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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 ]
 Charlie-Boo Posts: 1,618 Registered: 2/27/06
Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle

Posted: Feb 3, 2013 11:19 PM

On Feb 3, 9:02 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 4, 9:12 am, Charlie-Boo <shymath...@gmail.com> wrote:
>
>
>
>
>
>
>
>
>

> > On Feb 3, 4:56 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > > 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)

If wffs are built on relations then { x | x ~e x } is not a wff
because ~e is not a relation.

We don?t need ZF - at all. All we need is Naïve Set Theory, a
complete formal definition of wff and recognition that x ~e x is not a
relation due to diagonalization on sets.

Logic = Set Theory

Logic = NOT AND OR EXISTS simple, easy

ZF Set Theory = a dozen messy axioms for which people can?t even agree
on the specifics ??

There are a dozen set theories and a dozen interpretations of the most
popular set theory, and 2 or 3 versions of it (with or without Choice,
etc.) none of which decide any of the important questions of set
theory due to exhaustive work (a waste!) by Godel and Cohen.

C-B

> 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
> or my record management addon.
>
> 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