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fom
Posts:
1,037
Registered:
12/4/12
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Re: Cantor's absurdity, once again, why not?
Posted:
Mar 14, 2013 2:52 PM
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On 3/14/2013 5:52 AM, WM wrote:
> On 14 Mrz., 11:17, fom <fomJ...@nyms.net> wrote:
>> On 3/14/2013 4:47 AM, david petry wrote:
>>
>>
>>
>>> In a previous aritcle a while back, "marcus_b" wrote:
>>
>>> ** start quote **
>>> In math, the great pons asinorum now is Cantor's diagonal proof. There seem to be scads of people out there who just cannot quite get it and who yearn to achieve their rightful 15 minutes of fame by trying to shoot it down, thus thrusting themselves ahead of Cantor in the pantheon of mathematical geniuses. Can you shed some light on the motivation here?
>>> ** end quote **
>>
>>> The "cranks" who insist on pointing out the absurdity of Cantor's argument are puzzled that mathematicians "cannot quite get it".
>>
>>> Cantor's argument relies on accepting the notion of an actual infinite, and that's problematic.
>>
>> If you are going to paraphrase Cantor's argument, please do
>> so correctly.
>>
>> Cantor's "argument" is an argument scheme.
>>
>> It is an argument for constructing a counter-example
>> for some particular claim.
>>
>> A particular claim must be made before Cantor's argument
>> can even apply.
>>
>> That particular claim is that there is a single infinity
>> that is referred to in language as an object.
>
> No. That particular claim is that infinity can be complete
Wrong. The completeness issue is entirely separate
from the diagonal proof.
It is clear that you completely fail to understand
that. Whether this is because your general feelings
concerning infinity make you unable to see the difference
or simply because you are pursuing an agenda makes
no difference.
In the Grundlagen (or, at least in the translations which
my ignorance forces me to use), Cantor explains in
detail why the logical construction of real numbers
from sets of rationals is reasonable and how one should
think about accepting the construction as legitimate.
Nor can one attribute the completeness issue to Cantor
alone since Dedekind was addressing the same issue
differently.
You would be correct to say that Cantor believed in
a completed infinity so that the diagonal argument
motivated his further researches. But, you need
to differentiate what the proof does and how it
does it from other mathematics that involves
completed infinities.
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