Re: Why does everyone do it?

In article
<484f7529-1408-4fbd-aaa5-917e54f154a1@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
julio@xxxxxxxxxxxxx wrote:

On 7 Aug, 11:31, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Wed, 6 Aug 2008 13:38:59 -0700 (PDT), ju...@xxxxxxxxxxxxx wrote:
On 6 Aug, 21:26, Mariano Suárez-Alvarez
<mariano.suarezalva...@xxxxxxxxx> wrote:
On Aug 6, 5:14 pm, ju...@xxxxxxxxxxxxx wrote:
On 5 Aug, 19:23, mike3 <mike4...@xxxxxxxxx> wrote:

Hi.

What is it about Cantor's theories that makes everyone want to try
and
"critique"
them, anyway? And why do they always seem to generate long
discussions?
Why was it that what appears to be the longest thread here (9018
msgs)
started
off with a Cantor Critique?

Because that is where lie the foundations of contemporary mathematics,
and on the correctness of those foundations relies the correctness of
the whole building.

Actualy, I think that it is a subject that appears
much more accessible and should-be-common-sense

Pardon me, but this is BS. What is at stake _is_ very significant,

Of course the question of whether Cantor's proof of the
uncountability of the reals is correct is a very important
question.

But it's also a trivial question. Yes, the proof is correct.


Maybe it is not just a question of "correctness". Correctness is not
an absolute. Maybe is about "comprehension".

First, the matter -- as I get it -- boils down to the axioms one
happens to choose, and there is not only the ZF family. Nor deduction
from the axioms can make up any "evidence": axioms do need to be
"accepted".

Then, even "accepting" the Powerset Axiom, I still can't find anything
trivial in getting the result |P(N)|>|N|.

We all know that. It doesn't matter. There are people who
cannot understand that 2 + 2 = 4, and who will never understand
that no matter how hard they try. The existence of such people
doesn't mean there's anything non-trivial about adding 2 plus 2.

The present situation is worse, since as far as we can see you
haven't been trying to understand the correct proof, instead
you've been trying to make people believe your proof that it's
false (which "proof" is incoherent nonsense).

The definition of "trivial" is not "everyone, with no exceptions,
believes it". Nothing you've said about all this has any effect
whatever on the fact that the proof that |P(A)| > |A| is trivial.

Actually: I can't find
anything trivial in the very diagonal argument! Because the formal
procedures of proof are not always so clear-cut as one would naively
suppose, are they? The nearest is the furthest, and so I guess I am
just still learning.

BTW, I believe I am agreeing with Hans the Bruijn in the substance.
(To add my 2c to the polemic: each coin has two sides and, as a matter
of fact, counter-crankhood is no exception.)

-LV


despite that some might find the argument trivial. And it even isn't.

Not sure which "argument" you're referring to. The argument showing
that |P(A)| > |A| is in fact trivial. We see a lot of explanations why
it's wrong here on sci.math. Those explanations are always either
wrong or not-even-wrong ("not-even-wrong" meaing that the
supposed argument is so incoherently presented that one cannot
pinpoint the error because it's not clear what the statements in
the argument even _mean_.)

Your problem, around here, is that you have lost the sensibility -- or
the energy -- to appreciate the difference(s).

-LV

(I was
taught the elements of set theory in kindergarden, and
I was shocked when I was given the technical definition
of cardinal numbers to find that it was essentially
the same notion I had been introduced to when I was 4
or 5)

It is quite unlikely that someone is going to
start a thread providing a critique of the proof
of the John-Nirenberg inequality, of the Cunz-Quillen
theorem stating that cyclic homology satisfies
excision, of the approach taken by Berthelot in
constructing crystalline cohomology or on the soundness
of Drinfel'd approach to the study of the absolute Galois
group through the theory of quantum groups. Doing so
would require years and years of study in
order to even construct a mental picture of what it
is that one is attempting to do in those contexts.

-- m

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)

--
David C. Ullrich
.

Relevant Pages

  • Re: Why does everyone do it?
    ... Why was it that what appears to be the longest thread here ... off with a Cantor Critique? ... and on the correctness of those foundations relies the correctness of ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: Why does everyone do it?
    ... Why was it that what appears to be the longest thread here ... off with a Cantor Critique? ... and on the correctness of those foundations relies the correctness of ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: Why does everyone do it?
    ... and on the correctness of those foundations relies the correctness of ... It is stupid to be talking about what is irrelevant, ... So then what were you saying was bad about this claim?: ...
    (sci.math)
  • Re: Why does everyone do it?
    ... off with a Cantor Critique? ... and on the correctness of those foundations relies the correctness of ...
    (sci.math)
  • Re: Public disclosure of discovered vulnerabilities
    ... for that matter. ... using programming paradigms which permit proof of correctness. ... which anyone doing a mechanical analysis of the code can ... (or anyone compiling with a different compiler or on a ...
    (sci.crypt)