We’re talking about J. Anthony Lucas’s classic argument that Gödel’s Second Incompleteness Theorem rules out man-machine equivalence. This is an argument that Penrose revived and popularized in the 1990s. This fallacious argument is a thoroughly dead horse. But I’ll give it another beating here. Do note that the Lucas-Penrose argument is a completely distinct issue from PenroseHameroff speculation that the brain can act as a coherent quantum computer. It’s to Penrose’s credit that he’s associated with multiple controversial ideas!
Lucas, J. R. (1990). A Paper Read to the Turing Conference at Brighton on April 6th, 1990. Retrieved from: http://users.ox.ac.uk/~jrlucas/Godel/brighton.html
Putnam, H. (1964). Minds and Machines. In: R. Anderson, Minds and Machines (pp. 43–59). Upper Saddle River: Prentice-Hall.
Rucker, R. (2005). Infinity and the Mind (3rd ed.). Princeton: Princeton University Press.
Rucker, R. (2016). The Lifebox, the Seashell, and the Soul. Edinburgh: Transreal Fiction.