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 project
Here 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. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([EMAIL PROTECTED])
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