```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 toprove.Let:LANGUAGE 1     LANGUAGE 2seta(x)        <->       x e setaproof(x)       <->       x e proofproveby(x,y)  <->    (x,y) e provebyrussell(x)      <->    not( x e x)-------------------In ZFC you "UNSTRATIFY" Russel's setbut 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
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