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Topic: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes

Replies: 53   Last Post: Feb 13, 2013 3:53 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes

Posted: Feb 3, 2013 4:56 PM

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_rules

In PROLOG we use lowercase words for TERMS
and uppercase words for VARIABLES

ATOMIC PREDICATE

p( a1, a2, a3, ... an)

where ak is either a term or a variable.
p is also a term.

The connectives are superfluous, just use

if( X, Y )

not( X )

and( X, Y)

which are special predicates in that their arguments are predicates
themselves.

-----

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

Date Subject Author
2/1/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 camgirls@hush.com
2/4/13 Charlie-Boo
2/4/13 billh04
2/4/13 Charlie-Boo
2/4/13 William Hale
2/4/13 Lord Androcles, Zeroth Earl of Medway
2/9/13 Graham Cooper
2/5/13 Charlie-Boo
2/4/13 Graham Cooper
2/5/13 Charlie-Boo
2/5/13 Graham Cooper
2/5/13 Brian Q. Hutchings
2/6/13 Graham Cooper
2/6/13 Charlie-Boo
2/4/13 fom
2/4/13 Charlie-Boo
2/4/13 fom
2/5/13 Charlie-Boo
2/7/13 fom
2/9/13 Charlie-Boo
2/9/13 Graham Cooper
2/11/13 Charlie-Boo
2/10/13 fom
2/10/13 Graham Cooper
2/10/13 fom
2/10/13 Graham Cooper
2/11/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 Graham Cooper
2/13/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 fom
2/5/13 Charlie-Boo
2/5/13 fom
2/6/13 fom
2/11/13 Charlie-Boo
2/11/13 fom
2/13/13 Charlie-Boo
2/13/13 fom
2/4/13 Graham Cooper
2/4/13 Charlie-Boo
2/5/13 Charlie-Boo