A dilemma about consistency
Lucas's dialectical argument against mechanism runs into a problem about how the mechanist knows whether or not his models are consistent (see detailed text).
Either, the mechanist knows all consistent machines

In which case, the mechanist has a decision procedure for logic.

But according to Church's theorem this is impossible. So the mentalist has no opponents at all.

Or, the mechanist doesn't know all consistent machines,

In which case, the mentalist's ability to refute the mechanist doesn't imply that no consistent machine can prove as much as the mentalist can.
 
In either case, the mentalist can't defeat his mechanist opponent.

Hao Wang (1974).

Note: also see the "Is the use of consistency in the Lucas argument problematic?" arguments on this map.
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Artificial Intelligence »Artificial Intelligence
Are thinking computers mathematically possible? [7] »Are thinking computers mathematically possible? [7]
No: computers are limited by Gödel's theorems »No: computers are limited by Gödel's theorems
Argument from Gödel's theorem is dialectical »Argument from Gödel's theorem is dialectical
A dilemma about consistency
Lucas claims less than Wang's dilemma suggests »Lucas claims less than Wang's dilemma suggests
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