From: [hidden email] [mailto:[hidden email]] On Behalf Of Nicholas Thompson
Sent: Wednesday, October 01, 2008 11:18 PM
To: [hidden email]
Subject: [FRIAM] Wittgenstein
I have put the following material in an email message because is suspect it would fascinate some of you., and given that you are mostly people with real jobs and given that the information comes from the guts of a 700 page book, I suspect that many of you would be unlikely to stumble on it on your own.I have, as I have said, been reading Monk's biography of W. In it we learn many weird things, for instance, that W. turned up at Russell's door in Cambridge in 1911 or so, an callow Austrian lad, who had graduated from a technical school and got a job making kites in Manchester. Within a year, Russell was ruminating about whether he should turn his entire project in the foundations of mathematics over to W. and do something else himself.By 1937, W. had developed enormous contempt for the whole foundationalist project. As luck would have it, both he and Turing were giving relevant lectures at Cambridge and Turing came to hear W. talk. W. (never a particularly nice man) took the occasion to beat on Turing about the absurdity of the foundationalist projectHere is a quote from Monk, p. 418."Wittgensteins technique was not to reinterpret certain particular proofs, but, rather, to redescribe the whole of mathematics in such a way that mathematical logic would appear as the philosophical aberration he believed it to be, and in a way that dissolved entirely the picture of mathematics as a science which discovers facts about mathematical objects . I shall try again and again, he said, to show that what is called a mathematical discovery had much better be called a mathematical invention. There was, on his view, nothing for the mathematician to discover. A proof in mathematics does not establish the truth of a conclusion; if fixes, rather, the meaning of certain signs. The inexorability of mathematics, therefore, does not consist in certain knowledge of mathematical truths, but in the fact that mathematical propositions are grammatical. To deny, for example, that two plus two equals four is not to disagree with a widely held view about a matter of fact; it is to show ignorance of the meanings of the terms involved. Wittgenstein presumably thought that if he could persuade Turing to see mathematics in this light, he could persuade anybody."
Turing apparently gave up on W. a few lectures later.
I have to admit the distinction that W. is making here does not move me particularly. It seems to me as much of a discovery to find out what is implied by the premises of a logical system as to find out how many electrons there are in an iron atom, and since logic is always at work behind empirical work, I cannot get very excited about the difference. Perhaps because I am dim witted.
No response necessary.
Nick
Nicholas S. ThompsonEmeritus Professor of Psychology and Ethology,Clark University ([hidden email])
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