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


Re: Realworld example of the liar paradox
Posted:
Jul 6, 2013 8:01 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 } >
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.

