fom
Posts:
1,969
Registered:
12/4/12


Re: Realworld example of the liar paradox
Posted:
Jul 6, 2013 7:45 PM


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.

