```Date: Feb 3, 2013 4:56 PM
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 4, 7:18 am, Charlie-Boo <shymath...@gmail.com> wrote:> On Feb 3, 4:03 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:>>>>>>>>>> > On Feb 4, 3:01 am, Charlie-Boo <shymath...@gmail.com> wrote:>> > > On Feb 1, 3:35 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:>> > > > On Feb 2, 4:09 am, Charlie-Boo <shymath...@gmail.com> wrote:>> > > > > There is a peculiar parallel between Semantic Paradoxes, Set Theory> > > > > Paradoxes and ordinary formal Arithmetic.>> > > > > Consider the following 3 pairs of expressions in English, Set Theory> > > > > and Mathematics:>> > > > > A> > > > > This is false.> > > > > This is true.>> > > > > B> > > > > 1/0> > > > > 0/0>> > > > > C> > > > > {x | x ~e x} e {x | x ~e x}> > > > > {x | x e x} e {x | x ~e x}> > > > > {x | x ~e x} e {x | x e x}> > > > > {x | x e x} e {x | x e x}>> > > > > A is the Liar Paradox, B is simple Arithmetic, and C is Russell?s> > > > > Paradox.>> > > > This is Russells Paradox>> > > >  {x | x ~e x} e {x | x ~e x}> > > >  <->> > > > {x | x ~e x} ~e {x | x ~e x}>> > > > To make a consistent set theory the formula  { x | x ~e x }> > > > must be flagged somehow.>> > > How do you define a wff - precisely?  That is the problem.  Frege was> > > right, Russell was wrong, and all you need is an exact (formal)> > > definition of wff.>> > > C-B>> > in the usual manner by Syntactic construction.>> > IF  X  is a WFF> >   THEN  ALL(Y) X  is a WFF>> > and so on.>> The problem isn't with the connectives.  What can X be for starters -> the most primitive wffs from which we build others?>> C-B>>>http://en.wikipedia.org/wiki/First_order_logic#Formation_rulesIn PROLOG we use lowercase words for TERMSand uppercase words for VARIABLESATOMIC PREDICATEp( a1, a2, a3, ... an)where ak is either a term or a variable.p is also a term.The connectives are superfluous, just useif( X, Y )not( X )and( X, Y)which are special predicates in that their arguments are predicatesthemselves.-----For Quantifiers, all solved variables EXIST()and I need a routine for SUBSET( var, set1, set2 )which can do quantifier ALL(var).A(x):D  P(x)<=>{ x | x e D }  C  { x | P(x) }Now all Predicate Calculus can be expressed in Atomic Predicates.p(a,b,c)Herc
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