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CONSISTENCY AND INCOMPLETENESS
Posted:
Jul 18, 1996 2:49 PM


(1) The consistency of a rich enough system S cannot be proved in S.
Moreover,
(2) If S is consistent it is not complete
PROOF Of (1). If consistency of S can be proved at all, in general, it would be via constructing a model of S.
So, let me prove that a model of system S mentioned above cannot be proved within S . Instead of giving a proof covered with 20 tons of cold lava and obfuscating the whole issue, I will give you an example.
Let S be the system describing the planet Earth. It is impossible to construct a model, i.e., a GLOBE, G on planet Earth which will model the (new) planet Earth system S + G . Because now on planet Earth you have put a Globe G and that glob G which was supposed to model planet Earth does not describe S + G. (and no finitely many repetition of S+ G+ G' + ...+G' will do the job). However, the consistency of S can be proved outside S. Indeed on planet Moon you can construct the Globe G which will faithfully describe S.
PROOF OF (2). If the system S mentioned above is consistent then it is not complete. Indeed, you can always enlarge S to the a consistent system S+H where H is a Globe of S constructed on the Moon, and repeat the process to show that you will never obtain a complete consistent system extending a sufficiently rich enough consistent system S.
Alexander Abian: Equivalence of Mass and Time Albert Einstein: Equivalence of Mass and Energy THERE WAS NO BIG BANG. THERE WAS A BIG SUCK INTO THE VOID OF SPACE

 TIME IS MASS. ABIAN MASSTIME EQUIVALENCE FORMULA T=(10^18)Log(1m/Mo) SECONDS ALTERING EARTH'S ORBIT AND TILT  STOPPING GLOBAL DISASTERS AND EPIDEMICS. ALTERING THE SOLAR SYSTEM. REORBITING VENUS INTO A NEAR EARTHLIKE ORBIT TO CREATE A BORN AGAIN EARTH.



