2009/6/5 Torgny Tholerus <torgny.domain.name.hidden>:
>
> Kory Heath skrev:
>> On Jun 4, 2009, at 8:27 AM, Torgny Tholerus wrote:
>>
>>> How do you handle the Russell paradox with the set of all sets that
>>> does
>>> not contain itself? Does that set contain itself or not?
>>>
>>> My answer is that that set does not contain itself, because no set can
>>> contain itself. So the set of all sets that does not contain
>>> itself, is
>>> the same as the set of all sets. And that set does not contain
>>> itself.
>>> This set is a set, but it does not contain itself. It is exactly the
>>> same with the natural numbers, BIGGEST+1 is a natural number, but it
>>> does not belong to the set of all natural numbers. The set of all
>>> sets
>>> is a set, but it does not belong to the set of all sets.
>>>
>>
>> So you're saying that the set of all sets doesn't contain all sets.
>> How is that any less paradoxical than the Russell paradox you're
>> trying to avoid?
>>
>
> The secret is the little word "all". To be able to use that word, you
> have to define it.
I call that secret bullshit, and to understand that word (bullshit),
you have to define it.
Sorry but I think we're talking in english here, all means all not
what you decide it means.
Quentin.
> You can define it by saying: "By 'all sets' I mean
> that set and that set and that set and ...". When you have made that
> definition, you are then able to create a new set, the set of all sets.
> But you must be carefull with what you do with that set. That set does
> not contain itself, because it was not included in your definition of
> "all sets".
>
> If you call the set of all sets for A, then you have:
>
> For all x such that x is a set, then x belongs to A.
> A is a set.
>
> But it is illegal to substitute A for x, so you can not deduce:
>
> A is a set, then A belongs to A.
>
> This deductuion is illegal, because A is not included in the definition
> of "all x".
>
> --
> Torgny Tholerus
>
> >
>
--
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Received on Fri Jun 05 2009 - 11:25:09 PDT