing precisely what fell outside it. Everything he cared about most was there. The book's cold machinery of facts and pictures was built, all along, for the sake of what it would refuse to say.

Chapter 05: What Cannot Be Said

By its author's own reckoning, everything important in the Tractatus happens at its edge. The machinery of facts and pictures fills the pages, but the point of the book lies in what the machinery cannot reach, and Wittgenstein built the whole apparatus the way a jeweler builds a setting, for the sake of the empty space at the center. The key to this side of the book is a distinction that looks small and turns out to govern everything, the distinction between what language says and what language shows.

A sentence, on the picture theory, says that things stand a certain way. But in order to say it, the sentence must have a structure, and that structure is not one more thing the sentence says. It is what the sentence does its saying with. Consider a map. The map says that the coastline bends here and the mountains rise there, and it can say these things because it is drawn to a projection, a rule connecting paper to terrain. But nowhere on the map is the projection itself drawn. The projection is not in the picture. It is how the picture is a picture at all, and it is visible only in the working of the map, never among its contents. So it is, Wittgenstein argued, with language as a whole. Every sentence displays its logical form, the shared skeleton that makes it a model of the world, but no sentence can state that form, because stating it would require a position outside language, a place to stand beyond the very medium of standing anywhere. What can be shown cannot be said. The deepest features of reality, the ones philosophy most wants to put into words, do not appear in true sentences. They appear in the fact that there are sentences at all.

From this thought the book draws a famous and vertiginous consequence. The limits of my language mean the limits of my world. Whatever I can think, I can think only in the forms my language provides, and whatever lies beyond those forms is not something I can mean, or wonder about, or even gesture toward, since the gesture too would be made of language. There is no balcony from which to survey the boundary from outside. And at this dizzying altitude Wittgenstein places one of the strangest remarks in the book, the remark about the self. There is a truth in solipsism, he says, in the old philosophical suspicion that only my world exists, but it is a truth that cannot be said, only shown. Look for the self in the world and you will not find it. Among all the facts, the hammer on the table, the rain on the window, the body in the chair, there is no fact that is the I who is having this world. The thinking subject is not an item within experience. It is the point from which experience opens, a limit of the world rather than a part of it, the way the edge of the page is not one of the words. What the solipsist means is quite correct, he wrote. It only cannot be put into words.

Now the ethical center of the book comes into view. Imagine the complete ledger of facts, every true sentence that could ever be written, the position of every particle, the history of every action, the firing of every nerve. Wittgenstein's claim is that in that total inventory you would find no entry that reads, and this was good, or this mattered, or this ought not to have happened. The ledger records that a man sheltered a stranger and that another betrayed one, but goodness and betrayal as values, as things that count, appear nowhere in it, because value is not one more fact alongside the others. If it were, it would be an accident, something that merely happens to be the case, and the whole force of good and evil is that they are not accidents of that kind. So ethics, he concluded, cannot be put into words. Ethics does not describe a special region of the world. It concerns the world as a whole and the will that meets it, and it shares this position outside the sayable with beauty, for at bottom, he thought, ethics and aesthetics are one. Nothing in the facts changes when a person becomes good. What changes is something no fact can register. The world of the happy man, he wrote, is a different one from the world of the unhappy man, though every object in it stands exactly where it stood.

In the same high, thin air the book places its few sentences about death and about God. Death is not an event in life, he wrote. We do not live through it, and so it is not one of the experiences the ledger could record. And of God he says almost nothing except where God is not. How things are in the world is a matter for the sciences. God does not show himself in the world. What is religious, what he calls the mystical, is not any fact within the world but something that no inquiry can reach because no inquiry can even formulate it. It is not how the world is that is mystical, but that it is. That anything exists at all, that there is a world rather than nothing, is not a state of affairs among others, not a question physics has merely failed so far to answer. It cannot be asked in a meaningful sentence, and yet, Wittgenstein insists, it presses on us. He calls it the feeling of the world as a limited whole. A man can stand inside the totality of facts and feel the totality itself as something given, handed over, unexplained and unexplainable. The book does not say what to do with that feeling. By its own rules, there is nothing that can be said.

Wittgenstein knew exactly how strange this position was, and in December of 1919 he tried to explain it to the one man best equipped and least disposed to receive it. He and Russell met in The Hague, in neutral Holland, and spent a week going through the book line by line. For Russell the treasure was the logic, the account of the proposition and the tautologies, the solution to his own deepest technical problems. He found the rest alarming. His brilliant student, he reported to friends, had become a complete mystic, deep in Kierkegaard and the religious poets, seriously contemplating a monastery, and maintaining in earnest that the most important matters lay beyond speech. Russell admired the mind and deplored the conclusion, and he would treat the book ever after as a great work of logic with an unfortunate religious shadow over its final pages. Wittgenstein, for his part, watched the person he most respected in philosophy embrace the setting and miss the jewel. It was the first and the defining instance of what would become the permanent fate of the book, to be loved with precision for everything its author considered preliminary.

And the author had, in fairness, made understanding nearly impossible, because near the end of the book he turns its full strictness on itself. The sentences of the Tractatus are not pictures of facts. They are sentences about logical form, about the limits of language, about value, exactly the kinds of sentence the book rules out. Wittgenstein does not flinch. Whoever understands me, he writes, finally recognizes my propositions as nonsensical, and uses them as rungs, climbing up through them and beyond them, and then he must throw away the ladder after he has climbed it. The book is a ladder, and a ladder is not a place to live. It exists to be used and discarded, leaving the climber standing somewhere no sentence could have carried him, seeing the world rightly. Whether this is profundity or an elegant self-contradiction has been argued for a hundred years. What is certain is that he meant it.

Then comes the final numbered remark, the seventh of the cardinal sentences, standing alone without commentary, the most famous line he ever wrote. What we cannot speak about we must pass over in silence. Generations of readers have heard in it a shrug, a tidy positivist dismissal, as if it said that whatever cannot be measured does not matter. He meant the opposite. The silence of the Tractatus is not the silence of an empty room. It is the silence kept in front of something, the hush of a man who has walked the boundary of language for 200 pages precisely in order to protect what lies beyond it from the chatter of philosophers, his own chatter included. The things that cannot be said, the worth of a life, the existence of the world, the good and the beautiful and God, are not casualties of the system. They are what the system was built to guard. The last sentence of the book is a door being closed, very quietly, on the holiest room in the house.

Chapter 06: The End of Philosophy

No publisher wanted the book that claimed to end philosophy. Through 1919 and 1920, while Wittgenstein lived in postwar Vienna in self-imposed poverty, the manuscript went out and came back. One firm would take it if the author paid the costs, and he refused on principle, saying that writing the book had been honest work but that paying the world to read it would be indecent. Another would take it with a long introduction by Bertrand Russell, whose name now carried international glamour, and that bargain would in time be struck, at a price Wittgenstein found bitter.

In the middle of these humiliations he sent the manuscript to a man who had no money and no power to help him, Ludwig von Ficker, the editor of a small Austrian literary journal he admired, and the same man who years before had quietly distributed his anonymous gift among the poets. Ficker plainly could not print a treatise on logic, and Wittgenstein seems to have known it. What the approach produced instead was a letter, and the letter has become the indispensable key to the book. Do not worry, Wittgenstein told him, that you cannot understand the contents. The point of the book is an ethical one. He had once planned, he said, to put a sentence into the preface explaining it, and the sentence was this. My work consists of two parts, the one presented here, and everything I have not written. And it is precisely this second part that is the important one. The book draws the limits of the ethical from the inside, he explained, and everything chattered about ethics by others, he was silent about. A treatise of logic, offered to a literary editor, described by its own author as an act of ethics performed by silence. Philosophers would spend the next century cataloguing its theory of the proposition. The author had told a provincial magazine editor, in a private letter, that they would be cataloguing the frame and missing the painting.

Publication, when it finally came, arrived as farce. Russell wrote his introduction, generous, lucid, and devoted almost entirely to the logical machinery. Wittgenstein read it in German translation and was appalled, finding in it, beneath the elegance, superficiality and misunderstanding, and for a while he preferred no publication at all to publication wearing that preface. Exhaustion won. He told Russell, in effect, to do as he liked with the thing. The first printing then appeared in 1921 in an obscure German annual of natural philosophy, riddled with misprints, set without his corrections, and he disowned it as little better than piracy. Only in 1922 did the book receive the form the world now knows, a slim London edition with German and English on facing pages. The translation was prepared under the editor C. K. Ogden, with much of the real work done by a Cambridge undergraduate still in his teens, Frank Ramsey. And it was G. E. Moore who proposed that the English edition carry a sonorous Latin title in the manner of Spinoza, which is how a slender German treatise became, forever, the Tractatus.

The preface Wittgenstein himself wrote for it contains 2 sentences that should be read together, because between them they explain the next 8 years of his life. The first is as proud a claim as any philosopher has made in print. The truth of the thoughts communicated here, he wrote, seems to me unassailable and definitive, and the problems of philosophy have, in essentials, been finally solved. Not advanced, not illuminated. Solved, finally, in their essentials, by a man in his early thirties, in 80 pages. But the second sentence undercuts the triumph with a strange, deliberate sadness. The value of this work, he went on, consists in showing how little is achieved when these problems are solved. The great questions of logic and language had been answered, and the answer revealed that they had never been the great questions. Everything that makes a life worth living stood exactly where it had always stood, untouched, on the far side of the boundary, beyond the help of any treatise.

Taken at his word, he had no choice about what to do next. A man who believes the problems are solved cannot go on being a philosopher, any more than a doctor can go on treating a patient he has pronounced cured. To stay in the subject would be to join the chatter, to make a career of decorating a finished building, and his whole nature revolted at the thought. Nor did he believe, after Tolstoy and the war, that a life of leisure was permitted to him, and he had in any case given away the money that would have funded one. What he wanted now was work that was plainly useful and plainly humble, work among people far from Cambridge and from drawing rooms in Vienna, where what remained of a man was only what he could honestly do. The author of the Tractatus was 32 years old, his book was in print in 2 languages, his teacher believed him the most advanced philosophical mind in Europe, and he was done. He walked away from the subject he had completed, and went looking for a job.

Chapter 07: The Lost Decade

For most of the 1920s, the man Russell considered the most advanced philosophical mind in Europe taught children their letters in poor mountain villages. The job he had gone looking for was village schoolmaster, and to get it he enrolled, a decorated officer and published author in his early thirties, at a teacher training college in Vienna, sitting through courses on classroom method among earnest eighteen year olds. His family watched in pain. One of his sisters told him that using a mind like his to teach peasant children was like using a precision instrument to open crates. He answered with an image of his own. You remind me, he said, of somebody looking out through a closed window who cannot explain the strange movements of a passer-by. He cannot tell what sort of storm is raging out there, or that this person might only be managing, with great effort, to stay on his feet. He was not wasting himself, he meant. He was surviving.

He asked for the poorest and most remote postings, and he got them, a string of villages in the hills south of Vienna where the farmers scratched a living and the children came to school smelling of the cowshed. He lodged in cramped rooms, ate badly, and lived on a schoolmaster's wage as if the fortune had never existed. And by every honest account, including the hostile ones, he was an extraordinary teacher when a child gave him an opening. He despised the official drill of memorization and taught by building and doing. His classes assembled the skeleton of a cat from bones they cleaned themselves. They built working model steam engines, identified the plants of their own hillsides, learned the architecture of Vienna before he took them, at his expense, to see it. He taught algebra to farm children on the conviction that nothing real was beyond them, and for the quick and hungry ones, many of them the poorest in the class, those years were a door thrown open. Some of them, interviewed half a century later as old men and women, still spoke of him with wonder.

But the same furnace that warmed the gifted scorched the slow. He could not comprehend a child who did not want to understand, and his impatience came out through his hands. Corporal punishment was the ordinary currency of Austrian village schools in those years, but his went beyond the ordinary, an ear boxed too hard, hair pulled, and the village distrusted him besides. The farmers needed their children for field work and resented the ambition of this strange, fierce gentleman who did not drink and did not socialize and plainly belonged to some other world. His letters from those years, many of them to Paul Engelmann, a young architect he had befriended during the war, swing between flickers of contentment and a despair that more than once circled the thought of suicide. He had come to the villages to be useful and ordinary. The villagers could see what he could not quite admit, that he was neither.

One lasting good came out of the classrooms. His pupils could not afford dictionaries, so he compiled one for them, a spelling word list fitted to the actual vocabulary of Austrian village life, and it was published in 1926 for use in elementary schools. Alongside the Tractatus, it is the only other book he published in his lifetime, and he was prouder of it than the comparison would suggest. A treatise on the limits of language, and a word list for children learning to spell. The shelf of his published life's work consists of those 2 volumes, and the second is not the joke. It is the clue.

The end of his teaching career came in April of 1926, in the last and unhappiest of his village posts, and it came through his hands. A frail eleven year old boy named Josef Haidbauer hesitated over his answers, and Wittgenstein struck him on the head, hard enough that the child collapsed. The boy came around, but the village had its case at last, and a legal hearing followed. The court ordered a psychiatric examination, the proceedings cleared him of criminal wrongdoing, and the verdict scarcely mattered, because he had already handed in his resignation, and because of what he had done in the hearing room itself. Asked about his punishments, he had told less than the truth, minimizing a harshness that he knew had been real. The blow ended his career as a schoolmaster. The half lie, from a man whose entire being was organized around the demand for total honesty, went on burning in him for more than a decade, and it would be years before he found a way to answer for it.

That summer he reached one of the lowest points he would ever touch. He presented himself at a monastery on the edge of Vienna and asked about taking orders, not for the first time in his life, and was steered away, reportedly by a superior wise enough to see that the motive was flight rather than vocation. Instead they gave him work in the monastery garden, and for some months the author of the Tractatus dug beds and pruned trees and slept in the toolshed of the garden, which seems to have done him more good than any position of honor ever did. His mother died that same year, and the family gathered, and the surviving children, all middle aged now, found themselves bound to one another more gently than the old palace of their childhood had ever allowed.

It was his sister Margarete, the boldest and most modern of the family, who found the bridge back. She was building a great townhouse in Vienna and had engaged Engelmann, Wittgenstein's wartime friend and a student of the city's most radical architect, to design it. Knowing her brother needed saving, she invited him into the project, and the project swallowed him whole. He began as a consulting partner and ended, by force of nature, as the governing intelligence of the building, credited as its architect alongside Engelmann. The house still stands, a composition of plain rectangular volumes without a single decoration, and what he gave it was not the general design but its exactness. He designed the door handles, unpainted tubes of metal bent with a precision that took months to get from the founders. He designed the radiators, and because no firm in Austria could cast them to his tolerances, the radiators took a year. Witnesses remembered him having a ceiling raised by three centimeters when the cleaning of the finished building had already begun, a correction invisible to any eye but his, and non-negotiable. The engineer who had once designed propellers, and the logician who had once demanded that analysis bottom out in perfect simples, was now enforcing logical form on window frames.

His sister Hermine, watching the building rise, gave it the name that has stuck to it ever since. It seemed to her not so much a house as logic become house, and she confessed that, for all its perfection, it seemed a dwelling more suited to gods than to a creature like herself, with her small human comforts and her clutter. Wittgenstein himself, years later, judged the building with the same cold justice he applied to everything he had made. The house, he said, was the product of a sensitive ear and good manners, the expression of real understanding. But primal life, wild life seeking to break out into the open, that, he admitted, was missing. It was the most precise self-portrait he ever drew. He had spent a decade trying to become a simple, useful, finished man, in the schoolroom, in the garden, in the perfect house, and the wild life in him had not broken out, only waited. It was waiting for the only work that had ever been large enough to hold it, and by the time the last radiator was finally fitted, that work had begun, very quietly, to call him back.

Chapter 08: The Great Misreading

While Wittgenstein was perfecting door handles, the Tractatus was acquiring disciples he had never met, a few streets away in his own city. Around the middle of the twenties, the philosopher Moritz Schlick, who held a chair at the University of Vienna, gathered a remarkable discussion group of philosophers, mathematicians, and scientists that would become famous as the Vienna Circle. They were men in love with the exactness of science and in revolt against the fog of traditional philosophy, and when they discovered the Tractatus they treated it as their founding scripture. For two academic years running they read it aloud in their meetings, sentence by numbered sentence, debating each remark like scholars of a sacred text. No book mattered more to them, and no book, as it turned out, did they more completely misunderstand.

The Circle's own program crystallized into one of the most influential doctrines of the century, logical positivism, and its heart was a single sharp test called the verification principle. The meaning of a statement, the positivists held, is its method of verification. Tell me what observations would show your claim true or false, and you have told me what it means. If no observation could ever bear on it either way, then it is not a deep statement, or a difficult one, or a poetic one. It is not a statement at all. It is noise shaped like a sentence. Armed with this test, they set about the demolition of metaphysics with real joy. Claims about the Absolute, about the soul, about the meaning of being, about God, all failed the test and were ruled meaningless, not false but empty, the verbal residue of confused grammar. Philosophy, on their program, would survive only as a service trade, the logical analysis of scientific language. Everything else that had worn the name for 2,000 years was to be swept away.

It is easy to see what they found in the Tractatus. Here was a book that drew the limits of language with mathematical rigor, showed the truths of logic to be tautologies, confined meaningful propositions to pictures of facts, the very territory of the sciences, and ended by consigning ethics, God, and the meaning of the world to the unsayable. Its famous closing sentence about silence they read as the most elegant dismissal ever written, a courteous death sentence for everything unverifiable. The book even seemed to hand them their method. What the Tractatus called the unsayable, they renamed the meaningless, and assumed the two words said the same thing. On their reading, the final page was a shrug. On the author's, as the letter to Ficker had already made plain, it was a genuflection. Rarely in the history of thought have so many brilliant people memorized a book while inverting its point.

Schlick, to his credit, wanted the man and not just the text, and he pursued the reclusive heir with extraordinary patience. When a first meeting was finally arranged, in 1927, Schlick's wife recalled that he left the house with the reverential air of a pilgrim setting out for a shrine. The pilgrim got his audience, on conditions. Wittgenstein would not attend the Circle itself, and would meet only a small, hand-picked company, Schlick himself, the gentle and devoted Friedrich Waismann, for a time the young Rudolf Carnap. Even then he would often refuse to discuss philosophy at all. He talked about music, about architecture, about whatever was actually alive in him that week. And on some evenings, facing the most rigorously anti-metaphysical minds in Europe, he chose a different instruction. He turned his chair to face the wall, so that he would not have to see their faces, and read aloud to them from the poems of Rabindranath Tagore, the Bengali mystic, verses about God and the soul and the beloved. The men who had proved that such sentences were meaningless sat in silence and listened.

Carnap, the most penetrating of them, eventually understood what he was looking at, and said so with the honesty of his school. Wittgenstein's relation to the things he would not discuss, Carnap realized, was not that of a scientist disposing of error. His attitude, his whole bearing toward problems and people, was closer to that of a creative artist, almost, Carnap said, to that of a religious man. The difference can be put simply. The Circle believed that where language ends, nothing begins, that the unsayable is empty and the silence beyond the boundary is the silence of a vacant lot. Wittgenstein believed that everything of ultimate importance lay in exactly that silence, and that the boundary wanted guarding, not because what lay beyond it was worthless but because words would profane it. They had read his fence as a demolition order. He had built it around the only ground he considered holy.

The misunderstanding would have mattered less if the Circle had remained a Viennese debating club. Instead, its members scattered ahead of the catastrophe of the thirties into the universities of Britain and America, and they carried logical positivism with them, and the Tractatus pinned to its banner. For a generation of English-speaking philosophers, Wittgenstein's first book was simply the positivist manifesto, the great machine for liquidating metaphysics, and its author the patron saint of a movement whose central conviction he regarded with something close to contempt. He bore it, on the whole, in silence of his own. But the episode set the pattern of his entire reception, the pattern The Hague had begun. He would be celebrated, all his life and long after it, with great precision, for the wrong thing.

Chapter 09: The Return

In the third week of January, 1929, the economist John Maynard Keynes sat down and wrote a short letter to his wife. Well, God has arrived, it said. I met him on the five fifteen train. God was a lean Austrian of thirty-nine in a worn jacket, carrying very little luggage, and his arrival in Cambridge that evening turned out to be one of the hinges of twentieth century thought. Wittgenstein had told his friends he was coming for a short visit. He remained, with interruptions, for the rest of his life, and the work he did after stepping off that train was aimed, with gathering force, at the destruction of the book that had made him a legend.

The return had been preparing itself for years, and the first agent of it was the young man who had helped translate the Tractatus as a teenager. Frank Ramsey had grown from Ogden's prodigious assistant into the most gifted philosopher and mathematician of his Cambridge generation, and he took the book seriously in the only way Wittgenstein ever respected, by attacking it. While Wittgenstein was still teaching school, Ramsey had traveled out to the Austrian mountain village where he was posted and spent a fortnight going through the text with its author line by line, hours a day, probing the joints. And Ramsey's deepest objection was not technical but moral. If philosophy ends by declaring its own propositions nonsense, Ramsey wrote, then we must take that conclusion seriously, and we cannot go on pretending, as Wittgenstein does, that it is important nonsense. Philosophy must be of some use, or it is a disease one ought to be cured of, and a theory you cannot state is a theory you do not have. The jab lodged like a splinter. Wittgenstein had answered the great ladder passage to his own satisfaction once. Under Ramsey's flat, friendly insistence, the answer began very slowly to come apart.

The second agent was a lecture. In March of 1928 the Dutch mathematician Brouwer came to Vienna to speak on the foundations of mathematics, defending his heretical vision of mathematics not as a frozen realm of eternal truths but as a living construction of the human mind, built out in time, with no guarantee that every question already has an answer waiting. Wittgenstein went, in the company of friends from Schlick's company, and something in him caught fire. The friends remembered him afterward in a coffee house, talking philosophy with a vehemence they had never seen, sketching, objecting, alive. Whether he agreed with Brouwer mattered less than what the evening proved, that the subject he had pronounced finished could still seize him by the throat. The house was built, the schoolrooms were behind him, the decade of penance was over, and within the year he was on the train to Cambridge.

His situation on arrival had a comic edge that the university solved with a straight face. The most famous philosopher in Europe had no doctorate, no degree of any kind, and no formal standing, and he needed an income, having permanently disposed of the alternative. The solution was to register the author of the Tractatus as a research student and award him the doctorate for the book itself. The oral examination took place in June of 1929, and the examiners were Russell and Moore, two of the most eminent philosophers alive, formally interrogating a friend about a work they had been studying for a decade. The story that everyone tells, and that no one can verify, is that the candidate ended the proceedings by clapping his examiners on the shoulder and saying, don't worry, I know you'll never understand it. What is certain is the sentence Moore put into his official examiner's report, perhaps the driest ever filed in that university. It is my personal opinion, Moore wrote, that Mr Wittgenstein's thesis is a work of genius, but be that as it may, it is certainly well up to the standard required for the Cambridge degree of Doctor of Philosophy. Trinity College gave him a research grant, and in time a fellowship. The system had found a drawer to put him in. What it had actually acquired was a man in the early stages of turning against everything the drawer was labeled with.

The technical crack had already appeared, and it is worth slowing down for, because it is the precise point at which one of the most confident systems in the history of philosophy began to fail, and its author, almost alone among philosophers, chose to follow the failure rather than defend the system. The Tractatus required that elementary propositions be independent of one another. Each minimal picture was to say its one thing, and logic, being empty tautology, was to generate no necessities beyond the bare combinations of yes and no. All genuine necessity was to be logical necessity. Now consider a simple statement, that this spot in my visual field is red. It seems as elementary as anything could be. But if the spot is red, it cannot also be blue. That is not a prediction or a habit. It is a necessity, as hard as any law of logic. And yet it is not a tautology, not a hollow truth of the and, or, not machinery. One apparently elementary proposition excludes another, which the system said could never happen. Wittgenstein tried the obvious repair, analyzing color statements into deeper components that would make the exclusion logical after all, and the repair failed, and he saw that the failure was not local. Necessities of this kind are everywhere. A thing cannot be in two places at once. A tone cannot be both higher and lower than another. A rod cannot be both one meter long and two meters long. Wherever language measures the world along a scale of any kind, color, pitch, length, weight, its statements come not as independent atoms but in organized systems, each member excluding its neighbors, and the exclusions are part of the meaning. The clean division between empty logic and independent fact, the load-bearing wall of the entire Tractatus, did not hold.

What deserves notice is not only the crack but his conduct in front of it. Most system builders, confronted with a counterexample at the foundation, spend their maturity on increasingly ingenious defenses, and the history of philosophy is in large part a museum of such defenses. Wittgenstein did the rarer thing. He had written that the truth of his thoughts was unassailable and definitive, and when he found them assailed by a colored spot, he let the verdict stand against himself, publicly, at the height of his fame, and began again as a beginner. Whatever else changed in him across the great divide of his thought, this did not. He had always held that a philosopher's first duty is honesty about his own confusion, and now the confusion was his, and he treated himself as exactly the patient he would later teach others to treat. In 1929 he wrote up the problem honestly in a short paper called Some Remarks on Logical Form, composed for a meeting of a learned society. It was the only academic article he ever published, and he repudiated it before he even delivered it, standing up at the meeting and talking about something else entirely. He had seen that the wall could not be patched. The building had to come down.

While the logic cracked from inside, a friend was striking the foundations from a direction no logician would have thought to guard. Piero Sraffa was an Italian economist at Cambridge, a friend of imprisoned anti-fascists and a mind of merciless concreteness, and he and Wittgenstein walked and argued for years. The story of their most famous exchange comes down in several versions, but its core is constant. Wittgenstein was defending the central doctrine of his book, that a proposition and what it describes must share the same logical form, the same skeleton. Sraffa said nothing for a moment. Then he brushed the underside of his chin with the tips of his fingers, an Italian gesture of contempt that every Neapolitan understands at sight, and asked, what is the logical form of that? The gesture meant something. It said something, and said it precisely, to anyone raised where it was current. And it had no picture structure at all, no parts mirroring parts, nothing the Tractatus could parse. Its meaning was not a shadow cast by skeletal form. Its meaning was its use among people, in a shared life where flicking your fingertips out from under your chin counts as a retort. Wittgenstein said later that those conversations made him feel like a tree with all its branches cut, and he meant it as the highest compliment in his vocabulary. Sraffa, he said, had given him an anthropological way of seeing philosophical problems, the habit of asking not what a sign mirrors but what people are doing with it, the way a field researcher would watch a tribe, attending to the customs in which the noises and marks are embedded. Years afterward, in the preface of his second great book, he wrote that he owed to Sraffa's criticism the most fruitful ideas in it, an acknowledgment he extended to no philosopher. The whole second half of his life's work is folded into that shift.

One more thing happened in those first Cambridge months, and Wittgenstein never stopped feeling its weight. In January of 1930, Frank Ramsey went into hospital with jaundice, was operated on, and died. He was 26 years old. The man who had carried the Tractatus into English as a teenager, and whose blunt objections had helped pull its author back into philosophy, did not live to see a line of what came next. Wittgenstein visited him in the hospital during those final days, and grieved for him afterward in his own unsparing, wordless way. Of the voices that had called him back, one had been silenced almost at the moment the return began.

So the man who stepped off the five fifteen as a living monument spent his first Cambridge years quietly becoming that monument's most dangerous enemy. He had come back, he thought, to make a correction. What he found was that the correction would not stop spreading, that the fault ran from the color of a spot in the visual field down through the deepest assumption he had ever made, the assumption that language has a single essence that logic can lay bare. Everything would have to be thought again, from the ground, with a patience he had never needed before. The thinking would take the remaining 22 years of his life, and it would not look like anything that had ever been called philosophy.

Chapter 10: Philosophy as Therapy

The lectures Wittgenstein gave at Cambridge through the 1930s resembled no other teaching in the university, and possibly none in the history of the subject. They were held not in a lecture hall but in his own rooms at the top of a tower in Trinity College, rooms furnished with almost nothing, a camp bed, a card table, a safe for his manuscripts, and a number of folding deck chairs which he set out for the class. There was no lectern, no notes, no syllabus, and in the ordinary sense no lecture. He thought, out loud, in front of the room, about a problem that was actually tormenting him, and the class watched a man wrestle in real time with his whole strength. There were long silences, some of them agonizing, in which he sat gripping his forehead, forbidding interruption, hunting a thought. There were sudden eruptions, at the class, at a student's answer, most violently at himself. He would mutter, I'm a fool, or declare the entire session worthless, or stop dead and say he could not go on, and go on. Students left those afternoons exhausted, sometimes shaken, occasionally converted for life. He told them repeatedly not to become philosophers. Attendance was by his permission, and the permission, once granted, felt like a sentence as much as a privilege.

Out of this unrepeatable classroom came two of the strangest publications never published. In the early thirties, finding his class too large for real work, Wittgenstein dictated a set of notes to a smaller group and had copies typed and bound, and the set circulated in blue paper covers under the name the Blue Book. A second, more careful dictation followed, bound in brown, the Brown Book. He published neither. They were copied, passed hand to hand, loaned and borrowed across two continents like manuscripts in a closed medieval guild, and for years they were the only access the wider philosophical world had to what was happening in that tower room. The rumor they carried was hard to credit. The author of the Tractatus, the legend of exact logic, was now talking about builders shouting for slabs, about children's games, about what we actually say when we teach a word, and he appeared to be claiming that the whole magnificent tradition of philosophical theory was a kind of illness of language.

One of the hands those dictations passed through belonged to Francis Skinner. Skinner had come up to Trinity as a mathematician of real brilliance, fell under Wittgenstein's influence in his early twenties, and became, through the middle thirties, the closest companion of his life, taking down the Brown Book from his dictation, walking with him, planning with him, loving him with a wholehearted devotion that Wittgenstein, by his own anguished account, never managed to repay in kind. True to the master's conviction that academic life corrupts, Skinner abandoned his mathematical career, over the horrified protests of his family, and apprenticed himself as a mechanic in an instrument factory. In 1941 he died suddenly, of polio, in his late twenties, and Wittgenstein, who had grown colder toward him in the final years and knew it, carried the guilt of that coldness for the rest of his life. Among the few possessions he kept to the end were Skinner's letters.

What the Blue Book announced, beneath its homely examples, was a change in the very aim of philosophy, and the change begins with a diagnosis. Philosophers, Wittgenstein argued, suffer from a craving for generality. We are mesmerized by the method of science, which takes 10,000 falling bodies and finds the one law inside them all, and we assume that understanding always looks like that, the many reduced to the one. So when philosophy asks, what is knowledge, what is time, what is beauty, it takes for granted that there must be some single hidden essence, common to every case, waiting to be distilled into a definition, and it treats the particular cases, the places where the words actually live, with contempt, as mere instances cluttering the path to the general formula. The craving feels like depth. It is, he came to think, the engine of two and a half thousand years of elegant confusion, the manufacture of questions that have the grammatical shape of scientific questions and no possible scientific answer, questions that stand to real inquiry the way a knot stands to a thread.

And if the problems are knots, the work of philosophy changes its character completely. You do not answer a knot. You untie it. The new method had no doctrines to offer, no theses, no discoveries, and Wittgenstein was explicit that if anyone tried to advance a thesis in philosophy, it should be something everyone would admit, too obvious to debate. The work consists in description, in laying out plainly the ways our words are actually used, until the spell breaks. Philosophy, he wrote, leaves everything as it is. It does not correct the physicist or the mathematician or the man in the street, because nothing is wrong with what any of them are doing. What is wrong is what happens when language goes on holiday, when words that work perfectly in the traffic of life are taken out of that traffic and asked questions they were never built to answer. Philosophy, in the sentence that names the whole later project, is a battle against the bewitchment of our intelligence by means of language. The enemy is not error but enchantment, and you do not refute an enchantment. You wake from it, slowly, by being shown, case after patient case, what is actually in front of you.

He knew precisely where the deepest enchantments come from, because he had spent his youth inside one. A picture held us captive, he wrote, and we could not get outside it, for it lay in our language, and language seemed only to repeat it to us inexorably. A picture, some compelling image of how things must be, installs itself in the grammar of our words, and from then on every sentence we form seems to confirm it, because the picture is doing the seeing. The man who wrote that sentence was describing, among other patients, himself. The picture theory of the Tractatus, the vision of language as a mirror of facts whose essence logic could expose, had been exactly such a captivity, an image so deep in the forms of language that it felt less like a theory than like sight itself. He had not been refuted out of it, and this is the point of the whole method. He had been shown out of it, by a gesture that had meaning and no logical form, by a color that excluded its neighbor without asking logic's permission, by case after case that the picture could not hold. Now he set about doing for philosophy at large what Sraffa's flicked fingers had done for him.

So the figure in the deck chair classroom was something genuinely new under the sun, a thinker of the first rank whose entire teaching was a method and whose method was a treatment. He compared the philosopher's handling of a question to the treatment of an illness, and he meant the comparison to cut deep. Illnesses are not refuted. They are treated, patiently, one patient at a time, and different sicknesses want different therapies. The prophet of 1918 had handed down final verdicts from the high country of logic. The man in the tower room worked like a clinician, slowly, descriptively, without a system, on the confusions of one example after another. What he was assembling, through those years of lectures and dictations and discarded drafts, was the book in which the treatment would be performed in full view, on the grandest patient available, the human language itself.

Chapter 11: Language Games

Philosophical Investigations, the book that occupied the last two decades of Wittgenstein's life, reached the world in 1953, 2 years after his death, and it opens not with a thesis but with a memory belonging to a saint. The first words on the first page are a quotation from Augustine's Confessions, a passage in which the old bishop recalls how he learned to speak as an infant. My elders, Augustine remembers, would name some object and turn toward it, and I saw this and grasped that the thing was signified by the sound they uttered, and so, hearing words repeatedly in their places in various sentences, I gradually learned to understand what objects they signified, and used these signs to express my own desires. It is a tender, innocent piece of reminiscence, and Wittgenstein chose it as the entrance to his book because of what lies coiled inside it unnoticed. Augustine is not stating a theory. He is doing something more powerful. He is taking a particular picture of language so completely for granted that it does not occur to him that anything else is conceivable. In that picture, every word is a name, naming is the essence of language, the meaning of a word is the object it stands for, and sentences are combinations of names. Learning to talk is learning the labels on the world's furniture.

Wittgenstein begins there because that picture, refined through twenty centuries and pushed to its ultimate rigor, was the picture theory of his own first book. The Investigations opens, in other words, with the author placing his own life's first work at the head of the indictment, traced back to its most ancient and innocent root. And his way of loosening the picture's grip is not a counterargument. It is a story.

Imagine, he says, a language for which the Augustinian picture is actually right, completely right. A builder is putting up a structure, working with an assistant. The language between them consists of exactly four words, block, pillar, slab, beam. The builder calls out one of the words, and the assistant brings the stone he has learned to bring at that call. Conceive of this, Wittgenstein insists, as a complete primitive language, not a fragment of ours but the whole speech of a tribe, the entire verbal life of these people. Children there are trained to fetch at the sound, the way children everywhere are trained, by guidance and repetition and correction. Now ask the simple question. What does the word slab mean in that language? Saying that it names a certain kind of stone already says too little, because the call does not function as a label pasted on an object. It functions as an order. The whole meaning of the cry slab, in the only language these people have, is what it does between them, the fetching it commands, the work it moves forward. Its meaning is not a thing it points at. Its meaning is the part it plays.

From this tiny imagined tribe Wittgenstein draws the central instrument of his later philosophy. He calls the builders' language a language-game, and the term then widens, deliberately, to cover something vast. A language-game is any of the countless patterns in which words are woven together with actions, with circumstances, with human life. Giving orders and obeying them is a language-game. So is describing the look of an object, and reporting an event, and speculating about one, and forming a hypothesis and testing it, and making up a story, and reading one aloud, and acting in a play, and singing rounds, and guessing riddles, and telling a joke, and solving an arithmetic problem, and translating, and asking, and thanking, and cursing, and greeting, and praying. He pours out the examples in exactly this way, a tumbling abundance of them, and the abundance is the argument. Step back from the cases and ask what single thing all of them are doing, what the essence of language is, and the honest answer is that the question has lost its grip. There is no one thing. Speaking is not one activity with one function, the picturing of facts or anything else. It is a teeming family of activities, as various as the rest of human behavior, because it is not separate from the rest of human behavior. The speaking of a language, he writes, is part of an activity, woven into the whole fabric of how its speakers live. New games are born, mathematics gains a branch, slang invents itself, old games fall out of use and are forgotten. Language is not a crystal. It is more like a living thing.

And with the games in view, the famous sentence of the later philosophy can be said. For a large class of cases in which we employ the word meaning, though not for all, the meaning of a word is its use in the language. Not the object it stands for, not an idea hovering in the mind of the speaker, not a shadow cast by logical form. Its use. Think of a chess piece, he suggests. If someone asks what the king in chess is, you could point at the carved figure, but the figure is not the answer, since a button or a bottle cap could serve as the king tomorrow. What the king is, is its powers in the game, the moves it may make, the threats it answers, the role the rules give it. A word is like that. To know the meaning of a word is not to have its object in view or its definition by heart. It is to be able to do things with it, to know your way around its game, and that is exactly what we test when we test whether a child has learned a word. We do not peer into the child. We watch what the child can do.

The Augustinian picture survives on an illusion of uniformity, and Wittgenstein attacks the illusion with the homeliest images he ever used. Think of the tools in a toolbox, he says, the hammer, the pliers, the saw, the screwdriver, the ruler, the glue pot, the nails and screws. How different the functions of these objects are, and how alike words look, spoken one after another in a sentence or printed in a row on a page. The uniform appearance of words is like the row of handles in the cab of a locomotive. They all look alike, being handles shaped for a hand, but one is the handle of a crank that opens a valve by degrees, another works a switch with only two positions, another is a brake lever that works the harder you pull, another a pump handle that acts only while you move it. A man who assumed that all the handles must work the same way, because they look the same, would crash the train. Philosophy, on Wittgenstein's diagnosis, has been crashing the train for millennia, taking words as different in function as is, true, mind, time, and good, and assuming that each must work like a label on an object, because all of them sit in sentences the same way.

At this point a reasonable listener objects, and the book voices the objection in its own pages. Surely this is too loose. If the uses of words are this various, language ought to be chaos, and it is not, so there must be something common to all the uses of a word, some shared core that makes them uses of one word. Here Wittgenstein produces the most influential single passage of his later thought, and the example he chooses is buried in his own terminology. Take the word game. Board games, card games, ball games, the Olympic games, a child throwing a ball at a wall, ring-a-ring-a-roses. What is common to them all? Do not say there must be something common, he warns, or they would not all be called games. Look and see whether there is. Is it winning and losing? The child at the wall neither wins nor loses, and neither does the circle of children singing. Is it skill? There is skill in chess and little in a dice game, and the skills are not the same skill. Amusement? Competition between players? Each candidate fits some games and fails others. What looking actually reveals, he says, is a complicated network of similarities, overlapping and criss-crossing, large likenesses and small ones, with no single thread running through the whole. He gives the network a name that has entered the language of every discipline since. Family resemblances. The members of a family are visibly akin, this one has the mother's eyes, that one the father's build, two share a temperament, none shares everything, and there need be no one feature stamped on every face. Games form a family. And so, he argues, do most of the concepts that matter to us, including the very concepts philosophy has spent its history trying to define into a single essence, knowledge, language, number, good. The instruction he gives, four words long, is the whole later method in miniature. Don't think, but look.

A concept held together by family resemblance has blurred edges, and Wittgenstein insists the blur is not a defect. Is a blurred photograph a picture of a person at all, he asks, and is it always an improvement to trade a blurred picture for a sharp one? Isn't the blurred one often exactly what we need? If I tell you to stand roughly there, the instruction works, and a millimeter-precise replacement would not serve better, only differently. Exactness is relative to a purpose. The demand that every genuine concept have a sharp boundary is not a discovery about meaning. It is a preference, dressed up as a requirement, and most of human language ignores it and thrives.

He knew, none better, where the preference comes from, because he had spent his youth obeying it. Logic had seemed to him something sublime, a pure crystal, hard and prior to all experience, and actual language, with its blur and its drift, had seemed a degraded approximation that analysis would redeem. The Investigations contains his verdict on that whole aspiration, in the most physical image he ever wrote. We have got onto slippery ice, he says, where there is no friction, and so in a certain sense the conditions are ideal, but just because of that, we are unable to walk. We want to walk, so we need friction. Back to the rough ground. The crystalline purity had not been a discovery about language but a demand placed on it, and the demand had made thought frictionless and therefore useless, elegant skating above a world it never touched. The rough ground, the actual mixed practices of speaking human beings, is not the degraded case. It is the only ground there is, and the only place where words have traction, because it is where they have work.

What is left of the old majestic question, what is language, once the essence has been let go? Near the beginning of the book Wittgenstein answers with a picture of his own, offered gently, and it is the right image to rest on. Our language, he says, can be seen as an ancient city, a maze of little streets and squares, of old houses and new ones, of buildings added onto in different centuries, and this whole surrounded by a multitude of newer boroughs with straight, regular streets and uniform houses, the suburbs of chemistry and calculus and legal jargon. No one planned the old town. No single principle explains its layout. And it is not a ruin or a problem to be corrected. It is where the life of the people actually happens, knitted by 10,000 paths worn into usefulness by feet. The Tractatus had wanted to map the city onto a perfect grid. The Investigations walks its streets, one game at a time, asking of each corner only the modest, bottomless question that had replaced the dream of essence. What do we actually do here?

Chapter 12: Following the Rule

Buried in the middle of Philosophical Investigations is an argument about something as humble as continuing a series of numbers, and a good many philosophers regard it as the deepest thing Wittgenstein ever wrote. It concerns what it is to follow a rule, and it matters because, on the view the book has been building, rules are everywhere. To use a word correctly is to follow the customs of its use. To add, to measure, to promise, to play, to reason at all, is to go on in the right way rather than the wrong one. Every order, every definition, every signpost on a country road presupposes that a human being can take in something finite, a sound, an explanation, a painted arrow, and be guided by it through an open future of cases that no one has listed in advance. We do this so constantly and so easily that it seems beneath examination. Wittgenstein examines it, and the floor opens.

He stages the problem as a scene of teaching. A teacher is training a pupil to write out a series by the rule, add two. The pupil writes, two, four, six, eight, and continues, correct at every step, through hundreds of cases, and we are satisfied that he has understood. Then, somewhere past 1,000, he writes 1,000 four, 1,000 eight, 1,000 twelve. We stop him. Look what you are doing, we say, you were meant to add two. And the pupil, sincerely puzzled, answers, I am adding two. I am going on exactly as I did before. It emerges that he understood the instruction, all along, as something like, add two up to 1,000, and four after that, and his hundreds of correct steps were correct by his reading as much as by ours. Now, how do we show him that he is wrong? Everything we actually gave him, the spoken rule, the worked examples, the nods of approval, fits his interpretation as perfectly as it fits ours. We can repeat the explanation in other words, but those words too must be taken some way, and his way of taking things is precisely what is in question. We meant him, of course, to go on writing 1,000 two. But what did that meaning consist of? We were not thinking of the step from 1,000 when we taught him. No one can think of every step. The rule has infinitely many applications, and our minds visited only a handful.

The point of the deviant pupil is not that such pupils exist. The point is that we cannot say what he lacks without discovering that we cannot find it in ourselves either. When I learned addition, I encountered a finite number of examples, a finite amount of explanation. Ahead of me lay endless cases I had never considered. What fact about me, at that moment, made it true that by add two I meant the function that says 1,000 two at the thousandth step, rather than some bent alternative agreeing with everything I had done so far and diverging beyond it? A formula in my head? The formula is a string of signs, and signs can be read in deviant ways too. An interpretation, then, a gloss telling me how to take the formula? But an interpretation is just more signs. It hangs in the air along with what it interprets, Wittgenstein says, and cannot give it any support. Each interpretation calls for another, and somewhere the chain has to end in something that is not an interpretation at all, or it never ends. Pressed to its limit, the problem becomes the paradox he states in one of the most discussed sentences of the book. No course of action could be determined by a rule, because every course of action can be made out to accord with the rule. And if anything can be made to accord, then accord has lost its meaning, and with it, it seems, meaning itself. The simplest arithmetic begins to look like a miracle performed without a mechanism.

Wittgenstein's answer to the paradox is characteristic of him. He does not produce the missing mechanism. He rejects the demand for one. The paradox arises, he says, from the assumption that grasping a rule must be a matter of interpretation, of having the right gloss installed in the mind. The escape is to see that there is a way of grasping a rule which is not an interpretation at all, and it is the one in plain sight. It is exhibited in what we do, in what we call obeying the rule and going against it, in actual cases, day after day. Following a rule is a practice, he writes, and the word is doing real work. A practice is not a private flash of insight. It is a custom, a use, an institution, something with a history and a community and a training. The child is not given a metaphysical rail to clamp onto. The child is trained, by example and correction, drilled in counting as we count, until going on this way becomes second nature, and the training succeeds because human beings, overwhelmingly, respond to it alike. And when I, the trained adult, follow the rule, I do not consult anything. When I obey a rule, I do not choose, he writes. I obey the rule blindly. The blindness is not a defect. It is what mastery is. The deliberating, interpreting picture was the fantasy, the imagined machinery behind a competence that never needed it.

He knew where the fantasy came from. We picture the rule as a machine that already contains all its movements, as rails invisibly laid to infinity, so that the right continuation at every step has somehow been traced out in advance, in some harder-than-physical medium, waiting for us. The picture is majestic and explains nothing. There are no such rails. What there is, instead, is something Wittgenstein asks us to find sufficient, and many readers feel a chill at this point in the book. Justifications run out. If I have exhausted the justifications, he writes, I have reached bedrock, and my spade is turned. Then I am inclined to say, this is simply what I do. The teacher who has explained, demonstrated, corrected, and explained again has nothing further behind the explanations. At the bottom of every rule there is not a deeper rule but a way of acting, ungrounded, shared, and stable.

Stable because shared, and here the argument reaches the concept that anchors the whole of his later thought. If rules rest on nothing but how we go on, does correctness collapse into popularity? Is 1,000 two the right answer merely because most of us say so? Wittgenstein's reply draws a careful line. What human agreement settles is not which opinions are true. It is the framework within which true and false get their grip. People agree in the language they use, he says, and that is not agreement in opinions but in form of life. A form of life is his name for the immense, mostly invisible bedrock of shared human nature and shared practice on which every language-game stands, the fact that we naturally point and follow pointing, that we react alike to training, that our memories and perceptions run in step closely enough for counting and measuring and promising to exist at all. Within the practice of arithmetic, the answer is not up for a vote, and no community decision could make the bent continuation correct. But that there is such a practice, that creatures like us converge so totally that disputes over sums are almost unknown among the billions who calculate, this quiet, oceanic agreement is the loom on which the hardness of arithmetic is woven. Logical necessity is not held up from below by iron. It is held taut from all sides, by us.

Some readers find vertigo in this, the sense of a floor replaced by a net of hands. Wittgenstein, by every sign, found peace in it. The craving had been for a foundation beneath human practice, some rail or crystal that would guarantee our going on, and the craving was one more case of language sending us to look for a something where no something was missing. Nothing is missing. The series continues, the sums come out, the children learn, the spade rings on bedrock, and the bedrock is enough, because it is not beneath our life. It is our life.

Chapter 13: The Beetle in the Box

Nothing in a human life seems more obviously private than a sensation. My headache is mine. You may infer it from my squint, sympathize with it, even cause it, but you cannot have it, and it seems natural to conclude that I alone really know it, by simply having it, while everyone else is guessing from the outside. From there it is one small step to a picture of how the words for sensations work. I feel something, I attend to it, I attach a name to it, and ever afterward the word pain, in my mouth, means this, the felt thing itself, known to me by direct acquaintance and forever hidden from you. It is the Augustinian picture of naming turned inward, the label pasted not on an object in the world but on an object in the soul. Almost everyone who has ever reflected on the mind has held some version of this picture. The most famous argument of Philosophical Investigations is a patient, relentless demonstration that it cannot be right, and the demonstration has been fought over by philosophers for 70 years under a name Wittgenstein never used, the private language argument.

Be precise about the target, because it is easy to aim the argument at the wrong thing. A private language, in the sense at issue, is not a secret code, not a diary in invented symbols, not the muttering a hermit does alone. Codes can be cracked and hermits can be overheard, because such languages are tied, however covertly, to the common world. The private language Wittgenstein has in view is private in a far stronger sense. Its words are to refer to what only the speaker can know, his immediate private sensations, so that no other person could so much as understand it, even in principle. Not a language no one else happens to learn, but a language no one else could learn. If the natural picture of sensation words is correct, then each of us already speaks such a language at the core of our speech, and our public words for pain and joy are mere exports from it. The question is whether the idea so much as makes sense.

So Wittgenstein runs the experiment. Imagine, he says, that I resolve to keep a diary about the recurrence of a certain sensation. I will associate it with the sign S, and write S on a calendar for every day on which I have the sensation. I cannot define S out loud for anyone, by hypothesis. I cannot even define it for myself in ordinary words, since ordinary words belong to the public language and would tie my sensation into the common world. All I can do is a kind of inward ceremony. I concentrate my attention on the feeling, and inwardly point to it, and undertake, solemnly, to call this S from now on. There. It feels as if something has been accomplished, a meaning established, a private institution founded.

Now the argument arrives, and it is short. What has the ceremony actually set up? A definition, even the humblest, establishes a technique, a way of using a word that can be gotten right or wrong on future occasions. That is what makes it a definition rather than a mood. So suppose next Tuesday I have a feeling and write S. The question that kills the project is simple. What is the difference between my using S correctly and my merely believing I am using it correctly? I want to say, I remember that this is the same sensation as before. But my memory of the original sensation is itself just another item in my private theater, with nothing to check it against except more of itself. In the public world, memories can be audited. I remember the train leaving at five, and the timetable, the station clock, the testimony of other passengers can convict my memory of error. Inside the sealed diary of S, there is no timetable, no clock, no witness. Appealing to my memory of S to validate my use of S, Wittgenstein says, is like buying several copies of the morning paper to assure oneself that what it said was true. Whatever is going to seem right to me is right, he concludes, and that only means that here we cannot talk about right. Without a possible distinction between being correct and seeming correct, there is no correctness, and without correctness there is no meaning. The inward ceremony established nothing, not because my attention wavered or my memory is weak, but because there was nothing of the right shape for it to establish. Wittgenstein has a small, devastating question for all such ceremonies of the inner life. Why can't my right hand give my left hand money? The right hand can place the coins in the left, the left can even write a receipt, and yet nothing has been given, because giving is not a movement of coins but a transaction between parties, and one person is not two parties.

The inward naming of S is the same pantomime one level up, all the gestures of a definition with none of its substance. The private institution has one member, one rule, and no difference between keeping the rule and breaking it, which is to say, no rule.

Hear what the argument does not say, because it has been slandered on this point for decades. It does not say that sensations do not exist, that pain is nothing but wincing, that the inner life is a fiction. Wittgenstein anticipated the accusation in the book itself, an imagined interlocutor crying out that he is denying the sensation, and his reply is exact. The sensation is not a something, he says, but not a nothing either. The conclusion was only that a nothing would serve as well as a something about which nothing could be said. The point is not that there is no pain. The point is that the word pain does not get its meaning by labeling a hidden object, and that when philosophy models the inner life on object and name, it produces a something that does no work, a wheel that turns nothing. Our real sensation words are learned and live in the open. The child falls and cries, and the adults teach it words that take up the work of the cry, so that saying it hurts becomes part of the natural history of hurting, woven into comfort and treatment and apology. The word reaches the feeling not by private baptism but by being grafted, in public, onto the natural expressions of the feeling. That, in outline, is how the words for the inner earn their living. What the diary establishes is the demolition. Meaning cannot be founded in a place where no one, not even the founder, can ever check what was founded.

Then, to show what his conclusion means, Wittgenstein built one of the great thought experiments in philosophy, small enough to carry in a pocket. Suppose, he says, that everyone has a box with something in it, and we all call the something a beetle. No one can ever look into anyone else's box, and everyone says he knows what a beetle is only by looking at his own. Now, if these people use the word beetle in their common life, trading it in sentences, teaching it to children, what does the word mean? It cannot mean the thing in the box, whatever each box privately holds. One man's box might hold something quite different from another's. The contents might be constantly changing. A box might be empty. None of this would make the slightest difference to how the word works between them, and so, Wittgenstein says, the thing in the box has no place in the language-game at all, not even as a something, for the box might even be empty. If we construe the grammar of sensation words on the model of object and name, the object drops out of consideration as irrelevant. The moral is not that our boxes are empty. The moral is a diagnosis by reduction. Since the word pain plainly does work between us, does it in hospitals and families and law courts, it cannot be working the way the beetle picture says, as each speaker's label for an unshareable exhibit. What we share, what the word lives on, is the public game, the circumstances and expressions and consequences, not a comparison of hidden specimens that no one has ever performed.

The argument even reaches back and corrects the innocent sentence that started it, the claim that I alone really know my pain. Wittgenstein's remark is that this can be said of me only as a joke. Knowing belongs where doubting belongs. I know the train leaves at five, because I checked, and I might have been wrong. But I do not check my pain, cannot doubt it, cannot be mistaken about it in the way knowledge requires, and so the solemn declaration that I know I am in pain says nothing at all, while the humbler truth underneath it is one of grammar. It makes no sense to doubt first-person pain, and what is senseless to doubt is not thereby known. It is simply had, and said. The fortress of inner certainty that philosophy spent three centuries defending turns out to be a misprinted sentence.

There is a question and answer in the Investigations that reads like a motto for everything Wittgenstein did after his return, and it belongs to this argument above all. What is your aim in philosophy, he asks. To show the fly the way out of the fly-bottle. The fly-bottle was a common piece of household glassware once, a trap baited with something sweet, easy to enter and almost impossible to leave, because the fly, once inside, beats forever toward the light through the glass, and the one direction it never tries is the dark opening through which it came. The philosopher haunted by the privacy of the mind is the fly. How can I ever really know that others feel? Might the color I see as red be the color you see as green, with no possible test? Am I alone behind my eyes? These questions feel profound, and they sting like profundities, and on Wittgenstein's diagnosis they are the buzzing of a creature sealed in glass by a picture, the name-and-object picture carried into the soul, which makes every mind a box and every word a beetle. There is no way forward through that glass, no theory that answers the skeptic on his own terms, because the terms are the trap. The way out is the way in, walked backward. Return to where the words were learned, the fall, the cry, the comfort, the shared life in which pain has its home, and the questions do not get answered. They get unasked. The glass was never locked. It was only lit.

Chapter 14: The Duck and the Rabbit

There is a simple line drawing, first printed in a German humor magazine in the 1890s, that found its way into Wittgenstein's late writing and has lived there ever since. Looked at one way, it is a duck, the head in profile, the long bill pointing away to the left. Looked at another way, the same lines are a rabbit, and what had been the bill becomes a pair of ears laid back along the head. Nothing on the paper moves. Every line keeps its exact place, and the eye keeps receiving exactly the same ink. And yet, as anyone who has met such figures knows, the image flips. One moment it is a duck, the next a rabbit, and you can feel the change happen, even though you would swear, truthfully, that nothing whatever has changed.

Wittgenstein turned this toy over for years, in the writings assembled after the Investigations as its second part, because it sits exactly on a seam in our concept of seeing. Notice that we use the word see in two ways that feel utterly different. I see a duck, says one observer of the figure, and reports what is before him. Now I see it as a rabbit, says another, and reports something stranger, a perception that admits in the same breath that the object never altered. Wittgenstein calls the second phenomenon the noticing of an aspect, and the moment of the flip the dawning of an aspect, and he is careful, in his patient way, to refuse both of the easy stories about it. It is not a change in the object, since the lines are fixed. But neither is it a piece of reasoning, an inference laid on top of neutral data, for you do not conclude that the figure could be a rabbit, the way you might conclude that a distant shape could be a deer. You see the rabbit. The thought and the sight arrive fused, and the experience belongs fully to neither category our language keeps ready. Seeing an aspect is something the eye and the mind do together, and our concepts strain to hold it.

What makes this more than a parlor curiosity is that aspect seeing is not a special performance reserved for trick drawings. It is the ordinary texture of human perception, invisible because it never stops. We do not receive patches of color and infer a friend's face. We see the friend, the welcome in his expression, the tiredness around his eyes. We see the drawing of a cube as a cube, the photograph as a person, the scrawled letters as a word, and in none of these cases does it feel like interpretation, because continuous, settled aspect perception is simply what seeing is like for creatures trained as we are trained. The flip of the duck and rabbit matters because it is the one place where the seam shows, where seeing-as catches its own reflection. For an instant we watch our own act of taking, the contribution we are always making and never noticing, and then the figure settles and the act disappears into its result again.

To bring out what is at stake, Wittgenstein imagines a deficit. Suppose a person who is in no way blind, whose eyes test perfectly, who can describe the duck-rabbit figure with complete accuracy, list its lines, even tell you that some people call it a duck picture and others a rabbit picture. But the flip never happens for him. Nothing dawns. He can classify but never see one thing in another. Wittgenstein calls this condition aspect blindness, and asks what such a person would be missing. Not information, since he can state every fact. Not acuity, since his eyes are sound. What he lacks is a whole dimension of relationship to what he sees, the dimension in which pictures resemble, evoke, fit, and come alive. He could match a portrait to a face by measurement, but the portrait would never look like anyone to him. He would live among signs and surfaces that all worked, and none of them would ever shine.

And the deficit, Wittgenstein saw, would not stop at pictures. Words have aspects too. Say a familiar word aloud 10 times, and feel it go strange in the mouth, suddenly a mere noise, its meaning drained out, like a face stared at too long. Or notice how the name of a composer can seem to fit his music, how a word in a poem feels chosen for its physiognomy and not just its function, how the same word said as a name and said as a description carries a different experience with it. Wittgenstein spoke of experiencing the meaning of a word, and imagined the corresponding blindness, a person who used every word correctly, paid out language like a machine paying out rope, and never once felt a word as apt, heavy, comic, or beautiful. Such a person could transact all the business of language. What he could not do is love it, and poetry, for him, would be a ledger that scanned.

The duck and the rabbit earned their place as the quiet emblem of Wittgenstein's whole later life. He had come to believe that the deepest changes a mind can undergo are of exactly this form. The facts stay where they were. Every line keeps its place, nothing new is discovered, and yet everything is suddenly different, because an aspect has dawned and the whole is organized another way. His own passage from the crystal of logic to the rough ground had been such a flip, not a new fact but a new way of taking all the old ones. What he offered his students, in the end, was rarely an argument and never a doctrine. It was the patient arrangement of what they already knew, turned and turned again, until the bill became ears, and they saw.

Chapter 15: The Inner and the Outer

Modern philosophy has lived for three centuries inside a picture of the mind that Descartes made canonical, and it can be drawn in a sentence. Each of us is an inner theater, a hidden stage on which sensations and thoughts and feelings perform before an audience of exactly one, while the body stands outside like the wall of the playhouse, transmitting muffled reports of the show to the strangers in the street. On this picture, what I really am goes on in the dark behind my face. Other people get the poster, never the play. The picture is so deep in our language that it can pass for common sense, in phrases like keeping something inside, or never knowing what goes on in another's head. The last decade of Wittgenstein's thought was, among other things, a sustained campaign against this geometry of the person, and the campaign is easy to misread. He is not denying that we have inner lives, any more than the argument about the diary denied sensations. He is redrawing the map on which the inner life is located, and the redrawing begins with a question of grammar.

Listen to the sentence, I am in pain, and ask what kind of sentence it is. The theater picture says it is a report, a bulletin from the private stage, exactly like, there is a fire in the next room, except that only one observer can ever check it. But watch how the sentence actually behaves. A report is gathered from evidence, can be carelessly mistaken, can be double-checked before filing. None of this fits. I do not examine myself and conclude that pain is present, I do not say, I think I am in pain but let me look again, and where checking makes no sense, reporting is the wrong category. The utterance functions less like a bulletin and more like conduct, a piece of pain-behavior that the language has refined, continuous with the groan it often replaces and the grimace it accompanies. Wittgenstein's word for such first-person utterances is avowals. They are expressions of the inner, not descriptions of it. And this single grammatical observation dissolves the famous asymmetry that haunted the theater picture. Why can I say how I feel without evidence, while you must watch and infer? Not because I have a front-row seat and you are outside the building, but because the first person and the third person play different parts in one public game. From me, the words are expression. From you, words about me are description. Two roles, not two locations.

The same redrawing transforms the question of how anyone knows the mind of another. On the theater picture this is a scandal, a leap from observed body to hidden guest, never justified, merely habitual. Wittgenstein turns the scandal around. If I see someone writhing in pain from an evident cause, he says, I do not think, all the same, his feelings are hidden from me. The doubt the philosopher recommends is one that no human being actually has, or could live with, and our certainty about one another does not behave like a conclusion at all. My attitude toward him, Wittgenstein writes of a fellow human, is an attitude toward a soul. I am not of the opinion that he has one. Opinions are adopted on evidence and abandoned under counter-evidence, but my response to your wince, your laugh, your voice, lies deeper than opinion, in the natural reactions of my kind, the recoil at another's wound, the answering smile that an infant gives a face within weeks of birth. Treating you as minded is not a theory I hold about you. It is the way creatures like us meet, the given on which every later doubt or theory has to stand.

His most compressed formula for the new geometry is also one of his most quoted sentences. An inner process stands in need of outward criteria. Take understanding, or remembering, or expecting, the workhorse concepts of the mental. What settles whether a pupil has understood a formula? The theater picture says, a private event of understanding, a click behind the eyes. But the click, even when there is one, settles nothing, because a person can feel the click and still go on wrongly, and another can feel nothing and go on right, and what we actually call understanding is the going on, the mastery displayed across time. The identity of the inner is woven into its outward life, into circumstances and abilities and consequences, and severed from that weave the inner notions lose their sense, not their privacy. This is not behaviorism, the doctrine that mind is nothing but movement, and Wittgenstein took care to mark the difference. Criteria can be feigned, and pretense is real. But notice that pretense itself is possible only inside a complicated form of life, a practice that takes training, context, and a future in which the mask can slip. A dog, he observes, cannot simulate pain, not because dogs are too honest but because the surroundings that give simulation its sense, rehearsal, audience, motive, unmasking, are missing from a dog's life. Even deception, the theater picture's favorite witness, testifies against the theater. Lies are performances in the public world, not leaks from the private one.

Wittgenstein sharpened these thoughts against the best psychology he could find, and for years the book he set his students was the great Principles of Psychology of William James. He admired James the man, and as a young student he had told Russell that James's study of religious experience had actually made him a little better, the highest praise he gave any book. But James the methodologist became his chosen sparring partner, because James practiced introspection with complete seriousness, turning his attention inward to catch the self in the act of being a self, and reporting, with marvelous honesty, that what he found were mostly peculiar motions in the head and between the head and the throat. There, said Wittgenstein, is the whole lesson. James went looking for the referent of the word self the way one looks for the source of a draft, and found muscle sensations, because that is what attending hard to oneself turns up. The experiment did not reveal the meaning of the word self. It revealed the state of a philosopher's attention. Introspection is a fine way to notice what crossing your eyes feels like, and a hopeless way to discover what mental words mean, since their meaning was never deposited inside, but lives in the games we play with them between us.

The limits of those games, and their dependence on a shared life, produced the single most famous sentence of his late period. If a lion could talk, we could not understand him. The remark sits beside another, less quoted and more tender. One human being, he notes, can be a complete enigma to another. We learn this when we come into a strange country with entirely strange traditions, and, even given mastery of the country's language, we still cannot find our feet with them. Understanding speech was never just decoding sounds. Words take their sense from the life around them, from what its speakers fear, honor, play, and repeat, from the whole tapestry in which the form of life embeds each phrase. The lion's life, structured by appetites and perceptions we share only distantly, would give his sentences supports we cannot stand on. The grammar might parse. The feet would never be found. And between humans the same truth operates in mercifully smaller degrees. Understanding one another is not the telepathic inspection of theaters. It is the slow, never-finished business of coming to share enough life for the words to sit in.

All of which gathers into the gentlest sentence Wittgenstein ever wrote about the soul, and the right one to end on. The human body is the best picture of the human soul. Not its container, not its disguise, not the wall of the playhouse. Its picture. If you want to know what a soul is, do not peer behind the face, because behind the face there is only anatomy, and the anatomy is not the secret. Look at the face. Grief is not the invisible cause hidden somewhere back of the tears. Grief is what you are seeing when you see a person weep in that way, in that life, with that history, and a man's tenderness is in how his hand steadies a child, visible, public, and as deep as anything hidden could ever have been. The theater picture promised depth and delivered a locked room that made every person a stranger. Wittgenstein closes the room and gives the depth back to where human beings actually live, to faces and voices and hands, which is where, all along, we had been reading one another, soul to soul, in plain sight.

Chapter 16: The Ceremonial Animal

In the early 1930s Wittgenstein read, with mounting indignation, the most famous anthropology book of his age, and the notes he made on it contain some of the most revealing pages he ever produced. The book was The Golden Bough, by Sir James Frazer, a vast and elegant compendium of the world's magic and ritual, organized around a single haunting image. In a sacred grove in ancient Italy, Frazer relates, there stood a priesthood that could be obtained in only one way. The candidate killed the priest, and then held the office, sword in hand, waiting for the man who would someday kill him. Around this dark anchor Frazer assembled rain dances and harvest effigies, fire festivals and corn spirits, from every continent, and he explained them all with one confident theory. Magic, he argued, is primitive science. The savage believes, mistakenly, that imitating rain brings rain, that burning an enemy's image harms the enemy. Ritual is technology that does not work, and the history of mankind is a slow graduation from magic through religion to the laboratory.

Wittgenstein thought this explanation was not merely wrong but blind, and his contempt for it had an unusual temperature. Frazer, he wrote, is more savage than most of his savages. The theory fails first as simple observation. Consider the rain dance, Frazer's showpiece of failed technology. The peoples who hold rain ceremonies hold them, Wittgenstein noted, when the rainy season approaches, when the rain is in a sense already coming, and not in the parched heart of the dry months when magical technology would be most urgently needed. They are not stupid. The same communities that dance for rain till their fields with perfect practical intelligence, build huts that stand, track game by real signs, and drop techniques that fail. If ritual were engineering, its practitioners, the most ruthlessly pragmatic people on earth where survival is concerned, would have noticed within a generation that it does not deliver. Whatever the ceremony is doing, it is not trying and failing to be irrigation.

What is it doing, then? Wittgenstein answers with examples from our own lives, because his deepest objection to Frazer is the pretense that ritual is something other people do. A man kisses the photograph of the woman he loves. He does not believe, not even a little, that the kiss is felt at a distance or that it improves his prospects. The act is not based on a belief and aims at no effect. It aims at a kind of satisfaction, Wittgenstein says, and achieves it, or rather, it does not aim at anything at all. We act in this way, and then feel satisfied. A mourner does not test the efficacy of laying flowers on a grave. A man who strikes the table in rage is not attempting carpentry. These are expressions, gestures in a language older than language, and the rain dance belongs with them, a community turning to face the sky at the turning of the year, enacting its need and its dependence, the way a face enacts grief. Magic, he suggests, gives a wish a body. The error was to read a poem as a failed instruction manual. And his summary phrase deserves to be famous. Man, he wrote, is a ceremonial animal.

Beneath the local correction lies a challenge to the whole idea of what it is to understand human things. Frazer explains each rite by conjecturing its history, the primitive theory from which it descended, and Wittgenstein observed that even where such hypotheses are right they leave the real question untouched. Take the fire festivals of old Scotland, in which villagers drew lots and the loser leapt 3 times through the flames, a game that Frazer traces back, plausibly enough, to human sacrifice. What unsettles us about the rite, Wittgenstein points out, is not the conjectured archaeology, which is merely probable and merely past. It is the thing itself, present before us, the lot, the chosen one, the fire, and what they stir in us, because we carry within ourselves whatever made such practices possible. The deep and the sinister in the ceremony do not become apparent from the history of the external action. We ascribe them from an experience in our own souls. Understanding here is not tracing causes. It is finding the rite in ourselves, recognizing our own ceremonial nature in the strange mirror, feeling the kinship that makes the strange intelligible. For work of that kind, Wittgenstein proposed a different ideal, which he called a surveyable presentation, an arrangement of the material, case set beside case, our kisses beside their effigies, our flowers beside their fires, that lets connections show themselves until the practice no longer looks like an error in need of correction but like a possibility of human life in need of acknowledgment.

The pages on Frazer are short, and they cast a long shadow, because the mistake they diagnose is not confined to Victorian anthropology. It is the standing temptation of every human science, the assumption that to understand people is always to explain them as one explains weather, by causes and laws, and that description without hypothesis is somehow not yet knowledge. Against this, Wittgenstein held up a humbler and harder ideal. Some things are understood not when they are explained but when they are seen rightly, placed among their kin, brought close enough to our own life that we stop asking what malfunction produced them. The rain dancer and the man kissing a photograph are not failed scientists. They are our family, doing what the ceremonial animal does, giving form to what it cannot engineer, its love, its dread, its dependence on skies it did not make. A philosophy that began by guarding the unsayable had found, in the dances of strangers, one more language that says nothing and shows everything.

Chapter 17: Inventing Mathematics

In the spring of 1939, the two most original minds in Cambridge sat in the same small classroom, on opposite sides of a question that sounds like a joke and is not. The question was whether mathematics could fall down. Wittgenstein, newly elected to his chair, was giving a course of lectures on the foundations of mathematics, thinking aloud in his usual way before a handful of students. Among the students that term was a young fellow of King's College named Alan Turing, who 3 years earlier had written the paper that invented the modern idea of the computer, a paper which answered one of the deepest open questions in logic by imagining a machine that reads and writes marks on an endless tape. Turing was not there to take notes. He was there to disagree, and Wittgenstein knew his value perfectly. When Turing once remarked that he would miss the next session, Wittgenstein told the class, in effect, that there was little point holding it, since the others would agree with everything he said.

The collision came over contradiction, and to feel its force one must remember what contradiction meant to that generation. The paradox that had wrecked Frege's system sat in living memory like a crater, and the great programs of the age, Russell's among them, had been built to wall such fissures out of mathematics forever. The orthodoxy, shared by nearly every working logician, held that an inconsistency anywhere poisons everything, because from a contradiction, by the standard rules, any statement whatever can be derived. Let one false coin into the treasury and the whole currency is worthless. Hidden somewhere in the systems we trust, an undetected contradiction would mean that arithmetic itself was bankrupt and had merely not yet noticed. Hence the anxious, heroic projects to prove mathematics consistent, to certify the treasury once and for all.

Wittgenstein, in front of his class, calmly declined the entire picture. Why, he asked, is everyone so afraid of contradictions? Suppose a contradiction did turn up in the depths of arithmetic. What would actually happen? Turing gave the orthodox answer in its most practical form. If you used a calculus that contained a hidden contradiction to do real work, he said, then something could go wrong in reality. A bridge designed with it might fall down. And there the issue stood, sharp as it has ever been put. Wittgenstein's reply ran along lines like these. Bridges fall because measurements are wrong, because materials fail, because the physics was misjudged, and a bridge built with sound engineering does not collapse on the day a logician discovers a paradox in set theory. A contradiction in a calculus is not a charge of explosive buried in the concrete. It is a place where the rules, as written, give conflicting instructions, like a signpost pointing both ways at once, and what happens when human beings reach such a place is perfectly familiar. They stop. They notice. They make a ruling, the way a game whose rules conflict in some strange position gets a new rule, and then they go on calculating, exactly as before everywhere else. The fear that one local conflict licenses everything everywhere takes the formal derivation rules with a superstitious literalness, as if the calculus used us rather than the other way around. He spoke, in his writing on the subject, of the superstitious dread and veneration of contradiction among mathematicians, and he chose the religious vocabulary deliberately. A contradiction was being treated as a demon, when it is more like a pothole. Turing was not convinced, and said so, term after term, with a directness almost no one else dared use in that room. He eventually stopped attending. The argument between their positions has continued in the philosophy of logic ever since, with honors still disputed.

Behind the local quarrel stood Wittgenstein's larger heresy, his assault on the most natural picture of mathematics anyone has, the picture most mathematicians privately love. On that picture, mathematical reality is a landscape, timeless and independent, its truths in place before any human counted, and the mathematician is an explorer who discovers what was always there, the way an astronomer finds a comet. Proof, on this picture, is a telescope, a way of seeing into the eternal. Wittgenstein proposed the reversal that still scandalizes. The mathematician, he wrote, is an inventor, not a discoverer. A new proof does not uncover a path that was lying in the dark. It builds a road, and the road changes the landscape. Before the proof, he argued, the proposition did not stand there fully formed, merely unverified, like a sealed letter waiting to be opened. The proof gives the proposition its place, its connections, its very sense, by forging a new technique, a new way of operating with signs that we then adopt as binding. What the proof produces is not news from a far country. It is a new instrument in the toolbox of the practice, and the feeling of eternal necessity that attends it is the depth of our commitment to the technique, not the gravity of an abstract realm. Mathematical propositions, on this view, do not function like descriptions at all. They function like standards, the way rules of measurement do. We do not check arithmetic against the world. We measure the world with arithmetic, which is why no experience refutes a multiplication table, and why its hardness is the hardness of an adopted measure, kept rigid because everything else is judged by it.

He insisted, just as he had about sensations, on what this view does not say. It does not say that mathematics is arbitrary, that we could decree the sums to come out otherwise the way a club amends its bylaws. The techniques are constrained from every side, by their uses in counting and building and predicting, by their dovetailing with one another, and beneath everything by the bedrock of agreement in how trained human beings go on, the same ground on which rule-following itself stands. Nor did he have the slightest quarrel with mathematics as practiced. The calculations are in perfect order. What he rejected was the mythology that grows around the practice, the prose in which mathematicians describe themselves as in contact with eternal objects. What a mathematician is inclined to say about the reality of mathematical facts, he remarked, is not itself a philosophy of mathematics, but material for philosophical treatment. The work is sound. The dream the worker dreams about the work is the patient.

From this height, the great foundations crisis, the crisis that had set his whole life in motion, receives its quietus. The programs of Frege and Russell had assumed that arithmetic was an edifice in danger, needing logic poured beneath it as underpinning. Wittgenstein's late verdict is contained in a single image. The mathematical problems of what is called foundations, he wrote, are no more the foundation of mathematics than the painted rock is the support of a painted tower. The picture of arithmetic trembling until logicians certify it has the whole order of dependence backward. Counting, calculating, measuring, the techniques drilled into every child and exercised in every market and workshop on earth, are among the most stable practices our species possesses, and they were stable for millennia before symbolic logic existed. Set theory's paradoxes never made a single shopkeeper miscount the change. The anxiety was real, but it was a philosopher's anxiety, generated by the demand that practice hang from a sky-hook of pure logic, and it is treated, like every illness in his late philosophy, not by building the sky-hook but by showing that nothing was ever hanging.

He wrote more on mathematics than on any other single subject, hundreds of pages of remarks published after his death, and it is the least loved part of his legacy. Mathematicians have largely ignored it, logicians have often been hostile, and even sympathetic philosophers call it his most contested work. Perhaps that is fitting. The lectures of 1939 had set the pattern, the philosopher and the engineer of the computable, each unable to move the other, each in possession of a piece of the truth too large to hand across the room. Turing went off to build the machines that won a war and inherited the earth. Wittgenstein went on writing, in notebooks no one would read for decades, that the majesty of mathematics is not in the heavens, and never needed to be, because a necessity built out of human agreement, one that has held every bridge we have ever trusted, is majesty enough.

Chapter 18: The Riverbed

The last philosophy Wittgenstein ever wrote was an answer to a man holding up his hands. In 1939, before a learned audience in London, G. E. Moore had delivered one of the most discussed performances in modern philosophy, a proof, he said, of the existence of the external world. The skeptics had argued for three centuries that the world outside the mind might be a dream, and that no one could strictly know otherwise. Moore's proof consisted of raising his right hand and saying, here is one hand, then raising his left and saying, and here is another. Two human hands exist, therefore an external world exists, and the proof, he announced with complete seriousness, was perfectly rigorous. Elsewhere Moore had drawn up a list of things he claimed to know with certainty, that the earth existed for many years before his birth, that he had never been far from its surface, that he had a body, that other people exist and have thoughts. Philosophers found the performance maddening in a way they struggled to articulate. The proof refuted no skeptic, and yet no one could quite say what was wrong with it, and the hands hung in the air of the subject for a decade.

Wittgenstein thought about those hands during the last 2 years of his life, and the notes he wrote, on scraps and in notebooks, in Vienna and Oxford and finally in the doctor's house in Cambridge, were gathered after his death into the book called On Certainty. It is the most unified thing he ever wrote, composed with death visibly approaching, and it carried his late method into the oldest question in the subject, the question of whether we can be certain of anything at all. His verdict on Moore has the double edge his verdicts usually had. Moore, he thought, had grasped something enormous, and had misdescribed it completely.

The misdescription lay in one word. Moore said he knew these things, and the grammar of knowing, the same grammar that had earlier unmasked the fortress of inner certainty, will not bear the weight. Where the word know does honest work, certain other words work alongside it. I know the shop closes at six because I checked, and I could in principle be wrong, and you could ask how I found out, and I could find out better. Now try to run that machinery on Moore's sentence. How did he find out that he has two hands? What would checking be, and what would discovering a mistake be? If a man looks at his own raised hand in good light and is not sure, we do not send him for more evidence, because there is no court more authoritative than the one already in session. And where doubt has lost its sense, the claim to knowledge has lost its sense too, not because we are ignorant but because the whole machinery of evidence, checking, and error has nothing here to grip. Moore was answering the skeptic by trumping a meaningless doubt with a meaningless certainty, one player making an illegal move and the other solemnly capturing the piece.

But the deep question is what Moore's certainties are, if they are not knowledge, and here Wittgenstein produced the idea for which the little book is famous. Consider everything you would call inquiry, asking, testing, verifying, doubting, proving. Every one of these activities, he observed, happens against a background that is not itself being tested. The scientist who doubts a measurement does not simultaneously doubt that his instruments exist, that the world is older than this morning, that words mean today what they meant yesterday. He could not. The questions we raise, he wrote, depend on the fact that some propositions are exempt from doubt, as it were like hinges on which those questions turn. If you want the door to move, the hinges must stay put. That the earth exists, that I have a body, that things do not pop out of existence when no one looks, these are the hinges of all our asking, and their certainty is not an achievement of inquiry. It is what makes inquiry possible at all. Moore's list was not a list of his best-established findings. It was an inventory of hinges, and his mistake was to present the door frame as if it were the prize trophy of the hunt.

This reverses the picture of doubt that philosophy had carried since Descartes made systematic doubting the badge of rigor. The skeptic presents doubt as the natural starting point, the default from which belief must earn its way up. Wittgenstein points out that in any actual human life, the order is the opposite. A child does not begin by doubting and gradually concede. The child learns by believing the adult, swallowing whole the words, the names, the ways of going on, and doubt arrives later, as a refinement, a special move within a practice already mastered. You cannot teach a child to doubt before you have taught it everything else, because doubting is a technique, with rules, learned like the rest. And a doubt that tried to doubt everything at once would not be a superhumanly rigorous doubt. It would not be a doubt at all, because it would have devoured the background that gives doubting its meaning, like a fire praised for its honesty as it burns down the courthouse. The skeptic's universal doubt is not the hardest test our beliefs can face. It is a wheel disconnected from the mechanism, spinning impressively, moving nothing.

Yet Wittgenstein was no dogmatist about the hinges, and the image he found for their strange status is among the most beautiful he ever made. Think of our whole system of conviction, he suggests, as a river. The moving water is the ordinary traffic of empirical belief, the propositions we test, revise, and abandon with the day's evidence. But the water moves between banks and over a bed, and the riverbed is the mass of hardened conviction that does not move, that gives the flow its channel. Now look closer at the bed. Part of it is rock, subject to no alteration, or to one so slow it cannot be observed. Part of it is sand, which washes away here and is deposited there, so that over generations the channel itself migrates. Propositions can change their state. What was once fluid hypothesis hardens into channel, what was once bedrock, the ancient certainties of myth and cosmology, softens, washes out, and is replaced. There is not, and there does not need to be, a sharp line between the bed and the stream. It is the spade-turning bedrock of his rule-following thoughts again, now mapped as a landscape, and given a history. Our certainties are neither eternal foundations nor arbitrary fashions. They are the slowly shifting bed of a very old river, absolutely solid from the standpoint of any swimmer, and never finally still across the centuries.

How does a human being come to have a riverbed at all? Not, Wittgenstein says, by accumulating certainties one at a time, each examined at the gate. When we first believe anything, he wrote, what we believe is not a single proposition but a whole system of propositions, and light dawns gradually over the whole. The child taking in its world is not stacking verified bricks. It is being given, all at once and in use, a world-picture, earth and hands and mothers and words and yesterday and tomorrow, a nest of convictions inside which every particular fact will afterward find its place. Nothing in the nest was proved, and the nest is not thereby a scandal, because proof lives inside it, the way moves live inside a game. Testing has an end, he wrote, and the end is not an ungrounded presupposition propping everything like a bad foundation stone. The end is an ungrounded way of acting, the trust of the hand that takes the cup, the foot that takes the stair, the speech that takes the meaning of its own words for granted and thereby manages to say anything at all.

This is why a person who actually denied the hinges would not strike us as a bolder thinker. If a man told us in earnest that the world began 50 years ago, complete with fossils and memories, or that he was not sure he had a body, we would not reach for counter-evidence, because every piece of evidence we could offer stands on the very floor he has announced he does not stand on. We would suspect madness, or joke, or some use of words we had not yet understood. Between people who share a riverbed, argument is possible. Where the beds themselves diverge, what remains is not refutation but something Wittgenstein names with complete honesty, persuasion, the slow work of bringing another into a practice, as one brings up a child. I said I would combat the other man, he writes, imagining a meeting with people whose deepest certainties differ from ours, but wouldn't I give him reasons? Certainly, he answers himself, but how far do they go? At the end of reasons comes persuasion, and he adds, with a coolness that has troubled his readers ever since, think what happens when missionaries convert natives. He is not recommending the missionaries. He is refusing to flatter us, because the uncomfortable truth he has uncovered holds for our own riverbed too. We did not reason our way into the bed of our convictions, and the person who stands fully outside it cannot be reasoned into it, only invited, trained, slowly immersed. It is an unsettling honesty, and he does not soften it. At the bottom of the best-grounded life there is not a proof. There is a way of living that holds the proofs.

He wrote these thoughts during the final stretch in the house of his doctor, working in a notebook as the cancer advanced, and the work did not trail off. It sharpened. The last entry was set down 2 days before his death, and it worries, with perfect lucidity, at a final wrinkle of the problem, whether a man who says he is dreaming, even if he is in fact dreaming, could mean what he says. The dying man examining the certainty of the waking world, 2 days from leaving it, was not performing courage. He was simply continuing, the water still moving in its channel, the bed holding. The young engineer had gone to Cambridge to find the unshakable foundation beneath human thought, and the whole of modern philosophy had been one long anxiety about that missing foundation. The old man's answer, finished almost at the hour of his death, is that the anxiety mistook the kind of creature we are. Nothing holds up the river. The river holds the river, bank and bed and moving water together, and it has carried everything we have ever known, and it is enough.

Chapter 19: The Walls of the Cage

In November of 1929, a few months after his return to Cambridge, Wittgenstein did something he never did again in his life. He gave a popular lecture. The audience was a student society open to the general university public, the subject was ethics, and the text he prepared, the only one of his unpublished writings he ever polished for ordinary listeners, is the closest he ever came to saying plainly what he believed about value. It begins with a distinction anyone can follow. We use words like good and right constantly in a relative sense. This is a good chair means it serves the purposes of sitting. He is a good tennis player means he meets a certain standard. This is the right road means it gets you to the station. Every such judgment, Wittgenstein observed, can be restated as a plain statement of fact about how things serve purposes, and loses nothing. But ethics, the thing that had stood behind his silence since the Tractatus, is not in this business at all. Ethics speaks of absolute value, the absolutely right road that one would have to take regardless of any purpose, the good that matters not for something but in itself. And no statement of fact, he argued, can ever be or imply a judgment of absolute value. It was the old verdict of the Tractatus delivered to a live audience, the ledger of facts with no entry for the good.

Then the lecture does something theories never do. It turns personal. Since he cannot define absolute value, Wittgenstein instead describes the experiences he himself reaches for when he wants to fix his mind on it. The first is the one he names his experience above all others. I wonder at the existence of the world. It is the lived, breathing counterpart of what the Tractatus had called the mystical, no longer a remark at the limit of logic but something that happens to a man on an ordinary evening. The second he calls the experience of feeling absolutely safe, the state of mind in which one says, nothing can injure me, whatever happens. And having laid these treasures on the table, he calmly points out that both, as utterances, are nonsense. To wonder at the existence of the world is to wonder at something one cannot conceive being otherwise, which is not wondering. To be safe whatever happens is to be safe from nothing in particular, which is not safety. The very expressions that carry what matters most to him fail, and must fail, as language. Our words, he said, will only express facts, as a teacup will only hold a teacup full of water even if I were to pour out a gallon over it. And then comes the sentence that made the lecture immortal. This running against the walls of our cage, this drive in all of us to speak what cannot be said, is perfectly, absolutely hopeless. Ethics, so far as it springs from the desire to say something about the ultimate meaning of life, the absolute good, can be no science. But it documents a tendency in the human mind, he told his audience, which I personally cannot help respecting deeply, and I would not for my life ridicule it. The author of the doctrine of silence stood in front of a room of undergraduates and confessed that he, too, runs at the walls, and honors the bruises.

What this reverence was, in him, his friends struggled to name. He never belonged to a church, practiced no rite, and bristled at theological talk. Yet his closest companions sensed that something organized the whole man from below. The best evidence is a remark he made to Maurice Drury, a gentle Irish student who had become one of his most trusted friends, and who recorded his conversation for decades. I am not a religious man, Wittgenstein told him, but I cannot help seeing every problem from a religious point of view. Not a religious man, by the measures of creed and observance. And yet every problem, the logic, the language-games, the mathematics, seen from a place that only the word religious would name. He once told Drury that Drury's religious ideas seemed to him more Greek than biblical, while his own thoughts were 100 percent Hebraic, and his library of the heart ran accordingly, the Gospels he had carried since the Tolstoy of his war years, Kierkegaard, Augustine, Dostoevsky's monks. Wisdom, he wrote in a late notebook, is something cold, and to that extent stupid. Wisdom merely conceals life from us, the way cold gray ash conceals the glowing embers. Faith, by contrast, is a passion. He did not have the passion, or could not believe he had it. He spent his life circling its flame with the longest attention any modern philosopher has paid.

In 1938 he gave a small class of students his only sustained discussion of religious belief itself, and the lectures, preserved in their notes, apply the whole later philosophy to faith with startling results. Suppose a believer says he believes in a Last Judgment, a day on which the dead will rise and every life be weighed. And suppose Wittgenstein says, as he honestly must, that he does not believe this. Has he contradicted the believer? His answer is no, and the answer is the lecture. If the believer were making a prediction, a forecast like rain on Tuesday, then the unbeliever's denial would contradict it, and the right response would be to examine the evidence, and a belief held on such evidence as religion has would be, he says bluntly, the worst kind of reasoning. But watch how the belief actually lives. The believer does not treat the Judgment as a well-supported hypothesis, does not hedge it with probabilities, does not revise it with the journals. The picture of the Judgment stands before his mind whenever he is tempted, regulates his risks, colors his deathbed. It is not an opinion inside his life. It is a frame around the whole of it. And the unbeliever does not have a rival forecast. He simply does not have the picture, does not steer by it, and so the two men pass without colliding, like ships in different waters. By the same token, Wittgenstein had only contempt for the apologists who would make faith scientific, who treat God as a hypothesis that the fossils might confirm. If religious belief is presented as being reasonable in that way, he said, then it is presented as superstition. Faith is not bad science. It is not science at all, and the deepest believers, he noticed, have always said so themselves.

There is a late entry among his notebooks that shows what these distinctions cost him, and how little of an outsider he really was. What inclines even me, he wrote, to believe in the resurrection of Christ? He plays with the thought. If Christ did not rise, then he decomposed in the grave like every other man, and is a teacher like any other, and can help us no more, and we are orphaned and alone. Only love can believe the resurrection, he writes, and what fights and frets in him is not the evidence but the heart's refusal of orphanhood. He never said he believed. He said that if he could bring himself to it, everything would be different, and he lived his last years reading the Gospels in the mornings as other men read the news. Perhaps the truest summary is the one his own categories provide. Religion was, for him, the supreme case of what cannot be said and must show itself, and what it must show itself in is not argument but a life. Whether his own life showed it was a question he refused to answer for himself, and one his friends never settled either. The cage held him to the end. So did the conviction, never argued and never surrendered, that the walls were the most important thing in it.

Chapter 20: The Poker and the Confession

On the evening of October the twenty-fifth, 1946, the Cambridge Moral Sciences Club met in a crowded college room to hear a visiting speaker from London, Karl Popper, address the question of whether there are genuine philosophical problems. Wittgenstein was in the chair. The fire was burning, and beside it lay a poker. What happened in the next minutes has been disputed by eyewitnesses for the rest of their lives. By Popper's own account, published years later, Wittgenstein seized the poker and gestured with it to punctuate his interruptions, demanding an example of a genuine moral rule, whereupon Popper answered, not to threaten visiting lecturers with pokers, and Wittgenstein threw the poker down and stormed out. Other people in the room remembered it otherwise, the poker idle in his hand as he made a point, the famous retort delivered only after he had already left, the whole exchange less duel than commotion. A book was eventually written just to sort out the testimony, and could not. What no one disputed is what made the story immortal in the first place, the perfect fit between the scene and the man. Of course it was Wittgenstein with the poker. Nobody who had ever sat in a room with him needed convincing.

Because discussion, with him, was never an exchange of views. It was an emergency. He could not produce or endure the lubricated politeness of academic debate, the concessive nods, the witty deflations, the agreement to differ. A question on the table was a live thing, and a careless answer was a moral event, evidence of a soul not taking its one chance at thinking seriously. Visiting philosophers left Cambridge shaken. Colleagues learned to dread the silence that meant he was about to begin. He interrupted, he groaned, he told distinguished men that they were not thinking but performing, and he was harder on no one in any room than he was on himself, which is the single fact that made the rest bearable to those who loved him.

It also explains the strangest habit any great teacher ever had. He spent 20 years systematically persuading his best students not to become philosophers. The gifted ones, the very ones a normal professor would groom for the profession, were told to go and do something honest, medicine, manual work, anything where a person's seriousness is tested by reality rather than rewarded for fluency. The advice was not rhetorical. Maurice Drury, as devoted a student as he ever had, was steered by him out of academic philosophy and into medicine, and became a psychiatrist in Dublin, and Wittgenstein regarded that outcome as a triumph, visiting him, following his cases, telling him he was doing more good than a chair in philosophy would ever have allowed. The university, in his eyes, was a machine for turning the love of wisdom into a salaried performance, and he had seen what it did to the young. A philosophy that did not change how a person lived was, to him, worse than no philosophy, because it spent the sacred coin and returned counterfeit.

He submitted himself to his own court, and the great sitting of that court came in 1937. Through that winter he composed a formal confession, and then did the part that costs, insisting on reading it, face to face, to his friends and family, one after another. Those who heard it remembered their own discomfort more easily than the contents, and one of them admitted to receiving it coldly, having expected darker sins than the two that mattered most to him. The first was that he had allowed people to believe his descent was less Jewish than it was, passing in silence where honesty would have corrected. The second was the old matter of the village school, the lie told at the hearing, never out of his sight. Measured as the world measures, these were modest crimes. That was precisely his point. A man shows what he is in his treatment of the small dishonesties, the ones no one would ever catch, and he had caught himself, and sentence had to be served in the only currency truth accepts, humiliation willingly paid. Some of the friends found the performance excessive, even cruel to its audience. None of them ever again doubted that he meant what he taught.

The standard he was serving had been set early, and partly by a book. In the Vienna of his boyhood, a young philosopher named Otto Weininger had published a strange, brilliant, poisonous volume on sex and character, then killed himself at twenty-three in the house where Beethoven died, and the city never forgot it. Wittgenstein admired the book all his life, not for its doctrines, many of which were repellent, including a self-lacerating hatred of Jewishness that left marks on his own notebooks which historians still read with discomfort, but for its terrible premise. Genius, Weininger taught, is not a gift but a duty, the obligation laid on a man to become fully honest or to perish, with no third way. Wittgenstein took that sentence into himself before he was 20 and never put it down. It is the frame in which his harshness, his confession, his contempt for the academy, and his advice to flee philosophy all hang together. He was not demanding that his students be brilliant. He was demanding that they be real, and he asked nothing of them that he was not visibly bleeding to pay himself.

Of all the documents of this severity, the most useful is a letter, because it shows the demand in plain words. His friend Norman Malcolm once remarked, during the war, that a certain accusation was incompatible with the British national character, and Wittgenstein, by his own account, was made furious by the phrase. Years later he was still angry, and wrote to Malcolm about it. What is the use of studying philosophy, he asked, if all it does for you is enable you to talk with some plausibility about abstruse questions of logic, and if it does not improve your thinking about the important questions of everyday life, if it does not make you more conscientious than any journalist in the use of the dangerous phrases such people use for their own ends. There is the whole teacher in one sentence. Logic was the classroom. The examination was how a man talked about nations and neighbors when no philosopher was watching, and friendship with him meant sitting that examination for life. Those who endured it used a word about him that the poker story tends to hide, and the word was goodness. He was, said many who knew him best, the most demanding person they had ever met, and the nearest thing to a saint, and they did not seem to feel that the two reports needed reconciling.

Chapter 21: The Album

For the last 22 years of his life Wittgenstein wrote almost every day, and published none of it. What he left behind amounted to some 20,000 pages, an entire philosophical literature in manuscript, pocket notebooks and ledgers, typescripts dictated and corrected and dictated again, revisions of revisions, and one box filled with hundreds of paper slips, remarks scissored out of earlier typescripts and saved toward an arrangement he never made. The man whose first book had announced the final solution of philosophy's problems spent the second half of his life producing, at enormous labor, a body of work he could not bring himself to let go of, and the reasons lie as deep in him as anything he ever argued.

Start with the form, because the form was not a quirk but a confession. Everything he wrote after his return is built from the same unit, the short numbered remark, a paragraph or a few lines, polished like a stone, set beside other stones. He tried, by his own testimony, to do the normal thing, to weld his results into a continuous treatise where thought follows thought in orderly procession, and he found that whatever he forced into that shape went dead on the page. His thinking simply did not move in a column. It moved across country. In the preface he drafted for Philosophical Investigations he described the book with an honesty no author has improved on. The remarks in it, he said, are like sketches of landscapes made in the course of long and involved journeyings, the same points approached again and again from different directions, fresh sketches made, the best of them selected and arranged. The book, he wrote, is really only an album. The apology hides a claim, and the claim is pure later Wittgenstein. A subject whose essence is the patient description of cases, seen from more sides than any single path crosses, cannot be honestly written as a system, and a book that pretended otherwise would falsify in its very grammar the thought it carried. The album was not a failure to build the cathedral. It was the discovery that what he had to show was a landscape, and landscapes are not built.

But the form explains only why the work looked as it did, not why it stayed locked in the cupboard, and there the explanation is his perfectionism, a force in him so absolute that the word hardly serves. He rewrote endlessly. He abandoned a complete revision of one dictated book with a sentence scrawled across it declaring the whole attempt worthless. More than once he carried Philosophical Investigations to the edge of the press, into negotiation with publishers, and pulled it back, because somewhere in it a remark stood in the wrong place, or said a shade more than he knew, and a shade more than you know is, by the standard he served, a lie. Meanwhile his ideas escaped anyway, through lecture notes copied and recopied, through the talk of students, and reached the world, as he bitterly put it in that same preface, more or less mangled or watered down, a circulation that stung his vanity and offended his conscience at once. Even that sting could not force his hand. He instructed that the Investigations be published only after his death, and went on revising a book he knew he would never see.

To call this neurosis is to miss what he thought writing was. Working in philosophy, he noted to himself, is really more a working on oneself, on one's own way of seeing things, on what one demands of things. The sentence is the key to the cupboard. He did not experience a flawed remark as a technical defect awaiting repair. He experienced it as a symptom, the visible surface of some remaining confusion or vanity in the man who wrote it, and the revision of the page and the revision of the soul were, for him, a single operation that could no more be finished than a person can be finished. His notebooks mix logic with self-accusation on the same leaf because, in the workshop where he lived, they were the same material. A man who confesses to his friends in a formal sitting does not release approximations under his name. The famous severity he turned on students and colleagues was, on the page, turned inward to the last comma, and the result was a paralysis that was also, seen from inside, simple honesty. He could not say, this is finished and true, of anything, and he refused to say anything else with a title page.

The locked cupboard created the great question that has organized his readers ever since, the question of how many Wittgensteins there were. The outline is stark. A young man builds one of the most rigorous systems in the history of philosophy, declares the problems solved, and leaves. An older man returns and spends two decades dismantling that system in favor of patience, description, and the rough ground, with no system at all. No other major thinker has produced two bodies of work so opposed, each powerful enough to school a generation, and readers have quarreled ever since about whether the life of his mind is a story of rupture or of return. Those who say rupture point to the doctrines, nearly every load-bearing one of the first book rejected by name in the second. Those who say continuity point to everything beneath the doctrines, the same obsession with the limits of language, the same conviction that philosophy's troubles are troubles of expression, the same fierce protection of the ethical from the chatter of theory, the same man, in short, drawing a boundary and standing guard at it, first with logic, then with description. He took a side in this quarrel himself, quietly, in a wish he expressed about publication. The new book, he thought, ought really to appear together with the old one between a single pair of covers, because the new thoughts could be seen in the right light, he wrote, only by contrast with, and against the background of, his old way of thinking. He did not regard the Tractatus as a discarded error. He regarded it as the magnificent, indispensable wrong turn that gives the right road its meaning, his own best example of the captivating picture, preserved the way a recovered patient keeps the X-rays.

So the silence of his last decades, the publishing silence, was not modesty and not fear. It was the working face of his deepest belief about thought and character, that they are one substance, and that releasing careless words is a moral act of the same species as telling a careless truth. He had ended his first book with a sentence about silence and built his last years out of the practice of it, leaving the sketches, the slips, the journeys across the landscape, to be assembled by hands he trusted more than his own, once the man whose flaws might distort them was out of the way. Perfection was not vanity in him. It was the only honesty he recognized, and if its price was that the world would meet his life's work only over his grave, he had settled that account in advance, and considered it paid.

Chapter 22: Light in the Darkness

His will named three of his former students as the keepers of everything he had written, and the choice turned out to be one of the most consequential acts of his life. Elizabeth Anscombe, Rush Rhees, and Georg Henrik von Wright, a Catholic Englishwoman of formidable intellect, an American teacher of austere devotion who made his life in Wales, and a Finnish logician of immense patience, inherited the locked cupboard, and they spent the better part of their own careers turning it into a library. The Investigations came first, in German and English on facing pages like the Tractatus before it, and then, decade after decade, the rest followed, the remarks on mathematics, the volumes on the philosophy of psychology, the notes on certainty, the gathered reflections on culture and value, the box of slips printed as a book of its own, until by the end of the century the whole mountain of papers stood open to anyone, down to photographic copies of the notebooks themselves. It was Anscombe who carried the heaviest single load, the English translation of the Investigations, and her rendering became one of the famous translations of the age. The plain, springy, speaking English in which the world reads the builders and the beetle and the rough ground is her instrument, fashioned so well that for millions of readers her sentences simply are Wittgenstein, an author whose most read book exists in a voice he never heard.

The first wave of his influence had not even waited for the books. It traveled through the people who had sat in the deck chairs, and through their notes, and by the 1950s it had effectively captured English-speaking philosophy. At Oxford, which became the busiest philosophical center in the world in those years, Gilbert Ryle's demolition of the ghost in the machine and J. L. Austin's microscopic studies of what we say and when owed their confidence, and much of their method, to the example of the man in Cambridge, and the whole movement that historians call ordinary language philosophy worked land he had cleared. For a generation, the profession's center of gravity was the conviction he had taught it, that philosophical problems are creatures of language and that attention to use is the way to handle them. It is one of history's neater ironies. The man who told his best students to flee the profession, and who believed his thinking was certain to be misunderstood, became for 20 years the dominant force in the very academy he despised, imitated down to his gestures by men who had never met him.

Fashion turned, as he knew it would. From the 1960s onward, English-language philosophy re-armed itself with formal logic and allied itself ever more closely with the sciences, and the new temper had little patience for a thinker who taught that philosophy should describe rather than explain and that the deepest problems end not in theories but in peace. The naturalistic decades filed him, politely, as a historical figure, admired, anthologized, and quietly set aside. Yet even at the low tide of his professional standing, his arguments would not stay filed. In 1982 the logician Saul Kripke published a small book on the rule-following passages, reading them as the most radical skeptical paradox since Hume, and the book set off 20 years of debate in exactly the technical heartland that had moved on, conducted around a hybrid figure, half Kripke and half Wittgenstein, that the literature affectionately named by splicing their two names together. The private language argument has never left the syllabus. The duck and the rabbit sit in every psychology textbook. And philosophers of mind who would never call themselves his followers still work in the long shadow of his claim that the inner takes its identity from the outer, every time they argue about what a mental state could be.

The turn of the millennium then brought something nobody had predicted, a genuine professional revival. Epistemologists discovered that the hinges of his last notebooks offered a living research program, a way of treating the old skeptical puzzles that neither refutes the skeptic nor surrenders to him, and a school now works under the banner of that single image. Philosophers of perception and of cognitive science, rebelling against the picture of the mind as a computer sealed in the skull, found that the man who located meaning in shared practice had been there generations before them, and his late psychology reads today like an anticipation of whole movements that treat thinking as something done by embodied creatures in a world, not by a theater behind the eyes. When professional philosophers were polled at the century's end and asked to name the most important philosophical books of the hundred years just closing, the Investigations stood first, ahead of every system and every school, a verdict delivered by exactly the profession whose temper had set him aside. The stone the builders rejected had quietly become the measure.

Beyond the borders of philosophy, his ideas seeped outward the way groundwater moves, invisibly and everywhere. Anthropology and sociology absorbed the idea of forms of life, and fought for a generation over a book by his student's student Peter Winch arguing that understanding a society is mastering its games rather than measuring its behavior, a thesis that is the Frazer notes in modern dress. Theology found in him a way to speak of faith after the collapse of the old proofs, as practice and picture rather than hypothesis, and a school of religious thinkers built on the lectures about belief. Linguists, legal theorists, and literary critics took the tools wholesale, and family resemblance became common currency in every field that classifies anything, from biology to library science, while computer scientists wrestling with how machines might handle concepts without definitions rediscovered, sometimes knowingly, the analysis of the word game. Artists claimed him outright. He is the rare philosopher with a serious presence in novels, poems, paintings, and films, the subject of memoirs and plays, and when the literary world tells the story of his century, he appears in it as a character, the ascetic in the deck chair, as vivid as any he disliked reading about. The popular image owes most to a single book, the biography by Ray Monk that appeared four decades after his death, whose title, The Duty of Genius, names the Weininger standard he had carried since boyhood, and whose achievement was to show a mass readership what the friends had always insisted, that the life and the thought were one fabric and could only be told together.

If a single thread runs through everything he left, for the specialist and the night-time listener alike, it is his lifelong resistance to the idolatry of science. No philosopher respected the sciences more concretely, the engineer who had flown kites and machined propellers and designed laboratory apparatus with his own hands. What he fought was something else, the creeping conviction of the modern age that the scientific kind of understanding is the only kind there is, that explanation by law and mechanism exhausts what it means to know, and that whatever resists the method, value, ritual, faith, grief, the meaning of a word, the worth of a life, must be either reduced to mechanism or dismissed as noise. Nearly every battle in his career was a front in that one war. Against the positivists who would burn what cannot be verified. Against Frazer's blindness to the ceremonial animal. Against the dream that mathematics needs certification from a deeper science. Against the picture of the mind as a hidden mechanism awaiting its engineers. He wrote once that he felt himself a stranger to the main current of European and American civilization, with its worship of progress and its faith that the unexplained is merely the unexplained so far, and he did not expect the current to slow. It has not. Which is precisely why he has never become obsolete, and why his stock rises whenever a discipline grows sick from its own success at explaining, because he is the great modern witness for the parts of human life that are not problems awaiting solutions, and for the kind of clarity that comes not from a theory but from finally seeing what has been lying in front of us all along.

A century after his first book, the questions he worked have acquired an urgency he could not have foreseen and would have recognized instantly. Machines now produce fluent, grammatical, endlessly plausible language by the billion words an hour, and the world has begun asking, in earnest, what the difference is between producing sentences and meaning them. It is his question. Whether meaning lives in an inner light behind the words or in participation in the shared life where words have their work, whether use without a form of life is use at all, these are no longer seminar exercises but the practical philosophy of the age now arriving, and the deepest analyses anyone possesses of them were written in longhand, in numbered remarks, by a man in a deck chair who never touched a computer and taught the man who invented it.

He never expected any of this, and the proof is in the preface he left on the Investigations, the sentence with which his life's second book goes out to meet the world. It is not impossible, he wrote, that it should fall to the lot of this work, in its poverty and in the darkness of this time, to bring light into one brain or another, but of course it is not likely. In its poverty, he said, of the most influential philosophy book of its century. In the darkness of this time, he said, and meant it, a man who had watched his world burn twice. And then that last clause, with its perfect, characteristic refusal of consolation. It is not likely. He was wrong about the likelihood, and the way he was wrong is the right place to leave him. The light he doubted has gone on arriving for 70 years, not as systems or schools, which he never wanted, but the only way he believed light ever truly comes, into one brain or another, one reader at a time, a knot loosening, an aspect dawning, a fly finding the open mouth of the bottle. Somewhere tonight a student reads the builders and feels the floor of language shift under her feet. Somewhere a person in pain is met by another who does not peer behind the face but reads the face itself, and that, too, is his light, passed hand to hand in the dark he named. He had asked, at the end, that his friends be told he had a wonderful life. Part of the wonder is that it is not finished.