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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: 1,635 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 12:01 PM

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

>
>
>  {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

> e.g.in ZFC
>
> { x | x e y }   IFF  E(z)  y C z
>
> Axiom of Specification.
>
> there is no z such that RS C z
> so RS is impossible to define in ZFC.
>
> I'm working on an automated Proof By Contradiction of RS.
>
> You need to forward chain MODUS PONENS
> which is new to PROLOG LOGIC since it requires
> depth limiting.  (which is simple enough and we've
> got DL working on backward chaining MP already)
>
> 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