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Topic: Real-world example of the liar paradox
Replies: 6   Last Post: Jul 6, 2013 8:01 PM

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fom

Posts: 1,968
Registered: 12/4/12
Re: Real-world example of the liar paradox
Posted: Jul 6, 2013 8:01 PM
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On 7/6/2013 6:29 PM, grahamcooper7@gmail.com wrote:
> On Sunday, July 7, 2013 7:43:13 AM UTC+10, Spac...@hotmail.com wrote:
>> Russel's paradox is nothing,
>>
>> but a lack of proper verbal tensing

>
>
> Granted...
>
> The Set of all sets
> that don't contain themselves
> barring that set itself
>
> is a proper definition of a set.
>
> R = { X | ~XeX & ~X=R }
>


This is not a proper definition in
the usual sense of the word.

Remember, Skolem suggested that the
problem of "definiteness" associated
with Zermelo's original axiomatization
be dealt with by using only formal
language:

Ax(x=R <-> Ay( (y in x) <-> (~(y in y) /\ ~(y=x))))

looks unlikely with regard to uniqueness if it
is instantiable at all, and,

Ax(x=R <-> Ay( (y in x) <-> (~(y in y) /\ ~(y=R))))

is clearly circular.

Of course, it is how one chooses to look at
what constitutes a definition.





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