The implied threat of this has long been a cult-theme of sci-fie and gee-gosh-Sunday-supplements. But it has been boosted to national level by Time Magazine in its June x, 2000, cover-story on "Technology".Such talk IGNORES several caveats:
That's for starters. Later, I may think of more. Perhaps you can, also. However, until the woe-sayers have countered these cautionaries, we'll give them pause.
- Gödel's Theorem
- Tarski's version of it
- Frege's name-dualism
- language, metalanguage dualism
- Figure-Ground Dualism
- Strategy-Tactics Dualism.
GÖDEL'S THEOREM David Hilbert (x-y) showed that all mathematics can be mapped onto arithmetic. Hence, IF ARITHMETIC CAN BE PROVEN COMPLETE, THEN ALL MATHEMATICS IS COMPLETE. Now, COMPLETENESS MEANS THAT ALL THEOREMS OF A GIVEN SUBJECT CAN BE DERIVED FROM ITS AXIOMS.
Gödel formulated a clever system for ENCODING ALL THE LANGUAGE OF ARITHMETIC IN GÖDEL NUMBERS, WITH AN ALGEBRA OF EQUATIONS THAT HAS THESE NUMBERS AS ROOTS. But he showed that the LATTER ALGEBRA HAS AN EQUATION WHOSE SOLUTION CAN BE DECODED TO SAY THAT A THEOREM EXISTS WHICH IS BOTH TRUE AND NONDERIVABLE FROM THE AXIOMS. CONCLUSION: ARITHMETIC IS CONTRADICTORY OR INCOMPLETE.
Many thinkers have concluded this implication: PROOF OF COMPLETENESS WOULD MEAN THAT COMPUTERS COULD REPLACE HUMANS; FAILURE OF COMPLETENESS, THAT HUMANS CANNOT BE THUS REPLACED. This is not mentioned in the Time scaries.
TARKI'S "PARADOX" Said to be equivalent to Gödel's Incompleteness Theorem. I'll state my own version of it.
IN ANY GAME ALLOWING SUBSTITUTION OF ONE PLAYER FOR ANOTHER, THE REFEREE/UMPIRE CANNOT SUBSTITUTE FOR ANOTHER PLAYER.
Violation consequence? The REFEREE/UMPIRE COULD RULE THAT HIS/HER APPARENT VIOLATIONS OF THE RULES ARE LEGAL.
Now, I interpret this to mean that MAKING THE AXIOMS OF ARITHMETIC PART OF ARITHMETIC WOULD CORRUPT ARITHMETIC.
In terms of the Title-subject, CLAIMING ALL HUMAN CAPABILITIES TO BE COMPUTABLE DEBASES VALUE.
FREGE'S NAME-DUALISM Gotthold Frege(x-y) founded predicate logic along with his universal ("all") and existential ("at least one") operators. Frege also noted the dual aspects or modes of any NAME: USE and MENSION. Thus, with respect to the NAME, "Boston", if you say, "Boston is a nice city to visit", you treating the NAME "Boston" in its USE MODE; but if you say, "Boston is a 6 letter-word", you are treating the NAME "Boston" in its MENTION MODE.
I infer from this DUALISM that uniquely and creative human acts occur on the MENTION level, while PROGRAMMING is primarily on the USE level.
LANGUAGE-METALANGUAGE DUALISM