Re: Zenkin's paper on Cantor

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 09/30/04 

Date: Thu, 30 Sep 2004 10:28:05 -0500

On 30 Sep 2004 07:09:37 -0700, erayo@bilkent.edu.tr (Eray Ozkural
exa) wrote:

>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.

No, just trying to keep the wandering context straight.

>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.

Uh, right. Exactly what assumption in the proof concerns you?

>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.

Imagine our disappointment.

>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,

************************

David C. Ullrich