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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 7:45 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 }
>
>
>
> so what do we do... enforce the 'NAME =' ??
>
> so self reference is explicit?
>


That is what I did, remember?

You took one look and saw that "definiteness"
involved an infinity from the outset.

The "diversity" relation had been given by
a strict transitive order,

AxAy(xcy <-> (Az(ycz -> xcz) /\ Ez(xcz /\ -ycz)))

after a similar sentence to introduce membership
and a bunch of axioms to establish the expected
logic of identity, the universal class is defined
and posited by

Definition:
Ax(x=V() <-> Ay(-(ycx <-> y=x)))

Assumption:
ExAy(-(ycx <-> y=x))


Note, however, identity is only eliminable from
set theory if one admits the principle of identity
of indiscernibles. But, if that principle is
rejected, then there is no meaningful sense by
which an individual is introduced through definition.









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