
Re: This is False. 0/0 {x  x ~e x} e {x  x ~e x} A single Principle to Resolve Several Paradoxes
Posted:
Feb 9, 2013 8:09 PM


On Feb 10, 10:19 am, CharlieBoo <shymath...@gmail.com> wrote: > On Feb 7, 1:51 am, fom <fomJ...@nyms.net> wrote: > > > > > > > > > > > On 2/5/2013 9:32 AM, CharlieBoo wrote: > > > > On Feb 4, 4:26 pm, fom <fomJ...@nyms.net> wrote: > > >> On 2/4/2013 8:46 AM, CharlieBoo wrote: > > > >>> On Feb 4, 12:25 am, fom <fomJ...@nyms.net> wrote: > > >>>> On 2/3/2013 10:19 PM, CharlieBoo wrote: > > >>>> <snip> > > > >>>>>>>> In PROLOG we use lowercase words for TERMS > > >>>>>>>> and uppercase words for VARIABLES > > > >>>>>>>> ATOMIC PREDICATE > > > >>>>>>> ATOMIC PREDICATE meaning relation? > > > >>>>>>> CB > > > >>>>>> 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. > > > >>>> Wellformed formulas are built from the alphabet > > >>>> of a formal language. If the language contains > > >>>> a symbol of negation, then NOT(xex) will be a > > >>>> wellformed 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 0place. A set is 1place. 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. > > CB > >
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

