Re: Ultimate debunking of Cantor's Theory

On 15 Jul., 14:31, Albrecht <albst...@xxxxxx> wrote:
WM schrieb:

That is a very clear argument proving the nonfictional character of
true mathematics. There are no axioms required -

I'm convinced that axioms are useful and essential for doing
mathematics. The axioms are the link between the world of our
experience and the world of our thinking. To make deductions we must
have starting assumption.


But not arbitrary assumptions. Do you know the axioms of arithmetic
200 years ago? That was an extremely well developed science (or art).
But there was no axiom.

Cantor declared concerning arbitrary axioms which he denoted as
Hypothesen: "Hypothesen welche gegen diese Grundwahrheiten verstoßen,
sind ebenso falsch und widersprechend, wie etwa der Satz 2 + 2 = 5
oder ein viereckiger Kreis. Es genügt für mich, derartige Hypothesen
an die Spitze irgend einer Untersuchung gestellt zu sehen, um von vorn
herein zu wissen, daß diese Untersuchung falsch sein muss."

I fully agree with him.

The problem is the choice of reasonable axioms. And the only certain
method we have to prove the logical consequences which we have deduced
from starting axioms is the comparisation with the reality.
A method which mathematicians had used over thousends of years.

Not in arithmetic, because it seemed not necessary, but in geometry.

and in fact
concerning arithmetic they were only used to corrupt and pervert
mathematics. (Wenn's dem Esel zu wohl wird, geht er auf's Eis tanzen.)

History repeats itself: When Anaxagoras applied common sense to
explain how God Helios generated his light, when Galilei tried to
introduce experiments into physics, when Kepler dared to apply profane
calculations to the divine spheres of celestial bodies, when Galilei
tried to use the telescope in the same realm: It was always the
ossified gang of high priests who opposed and tried to prevent new
ways of science. Here we have the same situation again. Only
mathematics which can be performed and approved by computers deserves
this name. Everything else is matheology without any value.

Regards, WM

It seems to me that nowadays very many people which are engaged in
doing mathematics have lost the bottom under their feet since they are
too much busy in standing on the shoulder of giants.

An approved principle is: Head in clouds, feet on the ground. Alas
many of them are not tall enough, nevertheless prefer to remain in the
clouds.

Regards, WM

.

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