He began by trying to reduce all mathematics to logic and ended by finding most metaphysics to be nonsense

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If you would like to watch philosophers squirm--and who wouldn't?--pose this tough question: Suppose you may either a) solve a major philosophical problem so conclusively that there is nothing left to say (thanks to you, part of the field closes down forever, and you get a footnote in history); or b) write a book of such tantalizing perplexity and controversy that it stays on the required-reading list for centuries to come. Which would you choose? Many philosophers will reluctantly admit that they would go for option b). If they had to choose, they would rather be read than right. The Austrian philosopher Ludwig Wittgenstein tried brilliantly to go for a) and ended up with b).

The revolution in mathematical logic early in the 20th century opened up a delicious prospect: a rigorous science of meanings. Just as the atomic theory in physics had begun to break matter down into its constituent parts and show how they fit together to produce all the effects in nature, logic held out the promise of accounting for all meaningful texts and utterances--from philosophy and geometrical proofs to history and legislation--by breaking them into their logical atoms and showing how those parts fit together (in an ideal language) to compose all the meanings there could be.

As a young engineering student in England, Wittgenstein saw the hope of the new mathematical logic, and rushed to Cambridge to become the protege of Bertrand Russell, whose monumental Principia Mathematica (1913), written with Alfred North Whitehead, was an attempt to reduce all mathematics to logic. Wittgenstein's first book, published in England in 1922, the even more grandly titled Tractatus Logico-philosophicus, went even further, and was thought by him, and by some of his admirers, to have brought philosophy to an end, its key problems definitively solved once and for all. Some "philosophical" propositions could be readily expressed and evaluated within his system, and those that couldn't--among them, metaphysical riddles that had bedeviled philosophers for centuries--were nonsense.

Wittgenstein returned to Austria to become a schoolteacher. But the worm of doubt soon gnawed, and he returned to England in 1929 to declare dramatically that he had got it all wrong the first time. The "later Wittgenstein" spent the next 18 years agonizing in front of a small Cambridge seminar of devoted and transfixed students, who posed curious questions that he then answered--or pointedly did not answer--with wonderfully austere if often enigmatic aphorisms. An obsessive perfectionist, Wittgenstein worked and reworked his notes and left his second masterpiece, Philosophical Investigations, for posthumous publication in 1953. Both books will be required reading as far into the future as any philosopher could claim to see.

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