
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


On Feb 9, 8:09 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > 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* !!
There are a lot of premises there.
TOM can express "unprovable by JERRY". TOM can express truth in JERRY. (Uhoh, Tarski) JERRY can express "unprovable by TOM". JERRY can express truth in TOM. (Uhoh, Tarski)
But I use CBL where this is all easily formalized.
CB
> must be unrelated to logic! > > Herc > www.BLoCKPROLOG.com

