Ludwig Wittgenstein's contemporaries at Cambridge used sometimes to call him "God". They were joking, but only just. It would be hard to exaggerate the awe in which the Austrian-born philosopher was held by his disciples, especially those who had the privilege of sitting with him in his Trinity rooms, hushed and clenched with anxiety, waiting for him to drag some gnomic phrase from deep in his soul with as much visible agony as if he were tearing out a vital organ. Since his premature death in 1951, his work has inspired a vast quantity of exposition, and his life - at once a wonderful and a pathetic thing - a hefty number of biographies. He fascinates people who otherwise have no particular relish for modern philosophy, rather as TE Lawrence (another self-tormenting ascetic and serial hermit) may beguile those who otherwise care little for military history. Heideggereans, Sartreans, Derrideans and their gregarious like will sneer at the proposition, but he was probably the greatest philosopher of the last century.

And that is why it is odd to discover, or be reminded of the fact, that in his lifetime, Ludwig's fame was as nothing compared to that of his elder brother, the pianist Paul Wittgenstein (1887-1961). Paul, a passionate and gifted musician from his earliest days, lost his right arm when serving in the Austrian army in the first world war. Instead of giving in to self-pity and the bottle, he rigorously retrained himself to play the piano with one hand, and then commissioned a number of composers, from Hindemith to a very young Benjamin Britten, to write pieces suitable for his new talent. The most famous of these pieces was a pyrotechnical - and rather stirring - concerto by Ravel. Paul's life story was considered so universally inspiring that, in the 1950s, a Hollywood production company approached him with plans for a biopic. He spurned them, as Ludwig would surely have done in the highly unlikely event that Hollywood had ever taken him up as a potential screen hero. (Ludwig was eventually brought to the cinema in an inventive if micro-budgeted film by Derek Jarman. Worth checking out.)

One consequence of Alexander Waugh's The House of Wittgenstein is to bring the pianist out of the deep shadow thrown, since those glory days, by his prodigious philosopher brother. True, other members of the affluent Wittgenstein clan also inhabit a few of these pages, and a stranger group of excessively rich people it would be hard to imagine. The nervy offspring of Karl Wittgenstein, an iron-willed Viennese industrialist, Ludwig's eight siblings included Rudolf, a guilty homosexual who killed himself with a glass of milk and cyanide at the age of 22; Hans, a mathematical idiot savant whose first recorded word was said to be "Oedipus" (can this be true?) and who vanished without trace in 1902; and Margaret, or "Gretl", who as a teenager embroidered a cushion with a heart - not the conventional, curvy hearts-and-flowers kind, but the actual, blood-swollen organ. She might have felt at home in the Addams family.

Piquant as these minor players are, it is Paul and Ludwig who dominate the book. In some respects, the brothers could hardly have been more different. When the children came into enormous fortunes on the death of their father in 1913, Ludwig donated large amounts to various artists, and eventually gave almost everything away, living most of his years in poverty. Paul, ferociously right-wing, was also generous with his money, though most of his cash gifts went to anti-communist and anti-anarchist associations. Ludwig, although he took much of his political inspiration from late Tolstoy rather than Lenin or Trotsky, perversely approved of the Soviet regime long past the point where it had obviously become a murderous tyranny. The brothers were alike in their great physical courage as soldiers and prisoners of war, and in a sternness of character that makes them both a little frightening.

Waugh's history is assiduously researched and pacily written, at times to the point of being slangy. (He uses "busted" for "arrested", "rocket" for "reprimand", "scampered" for "fled".) Its chief virtue is that it pays due respect not merely to Paul Wittgenstein's talent and courage but to what earlier generations would have called his "gallantry": how anyone could have endured what he and his comrades did as prisoners in Siberia, and then seek to enlist again, is almost as far beyond comprehension as...well, as some people find Ludwig Wittgenstein.

Waugh seems happy to confess himself among the ranks of the baffled or sceptical, and to share Paul's view that, however dazzling his other talents, Ludwig Wittgenstein's linguistic philosophy was "pure nonsense". And this is unfair, not to say unworthy. To brood upon the plainly written, often cryptic propositions and queries of the Philosophical Investigations (Ludwig's posthumous masterpiece, only sketchily outlined by Waugh) is to have glimpses of the world under a new aspect: the same one we have always known, but transfigured. For a few readers, it can still feel like a divine revelation.


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