Word: wittgensteins
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...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...
...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 set out in particular to subvert the seductive theories about mind and consciousness that philosophers since Descartes had puzzled and battled over. Again and again in Philosophical Investigations, he catches his interlocutors in the act of being suckered by their overconfident intuitions about what their words mean--what their words must mean, they think--when they talk about what's going on in their own minds. As he says, "The decisive moment in the conjuring trick has been made, and it was the very one that we thought quite innocent." (Today's neuroscientists fall into these same traps with...
...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...
Happily, in those days before tape recorders, some of Wittgenstein's disciples took verbatim notes, so we can catch a rare glimpse of two great minds addressing a central problem from opposite points of view: the problem of contradiction in a formal system. For Turing, the problem is a practical one: if you design a bridge using a system that contains a contradiction, "the bridge may fall down." For Wittgenstein, the problem was about the social context in which human beings can be said to "follow the rules" of a mathematical system. What Turing saw, and Wittgenstein...