Monday, December 9, 2013

Gödel and mechanism

The Stanford Encyclopedia of Philosophy has a new entry on Gödel's Incompleteness Theorems (they also have an entry on Kurt Gödel himself). A subcategory of the article is on Gödelian arguments against mechanism, which, as is often the case, paints a somewhat bleak picture of such arguments' success. In addition to listing J.R. Lucas as a proponent of an anti-mechanist argument à la Gödel, the article also mentions mathematical physicist Roger Penrose who argued along these lines in The Emperors New Mind and Shadows of the Mind (and elsewhere). Two other philosophers the article points me to, who I was unaware had argued similarly, are John Searle in The Mystery of Consciousness and a couple of essays by Crispin Wright (along with a rebuttal by Michael Detlefsen). So I have some reading to do.


Gyan said...

The encyclopedia article cites Turing's refutation of the Goedelian argument against mechanism but omits to say that Lucas has replied to all of Turing's points. The situation is not bleak. See also Jaki's Mind, Brains and Computers. He also replies to Turing.

Curiously, Douglas Hofstadter uses Goedel to argue for a self-referential artificial intelligence. Thus, he accepts that there is a self-referential loop but assumes that this loop may be utilized for the AI.

Jim S. said...

I agree that the situation is not bleak. The article suggests that there is a general consensus on what is wrong with the Godelian argument, but actually there is widespread disagreement. Moreover, the argument is completely beholden to Turing: it needs Turing's "On Computable Numbers" to show that any mechanistic system is analogous to a purely deductive (thus formal) system, which therefore has no room for non-formalizable concepts, or any non-deductive form of reasoning like induction, abduction, or intuition. And Lucas cites Turing's "Computing Machinery and Intelligence" as a predecessor to his argument, as Turing argues there that the human mind is different (not "better") than any mechanistic system.