Re: Zenkin's paper on Cantor

From: Eray Ozkural exa (erayo_at_bilkent.edu.tr)
Date: 09/30/04 

Date: 30 Sep 2004 07:09:37 -0700

David C. Ullrich <ullrich@math.okstate.edu> wrote in message news:<gamnl094lct87n15dsksa378bgvfjfqdfr@4ax.com>...
> On 30 Sep 2004 02:15:41 -0700, erayo@bilkent.edu.tr (Eray Ozkural
> exa) wrote:
>
> >mtx014@linux.services.coventry.ac.uk (Robert Low) wrote in message news:<cjeq18$890$1@sunbeam.coventry.ac.uk>...
> >> Eray Ozkural exa <erayo@bilkent.edu.tr> wrote:
> >> >That is nice. So, I suppose trying to understand constructivists'
> >> >objections to some rather basic issues in set theory is not synonymous
> >> >to crackpottery, I suppose.
> >>
> >> No, it isn't. But neither is it saying that the diagonalization
> >> proof that the reals are uncountable is wrong because you can
> >> find a bijection; that *is* crackpottery.
> >
> >Let's be precise. I did not claim that. What I said was, look, here it
> >seems there is a bijection in the finite case, but must be eliminated
> >in the transfinite (if we are to be consistent with Cantor's theory).
>
> Uh, no. The claim that's relevant to the above, that is, the
> claim in the immediately preceding context, was that I must
> believe CH because set theorists do. I said "huh?" and you
> replied with the total irrelevance above.

You are taking things personal.

I have merely referred to the possibility that what may seem like a
simple proof, e.g. Cantor's theorem, in fact rests on assumptions of
set theory which are not trivial at all, assessing their
validity/truth might be just as hard as giving an answer to CH.

Some of the arguments about which axioms must be true, since they
cannot be proven, are appeals to intuition, and I see this as very
shaky. Indeed, in such situations, intuition of authority is seen as
preferable to one's own opinion, and that is precisely what I meant.

For the record, I do not have much to say about CH. That was just an
example for what must be a more difficult question. I am just saying
that it's not an easy matter, although it's fundamental and basic.

Anyway, I would prefer not to talk about this issue any further.

Regards, 

--
Eray Ozkural

Relevant Pages

  • Re: Zenkins paper on Cantor
    ... > exa) wrote: ... >>seems there is a bijection in the finite case, ... set theory which are not trivial at all, ... Indeed, in such situations, intuition of authority is seen as ...
    (sci.math)
  • Re: Distinct linear orderings on Z
    ... > possible for a bijection to exist between a set and a proper subset of ... That bijections can be used to establish an equivalence relation ... intuition can sometimes help find a proof or solve a problem. ... that boggle the visual intuition. ...
    (sci.math)
  • Re: Distinct linear orderings on Z
    ... >> possible for a bijection to exist between a set and a proper subset of ... That bijections can be used to establish an equivalence relation ... >intuition can sometimes help find a proof or solve a problem. ... >that boggle the visual intuition. ...
    (sci.math)