Although it's true—as Newman and Nagel claim— that a machine can't prove some undecidable propositions, a human can't prove those propositions either, unless he or she can first prove that the machine is consistent.
But is unlikely that a human would ever be able to carry out such a consistency proof unless the machine were very simple.
Hilary Putnam (1960).
**Note**: Also, see the *"Is the use of consistency in the Lucas argument problematic?" *arguments on this map. |