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For several terms at Cambridge in 1939, Ludwig Wittgenstein lectured

on the philosophical foundations of mathematics. A lecture class

taught by Wittgenstein, however, hardly resembled a lecture. He sat on

a chair in the middle of the room, with some of the class sitting in

chairs, some on the floor. He never used notes. He paused frequently,

sometimes for several minutes, while he puzzled out a problem. He

often asked his listeners questions and reacted to their replies. Many

meetings were largely conversation. These lectures were attended by,

among others, D. A. T. Gasking, J. N. Findlay, Stephen Toulmin, Alan

Turing.

[Cora Diamond (ed.): "Wittgenstein's Lectures on the Foundations of

Mathematics, Cambridge 1939 from the notes taken by R. G. Bosanquet,

Norman Malcolm, Rush Rhees, and Yorick Smythies", The University of

Chicago Press, Chicago (1975)]

http://www.amazon.com/Wittgensteins...ks&qid48181058&sr=8-1#reader

Imagine set theory's having been invented by a satirist as a kind of

parody on mathematics. – Later a reasonable meaning was seen in it and

it was incorporated into mathematics. (For if one person can see it

as a paradise of mathematicians, why should not another see it as a

joke?)

If it were said: "Consideration of the diagonal procedure shews you

that the concept "real number" has much less analogy with the concept

"cardinal number" than we, being misled by certain analogies, inclined

to believe", that would have a good and honest sense. But just the

opposite happens: one pretends to compare the "set" of real numbers in

magnitude with that of cardinal numbers. The difference in kind

between the two conceptions is represented, by a skew form of

expression, as difference of extension. I believe, and I hope, that a

future generation will laugh at this hocus pocus.

The curse of the invasion of mathematics by mathematical logic is that

now any proposition can be represented in a mathematical symbolism,

and this makes us feel obliged to understand it. Although of course

this method of writing is nothing but the translation of vague

ordinary prose.

"Mathematical logic" has completely deformed the thinking of

mathematicians and of philosophers, by setting up a superficial

interpretation of the forms of our everyday language as an analysis of

the structures of facts. Of course in this it has only continued to

build on the Aristotelian logic.

Rhees, von Wright, Anscombe (eds.): Ludwig Wittgenstein, Remarks on

the Foundations of Mathematics, Wiley-Blackwell (1991).

http://www.amazon.com/Remarks-Found...ks&qid48181778&sr=1-1

http://uk.geocities.com/frege@btinternet.com/cantor/wittgensteinquotes.htm#rfm

Gruß, WM

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