Re: Cardinality question



Eckard Blumschein wrote: 
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.

Do you understand what an axiom represents? It is an *assumed* rule for the system being worked in. You are free to use different axioms if you wish, but that will merely give you a different system. If you want different axioms, use different axioms. ZF is used by some people because it is consistent and because it corresponds closely to what those people have in mind for set theory.

> 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.


This statement seems odd.  How much mathematics have you taken?

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.

Numbers are invented by us, just like the rest of mathematics. Even something as simple as 1, 2 or 3 is an abstraction from reality.

--
Will Twentyman
email: wtwentyman at copper dot net
.

Relevant Pages

  • Re: Logarithm of transfinite numbers
    ... What argument and objection are you talking about? ... The only conclusion is that, in mathematics, it is not true. ... logic, then there is likely a problem in the higher level theory, ... more fundamental Peano axioms, mathematics chooses to stick with only ...
    (sci.math)
  • Re: Well Ordering the Reals
    ... most of the standard axioms would get scrapped ... you claim that set theory is ... theory in which to express virtually all of mathematics. ... S (call this function 'omega pre S'). ...
    (sci.math)
  • Re: Robot Evolution
    ... no. Goedel proved a very limited thing about ... generated from systems of axioms "at least as ... accomplish mathematical reasoning. ... "If human reasoning about mathematics is ...
    (sci.bio.evolution)
  • Re: Skolems Paradox and why is math the way it is?
    ... > This is not a job the axioms were ever meant to do. ... other person's interpretation require a winning strategy, no more, no ... I'm pretty sure than any model of set theory is intuitively ... figuring out how I tell what is real in mathematics. ...
    (sci.math)
  • Re: Godel proved maths inconsistent not incompleteness theorem
    ... It's the *axioms* ... Otherwise it's not an axiomatic system. ... generator to compare to a proof checker in the first place. ... The program was to be able to rewrite all mathematics starting using ...
    (sci.logic)