
Re: This is False. 0/0 {x  x ~e x} e {x  x ~e x} A single Principle to Resolve Several Paradoxes
Posted:
Feb 5, 2013 5:34 PM


On Feb 6, 12:10 am, CharlieBoo <shymath...@gmail.com> wrote: > On Feb 4, 4:14 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>> thm( X ) < if( not(X), P ) ^ if( not(X), not(P) ) >What does that say in English?
Negate an Hypothesis and prove it by contradiction
(~x>p) & (~x>~p) > x
[1]
> > Sure you can syntactically eliminate strings like "~e(X,X)" > > And don't forget strings that imply it. > > > in NFU Set Theory. > > > I'm working on using > > > NOT( PROVABLE( T ) ) <> DERIVE( NOT(T) )
[2]
a WFF 'T' is not "provable" (a True or False predicate) if there is a proof of NOT(T)
e.g. T = EXIST(rs) rs={xx~ex}
T is false hence there cannot be a proof of T
> > > EXISTS( SET( S ) ) <> PROVABLE ( EXIST (SET (S) ) ) > > AXIOM OF SET SPECIFICATION
[3]
> > What does this say in English? >
Set existence is dependant upon that set's existence being provable.

e.g. PROOF( NOT(EXIST(RUSSELLSSET)) by [1] NOT(PROVABLE(RUSSELLSSET)) by [2] NOT(EXIST(RUSSELLSSET)) by [3]

So far my PROLOG FORMAL SYSTEM has 1 type  PREDICATES with 2 variations
thm( .... predicate...) and not(.... predicate...)
I think by adding a SETorELEMENT type:
[X1] exist( rs )
I can finish my PROVABLESETTHEORY by using:
[X2] e(MEM,SET) : exist(MEM) , exist(SET)
then PROLOG should be able to INSTANTIATE rs into its e(X,X) definition just like you did here:
> Then I take it that: > if [ not [ e rs rs ]] [ e rs rs ] Line 1 X => rs > if [ e rs rs ] [ not [ e rs rs ]] Line 2 X => rs
by using rule [X2] and the fact exist(rs)
it should be able to derive the contradiction... and keep the Theory consistent via that!
Herc

