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Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle
to Resolve Several Paradoxes
Posted:
Feb 11, 2013 1:59 PM
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On Feb 9, 8:09 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
> On Feb 10, 10:19 am, Charlie-Boo <shymath...@gmail.com> wrote:
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> > 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>
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> > > >>>>>>>> In PROLOG we use lowercase words for TERMS
> > > >>>>>>>> and uppercase words for VARIABLES
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> > > >>>>>>>> ATOMIC PREDICATE
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> > > >>>>>>> ATOMIC PREDICATE meaning relation?
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> > > >>>>>>> C-B
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> > > >>>>>> 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.
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> > > >>>> 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.
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> > > >>> 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.
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> > > >> First, I was not in a good mood when I posted. So, I may
> > > >> have been too dogmatic.
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> > > >> What you seem to be objecting to is the historical development
> > > >> of a logical calculus along the lines of Brentano and DeMorgan.
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> > > 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.
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> > > > (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.)
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> > > How do you see Logic and Set Theory as being the same?
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> > 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.)
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> > So you have the same rules of inference: Double Negative, DeMorgan
> > etc. apply to propositions and sets.
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> > To prove incompleteness, Godel had to generalize wffs as expressing
> > propositions to expressing sets when the wff has a free variable.
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> > C-B
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> Yes but you change the rules of the game depending what you want to
> prove.
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> Let:
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> LANGUAGE 1 LANGUAGE 2
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> seta(x) <-> x e seta
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> proof(x) <-> x e proof
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> proveby(x,y) <-> (x,y) e proveby
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> russell(x) <-> not( x e x)
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> -------------------
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> In ZFC you "UNSTRATIFY" Russel's set
> but in all theories > PA you necessitate Godel's Statment!
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> Sheer blindness!
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> TOM: Jerry can't say this sentence is true!
> JERRY: Tom can't say this sentence is true!
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> TOM AND JERRY ARE *INCOMPLETE* !!
There are a lot of premises there.
TOM can express "unprovable by JERRY".
TOM can express truth in JERRY. (Uh-oh, Tarski)
JERRY can express "unprovable by TOM".
JERRY can express truth in TOM. (Uh-oh, Tarski)
But I use CBL where this is all easily formalized.
C-B
> must be unrelated to logic!
>
> Herc
> --www.BLoCKPROLOG.com
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