```Date: Feb 5, 2013 5:34 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 6, 12:10 am, Charlie-Boo <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={x|x~ex}T is falsehence 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(RUSSELLS-SET))    by [1]   NOT(PROVABLE(RUSSELLS-SET))         by [2]   NOT(EXIST(RUSSELLS-SET))        by [3]---------------------------------So far my PROLOG FORMAL SYSTEM has 1 type - PREDICATESwith 2 variationsthm( .... predicate...)andnot(.... predicate...)I think by adding a SETorELEMENT  type:[X1]exist( rs )I can finish my PROVABLE-SET-THEORY by using:[X2]e(MEM,SET)  :-  exist(MEM)  ,  exist(SET)then PROLOG should be able to INSTANTIATE rsinto 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 => rsby using rule [X2]  and the fact  exist(rs)it should be able to derive the contradiction...and keep the Theory consistent via that!Herc
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