Proof of human superiority relies on proof of consistency
Newman and Nagel's thesis results from a misapplication of Gödel’s theorem (see detailed text).
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.