(...) if there is a sufficiently large threat to XP that is left unpatched but does not affect Vista. careful there, you'll give them ideas.
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Turing did mention chess as a possible starting point in Computing Machinery and Intelligence. However, even he did not go as far as the grandparent poster in claiming to replicate sentience in anything that way.
In the light of this post, I feel like we have entered a Gödelian recursion, repeating the same things at different levels. So I will stop here and concede. I am actually a researcher working on strong AI so I already spend my working hours poring over these issues. I'd like to keep some of my free time actually free of work.
Thank you for a stimulating discussion.
I'm sorry, I did not exactly understand your first sentence. I'm not sure if this is what you were asking, but I'll try to explain. What I'm saying is that Gödel's theorem is a purely mathematical theorem that is only relevant to formal systems strong enough to support basic arithmetic. Anything it proves cannot be used to support facts outside the domain of arithmetic. One can be inspired by what they imply, but that does not equal proving those statements.
The argument you have mentioned makes clever use of circular logic to misdirect the reader. There are two possible cases:
(1) If T can prove the mathematical statements I can prove, it can use Gödel's technique just as well as me. After all, they are mathematical statements as well.
(2) If there exists a statement that T cannot prove but I can, then T does not represent me totally. However, I can always build another Turing machine, T-Prime, that can prove everything T could prove PLUS the statement that T failed to prove. This machine can now be said to represent me totally.
I'm sure you see where this is going. Use the incompleteness theorem to go beyond the limits of this machine, build T-Prime-Prime to solve that, use the theorem once more, build T-Prime-Prime-Prime to solve that and so on. There is no end to this recursion. The resolution "...hence I am not a Turing machine" cannot be reached. The resolution "I am a Turing machine" is not reached either. Once again, the proof is not there.
Can a human always stay one step ahead of a Turing machine, insofar as what propositions can be proven? As I've explained above, it is not the human that is always one step of the Turing machine. They are not ahead or behind each other in any way. The recursion is simply infinite.
I should have been more precise in my statements, I apologize for being unclear. When I said "Gödel's theorems have nothing to do with representing the human mind in any form", I should have emphasized the word representing. I did not mean that the incompleteness theorem is philosophically unrelated to the topic at hand. I merely said (and I reiterate):
They cannot be applied to the human mind for the purposes of answering the question of strong AI. I do not want to argue if the mind is a Turing machine or not. I just want to state that there is no proof in Gödel's, Lucas' or Franzen's works for this issue. Assuming the truth of the statement "the human mind can understand something a Turing machine can't" is a fallacy.
I am also aware of the 1951 lecture. However, that lecture or anything else produced by Gödel does not prove that a human can understand something that the Turing machine cannot. It does not disprove of the fact either. You are welcome to believe anything you want, but that does not change the fact that the proof simply does not exist.
Gödel's theorems have nothing to do with representing the human mind in any form. They cannot be applied to the human mind for the purposes of answering the question of strong AI. Basically, the only thing that Gödel's theorems do is carry the Liar's Paradox ("This sentence is false.") to the level of basic arithmetic. There is no magical process that proves or disproves anything about the human mind. The confusion stems from the fact that the mathematical terms "incomplete" and "inconsistent" seem to imply so much more when quoted in a non-mathematical context.
I would like to believe that we will achieve strong AI one day. However, referencing Gödel's incompleteness theorems just because they sound appropriate at first glance does not give any argument scientific credibility.
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Turing did mention chess as a possible starting point in Computing Machinery and Intelligence. However, even he did not go as far as the grandparent poster in claiming to replicate sentience in anything that way.
In the light of this post, I feel like we have entered a Gödelian recursion, repeating the same things at different levels. So I will stop here and concede. I am actually a researcher working on strong AI so I already spend my working hours poring over these issues. I'd like to keep some of my free time actually free of work. Thank you for a stimulating discussion.
The argument you have mentioned makes clever use of circular logic to misdirect the reader. There are two possible cases:
(1) If T can prove the mathematical statements I can prove, it can use Gödel's technique just as well as me. After all, they are mathematical statements as well.
(2) If there exists a statement that T cannot prove but I can, then T does not represent me totally. However, I can always build another Turing machine, T-Prime, that can prove everything T could prove PLUS the statement that T failed to prove. This machine can now be said to represent me totally.
I'm sure you see where this is going. Use the incompleteness theorem to go beyond the limits of this machine, build T-Prime-Prime to solve that, use the theorem once more, build T-Prime-Prime-Prime to solve that and so on. There is no end to this recursion. The resolution "...hence I am not a Turing machine" cannot be reached. The resolution "I am a Turing machine" is not reached either. Once again, the proof is not there. Can a human always stay one step ahead of a Turing machine, insofar as what propositions can be proven? As I've explained above, it is not the human that is always one step of the Turing machine. They are not ahead or behind each other in any way. The recursion is simply infinite.
I am also aware of the 1951 lecture. However, that lecture or anything else produced by Gödel does not prove that a human can understand something that the Turing machine cannot. It does not disprove of the fact either. You are welcome to believe anything you want, but that does not change the fact that the proof simply does not exist.
Gödel's theorems have nothing to do with representing the human mind in any form. They cannot be applied to the human mind for the purposes of answering the question of strong AI. Basically, the only thing that Gödel's theorems do is carry the Liar's Paradox ("This sentence is false.") to the level of basic arithmetic. There is no magical process that proves or disproves anything about the human mind. The confusion stems from the fact that the mathematical terms "incomplete" and "inconsistent" seem to imply so much more when quoted in a non-mathematical context.
For anyone who is interested in reading further, Gödel's Theorem: An Incomplete Guide to Its Use and Abuse contains a thorough discussion of the issue.
I would like to believe that we will achieve strong AI one day. However, referencing Gödel's incompleteness theorems just because they sound appropriate at first glance does not give any argument scientific credibility.