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.

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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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