I didn't realise people were making these arguments back in the sixties. I came across this in Penrose's much more recent books "The Emperor's New Mind" and to a lesser extent "The Shadow Of The Mind" which make similar arguments to this paper, appealing to incompleteness (and in the second book quantum mechanics) to argue against strong AI. Both books are well worth reading, but since I understand Turing machines are able to stimulate both quantum and classical machines I found it hard to find them truly convincing.