Date: Feb 6, 2013 1:29 AM
Author: Graham Cooper
Subject: Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle<br> to Resolve Several Paradoxes

On Feb 6, 2:01 pm, 1treePetrifiedForestLane <>
> Russell's paradoxes, mostly, are illinguistic,
> essentially not properly tensed.
> the village barber has to go to the next village,
> iff he doesn't want to do it, himself.


all(MAN) : men

if [ not [ shave MAN MAN ]] [ shave barber MAN ]

"if a man doesn't get a shave by himself
then the barber will shave him"


shave X barber?


Remove the ALL()

{ M | M e men } C { M | not(shave(M,M) -> shave(barber,M) }

i.e. not shaving yourself then the barber shaves you
holds for all men (atleast)

the Paradox still holds over all men, by the possibility of the
construction of the above formula.

if you know of an algorithmic process that parses this into

{ M | M=/=barber -> M e men }
C { M | not(shave(M,M) -> shave(barber,M) }

then you could dismiss it as being a paradox, but you'll probably have
to algorithmically detect the contradiction 1st in which case provable
set specification can eliminate the definition (rather than rewrite

not(provable(THM)) <-> derive(not(THM)) (eg a contradiction)

provable(THM) <-> exist(set(....THM))