Re: Raatikainen's critique of Chaitin

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 09/08/04 

Date: Wed, 08 Sep 2004 15:15:10 +0200

Mitch Harris <harrisq@tcs.inf.tu-dresden.de> writes:

> Jesse F. Hughes wrote:
>> Mitch Harris <harrisq@tcs.inf.tu-dresden.de> writes:
>>
>>
>>>Eray Ozkural exa wrote:
>>>
>>>>Just a thought. Why would someone think axiom of choice is true?
>>>
>>>1) because it hasn't been contradicted after lots of testing
>>>(Banach-Tarski makes one question it though)
>>
>> Testing? What sort of testing?
>
> use in proofs of important theorems.
>
>> What sort of contradiction do you expect?
>
> 0=1. Well, I don't expect it, but that's the kind of contradiction I
> would expect to get if the axiom of choice were not true.

But it's well known that if ZF (set theory) is consistent, then so is
ZFC (set theory with the axiom of choice). This proof is a bit more
comforting than "lots of testing". 

-- 
Jesse F. Hughes
                "A gorgeous display of homoerotic lust."
                 -- Review blurb found on the back of a 
                    Chinese black market "Dawn of the Dead" DVD

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