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:
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> > On 2/5/2013 9:32 AM, Charlie-Boo wrote:
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> > > On Feb 4, 4:26 pm, fom <fomJ...@nyms.net> wrote:
> > >> On 2/4/2013 8:46 AM, Charlie-Boo wrote:
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> > >>> 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
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> > >>>>>>> ATOMIC PREDICATE meaning relation?
>
> > >>>>>>> C-B
>
> > >>>>>> RELATION
> > >>>>>> p(a, b, e)
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> > >>>>> 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.
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> > > 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
--
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