Das Kalenderblatt 100827

26/08/2010 - 14:39 von WM | Report spam
Meine MathOverflow-Episode (27)

Es geht um einen Artikel von Jeremy Gray, "Did Poincare say 'set
theory is a disease'?", Math. Intelligencer 13 (1991), 19-22. Debunks
the myth that Poincare said, "Later generations will regard
Mengenlehre as a disease from which one has recovered." Meine erste
Antwort darauf war nach nur einer Stunde von einem automatisierten
Gedàchtnisstörungspolizisten gelöscht worden. Hier ist die zweite:

I am not used to be censored by stupid automata!

Therefore I repeat that I have said in "The future of
mathematics" (1908) "... it has come to pass that we have encountered
certain paradoxes, certain apparent contradictions that would have
delighted Zeno the Eleatic and the school of Megara. And then each
must seek the remedy. For my part, I think, and I am not the only one,
that the important thing is never to introduce entities not completely
definable in a finite number of words. Whatever be the cure adopted,
we may promise ourselves the joy of the doctor called in to follow a
beautiful pathologic case."

I do not remember whether I have said exactly what Jeremy Gray
believes to have "debunked". But it is clear that I ment it. Cantor
himself complains in a letter to Russell, written on Sept. 19, 1911:

"I am quite an adversary of Old Kant, who, in my eyes has done much
harm and mischief to philosophy, even to mankind; as you easily see by
the most perverted development of metaphysics in Germany in all that
followed him, as in Fichte, Schelling, Hegel, Herbart, Schopenhauer,
Hartmann, Nietzsche, etc. etc. on to this very day. I never could
understand that and why such reasonable and enabled peoples as the
Italiens, the English and the French are, could follow yonder
sophistical philistine, who was so bad a mathematician. And now it is
that in just this abominable mummy, as Kant is, Monsieur Poincare felt
quite enamoured, if he is not bewitched by him. So I understand quite
well the Opposition of Mons. Poincaré, by which I felt myself
honoured, so he never had in his mind to honour me, as I am sure. If
he perhaps expect, that I will answer him for defending myself, he is
certainly in great a mistake."

From that letter it is obvious that I must have had said something
that Cantor did not like very much.

Fortunately Cantor did not meet Russell. Cantor would have been very
disappointed: "The objections to the theory are [...] that a great
part of Cantor's theory of the transfinite, including much that it is
hard to doubt, is, so far as can be seen, invalid if there are no
classes or relations." [Bertrand Russell: "On some difficulties in the
theory of transfinite numbers and order types", Proc. London Math.
Soc. (2) 4 (1906) 29-53, Received November 24th, 1905. - Read December
14, 1905.]

And at least Skolem reports the "debunked" sentence:

Andere Mathematiker gingen so weit in skeptischer Richtung, daß sie
die Mengenlehre ganz verwarfen, so z. B. Poincaré. Er soll in einem
Vortrage auf dem internationalen Mathematikerkongreß in Rom 1908
gesagt haben, daß man einmal in der Zukunft dazu kommen würde, die
Mengenlehre als eine überwundene Krankheit anzusehen. (to consider set
theory as a disease from which one has recovered.) Skolem: "Über die
Grundlagendiskussionen in der Mathematik" (1929)

From these few quotes it is clear, that the T. Chow's question
suggests a falsehood. And he should be grateful that I have corrected
that. I do not hope that some matheologians here around will again
demonstrate that they belong to an intolerant and fanatic sect where
it is usual to suppress the truth.

Regards, HP

Gruß, WM
 

Lesen sie die antworten

#1 Jürgen R.
26/08/2010 - 16:19 | Warnen spam
WM wrote:
Meine MathOverflow-Episode (27)

Es geht um einen Artikel von Jeremy Gray, "Did Poincare say 'set
theory is a disease'?", Math. Intelligencer 13 (1991), 19-22. Debunks
the myth that Poincare said, "Later generations will regard
Mengenlehre as a disease from which one has recovered." Meine erste
Antwort darauf war nach nur einer Stunde von einem automatisierten
Gedàchtnisstörungspolizisten gelöscht worden. Hier ist die zweite:

I am not used to be censored by stupid automata!

Therefore I repeat that I have said in "The future of
mathematics" (1908) "... it has come to pass that we have encountered
certain paradoxes, certain apparent contradictions that would have
delighted Zeno the Eleatic and the school of Megara. And then each
must seek the remedy. For my part, I think, and I am not the only one,
that the important thing is never to introduce entities not completely
definable in a finite number of words. Whatever be the cure adopted,
we may promise ourselves the joy of the doctor called in to follow a
beautiful pathologic case."



Wenn man den von WM unterdrückten Anfang des zitierten Abschnittes liest,
ergibt sich ein völlig anderes Bild:

"I have spoken above of the need we have of returning continually
to the first principles of our science, and of the advantage of this
process to the study of the human mind. It is this need which has inspired
two attempts which have held a very great place in the most recent history
of mathematics. The first is Cantorism, and the services it has rendered
to the science are well known. Cantor introduced into the science a new
method of considering mathematical infinity, and I shall have occasion
to speak of it again in Book Il., chapter iii. One of the characteristic
features of Cantorism is that, instead of rising to the general by erecting
more and more complicated constructions, and defining by construction,
it starts with the genus supremum and only defines, as the scholastics
would have said, per genus proximum et differentiam specificam.
Hence the horror he has sometimes inspired in certain minds, such
as Hermite's, whose favourite idea was to compare the mathematical
with the natural sciences. For the greater number of us these prejudices
had been dissipated, but it has come about that we have run against
certain paradoxes and apparent contradictions..." usw

I do not remember whether I have said exactly what Jeremy Gray
believes to have "debunked". But it is clear that I ment it. Cantor
himself complains in a letter to Russell, written on Sept. 19, 1911:

"I am quite an adversary of Old Kant, who, in my eyes has done much
harm and mischief to philosophy, even to mankind; as you easily see by
the most perverted development of metaphysics in Germany in all that
followed him, as in Fichte, Schelling, Hegel, Herbart, Schopenhauer,
Hartmann, Nietzsche, etc. etc. on to this very day. I never could
understand that and why such reasonable and enabled peoples as the
Italiens, the English and the French are, could follow yonder
sophistical philistine, who was so bad a mathematician. And now it is
that in just this abominable mummy, as Kant is, Monsieur Poincare felt
quite enamoured, if he is not bewitched by him. So I understand quite
well the Opposition of Mons. Poincaré, by which I felt myself
honoured, so he never had in his mind to honour me, as I am sure. If
he perhaps expect, that I will answer him for defending myself, he is
certainly in great a mistake."

From that letter it is obvious that I must have had said something
that Cantor did not like very much.

Fortunately Cantor did not meet Russell. Cantor would have been very
disappointed: "The objections to the theory are [...] that a great
part of Cantor's theory of the transfinite, including much that it is
hard to doubt, is, so far as can be seen, invalid if there are no
classes or relations." [Bertrand Russell: "On some difficulties in the
theory of transfinite numbers and order types", Proc. London Math.
Soc. (2) 4 (1906) 29-53, Received November 24th, 1905. - Read December
14, 1905.]

And at least Skolem reports the "debunked" sentence:

Andere Mathematiker gingen so weit in skeptischer Richtung, daß sie
die Mengenlehre ganz verwarfen, so z. B. Poincaré. Er soll in einem
Vortrage auf dem internationalen Mathematikerkongreß in Rom 1908
gesagt haben, daß man einmal in der Zukunft dazu kommen würde, die
Mengenlehre als eine überwundene Krankheit anzusehen. (to consider set
theory as a disease from which one has recovered.) Skolem: "Über die
Grundlagendiskussionen in der Mathematik" (1929)

From these few quotes it is clear, that the T. Chow's question
suggests a falsehood. And he should be grateful that I have corrected
that. I do not hope that some matheologians here around will again
demonstrate that they belong to an intolerant and fanatic sect where
it is usual to suppress the truth.

Regards, HP

Gruß, WM

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