Jesse Mazer skrev:
>
>
>   
>> Date: Thu, 29 Nov 2007 19:55:20 +0100
>> From: [EMAIL PROTECTED]
>>
>>     
>> As soon as you say "the set of ALL numbers", then you are forced to 
>> define the word ALL here.  And for every definition, you are forced to 
>> introduce a "limit".  It is not possible to define the word ALL without 
>> introducing a limit.  (Or making an illegal circular definition...)
>>     
>
> Why can't you say "If it can be generated by the production rule/fits the 
> criterion, then it's a member of the set"? I haven't used the word "all" 
> there, and I don't see any circularity either.

What do you mean by a "well-defined criterion"?  Is this a well-defined 
criterion? :

The set R is defined by:

(x belongs to R) if and only if (x does not belong to x).

If it fits the criterion (x does not belong to x), then it's a member of 
the set R.

Then we ask the question: "Is R a member of the set R?".  How shall we 
use the criterion to answer that question?

If we substitute R for x in the criterion, we will get:

(R belongs to R) if and only if (R does not belong to R)...

What is wrong with this?

-- 
Torgny

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