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Do Gödellian arguments refute a computational model of the mind?

Gödel's incompleteness theorem has been used to claim that the human mind cannot be modeled with a computer. The outline of the argument is that humans have an inexplicable ability to intuitively recognize certain statements as true, even though, per Gödel's theorem, we have no logical basis to know such statements are true. The argument was first proposed by John Lucas in 1959, and since then many philosophers, mathematicians, and cognitive scientists have argued for and against his reasoning.

Implications to Other Questions

Is quantum mechanics needed to explain consciousness?
Could a computer ever be conscious?
Do Gödellian arguments refute a computational model of the mind?

Experts and Influencers

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Agree
Experts In Mathematics


J. R. Lucas    Philosophy Professor
Agree
Gödel's theorem must apply to cybernetical machines, because it is of the essence of being a machine, that it should be a concrete instantiation of a formal system. It follows that given any machine which is consistent and capable of doing simple arithmetic, there is a formula which it is incapable of producing as being true — i.e., the formula is unprovable-in-the-system-but which we can see to be true. It follows that no machine can be a complete or adequate model of the mind...
01 Jan 1963    Source


Roger Penrose    Mathematics Professor
Agree
...I regard the Gödel argument as showing that conscious understanding is something that cannot be properly imitated by a computer. ...if consciousness is part of physics—-describable by the “true” laws of physics—-then the true laws of physics must be non-computable. It is known (using Gödel-Turing-type arguments) that there are many areas of mathematics which are actually non-computable, so I am claiming that the true laws of physics (not yet fully known to us) must also be non-computable.
01 Jan 2007    Source



Deepak Chopra    Inventor of Quantum Healing
Agree
...the brain being a physical organ cannot process real creativity as per Gödel's Theorem ... or even have free will.
27 Mar 2010    Source


Disagree
Experts In Philosophy


Daniel Dennett    Philosophy Professor
Disagree
...even if mathematicians are superb recognizers of mathematical truth, and even if there is no algorithm, practical or otherwise, for recognizing mathematical truth, it does not follow that the power of mathematicians to recognize mathematical truth is not entirely explicable in terms of their brains executing an algorithm.
29 Sep 1989    Source


Experts In Cognition


Robin Hanson    Economics Professor
Disagree
Reviewers [of Penrose] knowledgeable about Godel's work ... have simply pointed out that an axiom system can infer that if its axioms are self-consistent, then its Godel sentence is true. An axiom system just can't determine its own self-consistency. But then neither can human mathematicians know whether the axioms they explicitly favor (much less the axioms they are formally equivalent to) are self-consistent. Cantor and Frege's proposed axioms of set theory turned out to be inconsistent...
01 Jan 1991    Source


David Chalmers    Philosophy Professor
Disagree
...the assumption that we know we are sound leads to a contradiction. [This is] the deepest flaw [in Penrose's position]. ... A reader who is not convinced by Penrose's Gödelian arguments is left with little reason to accept his claims that physics is noncomputable and that quantum processes are essential to cognition...
01 Jan 1995    Source



Douglas Hofstadter    Professor of Cognitive Science
Disagree
The repeatability of Gödel's argument is shown, with the implication that TNT is not only incomplete, but "essentially incomplete". The fairly notorious argument by J. R. Lucas, to the effect that Gödel’s Theorem demonstrates that human thought cannot in any sense be "mechanical", is analyzed and found to be wanting.
05 Feb 1999    Source



Comments

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1 Point      JGWeissman      25 Apr 2010      Stance on Question: Disagree
Gödel's incompleteness theorem shows that a sufficiently complex, consistent axiomatic system (that can describe the natural numbers) will have propositions that are true according to the axioms, but not provable by that system. These propositions are incredibly complicated, constructed out of a clever mapping of numbers and arithmetic operators to the language and rules of inference of the axiomatic system, to get a proposition about the existence of a number with certain properties, which corresponds to a reasonable way of cashing out the self reference in a statement like "This statement is not provable within the axiomatic system". Gödel also showed that an expanded axiomatic system can prove these statements (though it also has its own statements which are true but it cannot prove).

It is certainly possible for the human mind to have such statements, that are true but it can't prove.


0 Points      Benja      25 Apr 2010      Editorial Comment


1 Point      Adam Atlas      25 Apr 2010      Stance on Question: Disagree
As far as I can tell, the Huge Mistake in this reasoning is the implicit but crucial jump from "a human's knowledge of some fact cannot be isomorphic to a formal proof" to "the human brain cannot be isomorphic to a formal system". The former is clearly true, at no detriment to the possibility of AI, and at only minor detriment to our ability to have useful knowledge. Our knowledge of anything, absolute mathematical certainties included, is imprecise and probabilistic. An AI with a similar (or preferably better) epistemology would very likely also be able, based on intelligent reasoning about formal deduction (not reasoning that looks like formal deduction from the inside), to come to very high or very low probability estimates for certain formally-undecidable statements, as this would not need to be isomorphic to any impossible proofs in the formal system it's ultimately implemented on.


0 Points      Benja      26 Apr 2010      Editorial Comment
FYI - I edited the wording of the question & description. Please let me know if I've diluted or distorted the meaning. You can click on the "history" to see the former wording, and of course you can simply re-edit the question.



1 Point      Adam Atlas      25 Apr 2010      Editorial Comment
Is there a standard procedure for citing quotes from books rather than websites? For now I just linked the Douglas Hofstadter quote to the Amazon.com page for GEB.

Also, I'll try to find a quote from him that better shows his actual arguments instead of just demonstrating that he disagrees.


0 Points      Benja      25 Apr 2010      Editorial Comment
Linking to Amazon is exactly what I've been doing for all book references - I should formalize that in the FAQ. When possible, I try to find a quote from a free article or interview online, to avoid frustration for anyone who wants to investigate the source. However, sometimes the best quote comes from a book.

Great question btw.