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CONSISTENCY AND INCOMPLETENESS
Posted:
Jul 18, 1996 2:49 PM
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(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 MASS-TIME EQUIVALENCE FORMULA T=-(10^18)Log(1-m/Mo) SECONDS
ALTERING EARTH'S ORBIT AND TILT - STOPPING GLOBAL DISASTERS AND EPIDEMICS.
ALTERING THE SOLAR SYSTEM. REORBITING VENUS INTO A NEAR EARTH-LIKE ORBIT
TO CREATE A BORN AGAIN EARTH.
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