Re: A Guide for Cantor Cranks

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Article #790

#790

From: Jim Burns
Date: Sun, 27 Mar 2011 21:46

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On 3/27/2011 3:23 PM, Transfer Principle wrote:
> On Mar 25, 7:50 am, MoeBlee<jazzm...@hotmail.com>  wrote:
>> On Mar 24, 7:05 pm, Albrecht<albst...@gmx.de>  wrote:
>>> I have the axiom of infinity in mind. And the combination of the
>>> power set axiom with the axiom of infinity. Without these axioms the
>>> interpretation of the diagonal argument of Cantor is completely
>>> different from the common interpretation.
>> Statements like that aren't constructive mathematics or finitist
>> mathematics or ultra-finitist mathematics. Just ignoramus mathematics.
>
> So merely stating that all known proofs in ZF of the existence
> of uncountable sets (i.e., what Cantor's diagonal argument is
> designed to prove) require both Infinity and Powerset is now
> considered "ignoramus mathematics"?
>
> Of course, if there really is a proof in ZF-Infinity or
> ZF-Powerset of the existence of uncountable sets, only then
> will I agree that Albrecht's post is "ignoramus mathematics."

Only then?

Would you be satisfied with ZF-Infinity
or ZF-Powerset (on Albrecht's behalf) even if
there were no naturals, integers or rationals,
which Albrecht does seem to find useful?

We may be getting into rarified philosophical
air here, distinguishing between being provable
to exist and not being provable not to exist,
but, if we avoid those heights, it looks
like his favorite numbers are unavailable
in those systems.

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From: Jim Burns <burns.87@osu.edu>
Newsgroups: sci.logic,sci.math,comp.theory,sci.physics,aus.science
Subject: Re: A Guide for Cantor Cranks
Date: Sun, 27 Mar 2011 17:46:48 -0400
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