The mystery, glamour, and romance that surround the name Ludwig Wittgenstein are now part of our intellectual heritage. There were arguably a dozen other thinkers in the twentieth century who were as original and influential, but few of them have as much mystique. This Viennese eccentric—who published only one book in his lifetime—has captured the imagination of people who hardly know what he is talking about. Alexander Waugh appears to be one of these, and that is no putdown. Bertrand Russell and his Cambridge colleague G. E. Moore, who had both been close to Wittgenstein, professed to be baffled by, but also in awe of, his ideas. He had little time for the history of philosophy. As for his own philosophy, he began his career by describing language as the logical representation or “picturing” of the world, which he understood as a collection of facts; but he later came to think of language more as a set of related practices than as a picture. Wittgenstein was a bundle of paradoxes: a philosopher who rejected much of what we usually think of as philosophy, a rigorous logician who was also a mystic.

In The House of Wittgenstein, Alexander Waugh doesn’t give pride of place to the greatest member of the Wittgenstein family. Instead, he takes the approach of the social and cultural historian and presents a meticulous, scrupulously researched account of what it was like to be a member of an exclusive Hapsburg clan of Jewish origin in the first half of the twentieth century. He is interested in the family’s special craziness, ambition, and pride. Ludwig and his seven siblings were the children of a steel and banking magnate who was also a violinist, art collector, and host to Mahler and Brahms. At the family’s palais there were seven grand pianos, imposing European paintings and sculptures, and lots of marble and heavy tapestries—enough grandeur to impress any aristocrat. But Ludwig’s father, Karl, was no aristocrat, and he wanted his five sons to be engineers and builders. Ludwig’s brothers Hans and Rudi—who were musically inclined and probably gay—both committed suicide before the Great War. They couldn’t satisfy the old man. Kurt did put in time in the steel business, but he too died by his own hand. The probable explanation: As an officer on the Italian Front he wouldn’t order his men to their deaths and therefore faced certain court-martial. Ludwig began as an engineer but soon turned to philosophy and wound up at Cambridge University, lecturing and arguing about the meaning and function of words. Paul—another disappointment to his father—was a pianist who lost an arm as an officer in Poland. He had the Wittgenstein drive, went through hell as a POW in Siberia, and became a famous one-handed concert performer. The self-effacing Hermine, who never married, was the family chronicler. Helene married a financial expert who managed the family’s interests for a time. Gretl, the bossiest of the children, was an exotic-looking young woman who was painted (not well, she thought) by Gustav Klimt. She married an unsuccessful American businessman and became an important philanthropist, society hostess, and art collector.

Wittgenstein family values included music, self-absorption, fighting with each other, Austrian patriotism and honor, and plenty of Jewish anti-Semitism. (Both Ludwig and Paul made sneering remarks about Jews.) The family had to save themselves after the Anschluss of 1938: they apparently had three Jewish grandparents and, despite their Catholic upbringing, were doomed under the Nuremberg Laws. The best-case scenario for Jews before the Final Solution was emigration at a price—which meant handing over most of one’s assets to the Reich. Next best was being declared a “half-breed” exception. Waugh does a superb job of chronicling the Byzantine complications of the Wittgenstein estate, the arguments between siblings over who should give up what, and all the terrifying and surreal implications of being part Jewish in Austria after the Anschluss. The family had the same lawyer as Sigmund Freud, the sinister Alfred Indra. But it took the Führer himself—after the family paid up, that is—to declare the Wittgensteins exceptions. Waugh’s narrative races along on a trail of forged passports, letters, and smuggled manuscripts (including some by Mozart). Gretl swings into action and winds up in jail.

Waugh has a fine cast to work with: sleazy lawyers on the make, a family that could lose everything, and the Nazis. But for all the intrigue, it’s still Ludwig who gives this book its real weight, even though he disappears for long stretches of the story. Paul’s quarrels with Maurice Ravel and Sergei Prokofiev just don’t do it. As Waugh admits, Paul was not a great artist. (One of his teachers had called him “The Mighty Key-Smasher.”) Ludwig, for all his arrogance, was a great soul and a great teacher. He became an ardent Tolstoyan Christian after discovering the master’s The Gospel in Brief in a little bookshop in Poland while on leave during the war. The way of Jesus—humility, renunciation, drawing close to God—was his answer to the horrors of his time. Being rich was intolerable, so he gave his share of the family money to his siblings and to creative people, including the poet Rainer Maria Rilke, the painter Oskar Kokoschka, and the architect Adolf Loos.

Waugh’s nice phrase for the sight of Wittgenstein at work—“the spectacle of his thinking”—captures the drama of his teaching. Wittgenstein’s Blue and Brown Notebooks—the record of his Cambridge lectures in the 1930s—“came to be regarded with the same reverence and mystical fascination as the apocalypse gospels that passed surreptitiously under the togas of ancient Christians during the period of Rome’s decline.”

There were sorrows and scandals. Wittgenstein admired the Soviet experiment, wanted to be a laborer in Russia, and has been associated with the infamous Cambridge spies. Waugh tells us that Ludwig had been in “close contact” with known agents. But whatever his real connection with this group was, Ludwig’s effort to transform philosophy partook of old Karl’s ambition and heroic single-mindedness.

Alexander Waugh is the son of the essayist and novelist Auberon and the grandson of Evelyn. He has written a brilliant book about his own family’s eccentricities, and he does equally well by the Wittgensteins. He is less successful at evoking the rich atmosphere of prewar Vienna and the excitements of Cambridge during one of its greatest periods as a center of learning. He includes too much business history and not enough cultural history. But that’s what happens when you don’t make Ludwig the protagonist of a book about the Wittgensteins.