As someone who took a number of mathetical logic classes between undergrad/graduate I always found this Gödel-sentence argument on the face-laughable, since the logical inconsistency was so easy to repair. My favorite critique of this was Hans Moravec's dialogue between Penrose and a robot AI, having resurrected his brain long past humanity's extinction: http://www.calculemus.org/MathUniversalis/NS/10/10moravec.ht...