• Philosopher and Mathematician Bertrand Arthur William Russell, 1872
• Philosopher Ludwig Josef Johann Wittgenstein, 1889

Russell led the British "revolt against idealism" in the early 20th century. He is considered one of the founders of analytic philosophy along with his predecessor Gottlob Frege and his protégé Ludwig Wittgenstein. He is widely held to be one of the 20th century's premier logicians. He co-authored, with A.N. Whitehead, Principia Mathematica, an attempt to ground mathematics on logic. His philosophical essay "On Denoting" has been considered a "paradigm of philosophy." His work has had a considerable influence on logic, mathematics, set theory, linguistics, computer science (type theory and type system) and philosophy, especially philosophy of language, epistemology and metaphysics.

Russell was a prominent anti - war activist; he championed anti - imperialism and went to prison for his pacifism during World War I. Later, he campaigned against Adolf Hitler, then criticized Stalinist totalitarianism, attacked the United States of America's involvement in the Vietnam War, and was an outspoken proponent of nuclear disarmament. In 1950 Russell was awarded the Nobel Prize in Literature, "in recognition of his varied and significant writings in which he champions humanitarian ideals and freedom of thought."

Bertrand Russell was born on 18 May 1872 at Ravenscroft, Trellech, Monmouthshire, Wales, into an influential and liberal family of the British aristocracy. His paternal grandfather, John Russell, 1st Earl Russell, was the third son of John Russell, 6th Duke of Bedford, and had twice been asked by Queen Victoria to form a government, serving her as Prime Minister in the 1840s and 1860s.

The Russells had been prominent in England for several centuries before this, coming to power and the peerage with the rise of the Tudor dynasty. They established themselves as one of Britain's leading Whig families, and participated in every great political event from the Dissolution of the Monasteries in 1536 – 40 to the Glorious Revolution in 1688 – 89 and the Great Reform Act in 1832.

Russell's mother, Katharine Louisa (1844 – 1874), was the daughter of Edward Stanley, 2nd Baron Stanley of Alderley, and the sister of Rosalind Howard, Countess of Carlisle. Kate and Rosalind's mother was one of the founders of Girton College, Cambridge.

Russell's parents were radical for their times. Russell's father, Viscount Amberley, was an atheist and consented to his wife's affair with their children's tutor, the biologist Douglas Spalding. Both were early advocates of birth control at a time when this was considered scandalous. John Russell's atheism was evident when he asked the philosopher John Stuart Mill to act as Russell's secular godfather. Mill died the year after Russell's birth, but his writings had a great effect on Russell's life.

Russell had two siblings: Frank (nearly seven years older than Bertrand), and Rachel (four years older). In June 1874 Russell's mother died of diphtheria, followed shortly by Rachel's death. In January 1876, his father died of bronchitis following a long period of depression. Frank and Bertrand were placed in the care of their staunchly Victorian grandparents, who lived at Pembroke Lodge in Richmond Park. His grandfather, who had been Prime Minister, died in 1878, and was remembered by Russell as a kindly old man in a wheelchair. His grandmother, the Countess Russell (née Lady Frances Elliot), was the dominant family figure for the rest of Russell's childhood and youth.

The countess was from a Scottish Presbyterian family, and successfully petitioned the Court of Chancery to set aside a provision in Amberley's will requiring the children to be raised as agnostics. Despite her religious conservatism, she held progressive views in other areas (accepting Darwinism and supporting Irish Home Rule), and her influence on Bertrand Russell's outlook on social justice and standing up for principle remained with him throughout his life — her favorite Bible verse, 'Thou shalt not follow a multitude to do evil' (Exodus 23:2), became his motto. The atmosphere at Pembroke Lodge was one of frequent prayer, emotional repression and formality; Frank reacted to this with open rebellion, but the young Bertrand learned to hide his feelings.

Russell's adolescence was very lonely, and he often contemplated suicide. He remarked in his autobiography that his keenest interests were in religion and mathematics, and that only the wish to know more mathematics kept him from suicide. He was educated at home by a series of tutors. His brother Frank introduced him to the work of Euclid, which transformed Russell's life.

During these formative years he also discovered the works of Percy Bysshe Shelley. In his autobiography, he writes: "I spent all my spare time reading him, and learning him by heart, knowing no one to whom I could speak of what I thought or felt, I used to reflect how wonderful it would have been to know Shelley, and to wonder whether I should meet any live human being with whom I should feel so much sympathy." Russell claimed that beginning at age 15, he spent considerable time thinking about the validity of Christian religious dogma, and by 18 had decided to discard the last of it.

Russell won a scholarship to read for the Mathematical Tripos at Trinity College, Cambridge, and commenced his studies there in 1890. He became acquainted with the younger George Edward Moore and came under the influence of Alfred North Whitehead, who recommended him to the Cambridge Apostles. He quickly distinguished himself in mathematics and philosophy, graduating as a high Wrangler in 1893 and becoming a Fellow in the latter in 1895.

Russell first met the American Quaker Alys Pearsall Smith when he was 17 years old. He became a friend of the Pearsall Smith family — they knew him primarily as 'Lord John's grandson' and enjoyed showing him off — and traveled with them to the continent; it was in their company that Russell visited the Paris Exhibition of 1889 and was able to climb the Eiffel Tower soon after it was completed.

He soon fell in love with the puritanical, high minded Alys, who was a graduate of Bryn Mawr College near Philadelphia, and, contrary to his grandmother's wishes, married her on 13 December 1894. Their marriage began to fall apart in 1901 when it occurred to Russell, while he was cycling, that he no longer loved her. She asked him if he loved her and he replied that he didn't. Russell also disliked Alys's mother, finding her controlling and cruel. It was to be a hollow shell of a marriage and they finally divorced in 1921, after a lengthy period of separation. During this period, Russell had passionate (and often simultaneous) affairs with a number of women, including Lady Ottoline Morrell and the actress Lady Constance Malleson.

Russell began his published work in 1896 with German Social Democracy, a study in politics that was an early indication of a lifelong interest in political and social theory. In 1896 he taught German social democracy at the London School of Economics, where he also lectured on the science of power in the autumn of 1937. He was a member of the Coefficients dining club of social reformers set up in 1902 by the Fabian campaigners Sidney and Beatrice Webb.

He now started an intensive study of the foundations of mathematics at Trinity, during which he discovered Russell's paradox, which challenged the foundations of set theory. In 1903 he published his first important book on mathematical logic, The Principles of Mathematics, arguing that mathematics could be deduced from a very small number of principles, a work which contributed significantly to the cause of logicism.

In 1905 he wrote the essay "On Denoting", which was published in the philosophical journal Mind. Russell became a fellow of the Royal Society in 1908. The first of three volumes of Principia Mathematica, written with Whitehead, was published in 1910, which, along with the earlier The Principles of Mathematics, soon made Russell world famous in his field.

In 1910 he became a lecturer in the University of Cambridge, where he was approached by the Austrian engineering student Ludwig Wittgenstein, who became his PhD student. Russell viewed Wittgenstein as a genius and a successor who would continue his work on logic. He spent hours dealing with Wittgenstein's various phobias and his frequent bouts of despair. This was often a drain on Russell's energy, but Russell continued to be fascinated by him and encouraged his academic development, including the publication of Wittgenstein's Tractatus Logico - Philosophicus in 1922. Russell delivered his lectures on Logical Atomism, his version of these ideas, in 1918, before the end of the First World War. Wittgenstein was still a prisoner of war.

During the First World War, Russell was one of the very few people to engage in active pacifist activities, and in 1916, he was dismissed from Trinity College following his conviction under the Defence of the Realm Act.

He was charged a fine of £100, which he refused to pay, hoping that he would be sent to prison, However, his books were sold at auction to raise the money. The books were bought by friends; he later treasured his copy of the King James Bible that was stamped "Confiscated by Cambridge Police."

A later conviction for publicly lecturing against inviting the US to enter the war on Britain's side resulted in six months' imprisonment in Brixton prison in 1918. He was reinstated in 1919, resigned in 1920, was Tarner Lecturer 1926, and became a Fellow again 1944 – 1949.

In August 1920 Russell traveled to Russia as part of an official delegation sent by the British government to investigate the effects of the Russian Revolution. He met Vladimir Lenin and had an hour long conversation with him. In his autobiography, he mentions that he found Lenin rather disappointing, sensing an "impish cruelty" in him and comparing him to "an opinionated professor". He cruised down the Volga on a steamship. Russell's lover, Dora Black, visited Russia independently at the same time — she was enthusiastic about the revolution, but Russell's experiences destroyed his previous tentative support for it. He wrote a book The Practice and Theory of Bolshevism about his experiences on this trip, taken with a group of 24 others from Britain, all of whom came home thinking well of the regime, despite Russell's attempts to change their minds. For example, he told them that he heard shots fired in the middle of the night and was sure these were clandestine executions, but the others maintained that it was only cars backfiring.

Russell subsequently lectured in Beijing on philosophy for one year, accompanied by Dora. He went there with optimism and hope, as China was then on a new path. Other scholars present in China at the time included Rabindranath Tagore, the Nobel laureate Indian poet. While in China, Russell became gravely ill with pneumonia, and incorrect reports of his death were published in the Japanese press. When the couple visited Japan on their return journey, Dora notified the world that "Mr. Bertrand Russell, having died according to the Japanese press, is unable to give interviews to Japanese journalists." The press, not appreciating the sarcasm, were not amused.

Dora was six months pregnant when the couple returned to England on 26 August 1921. Russell arranged a hasty divorce from Alys, marrying Dora six days after the divorce was finalized, on 27 September 1921. Their children were John Conrad Russell, 4th Earl Russell, born on 16 November 1921, and Katharine Jane Russell (Lady Katharine Tait), born on 29 December 1923. Russell supported himself during this time by writing popular books explaining matters of physics, ethics and education to the layman. Some have suggested that at this point he had an affair with Vivienne Haigh - Wood, first wife of T.S. Eliot.

Together with Dora, he founded the experimental Beacon Hill School in 1927. The school was run from a succession of different locations, including its original premises at the Russells' residence, Telegraph House, near Harting, West Sussex. On 8 July 1930 Dora gave birth to her third child, a daughter, Harriet Ruth. After he left the school in 1932, Dora continued it until 1943.

Upon the death of his elder brother Frank, in 1931, Russell became the 3rd Earl Russell. He once said that his title was primarily useful for securing hotel rooms.

Russell's marriage to Dora grew increasingly tenuous, and it reached a breaking point over her having two children with an American journalist, Griffin Barry. They separated in 1932 and finally divorced. On 18 January 1936, Russell married his third wife, an Oxford undergraduate named Patricia ("Peter") Spence, who had been his children's governess since 1930. Russell and Peter had one son, Conrad Sebastian Robert Russell, 5th Earl Russell, who became a prominent historian and one of the leading figures in the Liberal Democratic party.

During the 1930s, Russell became a close friend and collaborator of V.K. Krishna Menon, then secretary of the India League, the foremost lobby for Indian independence in Great Britain.

Russell opposed rearmament against Nazi Germany, but in 1940 changed his view that avoiding a full scale world war was more important than defeating Hitler. He concluded that Adolf Hitler taking over all of Europe would be a permanent threat to democracy. In 1943, he adopted a stance toward large scale warfare, "Relative Political Pacifism": war was always a great evil, but in some particularly extreme circumstances, it may be the lesser of two evils.

Before the Second World War, Russell taught at the University of Chicago, later moving on to Los Angeles to lecture at the UCLA Department of Philosophy. He was appointed professor at the City College of New York in 1940, but after a public outcry, the appointment was annulled by a court judgement: his opinions (especially those relating to sexual morality, detailed in Marriage and Morals ten years earlier) made him "morally unfit" to teach at the college. The protest was started by the mother of a student who would not have been eligible for his graduate level course in mathematical logic. Many intellectuals, led by John Dewey, protested against his treatment. Albert Einstein's often quoted aphorism that "Great spirits have always encountered violent opposition from mediocre minds ... " originated in his open letter in support of Russell, during this time. Dewey and Horace M. Kallen edited a collection of articles on the CCNY affair in The Bertrand Russell Case. He soon joined the Barnes Foundation, lecturing to a varied audience on the history of philosophy; these lectures formed the basis of A History of Western Philosophy. His relationship with the eccentric Albert C. Barnes soon soured, and he returned to Britain in 1944 to rejoin the faculty of Trinity College.

During the 1940s and 1950s, Russell participated in many broadcasts over the BBC, particularly The Brains Trust and the Third Programme, on various topical and philosophical subjects. By this time Russell was world famous outside of academic circles, frequently the subject or author of magazine and newspaper articles, and was called upon to offer opinions on a wide variety of subjects, even mundane ones. En route to one of his lectures in Trondheim, Russell was one of 24 survivors (among a total of 43 passengers) in an airplane crash in Hommelvik in October 1948. He said he owed his life to smoking since the people who drowned were in the non - smoking part of the plane. A History of Western Philosophy (1945) became a best seller, and provided Russell with a steady income for the remainder of his life.

In a speech in 1948, Russell said that if the USSR's aggression continued, it would be morally worse to go to war after the USSR possessed an atomic bomb than before it possessed one, because if the USSR had no bomb the West's victory would come more swiftly and with fewer casualties than if there were atom bombs on both sides. At that time, only the United States possessed an atomic bomb, and the USSR was pursuing an extremely aggressive policy towards the countries in Eastern Europe which it was absorbing into its sphere of influence. Many understood Russell's comments to mean that Russell approved of a first strike in a war with the USSR, including Nigel Lawson, who was present when Russell spoke. Others, including Griffin, who obtained a transcript of the speech, have argued that he was merely explaining the usefulness of America's atomic arsenal in deterring the USSR from continuing its domination of Eastern Europe.

In 1948, Russell was invited by the BBC to deliver the inaugural Reith Lectures — what was to become an annual series of lectures, still broadcast by the BBC. His series of six broadcasts, titled Authority and the Individual, explored themes such as the role of individual initiative in the development of a community and the role of state control in a progressive society. Russell continued to write about philosophy. He wrote a foreword to Words and Things by Ernest Gellner, which was highly critical of the later thought of Ludwig Wittgenstein and of Ordinary language philosophy. Gilbert Ryle refused to have the book reviewed in the philosophical journal Mind, which caused Russell to respond via The Times. The result was a month long correspondence in The Times between the supporters and detractors of ordinary language philosophy, which was only ended when the paper published an editorial critical of both sides but agreeing with the opponents of ordinary language philosophy.

In the King's Birthday Honours of 9 June 1949, Russell was awarded the Order of Merit, and the following year he was awarded the Nobel Prize in Literature. When he was given the Order of Merit, King George VI was affable but slightly embarrassed at decorating a former jailbird, saying that "You have sometimes behaved in a manner that would not do if generally adopted." Russell merely smiled, but afterwards claimed that the reply "That's right, just like your brother" immediately came to mind.

In 1952 Russell was divorced by Spence, with whom he had been very unhappy. Conrad, Russell's son by Spence, did not see his father between the time of the divorce and 1968 (at which time his decision to meet his father caused a permanent breach with his mother).

Russell married his fourth wife, Edith Finch, soon after the divorce, on 15 December 1952. They had known each other since 1925, and Edith had taught English at Bryn Mawr College near Philadelphia, sharing a house for 20 years with Russell's old friend Lucy Donnelly. Edith remained with him until his death, and, by all accounts, their marriage was a happy, close, and loving one. Russell's eldest son, John, suffered from serious mental illness, which was the source of ongoing disputes between Russell and John's mother, Russell's former wife, Dora. John's wife Susan was also mentally ill, and eventually Russell and Edith became the legal guardians of their three daughters (two of whom were later found to have schizophrenia).

In 1962 Russell played a public role in the Cuban Missile Crisis: in an exchange of telegrams with Soviet leader Nikita Khrushchev, Khrushchev assured him that the Soviet government would not be reckless. Russell also wrote to John F. Kennedy, who returned his telegram unopened.

According to historian Peter Knight, after the John F. Kennedy assassination, Russell, "prompted by the emerging work of the lawyer Mark Lane in the US ... rallied support from other noteworthy and left leaning compatriots to form a Who Killed Kennedy Committee in June 1964, members of which included Michael Foot MP, the wife of Tony Benn MP, the publisher Victor Gollancz, the writers John Arden and J.B. Priestley, and the Oxford history professor Hugh Trevor - Roper. Russell published a highly critical article weeks before the Warren Commission Report was published, setting forth 16 Questions on the Assassination and equating the Oswald case with the Dreyfus affair of late 19th century France, in which the state wrongly convicted an innocent man. Russell also criticized the American press for failing to heed any voices critical of the official version.

Russell spent the 1950s and 1960s engaged in various political causes, primarily related to nuclear disarmament and opposing the Vietnam war (Russell Vietnam War Crimes Tribunal). The 1955 Russell – Einstein Manifesto was a document calling for nuclear disarmament and was signed by 11 of the most prominent nuclear physicists and intellectuals of the time. He wrote a great many letters to world leaders during this period. He was in contact with Lionel Rogosin while the latter was filming his anti - war film Good Times, Wonderful Times in the 1960s. He became a hero to many of the youthful members of the New Left. In early 1963, in particular, Russell became increasingly vocal about his disapproval of what he felt to be the US government's near genocidal policies in South Vietnam. In 1963 he became the inaugural recipient of the Jerusalem Prize, an award for writers concerned with the freedom of the individual in society. In October 1965 he tore up his Labour Party card because he suspected the party was going to send soldiers to support the US in the Vietnam War.

Russell published his three volume autobiography in 1967, 1968, and 1969. On 23 November 1969 he wrote to The Times newspaper saying that the preparation for show trials in Czechoslovakia was "highly alarming". The same month, he appealed to Secretary General U Thant of the United Nations to support an international war crimes commission to investigate alleged torture and genocide by the US in South Vietnam. The following month, he protested to Alexei Kosygin over the expulsion of Aleksandr Solzhenitsyn from the Writers Union.

Russell made a cameo appearance playing himself in the anti - war Hindi film “Aman” which was released in India in 1967. This was Russell’s only appearance in a feature film.

On 31 January 1970 Russell issued a statement which condemned Israeli aggression in the Middle East and called for Israeli withdrawal from the Israeli occupied territories. This was Russell's final political statement or act. It was read out at the International Conference of Parliamentarians in Cairo on 3 February 1970, the day after his death.

Russell died of influenza on 2 February 1970 at his home, Plas Penrhyn, in Penrhyndeudraeth, Merionethshire, Wales. His body was cremated in Colwyn Bay on 5 February 1970. In accordance with his will, there was no religious ceremony; his ashes were scattered over the Welsh mountains later that year.

In 1980 a memorial to Russell was commissioned by a committee including the philosopher A.J. Ayer. It consists of a bust of Russell in Red Lion Square in London sculpted by Marcelle Quinton.

Russell is generally credited with being one of the founders of analytic philosophy. He was deeply impressed by Gottfried Leibniz (1646 – 1716), and wrote on every major area of philosophy except aesthetics. He was particularly prolific in the field of metaphysics, the logic and the philosophy of mathematics, the philosophy of language, ethics and epistemology. When Brand Blanshard asked Russell why he did not write on aesthetics, Russell replied that he did not know anything about it, "but that is not a very good excuse, for my friends tell me it has not deterred me from writing on other subjects."

Russell described himself both as an agnostic and an atheist. For most of his adult life Russell maintained that religion is little more than superstition and, despite any positive effects that religion might have, it is largely harmful to people. He believed religion and the religious outlook (he considered communism and other systematic ideologies to be forms of religion) serve to impede knowledge, foster fear and dependency, and are responsible for much of the war, oppression, and misery that have beset the world. He was a member of the Advisory Council of the British Humanist Association and President of Cardiff Humanists until his death.

Political and social activism occupied much of Russell's time for most of his life, which makes his prodigious and seminal writing on a wide range of technical and non - technical subjects all the more remarkable. Russell remained politically active almost to the end of his life, writing to and exhorting world leaders and lending his name to various causes. He was noted for saying "No one can sit at the bedside of a dying child and still believe in God."

Russell determined man to be "the product of causes ... his origin, his growth, his hopes and fears, his loves and his beliefs, are but the outcome of accidental collocations of atoms, that no fire, no heroism, no intensity of thought and feeling, can preserve an individual life beyond the grave; that all the labors of the ages, all the inspiration, all the noonday brightness of human genius are destined to extinction in the vast death of the solar system, that the whole temple of man's achievement must inevitably be buried beneath the debris of a universe in ruins — all these things, if not quite beyond dispute, are so nearly certain, that no philosophy which rejects them can hope to stand ... "

Born in Vienna into one of Europe's wealthiest families, he gave away his entire inheritance. Three of his brothers committed suicide, with Ludwig contemplating it too. He left academia several times: serving as an officer on the front line during World War I, where he was decorated a number of times for his courage; teaching in schools in remote Austrian villages, where he encountered controversy for hitting children when they made mistakes in mathematics; and working during World War II as a hospital porter in London, where he told patients not to take the drugs they were prescribed, and where no-one knew he was one of the world's most famous philosophers. He described philosophy, however, as "the only work that gives me real satisfaction."

His philosophy is often divided between his early period, exemplified by the Tractatus, and later period, articulated in the Philosophical Investigations. The early Wittgenstein was concerned with the logical relationship between propositions and the world, and believed that by providing an account of the logic underlying this relationship he had solved all philosophical problems. The later Wittgenstein rejected many of the conclusions of the Tractatus, arguing that the meaning of words is constituted by the function they perform within any given language - game.

Wittgenstein's influence has been felt in nearly every field of the humanities and social sciences, yet there are widely diverging interpretations of his thought. In the words of his friend and colleague Georg Henrik von Wright: "He was of the opinion... that his ideas were generally misunderstood and distorted even by those who professed to be his disciples. He doubted he would be better understood in the future. He once said he felt as though he were writing for people who would think in a different way, breathe a different air of life, from that of present - day men."

According to a family tree prepared in Jerusalem after World War II, Wittgenstein's paternal great - grandfather was Moses Meier, a Jewish land agent who lived with his wife, Brendel Simon, in Bad Laasphe in the Principality of Wittgenstein, Westphalia. In July 1808, Napoleon issued a decree that everyone, including Jews, must adopt an inheritable family surname, and so Meier's son, also Moses, took the name of his employers, the Sayn - Wittgensteins, and became Moses Meier Wittgenstein. His son, Hermann Christian Wittgenstein — who took the middle name "Christian" to distance himself from his Jewish background — married Fanny Figdor, also Jewish, who converted to Protestantism just before they married, and the couple founded a successful business trading in wool in Leipzig. Ludwig's grandmother, Fanny Figdor, was a first cousin of the famous violinist Joseph Joachim. They had 11 children — among them Wittgenstein's father. Karl Wittgenstein (1847 – 1913) became an industrial tycoon, and by the late 1880s was one of the richest men in Europe, with an effective monopoly on Austria's steel cartel. Thanks to Karl, the Wittgensteins became the second wealthiest family in the Habsburg Empire, behind only the Rothschilds. As a result of his decision in 1898 to invest substantially overseas, particularly in the Netherlands, Switzerland and the US, the family was to an extent shielded from the hyperinflation that hit Austria in 1922. Their wealth did still diminish due to post 1918 hyperinflation and the Great Depression, although even as late as 1938 they owned 13 mansions in Vienna alone.

Wittgenstein's mother was Leopoldine Kalmus. Her father was Czech Jewish and her mother was Austrian - Slovene Catholic — she was Ludwig's maternal grandparent and only non - Jewish grandparent, whose ancestry was Austrian and an aunt of the Nobel Prize laureate Friedrich Hayek on her maternal side. Ludwig was born at 8:30pm on 26 April 1889 in the so-called "Wittgenstein Palace" at Alleegasse 16, now the Argentinierstrasse, near the Karlskirche. Karl and Poldi, as she was known, had nine children in all. There were four girls: Hermine, Margaret (Gretl), Helene, and a fourth daughter who died as a baby; and five boys: Johannes (Hans), Kurt, Rudolf (Rudi), Paul — who became a concert pianist despite losing an arm in World War I — and Ludwig, who was the youngest of the family.

The children were baptized as Catholics, and raised in an exceptionally intense environment. The family was at the center of Vienna's cultural life; Bruno Walter described the life at the Wittgensteins' palace as an "all pervading atmosphere of humanity and culture". Karl was a leading patron of the arts, commissioning works by Auguste Rodin and financing the city's exhibition hall and art gallery, the Secession Building. Gustav Klimt painted Wittgenstein's sister for her wedding portrait, and Johannes Brahms and Gustav Mahler gave regular concerts in the family's numerous music rooms.

For Ludwig, who highly valued precision and discipline, contemporary music was never considered acceptable at all. "Music", he said to his friend Drury in 1930, "came to a full stop with Brahms; and even in Brahms I can begin to hear the noise of machinery." Ludwig himself had absolute pitch perception, and his devotion to music remained vitally important to him throughout his life: he made frequent use of musical examples and metaphors in his philosophical writings, and was unusually adept at whistling lengthy and detailed musical passages. He also learned to play the clarinet in his thirties.

Ray Monk writes that Karl's aim was to turn his sons into captains of industry; they were not sent to school lest they acquire bad habits, but were educated at home to prepare them for work in Karl's industrial empire. Three of the five brothers would later commit suicide. The Irish psychiatrist Michael Fitzgerald argues that Karl was a harsh perfectionist who lacked empathy, and that Wittgenstein's mother was anxious and insecure, unable to stand up to her husband. Johannes Brahms said of the family, whom he visited regularly: "They seemed to act towards one another as if they were at court". The family appeared to have a strong streak of depression running through it. Anthony Gottlieb tells a story about Paul practicing on one of the seven grand pianos in the Wittgensteins' main family mansion, when he suddenly shouted at Ludwig in the next room: "I cannot play when you are in the house, as I feel your skepticism seeping towards me from under the door!"

The eldest brother, Hans, was hailed as a musical prodigy. At the age of four, Waugh writes, Hans could identify the Doppler effect in a passing siren as a quarter - tone drop in pitch, and at five started crying "Wrong! Wrong!" when two brass bands in a carnival played the same tune in different keys. But he died in mysterious circumstances in May 1902, when he ran away to America and disappeared from a boat in Chesapeake Bay, most likely having committed suicide.

Two years later, aged 22 and studying chemistry at the Berlin Academy, the third eldest brother, Rudi, committed suicide in a Berlin bar. He had asked the pianist to play Thomas Koschat's "Verlassen, verlassen, verlassen bin ich ("Forsaken, forsaken, forsaken am I"), before mixing himself a drink of milk and potassium cyanide. He had left several suicide notes, one to his parents that said he was grieving over the death of a friend, and another that referred to his "perverted disposition". It was reported at the time that he had sought advice from the Scientific - Humanitarian Committee, an organization that was campaigning against Paragraph 175 of the German Criminal Code, which from 1871 until 1969 prohibited homosexual sex. His father forbade the family from ever mentioning his name again.

The second eldest brother, Kurt, an officer and company director, shot himself on 27 October 1918 at the end of World War I, when the Austrian troops he was commanding refused to obey his orders and deserted en masse. According to Gottlieb, Hermine had said Kurt seemed to carry "the germ of disgust for life within himself". Paul also considered suicide, as did Ludwig. Later Wittgenstein wrote: "I ought to have... become a star in the sky. Instead of which I have remained stuck on earth."

Wittgenstein was taught by private tutors at home until he was fourteen years old. Subsequently, for three years, he attended a school. After the deaths of Hans and Rudi, Karl relented, and allowed Paul and Ludwig to be sent to school. Alexander Waugh writes that it was too late for Wittgenstein to pass his exams for the more academic Gymnasium in Wiener Neustadt; having had no formal schooling, he failed his entrance exam and only barely managed after extra tuition to pass the exam for the more technically oriented K.u.k. Realschule in Linz, a small state school with 300 pupils. In 1903, when he was 14, he began his three years of formal schooling there, lodging nearby in term time with the family of a Dr. Srigl, a master at the local gymnasium, the family giving him the nickname Luki.

On starting at the Realschule, Wittgenstein had been moved forward a year. Historian Brigitte Hamann writes that he stood out from the other boys: he spoke an unusually pure form of High German with a stutter, dressed elegantly, and was sensitive and unsociable. Monk writes that the other boys made fun of him, singing after him: "Wittgenstein wandelt wehmütig widriger Winde wegen Wienwärts" ("Wittgenstein strolls wistfully Vienna - wards due to adverse winds"). In his leaving certificate, he received a top mark - 5 - in religious studies; a 2 for conduct and English, 3 for French, geography, history, mathematics and physics, and 4 for German, chemistry, geometry and freehand drawing. He had particular difficulty with spelling and failed his written German exam because of it. He wrote in 1931: "My bad spelling in youth, up to the age of about 18 or 19, is connected with the whole of the rest of my character (my weakness in study)."

There is much debate about the extent to which Wittgenstein and his siblings, who were of 3/4 Jewish descent, saw themselves as Jews, and the issue has arisen in particular regarding Wittgenstein's schooldays, because Adolf Hitler was at the same school for part of the same time. Laurence Goldstein argues it is "overwhelmingly probable" the boys met each other: that Hitler, vicious and aggressive, would have hated and envied Wittgenstein, a "stammering, precocious, precious, aristocratic upstart ...". Other commentators have dismissed as irresponsible and uninformed any suggestion that Wittgenstein's wealth and unusual personality may have fed Hitler's antisemitism, in part because there is no indication that Hitler would have seen Wittgenstein as Jewish.

Wittgenstein and Hitler were born just six days apart, though Hitler had been held back a year, while Wittgenstein was moved forward by one, so they ended up two grades apart at the Realschule. Monk estimates they were both at the school during the 1904 – 1905 school year, but says there is no evidence they had anything to do with each other. Several commentators have argued that a school photograph of Hitler may show Wittgenstein in the lower left corner, but Hamann says the photograph stems from 1900 or 1901, before Wittgenstein's time.

In his own writings Wittgenstein frequently referred to himself as Jewish, at times as part of an apparent self - flagellation. For example, while berating himself for being a "reproductive" as opposed to "productive" thinker, he attributed this to his own Jewish sense of identity, writing: "The saint is the only Jewish genius. Even the greatest Jewish thinker is no more than talented. (Myself for instance)." While Wittgenstein would later claim that "[m]y thoughts are 100% Hebraic", as Hans Sluga has argued, if so, "his was a self - doubting Judaism, which had always the possibility of collapsing into a destructive self - hatred (as it did in Weininger's case) but which also held an immense promise of innovation and genius."

It was while he was at the Realschule that he decided he had lost his faith in God. He nevertheless believed in the importance of the idea of confession. He wrote in his diaries about having made a major confession to his oldest sister, Hermine, while he was at the Realschule; Monk writes that it may have been about his loss of faith. He also discussed it with Gretl, his other sister, who directed him to Arthur Schopenhauer's The World as Will and Representation. As a teenager, Wittgenstein adopted Schopenhauer's epistemological idealism. However, after his study of the philosophy of mathematics, he abandoned epistemological idealism for Gottlob Frege's conceptual realism. In later years, Wittgenstein was highly dismissive of Schopenhauer, describing him as an ultimately "shallow" thinker: "Schopenhauer has quite a crude mind... where real depth starts, his comes to an end".

While a student at the Realschule, Wittgenstein was influenced by Austrian philosopher Otto Weininger's 1903 book Geschlecht und Charakter (Sex and Character). Weininger (1880 – 1903), who was both Jewish and homosexual, argued that the concepts male and female exist only as Platonic forms, and that the essence of woman is sexual. Whereas men are basically rational, women operate only at the level of their emotions and sexual organs. Jews, Weininger argued, are similar, saturated with femininity, with no sense of right and wrong, and no soul. Weininger argues that man must choose between his masculine and feminine sides, consciousness and unconsciousness, Platonic love and sexuality. Love and sexual desire stand in contradiction, and the love between a woman and a man is therefore doomed to misery or immorality. The only life worth living is the spiritual one — to live as a woman or a Jew means one has no right to live at all; the choice is genius or death. Weininger committed suicide, shooting himself in 1903, shortly after publishing the book. Many years later, as a professor at Cambridge, Wittgenstein distributed copies of Weininger's book to his bemused academic colleagues. He said that Weininger's arguments were wrong, but that it was the way in which they were wrong that was interesting.

He began his studies in mechanical engineering at the Technische Hochschule in Charlottenburg, Berlin, on 23 October 1906, lodging with the family of a professor there, Dr Jolles. He attended for three semesters, and was awarded a diploma on 5 May 1908, after developing an interest in aeronautics. He arrived at the Victoria University of Manchester in the spring of 1908 to do his doctorate, full of plans for aeronautical projects, including designing and flying his own plane. He conducted research into the behavior of kites in the upper atmosphere, experimenting at a meteorological observation site near Glossop. He also worked on the design of a propeller with small jet engines on the end of its blades, something he patented in 1911 and which earned him a research studentship from the university in the autumn of 1908.

It was at this time that he became interested in the foundations of mathematics, particularly after reading Bertrand Russell's The Principles of Mathematics (1903), and Gottlob Frege's Grundgesetze der Arithmetik, vol. 1 (1893) and vol. 2 (1903). Wittgenstein's sister Hermine said he became obsessed with mathematics as a result, and was anyway losing interest in aeronautics. He decided instead that he needed to study logic and the foundations of mathematics, describing himself as in a "constant, indescribable, almost pathological state of agitation". In the summer of 1911 he visited Frege at the University of Jena to show him some philosophy of mathematics and logic he had written, and to ask whether it was worth pursuing; the work did not survive, perhaps because, as he said, Frege wiped the floor with him. He wrote: "I was shown into Frege's study. Frege was a small, neat man with a pointed beard who bounced around the room as he talked. He absolutely wiped the floor with me, and I felt very depressed; but at the end he said 'You must come again', so I cheered up. I had several discussions with him after that. Frege would never talk about anything but logic and mathematics, if I started on some other subject, he would say something polite and then plunge back into logic and mathematics."

Wittgenstein wanted to study with Frege, but Frege suggested he attend the University of Cambridge to study under Russell, so on 18 October 1911 Wittgenstein arrived unannounced at Russell's rooms in Trinity College. Russell was having tea with C.K. Ogden, when, according to Russell, "... an unknown German appeared, speaking very little English but refusing to speak German. He turned out to be a man who had learned engineering at Charlottenburg, but during this course had acquired, by himself, a passion for the philosophy of mathematics & has now come to Cambridge on purpose to hear me." He was soon not only attending Russell's lectures, but dominating them. The lectures were poorly attended and Russell often found himself lecturing only to C.D. Broad, E.H. Neville, and H.T.J. Norton. Wittgenstein started following him after lectures back to his rooms to discuss more philosophy, until it was time for the evening meal in Hall. Russell grew irritated; he wrote to his lover Lady Ottoline Morrell: "My German friend threatens to be an infliction."

Russell soon came to believe that Wittgenstein was a genius, especially after he had examined Wittgenstein's written work. He wrote in November 1911 that he had at first thought Wittgenstein might be a crank, but soon decided he was a genius: "Some of his early views made the decision difficult. He maintained, for example, at one time that all existential propositions are meaningless. This was in a lecture room, and I invited him to consider the proposition: 'There is no hippopotamus in this room at present.' When he refused to believe this, I looked under all the desks without finding one; but he remained unconvinced." Three months after Wittgenstein's arrival Russell told Morrell: "I love him & feel he will solve the problems I am too old to solve ... He is the young man one hopes for." The role reversal between him and Wittgenstein was such that he wrote in 1916, after Wittgenstein had criticized his own work: "His criticism, 'tho I don't think he realized it at the time, was an event of first rate importance in my life, and affected everything I have done since. I saw that he was right, and I saw that I could not hope ever again to do fundamental work in philosophy."

In 1912 Wittgenstein joined the Cambridge Moral Sciences Club, an influential discussion group for philosophy dons and students, delivering his first paper there on 29 November that year, a four minute talk defining philosophy as "all those primitive propositions which are assumed as true without proof by the various sciences." He dominated the society and stopped attending entirely in the early 1930s after complaints that he gave no one else a chance to speak.

The club became legendary within philosophy because of a meeting on 25 October 1946 at Richard Braithwaite's rooms in King's, where Karl Popper, another Viennese philosopher, had been invited as the guest speaker. Popper's paper was "Are there philosophical problems?", in which he struck up a position against Wittgenstein's, contending that problems in philosophy are real, not just linguistic puzzles as Wittgenstein argued. Accounts vary as to what happened next, but Wittgenstein was apparently infuriated and started waving a hot poker at Popper, demanding that Popper give him an example of a moral rule. Popper offered one — "Not to threaten visiting speakers with pokers" — at which point Russell had to tell Wittgenstein to put the poker down and Wittgenstein stormed out. It was the only time the philosophers, three of the most eminent in the world, were ever in the same room together. The minutes record that the meeting was "charged to an unusual degree with a spirit of controversy".

John Maynard Keynes also invited him to join the Cambridge Apostles, an elite secret society formed in 1820, which both Russell and G.E. Moore had joined as students, but Wittgenstein did not enjoy it and attended infrequently. Russell had been worried that Wittgenstein would not appreciate the group's unseriousness, style of humor, or the fact that the members were in love with one another.

Wittgenstein later confessed that, as a teenager in Vienna, he had had an affair with a woman. Wittgenstein is also widely regarded to have fallen in love with at least three men: David Hume Pinsent in 1912, Francis Skinner in 1930, and Ben Richards in the late 1940s. Additionally, in the 1920s Wittgenstein became infatuated with a young Swiss woman, Marguerite Respinger, modelling a sculpture of her and proposing marriage, albeit on condition that they did not have children.

It was Russell who introduced Wittgenstein to David Pinsent (1891 – 1918) in the summer of 1912. A mathematics undergraduate and descendant of David Hume, Pinsent soon became Wittgenstein's closest friend. The men worked together on experiments in the psychology laboratory about the role of rhythm in the appreciation of music, and Wittgenstein delivered a paper on the subject to the British Psychological Association in Cambridge in 1912. They also traveled together, including to Iceland in September 1912 — the expenses paid by Wittgenstein, including first class travel, the hiring of a private train, and new clothes and spending money for Pinsent — and later to Norway. Pinsent's diaries provide valuable insights into Wittgenstein's personality - sensitive, nervous and attuned to the tiniest slight or change in mood from Pinsent. In his diaries Pinsent wrote about shopping for furniture with Wittgenstein in Cambridge when the latter was given rooms in Trinity; most of what they found in the stores was not minimalist enough for Wittgenstein's aesthetics: "I went and helped him interview a lot of furniture at various shops ... It was rather amusing: he is terribly fastidious and we led the shopman a frightful dance, Vittgenstein [sic] ejaculating "No — Beastly!" to 90 percent of what he shewed [archaic spelling] us!"

He wrote in May 1912 that Wittgenstein had just begun to study the history of philosophy: "[h]e expresses the most naive surprise that all the philosophers he once worshiped in ignorance are after all stupid and dishonest and make disgusting mistakes!" The last time they saw each other was at a Birmingham railway station on 8 October 1913, when they said goodbye before Wittgenstein left to live in Norway.

Karl Wittgenstein died on 20 January 1913, and on receiving his inheritance Wittgenstein became one of the wealthiest men in Europe. He donated some of his money, initially anonymously, to Austrian artists and writers, including Rainer Maria Rilke and Georg Trakl. Wittgenstein came to feel that he could not get to the heart of his most fundamental questions while surrounded by other academics, and so in 1913 he retreated to the village of Skjolden in Norway, where he rented the second floor of a house for the winter. He later saw this as one of the most productive periods of his life, writing Logik (Notes on Logic), the predecessor of much of the Tractatus.

At Wittgenstein's insistence, Moore, who was now a Cambridge don, visited him in Norway in 1914, reluctantly because Wittgenstein exhausted him. David Edmonds and John Eidinow write that Wittgenstein regarded Moore, an internationally known philosopher, as an example of how far someone could get in life with "absolutely no intelligence whatever". In Norway it was clear that Moore was expected to act as Wittgenstein's secretary, taking down his notes, with Wittgenstein falling into a rage when Moore got something wrong. When he returned to Cambridge, Moore asked the university to consider accepting Logik as sufficient for a bachelor's degree, but they refused, saying it was not formatted properly: no footnotes, no preface. Wittgenstein was furious, writing to Moore in May 1914: "If I am not worth your making an exception for me even in some STUPID details then I may as well go to Hell directly; and if I am worth it and you don't do it then — by God — you might go there." Moore was apparently distraught; he wrote in his diary that he felt sick and could not get the letter out of his head. The two did not speak again until 1929.

On the outbreak of World War I, Wittgenstein immediately volunteered for the Austro - Hungarian Army, first serving on a ship and then in an artillery workshop. In March 1916, he was posted to a fighting unit on the front line of the Russian front, as part of the Austrian 7th Army, where his unit was involved in some of the heaviest fighting, defending against the Brusilov Offensive. In action against British troops, he was decorated with the Military Merit with Swords on the Ribbon, and was commended by the army for "His exceptionally courageous behavior, calmness, sang - froid, and heroism", which "won the total admiration of the troops." In January 1917, he was sent as a member of a howitzer regiment to the Russian front, where he won several more medals for bravery including the Silver Medal for Valor, First Class. In 1918 he was promoted to lieutenant and sent to the Italian front as part of an artillery regiment. For his part in the final Austrian offensive of June 1918, he was recommended for the Gold Medal for Valor, one of the highest honors in the Austrian army, but was instead awarded the Band of the Military Service Medal with Swords — it being decided that this particular action, although extraordinarily brave, had been insufficiently consequential to merit the highest honor.

Throughout the war, he kept notebooks in which he frequently wrote philosophical reflections alongside personal remarks, including his contempt for the character of the other soldiers. He discovered Leo Tolstoy's The Gospel in Brief at a bookshop in Galicia, and carried it everywhere, recommending it to anyone in distress, to the point where he became known to his fellow soldiers as "the man with the gospels". In 1916 Wittgenstein read Dostoevsky's The Brothers Karamazov so often that he knew whole passages of it by heart, particularly the speeches of the elder Zossima, who represented for him a powerful Christian ideal, a holy man ″who could see directly into the souls of other people″. Russell said he returned from the war a changed man, one with a deeply mystical and ascetic attitude.

In the summer of 1918 Wittgenstein took military leave and went to stay in one of his family's Vienna summer houses, Neuwaldegg. It was there in August 1918 that he completed the Tractatus, which he submitted with the title Der Satz (The Proposition) to the publishers Johada and Siegel.

A series of events around this time left him deeply upset. On 13 August, his uncle Paul died. On 25 October, he learned that Johada and Siegel had decided not to publish the Tractatus, and on 27 October, his brother Kurt killed himself, the third of his brothers to commit suicide. It was around this time he received a letter from David Pinsent's mother to say that Pinsent had been killed in a plane crash on 8 May. Wittgenstein was distraught to the point of being suicidal. He was sent back to the Italian front after his leave and, as a result of the defeat of the Austrian army, was captured by Allied forces on 3 November in Trentino. He subsequently spent nine months in an Italian prisoner of war camp.

He returned to his family in Vienna on 25 August 1919, by all accounts physically and mentally spent. He apparently talked incessantly about suicide, terrifying his sisters and Paul. He decided to do two things: to enroll in teacher training college as an elementary school teacher, and to get rid of his fortune. In 1914, it had been providing him with an income of 300,000 Kronen a year, but by 1919 was worth a great deal more, with a sizable portfolio of investments in the US and the Netherlands. He divided it among his siblings, except for Margarete, insisting that it not be held in trust for him. His family saw him as ill, and acquiesced.

In September 1919 he enrolled in the Lehrerbildungsanstalt (teacher training college) in the Kundmanngasse in Vienna. His sister Hermine said that Wittgenstein working as an elementary teacher was like using a precision instrument to open crates, but the family decided not to interfere. Thomas Bernhard, more critically, wrote of this period in Wittgenstein's life: "the multi - millionaire as a village schoolmaster is surely a piece of perversity."

In the summer of 1920, Wittgenstein worked as a gardener for a monastery. At first he applied, under a false name, for a teaching post at Reichenau, was awarded the job, but he declined it when his identity as a Wittgenstein was discovered. As a teacher, he wished to no longer be recognized as a member of the famous Wittgenstein family. In response his brother Paul wrote: "It is out of the question, really completely out of the question, that anybody bearing our name and whose elegant and gentle upbringing can be seen a thousand paces off, would not be identified as a member of our family... That one can neither simulate nor dissimulate anything including a refined education I need hardly tell you."

In 1920, Wittgenstein was given his first job as a primary school teacher in Trattenbach, under his real name, in a remote village of a few hundred people. His first letters describe it as beautiful, but in October 1921, he wrote to Russell: "I am still at Trattenbach, surrounded, as ever, by odiousness and baseness. I know that human beings on the average are not worth much anywhere, but here they are much more good - for - nothing and irresponsible than elsewhere." He was soon the object of gossip among the villagers, who found him eccentric at best. He did not get on well with the other teachers; when he found his lodgings too noisy, he made a bed for himself in the school kitchen. He was an enthusiastic teacher, offering late night extra tuition to several of the students, something that did not endear him to the parents, though some of them came to adore him; his sister Hermine occasionally watched him teach and said the students "literally crawled over each other in their desire to be chosen for answers or demonstrations".

To the less abled, it seems that he became something of a tyrant. The first two hours of each day were devoted to mathematics, hours that Monk writes some of the pupils recalled years later with horror. They reported that he caned the boys and boxed their ears, and also that he pulled the girls' hair; this was not unusual at the time for boys, but for the villagers he went too far in doing it to the girls too; girls were not expected to understand algebra, much less have their ears boxed over it. The violence apart, Monk writes that he quickly became a village legend, shouting "Krautsalat!" when the headmaster played the piano, and "Nonsense!" when a priest was answering children's questions.

While Wittgenstein was living in isolation in rural Austria, the Tractatus was published to considerable interest, first in German in 1921 as Logisch - Philosophische Abhandlung, part of Wilhelm Ostwald's journal Annalen der Naturphilosophie, though Wittgenstein was not happy with the result and called it a pirate edition. Russell had agreed to write an introduction to explain why it was important, because it was otherwise unlikely to have been published: it was difficult if not impossible to understand, and Wittgenstein was unknown in philosophy. In a letter to Russell, Wittgenstein wrote "The main point is the theory of what can be expressed (gesagt) by prop[osition]s — i.e., by language — (and, which comes to the same thing, what can be thought) and what can not be expressed by pro[position]s, but only shown (gezeigt); which, I believe, is the cardinal problem of philosophy." But Wittgenstein was not happy with Russell's help. He had lost faith in Russell, finding him glib and his philosophy mechanistic, and felt he had fundamentally misunderstood the Tractatus.

An English translation was prepared in Cambridge by Frank Ramsey, a mathematics undergraduate at King's commissioned by C.K. Ogden. It was Moore who suggested Tractatus Logico - Philosophicus for the title, an allusion to Baruch Spinoza's Tractatus Theologico - Politicus. Initially there were difficulties in finding a publisher for the English edition too, because Wittgenstein was insisting it appear without Russell's introduction; Cambridge University Press turned it down for that reason. Finally in 1922 an agreement was reached with Wittgenstein that Kegan Paul would print a bilingual edition with Russell's introduction and the Ramsey - Ogden translation. This is the translation that was approved by Wittgenstein, but it is problematic in a number of ways. Wittgenstein's English was poor at the time, and Ramsey was a teenager who had only recently learned German, so philosophers often prefer to use a 1961 translation by David Pears and Brian McGuinness.

An aim of the Tractatus is to reveal the relationship between language and the world: what can be said about it, and what can only be shown. Wittgenstein argues that language has an underlying logical structure, a structure that provides the limits of what can be said meaningfully, and therefore the limits of what can be thought. The limits of language, for Wittgenstein, are the limits of philosophy. Much of philosophy involves attempts to say the unsayable: "what can we say at all can be said clearly", he argues. Anything beyond that — religion, ethics, aesthetics, the mystical — cannot be discussed. They are not in themselves nonsensical, but any statement about them must be. He wrote in the preface: "The book will, therefore, draw a limit to thinking, or rather — not to thinking, but to the expression of thoughts; for, in order to draw a limit to thinking we should have to be able to think both sides of this limit (we should therefore have to be able to think what cannot be thought)."

The book is 75 pages long — "As to the shortness of the book, I am awfully sorry for it ... If you were to squeeze me like a lemon you would get nothing more out of me", he told Ogden — and presents seven numbered propositions (1–7), with various sub-levels (1, 1.1, 1.11):

1. Die Welt ist alles, was der Fall ist.

   The world is all that is the case.

2. Was der Fall ist, die Tatsache, ist das Bestehen von Sachverhalten.

   What is the case — a fact — is the existence of states of affairs.

3. Das logische Bild der Tatsachen ist der Gedanke.

   A logical picture of facts is a thought.

4. Der Gedanke ist der sinnvolle Satz.

   A thought is a proposition with a sense.

5. Der Satz ist eine Wahrheitsfunktion der Elementarsätze.

   A proposition is a truth - function of elementary propositions.

6. Die allgemeine Form der Wahrheitsfunktion ist: . Dies ist die allgemeine Form des Satzes.

   The general form of a truth - function is: . This is the general form of a proposition.

7. Wovon man nicht sprechen kann, darüber muß man schweigen.

   What we cannot speak about we must pass over in silence

In September 1922 he moved to a secondary school in a nearby village, Hassbach, but the people there were just as bad — "These people are not human at all but loathsome worms", he wrote to a friend — and he left after a month. In November he began work at another primary school, this time in Puchberg in the Schneeberg mountains. There, he told Russell, the villagers were "one - quarter animal and three - quarters human".

Frank P. Ramsey visited him on 17 September 1923 to discuss the Tractatus; he had agreed to write a review of it for Mind. He reported in a letter home that Wittgenstein was living frugally in one tiny whitewashed room that only had space for a bed, washstand, a small table, and one small hard chair. Ramsey shared an evening meal with him of coarse bread, butter and cocoa. Wittgenstein's school hours were eight to twelve or one, and he had afternoons free. After Ramsey returned to Cambridge a long campaign began among Wittgenstein's friends to persuade him to return to Cambridge and away from what they saw as a hostile environment for him. He was accepting no help even from his family. Ramsey wrote to John Maynard Keynes: "[Wittgenstein's family] are very rich and extremely anxious to give him money or do anything for him in any way, and he rejects all their advances; even Christmas presents or presents of invalid's food, when he is ill, he sends back. And this is not because they aren't on good terms but because he won't have any money he hasn't earned ... It is an awful pity."

He moved schools again in September 1924, this time to Otterthal, near Trattenbach; the socialist headmaster, Josef Putre, was someone Wittgenstein had become friends with while at Trattenbach. While he was there, he wrote a 42 page pronunciation and spelling dictionary for the children, Wörterbuch für Volksschulen, published in Vienna in 1926 by Hölder - Pichler - Tempsky, the only book of his apart from the Tractatus that was published in his lifetime. A first edition sold in 2005 for £75,000.

An incident occurred in April 1926 and became known as Der Vorfall Haidbauer (the Haidbauer incident). Josef Haidbauer was an 11 year old pupil whose father had died and whose mother worked as a local maid. He was a slow learner, and one day Wittgenstein hit him two or three times on the head, causing him to collapse. Wittgenstein carried him to the headmaster's office, then quickly left the school, bumping into a parent, Herr Piribauer, on the way out. Piribauer had been sent for by the children when they saw Haidbauer collapse; Wittgenstein had previously pulled Piribauer's daughter, Hermine, so hard by the ears that her ears had bled. Piribauer said that when he met Wittgenstein in the hall that day: "I called him all the names under the sun. I told him he wasn't a teacher, he was an animal - trainer! And that I was going to fetch the police right away!"

Piribauer tried to have Wittgenstein arrested, but the village's police station was empty, and when he tried again the next day he was told Wittgenstein had disappeared. On 28 April 1926, Wittgenstein handed in his resignation to Wilhelm Kundt, a local school inspector, who tried to persuade him to stay, but Wittgenstein was adamant that his days as a schoolteacher were over. Proceedings were initiated in May, and the judge ordered a psychiatric report; in August 1926 a letter to Wittgenstein from a friend, Ludwig Hänsel, indicates that hearings were ongoing, but nothing is known about the case after that. Alexander Waugh writes that Wittgenstein's family and their money may have had a hand in covering things up. Waugh writes that Haidbauer died shortly afterwards of haemophilia; Monk says he died when he was 14 of leukaemia.

Ten years later, in 1936, as part of a series of "confessions" he engaged in that year, Wittgenstein appeared without warning at the village saying he wanted to confess personally and ask for pardon from the children he had hit. He visited at least four of the children, including Hermine Piribauer, who apparently replied only with a "Ja, ja", though other former students were more hospitable. Monk writes that the purpose of these confessions was not "to hurt his pride, as a form of punishment; it was to dismantle it - to remove a barrier, as it were, that stood in the way of honest and decent thought." Of the apologies, Wittgenstein wrote, "This brought me into more settled waters... and to greater seriousness."

The Tractatus was now the subject of much debate among philosophers, and Wittgenstein was a figure of increasing international fame. In particular, a discussion group of philosophers, scientists and mathematicians, known as the Vienna Circle, had built up largely as a result of the inspiration they had been given by reading the Tractatus. From 1926, with the members of the Vienna Circle, Wittgenstein would take part in many discussions. However, during these discussions, it soon became evident that Wittgenstein held a different attitude towards philosophy than the members of the Circle who his work had inspired. In his autobiography, Rudolph Carnap describes Wittgenstein as the thinker who gave him the greatest inspiration. However, he also wrote that "there was a striking difference between Wittgenstein's attitude toward philosophical problems and that of Schlick and myself. Our attitude toward philosophical problems was not very different from that which scientists have toward their problems." As for Wittgenstein:

His point of view and his attitude toward people and problems, even theoretical problems, were much more similar to those of a creative artist than to those of a scientist; one might almost say, similar to those of a religious prophet or a seer... When finally, sometimes after a prolonged arduous effort, his answers came forth, his statement stood before us like a newly created piece of art or a divine revelation... the impression he made on us was as if insight came to him as through divine inspiration, so that we could not help feeling that any sober rational comment of analysis of it would be a profanation.

In 1926, Wittgenstein was again working as a gardener for a number of months, this time at the monastery of Hütteldorf, where he had also inquired about becoming a monk. His sister, Margaret, invited him to help with the design of her new townhouse in Vienna's Kundmanngasse. Wittgenstein, his friend Paul Engelmann, and a team of architects developed a spare modernist house. In particular, Wittgenstein focused on the windows, doors, and radiators, demanding that every detail be exactly as he specified. When the house was nearly finished Wittgenstein had an entire ceiling raised 30mm so that the room had the exact proportions he wanted. Monk writes that "This is not so marginal as it may at first appear, for it is precisely these details that lend what is otherwise a rather plain, even ugly house its distinctive beauty.".

It took him a year to design the door handles, and another to design the radiators. Each window was covered by a metal screen that weighed 150 kg, moved by a pulley Wittgenstein designed. Bernhard Leitner, author of The Architecture of Ludwig Wittgenstein, said there is barely anything comparable in the history of interior design: "It is as ingenious as it is expensive. A metal curtain that could be lowered into the floor."

The house was finished by December 1928, and the family gathered there at Christmas to celebrate its completion. Wittgenstein's sister Hermine wrote: "Even though I admired the house very much.... It seemed indeed to be much more a dwelling for the gods." Wittgenstein said "the house I built for Gretl is the product of a decidedly sensitive ear and good manners, and expression of great understanding... But primordial life, wild life striving to erupt into the open - that is lacking." Monk comments that the same might be said of the technically excellent, but austere, terracotta sculpture Wittgenstein had modeled of Marguerite Respinger in 1926, and that, as Russell first noticed, this "wild life striving to be in the open" was precisely the substance of Wittgenstein's philosophical work.

At the urging of Ramsey and others, Wittgenstein returned to Cambridge in 1929. Keynes wrote in a letter to his wife: "Well, God has arrived. I met him on the 5.15 train." Despite this fame, he could not initially work at Cambridge as he did not have a degree, so he applied as an advanced undergraduate. Russell noted that his previous residency was sufficient for a PhD, and urged him to offer the Tractatus as his thesis. It was examined in 1929 by Russell and Moore; at the end of the thesis defense, Wittgenstein clapped the two examiners on the shoulder and said, "Don't worry, I know you'll never understand it." Moore wrote in the examiner's report: "I myself consider that this is a work of genius; but, even if I am completely mistaken and it is nothing of the sort, it is well above the standard required for the Ph.D. degree." Wittgenstein was appointed as a lecturer and was made a fellow of Trinity College.

From 1936 to 1937, Wittgenstein lived again in Norway, where he worked on the Philosophical Investigations. In the winter of 1936/7, he delivered a series of "confessions" to close friends, most of them about minor infractions like white lies, in an effort to cleanse himself. In 1938, he traveled to Ireland to visit Maurice O'Connor Drury, a friend who became a psychiatrist, and considered such training himself, with the intention of abandoning philosophy for it. The visit to Ireland was at the same time a response to the invitation of the then Irish Taoiseach, Éamon de Valera, himself a mathematics teacher. De Valera hoped Wittgenstein's presence would contribute to an academy for advanced mathematics.

While he was in Ireland in March 1938, Germany annexed Austria in the Anschluss; the Viennese Wittgenstein was now a citizen of the enlarged Germany and a Jew under the 1935 Nuremberg racial laws, because three of his grandparents had been born as Jews. The Nuremberg Laws classified people as Jews (Volljuden) if they had three or four Jewish grandparents, and as mixed blood (Mischling) if they had one or two. It meant inter alia that the Wittgensteins were restricted in whom they could marry or have sex with, and where they could work.

After the Anschluss, Paul left almost immediately for England, and later the US. The Nazis discovered his relationship with Hilde Schania, a brewer's daughter with whom he had had two children but whom he had never married, though he did later. Because she was not a Jew, he was served with a summons for Rassenschande (racial defilement). He told no one he was leaving the country, except for Hilde who agreed to follow him. He left so suddenly and quietly that for a time people believed he was the fourth Wittgenstein brother to have committed suicide.

Wittgenstein began to investigate acquiring British or Irish citizenship with the help of Keynes, and apparently had to confess to his friends in England that he had earlier misrepresented himself to them as having just one Jewish grandparent, when in fact he had three.

A few days before the invasion of Poland, Hitler personally granted Mischling status to the Wittgenstein siblings. In 1939 there were 2,100 applications for this, and Hitler granted only 12. Anthony Gottlieb writes that the pretext was that their paternal grandfather had been the bastard son of a German prince, which allowed the Reichsbank to claim the gold, foreign currency, and stocks held in Switzerland by a Wittgenstein trust. Gretl, an American citizen by marriage, started the negotiations over the racial status of their grandfather, and the family's large foreign currency reserves were used as a bargaining tool. Paul had escaped to Switzerland and then the US in July 1938, and disagreed with the negotiations, leading to a permanent split between the siblings. After the war, when Paul was performing in Vienna, he did not visit Hermine who was dying there, and he had no further contact with Ludwig or Gretl.

After G.E. Moore resigned the chair in philosophy in 1939, Wittgenstein was elected, and acquired British citizenship soon afterwards. In July 1939 he traveled to Vienna to assist Gretl and his other sisters, visiting Berlin for one day to meet an official of the Reichsbank. After this, he traveled to New York to persuade Paul, whose agreement was required, to back the scheme. The required Befreiung was granted in August 1939. The unknown amount signed over to the Nazis by the Wittgenstein family, a week or so before the outbreak of war, included among many other assets, 1700 kg of gold. There is a report Wittgenstein visited Moscow a second time in 1939, traveling from Berlin, and again met the philosopher Sophia Janowskaya.

Norman Malcolm, at the time a post - graduate research fellow at Cambridge, describes his first impressions of Wittgenstein in 1938:

"At a meeting of the Moral Science Club, after the paper for the evening was read and the discussion started, someone began to stammer a remark. He had extreme difficulty in expressing himself and his words were unintelligible to me. I whispered to my neighbor, 'Who's that?': he replied, 'Wittgenstein'. I was astonished because I had expected the famous author of the Tractatus to be an elderly man, whereas this man looked young - perhaps about 35. (His actual age was 49.) His face was lean and brown, his profile was aquiline and strikingly beautiful, his head was covered with a curly mass of brown hair. I observed the respectful attention that everyone in the room paid to him. After this unsuccessful beginning he did not speak for a time but was obviously struggling with his thoughts. His look was concentrated, he made striking gestures with his hands as if he was discoursing... Whether lecturing or conversing privately, Wittgenstein always spoke emphatically and with a distinctive intonation. He spoke excellent English, with the accent of an educated Englishman, although occasional Germanisms would appear in his constructions. His voice was resonant... His words came out, not fluently, but with great force. Anyone who heard him say anything knew that this was a singular person. His face was remarkably mobile and expressive when he talked. His eyes were deep and often fierce in their expression. His whole personality was commanding, even imperial."

Describing Wittgenstein's lecture program, Malcolm continues:

"It is hardly correct to speak of these meetings as 'lectures', although this is what Wittgenstein called them. For one thing, he was carrying on original research in these meetings... Often the meetings consisted mainly of dialogue. Sometimes, however, when he was trying to draw a thought out of himself, he would prohibit, with a peremptory motion of the hand, any questions or remarks. There were frequent and prolonged periods of silence, with only an occasional mutter from Wittgenstein, and the stillest attention from the others. During these silences, Wittgenstein was extremely tense and active. His gaze was concentrated; his face was alive; his hands made arresting movements; his expression was stern. One knew that one was in the presence of extreme seriousness, absorption, and force of intellect... Wittgenstein was a frightening person at these classes."

After work, Wittgenstein would often relax by watching Westerns, where he preferred to sit at the very front of the cinema, or reading detective stories. Norman Malcolm wrote that he would rush to the cinema when class ended.

By this time, Wittgenstein's view on the foundations of mathematics had changed considerably. In his early 20s, Wittgenstein had thought logic could provide a solid foundation, and he had even considered updating Russell and Whitehead's Principia Mathematica. Now he denied there were any mathematical facts to be discovered. He gave a series of lectures on mathematics, discussing this and other topics, documented in a book, with lectures by Wittgenstein and discussions between him and several students, including the young Alan Turing.

Monk writes that Wittgenstein found it intolerable that a war was going on and he was teaching philosophy. He grew angry when any of his students wanted to become professional philosophers.

In September 1941 he asked John Ryle, the brother of the philosopher Gilbert Ryle, if he could get a manual job at Guy's Hospital in London. John Ryle was professor of medicine at Cambridge and had been involved in helping Guy's prepare for the Blitz. Wittgenstein told Ryle he would die slowly if left at Cambridge, and he would rather die quickly. He started working at Guy's shortly afterwards as a dispensary porter, meaning that he delivered drugs from the pharmacy to the wards — where he apparently advised the patients not to take them.

The hospital staff were not told he was one of the world's most famous philosophers, though some of the medical staff did recognize him — at least one had attended Moral Sciences Club meetings — but they were discreet. "Good God, don't tell anybody who I am!" Wittgenstein begged one of them. Some of them nevertheless called him Professor Wittgenstein, and he was allowed to dine with the doctors. He wrote on 1 April 1942: "I no longer feel any hope for the future of my life. It is as though I had before me nothing more than a long stretch of living death. I cannot imagine any future for me other than a ghastly one. Friendless and joyless."

He had developed a friendship with Keith Kirk, a working class teenage friend of Francis Skinner, the mathematics undergraduate he had had a relationship with until Skinner's death in 1941 from polio. Skinner had given up academia, thanks at least in part to Wittgenstein's influence, and had been working as a mechanic in 1939, with Kirk as his apprentice. Kirk and Wittgenstein struck up a friendship, with Wittgenstein giving him lessons in physics to help him pass a City and Guilds exam. During his period of loneliness at Guy's he wrote in his diary: "For ten days I've heard nothing more from K, even though I pressed him a week ago for news. I think that he has perhaps broken with me. A tragic thought!" Kirk had in fact got married, and they never saw one another again.

While Wittgenstein was at Guy's he met Basil Reeve, a young doctor with an interest in philosophy, who, with Dr R T Grant, was studying the effect of shock on air raid casualties. When the blitz ended there were fewer casualties to study and in November 1942 Grant and Reeve moved to the Royal Victoria Infirmary, Newcastle upon Tyne, in order to study road traffic and industrial casualties. Grant offered Wittgenstein a position as a laboratory assistant at a wage of £4 per week, and he lived in Newcastle (at 28 Brandling Park, Jesmond) from 29 April 1943 until February 1944.

He resigned the professorship at Cambridge in 1947 to concentrate on his writing, and traveled to Ireland in 1947 and 1948, staying in Ross's Hotel in Dublin and a farmhouse in Red Cross, in County Wicklow, where he began the manuscript volume MS 137, Band R. Seeking solitude he moved to Rosro, a holiday cottage in Connemara owned by Maurice O'Connor - Drury.

He also accepted an invitation from Norman Malcolm, then professor at Cornell University, to stay with him and his wife for several months at Ithaca, New York. He made the trip in April 1949, although he told Malcolm he was too unwell to do philosophical work: "I haven't done any work since the beginning of March & I haven't had the strength of even trying to do any." A doctor in Dublin had diagnosed anemia and prescribed iron and liver pills. The details of Wittgenstein's stay in America are recounted in Norman Malcolm's Ludwig Wittgenstein: A Memoir. During his summer in America, Wittgenstein began his epistemological discussions, in particular his engagement with philosophical skepticism, that would eventually become the final fragments On Certainty.

He returned to London, where he was diagnosed with an inoperable cancer of the prostate, which had spread to his bone marrow. He spent the next two months in Vienna, where his sister Hermine died on 11 February 1950; he went to see her every day, but she was hardly able to speak or recognize him. "Great loss for me and all of us", he wrote. "Greater than I would have thought." He moved around a lot after Hermine's death staying with various friends: to Cambridge in April 1950, where he stayed with G.H. von Wright; to London to stay with Rush Rhees; then to Oxford to see Elizabeth Anscombe, writing to Norman Malcolm that he was hardly doing any philosophy. He went to Norway in August with Ben Richards, then returned to Cambridge, where on 27 November he moved into "Storey's End", at 76 Storey's Way, the home of his doctor, Edward Bevan, and his wife Joan; he had told them he did not want to die in a hospital, so they said he could spend his last days in their home instead. Joan was at first afraid of Wittgenstein, but they soon became good friends.

By the beginning of 1951 it was clear that he had little time left. He wrote a new will in Oxford on 29 January, naming Rhees as his executor, and Anscombe and von Wright his literary administrators, and wrote to Norman Malcolm that month to say, "My mind's completely dead. This isn't a complaint, for I don't really suffer from it. I know that life must have an end once & and that mental life can cease before the rest does." In February he returned to the Bevans' home to work on MS 175 and MS 176. These and other manuscripts were later published as Remarks on Colour and On Certainty. He wrote to Malcolm on 16 April, 13 days before his death: "An extraordinary thing happened to me. About a month ago I suddenly found myself in the right frame of mind for doing philosophy. I had been absolutely certain that I'd never again be able to do it. It's the first time after more than 2 years that the curtain in my brain has gone up. — Of course, so far I've only worked for about 5 weeks & it may be all over by tomorrow; but it bucks me up a lot now."

He began work on his final manuscript, MS 177, on 25 April 1951. It was his 62nd birthday on 26 April. He went for a walk the next afternoon, and wrote his last entry that day, 27 April. That evening, he became very ill; when his doctor told him he might live only a few days, he reportedly replied, "Good!". Joan stayed with him throughout that night, and just before losing consciousness for the last time on 28 April, he told her: "Tell them I've had a wonderful life." Norman Malcolm describes this as a "strangely moving utterance". Four of his former students arrived at his bedside — Ben Richards, Elizabeth Anscombe, Yorick Smythies and Maurice O'Connor Drury. Anscombe and Smythies were Catholics, and at the latter's request, a Dominican friar, Father Conrad Pepler, also attended. They were at first unsure what Wittgenstein would have wanted, but then remembered he had said he hoped his Catholic friends would pray for him, so they did, and he was pronounced dead shortly afterwards. He was given a Catholic burial at St. Giles's Church, Cambridge. Drury later said he had been troubled ever since about whether that was the right thing to do.

The Blue Book, a set of notes dictated to his class at Cambridge in 1933 – 1934, contains the seeds of Wittgenstein's later thoughts on language, and is widely read as a turning point in his philosophy of language.

Philosophical Investigations was published in two parts in 1953. Most of Part I was ready for printing in 1946, but Wittgenstein withdrew the manuscript from his publisher. The shorter Part II was added by his editors, Elizabeth Anscombe and Rush Rhees. Wittgenstein asks the reader to think of language as a multiplicity of language - games within which parts of language develop and function. He argues that philosophical problems are bewitchments that arise from philosophers' misguided attempts to consider the meaning of words independently of their context, usage, and grammar, what he called "language gone on holiday".

According to Wittgenstein, philosophical problems arise when language is forced from its proper home into a metaphysical environment, where all the familiar and necessary landmarks and contextual clues are removed. He describes this metaphysical environment as like being on frictionless ice: where the conditions are apparently perfect for a philosophically and logically perfect language, all philosophical problems can be solved without the muddying effects of everyday contexts; but where, precisely because of the lack of friction, language can in fact do no work at all. Wittgenstein argues that philosophers must leave the frictionless ice and return to the "rough ground" of ordinary language in use. Much of the Investigations consists of examples of how the first false steps can be avoided, so that philosophical problems are dissolved, rather than solved: "the clarity we are aiming at is indeed complete clarity. But this simply means that the philosophical problems should completely disappear."

Wittgenstein's influence has been felt in nearly every field of the humanities and social sciences, yet there are widely diverging interpretations of his thought. In the words of Georg Henrik von Wright, "He was of the opinion... that his ideas were generally misunderstood and distorted even by those who professed to be his disciples. He doubted he would be better understood in the future. He once said he felt as though he were writing for people who would think in a different way, breathe a different air of life, from that of present - day men."

In 1999, the Baruch Poll ranked the Investigations as the most important book of 20th century philosophy, standing out as "...the one crossover masterpiece in twentieth - century philosophy, appealing across diverse specializations and philosophical orientations".