Re: Cardinality question

On 4/12/2005 6:27 PM, Torkel Franzen wrote:
> Eckard Blumschein <blumschein@xxxxxxxxxxxxxxxxxxx> writes:
>
>> What about "my findings" the situation is opposite. In contrast to the
>> Cantorians I am open for any objection.
>
> Splendid! We must simply wait for posterity to find that there are
> no objections to your profound arguments, and to adjust their
> mathematics accordingly.

I am not sure what profound arguments you are referring to. What about
Cantor's basic mistakes, I got aware of telling very well known secrets
to those who are able to judge. However, there seems to be a variety of
personal arrangements whith these mistakes ranging from Ebbinghaus who
indirectly admitted the "obvious fallacy" but nonetheless alluded a "big
useful mathematical truth" to those physicists who revealed to be
unhappy with set theory but having not yet a better substitute.

So far I was unable to grasp the putative big truth. I see it rather an
pretended excuse for lacking courage and/or understandable adaptation.
It would not be wise writing books on nothing more than nonsense.
Moreover, the existing set theory is welcome in order to suppress
questions concerning some peculiarities of real "numbers". Axioms are
not to be questioned, basta. Caveats by Eberhard Illigens did not have
any effect against Cantor's authority. David Hilbert fortified his
"power of state" when he feared Weyl could be the revolution. Students
of mathematics have to learn so much arbitrarily sophisticated stuff
that their ability for developing independent criticism and creativity
is perhaps more damaged than by permanent consume of natriumglutamate.
In so far it would be illusory to wait for future generations.

Even if I do not expect any applause, I would like to doubt whether the
ubiquitously assumed idea that numbers are god-given numbers in every
respect is really best. When I missed humbleness, I meant that it is
perhaps suboptimal to "attack" infinity and continuum like a conqueror
commanding an army of uniformed numbers.

Eckard

Eckard

.

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