Date: Nov 17, 2012 10:10 PM
Author: INFINITY POWER
Subject: A HARD FLAW in Godel's Proof

THINKING CAPS ON!
ARGUE LOGICALLY!
ASSUME ANYTHING!
ROLLBACK ASSUMPTIONS LATER ON <<!

STEP 1:  DEFINE a 2 parameter predicate DERIVE(THEOREM, DERIVATION)

DERIVE(T,D) is TRUE IFF
  D contains a sequence of inference rules and substitutions
  and the final formula T in D is logically implied from the Axioms.

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STEP 2:  DEFINE a Godel Statement.

i.e.  Godel Statement named G =
    ALL(M)  ~DERIVE(G,M)

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STEP 3:  IS G A THEOREM?

ASSUME: YES G IS A THEOREM
    DERIVE(   G:ALL(M)~DERIVE(G,M)  , D )

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STEP 4:  UNIFY THE QUERY TO THE AXIOMS TO GET THE ANSWER

  GOAL :       DERIVE(  G:ALL(M)~DERIVE(G,M)   , D )
  SUBGOAL :    G:ALL(M)~DERIVE(G,M)

  (SUBGOALs are a Derivation Process that calculate reverse D in the trace)

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STEP 5:  REMOVE THE QUANTIFIER

  G:~EXIST(M)DERIVE(G,M)
  G: ~DERIVE(G,M)

M is a variable and Existential by Double Variable Instantiation Rule of 
UNIFY().

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STEP 6:  M IS A FREE VARIABLE

  G: ~DERIVE(G,M)

is a null statement that will return

SUBGOAL:  M?

i.e. When parsed by a clever logic compiler, Godel's Statement will return a 
Query in response

[PROVER]- "Why is sentence G not derivable?"


Herc

--
if( if(t(S),f(R)) , if(t(R),f(S)) ).
    if it's sunny then it's not raining
ergo
       if it's raining then it's not sunny