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Topic: A HARD FLAW in Godel's Proof
Replies: 7   Last Post: Dec 8, 2012 2:27 PM

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 INFINITY POWER Posts: 117 Registered: 11/1/11
A HARD FLAW in Godel's Proof
Posted: Nov 17, 2012 10:10 PM

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.

- - - - - - - - - - - - - -

STEP 2: DEFINE a Godel Statement.

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

- - - - - - - - - - - - - -

STEP 3: IS G A THEOREM?

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

- - - - - - - - - - - - - -

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)

- - - - - - - - - - - - - - -

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().

- - - - - - - - - - - - - - -

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

Date Subject Author
11/17/12 INFINITY POWER
11/17/12 Graham Cooper
11/19/12
11/18/12 Graham Cooper
11/18/12 Graham Cooper
12/8/12 Graham Cooper