The family into which Wittgenstein was born in 1889 was one of the wealthiest in Vienna, and young Ludwig grew up in a hothouse atmosphere of high culture and privilege. Brahms and Mahler were frequent visitors to the palatial family home, and Ludwig's brother Paul, a concert pianist who lost an arm in World War I, commissioned works for the left hand by Richard Strauss, Ravel and Prokofiev. It was during the war that Ludwig, a volunteer in the Austrian artillery, completed the "Tractatus" shortly before he was captured and taken prisoner. Always an ascetic, he gave away his inheritance, relying on the generosity of his Cambridge champions, Russell and John Maynard Keynes, to secure academic employment for him, living frugally and in later life being cared for by his disciples.

You know from the moment you open the "Tractatus" that it is something special. Each left-hand page is in German, facing its English translation on the right, and the sentences are numbered, using a hierarchical system that tells you this is a formal proof. The book begins straightforwardly enough: "1. The world is everything that is the case." (In German, it makes a memorable rhyming couplet: Die Welt ist alles, was der Fall ist.) And it ends with an ending to end all endings: "7. Whereof one cannot speak, thereof one must be silent."

In between, there is some tough sledding. Wittgenstein draws a distinction between what can be said, using words, and what can only be shown, and this raises the inevitable question: Does the "Tractatus," as a text, say things that can't be said? Maybe. The next-to-last proposition is a famous shocker: "6.54. My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) He must surmount these propositions; then he sees the world rightly."

Did this mean that the wonderful dream of logical atomism--a science of meanings — was hopeless? Or that there was much less to be said than one might have thought? Or what?

When Wittgenstein returned to philosophy in 1929, it was with the message that the rigorous methods of pure logic could get no grip on the problems of philosophy: "We have got on to slippery ice where there is no friction and so in a certain sense the conditions are ideal, but also, just because of that, we are unable to walk. We want to walk: so we need friction. Back to the rough ground!" Where before he had favored explicit logical rules, now he spoke of language games, governed by tacit mutual understanding, and he proposed to replace the sharp boundaries of set theory with what he called family resemblances. "Philosophy is a battle against the bewitchment of our intelligence by means of language," he declared, and language bewitches us by enticing us to concoct "theories" to solve philosophical problems that arise only "when language goes on holiday."

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