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

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

Posted: Feb 3, 2013 9:02 PM

On Feb 4, 9:12 am, Charlie-Boo <shymath...@gmail.com> wrote:
> On Feb 3, 4:56 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
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> > 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
>
> ATOMIC PREDICATE meaning relation?
>
> C-B

RELATION
p(a, b, e)

ATOMIC PREDICATE
p(a, b(c,d), e(f,g))

NON-ATOMIC PREDICATE
a(b) -> d(c)

NON-ATOMIC PREDICATE
All(a) p(a, b(c,d), e(f,g))

Relational Algebra is generally used to refer to ordinary tuples of
terms. e.g SQL Tables.

QUANTIFIED LOGIC

ALL(n):N EXIST(m):N m>n

------------------

AS A SUBSET

{ n | n e N } C { n | m>n }
every n here --- has a bigger m here

-----------------

AS A PROLOG PREDICATE

subset( N, nat(N), bigger(M,N) )

------------------

subset() is not easy to program though...

You can use the LISP addon to PROLOG

PROLOG+ A CONCEPT DATABASE MANAGEMENT LANGUAGE (DBML)

Y> next record
Y< prev record
Y>> last record
Y<< 1st record

AXIOM OF FINITE SUBSETS
-----------------------

subs(A,X,Y) <- e(A>>,X) ^ e(A,Y).

subs(A,X,Y) <- e(A,Y) ^ e(A>,X) ^ subs(A,X,Y).

ss(X,Y) <- e(A<<,X) ^ subs(A,X,Y).

This is just using PROLOG RECURSION to do a FOR LOOP

A>> last record
A> next record
A<< first record

AXIOM OF FINITE SET EQUALITY
----------------------------

equals(X,Y) <- ss(X,Y) ^ ss(Y,X).

Now you can do Set Theory and Logic all in Atomic Predicates!

In BLOCK PROLOG the above would be a rule:

equals X Y
ss X Y
ss Y X.

Herc
--
www.BLoCKPROLOG.com

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