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