Das Kalenderblatt 100207

06/02/2010 - 10:03 von WM | Report spam
For the sake of a historical fairness, it is appropriate to add, that
the famous Thesis by Aristotle "Infinitum Actu Non Datur", i.e. a
statement on the impossibility of the existence (i.e. about the
internal contradiction of the concept) of logical or mathematical
(i.e. only conceivable and not naturally existing) actually infinite
objects, was shared and supported, - in the course of the last 2300
years, - by such Aristotle's great like-minded person as Leibnis,
Cauchy, Gauss, Kant, Kronecker, Poincare, Brouwer, Weyl, Luzin, and
many other outstanding creators of classical logic and modern
classical mathematics as a whole!
Each of them was professionally studying (researching) the problem
of mathematical infinity, and there can be no doubt about the fact
that they understood the real Nature of the Infinity no less than
G.Cantor. This is especially so if the basic importance of the fact
that infinity as such does not depend on a progress and
"technological" equipment of science, since it was never and will
never become an object of instrumental researches - since even all
conceivable computers together, can never complete the enumeration of
all elements of the natural numbers series 1,2,3,… It is exactly for
this reason that all discussions about the impossibility of actual
infinity in the course of two millenniums and up to Cantor was
speculative in nature, did not depend on the obvious (in all other
relations) progress of science. It is only proved contradiction of
consequences, arising from the concept of actual infinity, could
become the "last argument" against using that concept in science. But
for that to happen, the discussion on the actual infinity needs to
overstep the limits of speculative reasonings, based on pure
subjective speculative preferences, and to come in the area of
argumentation, which is accessible for a strict logical analysis.
In that sense, the doubtless merit of Cantor is in the fact that,
he first, from more or less substantiated reasonings about the
possibility or impossibility of the actual infinity came over to its
explicit, operational usage within the framework of classical logic
and classical mathematics, and, by so doing, he, for the first time,
made accessible the results of such the "mathematical" (see above)
usage of the actual infinity conception for standardized methods of
logical and mathematical analysis. It is exactly this type of analysis
of logical aspects of Cantor's proof of the uncountablity theorem, -
which is more than corner stone of the whole Cantor's "transfinite
doctrine" and of all modern meta-mathematics, - carried out above,
shows that the major assumption of Cantor's proof as to the actual
infinity of the enumeration (1) leads to non-finite contradiction (2),
which has no relation to Reduction ad Absurdum method, while Cantor's
theorem itself about the uncountablity is simply wrong, from the point
of view of Aristotle's classical logic.
Why was such the analysis of Cantor's theorem not carried out in
time, i.e. at the end of the XIX Century? - This, according to Zigmund
Freud, is a very non-trivial topic for fundamental researched in the
field of "psycho-pathology of an ordinary (scientific)
consciousness".

[A Zenkin: FATAL MISTAKE OF GEORG CANTOR]

http://www.ccas.ru/alexzen/papers/C...antor.html

Gruß, WM
 

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#1 Rudolf Sponsel
06/02/2010 - 12:24 | Warnen spam
WM schrieb:
...

[A Zenkin: FATAL MISTAKE OF GEORG CANTOR]

http://www.ccas.ru/alexzen/papers/C...antor.html

Gruß, WM



Danke, kannte ich noch nicht (1997, 2000) aufgenommen:
http://www.sgipt.org/wisms/geswis/m...dgsidm.htm

*

Gibt es denn Hypothesen, wie es möglich ist, dass sich eine solch
impredikative, d.h. in sich widersprüchliche und damit völlig unsinnige
Begriffsbildung - etwas Unabschließbares als etwas Abgeschlossenes zu
definieren - durchsetzen kann? Wieso fàllt den meisten MathematikerInnen, die
doch das exakte Denken für sich besonders in Anspruch nehmen, nicht auf, was
sie da für einen grundlegenden Unsinn machen? Und vor allem: was bedeutet das
eigentlich für die Wissenschaft, wenn solche widerspruchsvollen
Begriffsschöpfungen so einfach durchgehen?

Gibt es Vergleichbares in den anderen Wissenschaften, etwa der Physik
(Ätherhypothese)?
In der Psychologie ist es die Faktorenanalyse, die vom Mekka
der mathematischen Numerologen um die Psychometrika (ab 1936) herum - unter
Mitwirken von Mathematikern mit Rang und Namen - hochgradigen Unsinn bis auf
den heutigen Tag propagiert/e. "Den" Signifikanztests könnte man hier auch
einordnen: wir testen unter bestimmten Annahmen A1, ob eine Annehme A2 besser
passt als Annahme A3 - nur über die Welt erfàhrt hierbei nichts.
Auch bei der Finanzkrise scheinen mir die MathematikerInnen mit der
Konstruktion von gemeinwohlgefàhrlichen Hirngespinsten sehr beteiligt ...

Rudolf Sponsel, Erlangen

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