So, you guys finally finished reading Roger Penrose’s The Emperor’s New Mind? What did you think of it?
(Since I forgot to record this lecture, the class responses are tragically lost to history. But if I recall correctly, the entire class turned out to consist of – YAWN – straitlaced, clear-thinking materialistic reductionists who correctly pointed out the glaring holes in Penrose’s arguments. No one took Penrose’s side, even just for sport.)
Alright, so let me try a new tack: who can summarize Penrose’s argument (or more correctly, a half-century-old argument adapted by Penrose) in a few sentences?
How about this: Gödel’s First Incompleteness Theorem tells us that no computer, working within a fixed formal system F such as Zermelo-Fraenkel set theory, can prove the sentence
G(F) = "This sentence cannot be proved in F."But we humans can just “see” the truth of G(F) – since if G(F) were false, then it would be provable, which is absurd! Therefore the human mind can do something that no present-day computer can do. Therefore consciousness can’t be reducible to computation.
Alright, class: problems with this argument?