Date: Feb 9, 2013 8:09 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 10, 10:19 am, Charlie-Boo <shymath...@gmail.com> wrote:

> On Feb 7, 1:51 am, fom <fomJ...@nyms.net> wrote:

>

>

>

>

>

>

>

>

>

> > On 2/5/2013 9:32 AM, Charlie-Boo wrote:

>

> > > On Feb 4, 4:26 pm, fom <fomJ...@nyms.net> wrote:

> > >> On 2/4/2013 8:46 AM, Charlie-Boo wrote:

>

> > >>> On Feb 4, 12:25 am, fom <fomJ...@nyms.net> wrote:

> > >>>> On 2/3/2013 10:19 PM, Charlie-Boo wrote:

> > >>>> <snip>

>

> > >>>>>>>> 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.

>

> > >>>> Well-formed formulas are built from the alphabet

> > >>>> of a formal language. If the language contains

> > >>>> a symbol of negation, then NOT(xex) will be a

> > >>>> well-formed formula.

>

> > >>> You have to define what value a symbol may have - how it is

> > >>> interpreted in your definition of a wff. You need to complete B

> > >>> below to see there is no paradox if you are consistent about what a

> > >>> wff may contain and what values it may equal after substitution

> > >>> (interpretation) if it contains variables for functions.

>

> > >> First, I was not in a good mood when I posted. So, I may

> > >> have been too dogmatic.

>

> > >> What you seem to be objecting to is the historical development

> > >> of a logical calculus along the lines of Brentano and DeMorgan.

>

> > I meant Bolzano here.

>

> > > The only objecting in my Set Theory proposal is perhaps objecting to

> > > the fact that ZF has a dozen messy axioms, a dozen competing

> > > axiomatizations, a dozen interpretations of the most popular

> > > Axiomatization, and (Wikipedia), The precise meanings of the terms

> > > associated with the separation axioms has varied over time. The

> > > separation axioms have had a convoluted history, with many competing

> > > meanings for the same term, and many competing terms for the same

> > > concept.

>

> > > (DeMorgan is an example of why Logic and Set Theory are the same thing

> > > and should be combined - same as Math and Computer Science etc.)

>

> > How do you see Logic and Set Theory as being the same?

>

> Both are concerned with mappings to {true,false}. A propositional

> calculus proposition is 0-place. A set is 1-place. A relation is any

> number of places. (A relation is a set - of tuples.)

>

> So you have the same rules of inference: Double Negative, DeMorgan

> etc. apply to propositions and sets.

>

> To prove incompleteness, Godel had to generalize wffs as expressing

> propositions to expressing sets when the wff has a free variable.

>

> C-B

>

>

Yes but you change the rules of the game depending what you want to

prove.

Let:

LANGUAGE 1 LANGUAGE 2

seta(x) <-> x e seta

proof(x) <-> x e proof

proveby(x,y) <-> (x,y) e proveby

russell(x) <-> not( x e x)

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

In ZFC you "UNSTRATIFY" Russel's set

but in all theories > PA you necessitate Godel's Statment!

Sheer blindness!

TOM: Jerry can't say this sentence is true!

JERRY: Tom can't say this sentence is true!

TOM AND JERRY ARE *INCOMPLETE* !!

must be unrelated to logic!

Herc

--

www.BLoCKPROLOG.com