Word: logical
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Dates: during 1990-1999
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This is the century that split the atom, probed the psyche, spliced genes and cloned a sheep. It invented plastic, radar and the silicon chip. It built airplanes, rockets, satellites, televisions, computers and atom bombs. It overthrew our inherited ideas about logic, language, learning, mathematics, economics and even space and time. And behind each of these great ideas, great discoveries and great inventions is, in most cases, one extraordinary human mind...
...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...
...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...
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...
...Wittgenstein's Cambridge seminar on the foundations of mathematics included a brilliant young mathematician, Alan Turing, who was giving his own course that term on the same topic. Turing too had been excited by the promise of mathematical logic and, like Wittgenstein, had come to see that it had limitations. But in the course of Turing's formal proof that the dream of turning all mathematics into logic was strictly impossible, he had invented a purely conceptual device--now known as a Universal Turing Machine--that provided the logical basis for the digital computer. And whereas Wittgenstein's dream...