Das Kalenderblatt 090724

23/07/2009 - 22:27 von WM | Report spam
OOOOOOOOOOOO
O O
O 50 O
O O
OOOOOOOOOOOO

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
 

Lesen sie die antworten

#1 WM
24/07/2009 - 21:43 | Warnen spam
On 23 Jul., 22:27, WM wrote:
OOOOOOOOOOOO
O                            O
O            50            O
O                            O
OOOOOOOOOOOO

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...matics-...

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...ttgenst...

http://uk.geocities.com//cantor/wit...es.htm#rfm




Der Link scheint defekt. Hier ist er korrigiert:

http://uk.geocities.com//cantor/wit...es.htm#rfm

Gruß, WM

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