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Re: Obections to Cantor's Theory (Wikipedia article)

Subject: Re: Obections to Cantor's Theory Wikipedia article
From: Martin Shobe
Date: Sat, 30 Jul 2005 13:14:05 GMT
Newsgroups: sci.math, sci.logic
On Fri, 29 Jul 2005 14:15:27 +0200, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

>Martin Shobe wrote:
>> On Fri, 29 Jul 2005 11:14:56 +0200, Han de Bruijn
>> <Han.deBruijn@xxxxxxxxxxxxxx> wrote:
>> 
>> 
>>>Martin Shobe wrote:
>>>
>>>
>>>>On Thu, 28 Jul 2005 15:56:32 +0200, Han de Bruijn
>>>><Han.deBruijn@xxxxxxxxxxxxxx> wrote:
>>>>
>>>>
>>>>>But without the claim that it
>>>>>is the one and only foundation possible. Why not have _several_ pillars
>>>>>that provide a foundation, instead of just one?
>>>>
>>>>Actually, I don't have a problem with that.  In a sense, we have that
>>>>now with set theory and category theory  (And lets not forget logic).
>>>>But while physics will continue to provide inspirition to mathematics,
>>>>it will not qualify as a foundation for methematics.  
>>>
>>>And I don't want that either. Read my lips:
>>>
>>>   A little bit of Physics would be NO Idleness in Mathematics
>>>
>>>See? Just that tiny pinch of salt in your otherwise tasteless soup.
>>>
>>>But nevertheless: *IN* your soup.
>> 
>> 
>> A "tiny pinch of salt"?  From the axioms I've seen you proposing that
>> would be more like a ten pound bag of rock salt added to single
>> serving.
>
>No, no. Nobody would like the soup anymore. Just a pinch.

Nobody likes the soup anymore.  The axiom that you seem most likely to
want to add (Ax x = {x}), has as a consequence that Ax Ay (x e y) =>
(x = y).  (It follows solely from the axiom and the definition of
{x}).  After that, you might as well not have sets at all.

Martin


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