The family of Karl Wittgenstein, who was one of Austria’s richest men when he died, in 1913, may deserve some gloomy sort of prize, the Palm of Atreus, perhaps. His youngest child, the philosopher Ludwig Wittgenstein, once asked a pupil if he had ever had any tragedies in his life. The pupil, evidently well trained, inquired what he meant by “tragedy.” “I mean suicides, madness, or quarrels,” replied Ludwig, three of whose four brothers committed suicide, two of them (Rudi and Hans) in their early twenties, and the third (Kurt) at the age of forty. Ludwig often thought of doing so, as did his surviving brother, Paul. A budding concert pianist when he lost his right arm to a Russian bullet, in 1914, Paul was imprisoned for a time in the infamous Siberian fortress where Dostoyevsky had set his novel “The House of the Dead.” Ludwig later claimed to have first entertained thoughts of suicide at around the age of ten, before any of his brothers had died. There were three sisters: Gretl, Helene, and Hermine. Hermine, the eldest child (she was born in 1874; Ludwig, the youngest, arrived fifteen years later), and the guardian of her father’s flame, never married. Helene was highly neurotic, and had a husband who suffered from dementia. Gretl was regarded as irritating by most people, including her unpleasant husband, who committed suicide, as did his father and one of his aunts. Bad temper and extreme nervous tension were endemic in the family. One day, when Paul was practicing at one of the seven grand pianos in their winter home, the Palais Wittgenstein, he leaped up and shouted at his brother Ludwig in the room next door, “I cannot play when you are in the house, as I feel your skepticism seeping towards me from under the door!”

Paul became a concert pianist despite losing an arm, and Ludwig shared his iron will. Yet their three brothers killed themselves. Illustration by David Hughes

All of this was before the Nazis got to work. The Wittgenstein children were brought up as Christians, but they counted as full Jews under the Nuremberg racial laws because three of their grandparents had been born Jewish and did not convert to Christianity until they reached adulthood. (The fourth, their maternal grandmother, had no Jewish ancestry.) After Germany annexed Austria, in 1938, the family money bought the lives of the three sisters—Paul had escaped, and Ludwig was safe in England—but at the cost of estranging several of the surviving siblings from one another. A few days before the invasion of Poland, in 1939, Hitler found the time to issue an order granting half-breed status to the Wittgenstein children, on the pretext that their paternal grandfather had been the bastard son of a German prince. Nobody believed this tale, but the arrangement enabled the German Reichsbank to claim all the gold and much of the foreign currency and stocks held in Switzerland by a Wittgenstein trust. The negotiations for this exchange seem to have involved a secret pact in which Gretl and Hermine sided with Nazi officials against Paul. After the war, Paul performed with his single hand at a concert in Vienna but did not visit Hermine, who was dying there; Ludwig and Paul had no contact after 1939; nor did Paul and Gretl. This was not a happy family.

Alexander Waugh, the author of “The House of Wittgenstein: A Family at War” (Doubleday; $28.95), is no stranger to family sagas. He belongs to the fourth generation of an English literary dynasty that includes the novelist Evelyn Waugh, who was his grandfather; his previous book, “Fathers and Sons,” is a memoir of the Waughs. The publishers of “The House of Wittgenstein” compare the “novelistic richness” of its style to Thomas Mann’s first novel, “Buddenbrooks: The Decline of a Family,” which was published in 1901. In fact, there are more than stylistic similarities between the Wittgensteins of Vienna and Mann’s invented north-German merchant dynasty. In Mann’s novel, the vitality and the solid businesslike virtues of the Buddenbrook family are sapped by introspection, homosexuality, loss of interest in commerce, overindulgence in art, and illness. If Karl Wittgenstein ever read it, he must have nodded in recognition. In a memoir that Hermine wrote in the nineteen-forties, she noted the “lack of vitality and will for life” that set her brothers apart from their father, and described his bitter disappointment that none of them wanted to continue his work in business. Like his wife and his children, Karl was highly musical, but he found his son Hans’s obsession with music to be morbid and strictly limited the amount of time the boy was allowed to play. Hans was a prodigy whose extraordinary musical perception became evident at the age of four; Gustav Mahler’s teacher, Julius Epstein, called him a genius. But Karl insisted that he follow a career in industry or finance. Rudi and Ludwig were homosexual, and Hans may have been, too.

There the parallels end. Thomas Mann traced the decline of the Buddenbrooks through four generations, but the Wittgensteins rose and fell within the span of two. Karl more or less built the family fortune himself. He was no stolid merchant but an audacious risk-taker, and something of a rebel in early life. At the age of seventeen, he absconded to New York, where he arrived in the spring of 1865 with a violin and no money. He worked as a waiter, then, among other things, he played in a minstrel band, a gig that came to an abrupt end when Abraham Lincoln was assassinated in a theatre and musical performances were banned. Karl was too ashamed to write to his family or answer their letters. It was only when he got a steady job as a teacher at a college in upstate New York that he recovered enough pride to agree to return.

His father was a land agent and a trader, and at first Karl was put to work on one of his rented farms. Then he briefly enrolled in Vienna’s Technical University. After dropping out, he took a series of engineering jobs. Energy and intelligence got him into management, audacious deal-making took him higher, and some capital from his wife (he married in 1874) provided the first grains of powder for an explosive entrepreneurial rampage. Waugh says that Karl Wittgenstein was a chancer, whose enormous fortune owed as much to the favorable outcomes of his gambles as to his hard work and his skills. That is implausible; nobody has quite such a consistent run of good luck. Karl was adept at swinging the odds in his own favor, and he knew exactly which chances to take—in particular, he appreciated the significance of technology more keenly than his competitors did. Announcing his death, in 1913, The Economist wrote that “the Austrian iron and steel trade owes its rapid growth and development solely to him.”

Newspaper articles by Karl Wittgenstein show that he believed in unfettered capitalism (though not in free trade) and was opposed to any legislation aimed at protecting consumers from cartels or fraud. Such laws, in his opinion, would interfere with the crucial work of vigorous entrepreneurs, who would ultimately raise the standard of living for everybody. An early master of the leveraged buyout, he no doubt cut some corners while assembling his ingeniously integrated empire of mines, iron- and steelworks, and hardware factories. He certainly reaped the benefits of monopoly wherever he could find them. In February of 1900, The Economist’s Austria-Hungary correspondent reported from Vienna that Herr Wittgenstein would “soon have the power of fixing iron prices in Hungary also, as he fixes them in Austria.”

Karl was no philanthropist on the scale of his American friend Andrew Carnegie. He was more of a patron—one of the main supporters of the Secession, Vienna’s Art Nouveau movement led by Gustav Klimt (who painted a portrait of Gretl, which she did not like). But the family’s cultural life really centered on the grand Musiksaal on the first floor of their main house. Brahms was a family friend. He dedicated his violin concerto to Karl’s first cousin Joseph Joachim, whose famous quartet played in the Musiksaal several times each year. Richard Strauss came and performed duets with the young Paul. Schoenberg attended the soirées several times; Mahler, whose music Ludwig later dismissed as “worthless,” once attended but was not invited again after he left before the end of the evening’s entertainment.

Music was more than entertainment for the Wittgensteins, though, and more than art. For one thing, it became a store of value. Pages from the Wittgenstein collection of autographed musical manuscripts flutter through this wonderfully told story. Scores by Brahms, Schubert, Wagner, and Bruckner are stuffed in a potting shed by a quick-thinking servant while an art historian from the Gestapo rummages through Gretl’s house. A Bach cantata, two Mozart piano concertos, a Haydn symphony, and one of Beethoven’s last piano sonatas are smuggled to Ludwig in Cambridge, where he places them in a bank safe-deposit box. Gretl’s younger son hides Schubert’s “Die Forelle,” Brahms’s “Handel Variations,” some Beethoven letters, Wagner’s sketches for “Die Walküre,” and more, under a pile of socks in his suitcase, and heads for the Vienna railway station. Music was also, Waugh writes, the only effective way in which the Wittgenstein children could communicate with their shy, nervous, and intensely musical mother. And music provided consolation and distraction from the tragedies of the family, about which they were mostly required to remain silent.

Sometime in 1901, Hans fled from his father and went to America, much as his own father had done thirty-six years earlier. In 1902, he disappeared, by most accounts, from a boat, which may have been in the Chesapeake Bay, perhaps on the Orinoco River in Venezuela, or in several other places. Wherever it was, no one doubted that he had committed suicide. Hans’s disappearance was a banned topic. Rudi was a twenty-two-year-old chemistry student in Berlin when he walked into a bar on a May evening in 1904, requested a sentimental song from the pianist, and then mixed potassium cyanide into a glass of milk and died in agony. The suicide note left for his parents said that he had been grieving over the death of a friend. A more likely explanation is that he thought he was identifiable as the subject of a published case study about homosexuality. After Rudi’s funeral, Karl forbade the family to mention him ever again. Waugh thinks that this enforced silence, which the dutiful Mrs.Wittgenstein supported, created a permanent rift between parents and children. The exact circumstances of Kurt’s suicide, which took place on the Italian front in 1918, are unknown. He was generally regarded as cheerful, but Hermine recorded that he seemed to carry “the germ of disgust for life within himself.”

Perhaps it was because Paul, after he lost his right arm, had the most tangible affliction in the family that he found the focus to remake himself. His determination to succeed on the concert stage was, in part, inspired by the example of Josef Labor, a blind organist and composer who was a favorite of the Wittgenstein family. Géza Zichy, a one-armed Hungarian count whose pianism had enthralled Liszt, was another encouraging model. Zichy wrote a self-help book for amputees, which explained, among other things, how to eat a crayfish and remove one’s underpants with only one arm. Paul worked furiously and ingeniously to develop techniques that would enable him to perform. The training began while he was still recovering from the amputation in a Russian prison hospital, tapping on a dummy keyboard that he had etched in charcoal on a crate. Later, on a real piano, he often practiced for up to seven hours at a sitting.

At the peak of his career, in the late nineteen-twenties and early thirties, Paul’s concerts drew wildly enthusiastic reviews from respected critics; the Grove Dictionary of Music describes Paul as having had “an amazing virtuosity which enabled him to overcome difficulties formidable even for a two-handed pianist.” During Ludwig’s lifetime, the pianist brother—his elder by just two years—was much the more famous of the two. It’s also true that Paul continued to perform after his abilities had declined, and his reputation declined accordingly. He made few recordings, and Waugh, who is also a composer and a music critic, remarks that most of them are bad.

His most lasting significance comes from having commissioned one-handed works from at least a dozen composers, including Richard Strauss, Sergei Prokofiev, Benjamin Britten, Paul Hindemith, and Maurice Ravel, whose Piano Concerto for the Left Hand remains widely performed. Strauss extracted a particularly large fee, and Britten, at least, affected to be in it just for the money. (“I have been commissioned by a man called Wittgenstein,” Britten wrote to his sister. “He pays gold so I’ll do it.”) Paul often insisted on changes to the music, especially when he thought that the orchestra had been overscored and would drown out his playing. (Britten groused, “The man really is an old sour puss.”) There was also a colorful dispute with Ravel, who complained for the rest of his life about his dealings with Paul. There was worse in store for poor Hindemith, who wrote his concerto in 1923: Paul couldn’t understand the composition, so he filed it away. It was discovered eight decades later, in a Pennsylvania farmhouse that had belonged to Paul’s widow, and given a belated world première by Leon Fleisher in Berlin in 2004. Paul couldn’t fathom Prokofiev’s concerto, either, and he shelved that, too. In 1950, Siegfried Rapp, a pianist who had lost his right arm in the Second World War, asked for permission to perform some of these works, many of which had been written a quarter of a century earlier. Paul usually bought exclusive performing rights for his commissions, and he said no. A few years later, Rapp obtained a copy of Prokofiev’s concerto from his widow and went ahead, anyway, infuriating Paul.

It is hard to warm to Paul’s refusal to let anyone else perform pieces that he wouldn’t play himself. (He even felt betrayed by composers who wanted to rearrange his commissions to produce two-handed versions.) And, despite giving evidence of Paul’s kindness and generosity to friends, pupils, and old retainers, Waugh makes no effort to conceal his hero’s estrangement from the compromises that lubricate everyday life. Bertrand Russell once wrote of Ludwig that no one could be more “destitute of the false politeness that interferes with truth.” This was at a time when Russell was still enraptured by the young Ludwig. Russell later grew less indulgent toward his erstwhile pupil, but he had identified a family characteristic: when they believed that an important principle was at stake—which, for them, was often—the Wittgensteins were not inclined to be nice.

Most of Paul’s eccentricities were perhaps the normal ones for a loner who had been brought up amid vast wealth. He was a fiercely private man who liked to book entire railway carriages for himself, even when travelling with his family. His wife, Hilde, who was half blind and had been his pupil, bore him two children in Vienna before their marriage; the elder child had been conceived shortly after their first piano lesson, when Hilde was eighteen years old and Paul was forty-seven. Because Hilde was not Jewish, Paul was open to charges of “racial defilement,” and in 1938 he fled Austria. When his wife and children arrived in the United States, in 1941, he set them up in a house on Long Island, which he visited on weekends from his apartment on Riverside Drive. Arriving in New York without a valet, he soon ran into trouble. When his clothes were stolen from a hotel—he had left them outside his room, presuming that someone would wash them—he sat around in bedsheets until a candidate for the post of personal assistant came up with the suggestion that more clothes be bought from a shop. She was hired. Another anecdote has him sallying forth into the street wearing a hat that was still attached to its box.

In the Wittgenstein family, it was not the philosopher who was the unworldly one. Ever since childhood, the last-born Ludwig had had a passion and a facility for mechanical things. At the age of ten, he constructed a working model of a sewing machine out of bits of wood and wire; while serving in the Austrian Army, he demonstrated a more dangerous practicality by improvising his own mortar in the field. After leaving school, Ludwig studied engineering in Berlin, specializing in hot-air balloons, and then moved to Manchester to work on aeronautical engines; in 1910, he patented an improvement in propeller technology. It was then that he heard of Bertrand Russell’s work on logic and decided to study with him in Cambridge.

Russell found him to be a tormented soul, unsure of his own abilities and unsure whether to be an engineer or a philosopher. Russell soon decided that Ludwig was the most perfect example of genius he had ever known, and persuaded him not to continue with engineering. “We expect the next big step in philosophy to be taken by your brother,” Russell told Hermine. But he feared that his new pupil was on the brink of suicide, as he explained in a letter to his mistress, Lady Ottoline Morrell. Ottoline wrote back that hot chocolate would calm Ludwig’s nerves, and enclosed a packet of cocoa tablets for Russell to give him.

If they ever reached Ludwig they did not do the trick. He continued to work with a feverish intensity on the problems of logic that he was discussing with Russell and to agonize about his life. The way those two topics were entangled in Ludwig’s mind can be seen from his “Tractatus Logico-Philosophicus,” a gnomic masterpiece that he completed as a soldier in 1918. The “Tractatus” is a mixture of logical symbols and mystical remarks in which Ludwig attempted to delineate the limits of language. Certain things could be expressed in language, and these were best understood in terms of the logical techniques developed by Russell, he maintained. But others—and these were the most important things in life—could not be expressed in language at all. Hence the book’s famous closing line: “Whereof one cannot speak, thereof one must be silent.” The problems of philosophy could thus be dispatched by being divided into those that could be perspicuously rendered into Russellian logic, and thereby answered fairly easily, and those about which nothing could be said.

Frank Ramsey, one of Ludwig’s most brilliant friends, who had reviewed the “Tractatus” in Britain’s main philosophical journal as an undergraduate, quipped that “what we can’t say we can’t say, and we can’t whistle it either.” Ramsey meant that Ludwig seemed to be cheating by trying to specify exactly what cannot be said. As it happens, Ludwig—who, unusually for a Wittgenstein, seems not to have mastered any musical instrument as a child—impressed his musical friends with displays of virtuoso whistling. Several Cambridge dons recalled hearing him whistle the solo part of an entire concerto while a pianist played the orchestral part. Whether or not Ramsey had this curious feat in mind, the Wittgensteins were certainly in the habit of using music to express what they couldn’t say in words.

After the “Tractatus,” having thus exhausted all philosophical problems, and been exhausted by them, Ludwig took a break. He worked as a schoolmaster for six years and then as an architect, designing and obsessively supervising the building of a house in Vienna for his sister Gretl. During the First World War, he had read Tolstoy’s “The Gospel in Brief” and other writings that extolled the wisdom of peasants. Resolving to lead a simple life, he gave his share of the family money to three of his siblings; since they were very rich already, he believed they could not be corrupted further by receiving his portion. Then, in 1927, his interest in philosophy was rekindled. This time, his view of language changed—the emphasis on Russellian logic was gone—but one key idea remained the same. Both his old and his new philosophy shared an inspiration that he had come across as a teen-ager in “The Principles of Mechanics,” by Heinrich Hertz, a German physicist. Hertz had suggested a novel way to deal with the puzzling concept of force in Newtonian physics: the best approach was not to try to define it but to restate Newton’s theory in a way that eliminates any reference to force. Once this was done, according to Hertz, “the question as to the nature of force will not have been answered; but our minds, no longer vexed, will cease to ask illegitimate questions.”

Ludwig’s big idea was to apply this method to philosophical problems. In his “Tractatus,” he had tried to show that some philosophical questions were illegitimate because they tried to say the unsayable. The new approach was gentler and more therapeutic. By painstakingly examining how language works in everyday life, Ludwig now believed that one could be cured of the misconceptions that give rise to philosophical puzzles, and thus stop worrying about them. That is what he toiled on, mostly in Cambridge, until his death, in 1951.

Does this actually work? Curiously, it is hard to say, because Ludwig seldom dealt explicitly with classical philosophical problems. His writings hardly ever mention the great philosophers of days gone by, except in passing. So one has to work out for oneself what, if any, bearing his explorations of the workings of language have on the ideas of Plato, Descartes, or Kant. Ludwig intended his technique to be revolutionary: “Why should philosophy in the age of airplanes and automobiles be the same as in the age when people travelled by coach or on foot?” the former aeronautical engineer asked. It remains a point of contention whether he really found an honest way to dispose of philosophical questions or merely succeeded in changing the subject of conversation by the sheer force of his personality.

There’s a telling description of genius by Arthur Schopenhauer, the German philosopher of romantic pessimism, whose work was well known to Ludwig, Paul, Gretl, and Hans: “Talent is like the marksman who hits a target which others cannot reach; genius is like the marksman who hits a target, as far as which others cannot even see.” That seems to have been the Wittgenstein way: trying to hit targets that others could not see. But if ordinary mortals cannot spot the bull’s-eye, how do they know whether it has been hit? According to Schopenhauer, they just have to accept the evidence of genius on faith, which is what Ludwig’s admirers often did. When Ludwig attacked some of Russell’s ideas, Russell wrote to Ottoline Morrell, “I couldn’t understand his objection—in fact he was very inarticulate—but I feel in my bones that he must be right.” Other philosophers who met Ludwig reported the same feeling.

It’s tempting to come away from the Wittgenstein saga with the thought that Karl, if only he had lived long enough, would have acknowledged the iron-willed independence of Paul and Ludwig as a reflection of his own, and given them his blessing. But that would probably be expecting too much of him. Tragic or not, no family has room for more than one Wittgenstein. ♦