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Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.h

by spot 16y ago

Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html

deleted 16y ago
[deleted]
justsee 16y ago
'have been debunked' - quite an emotionally laden phrase to introduce what is in fact an opposing view by another mathematician don't you think? The hostility the Strong AI camp have for Penrose's views is fascinating - it must be infuriating to have such a respected mathematician and physicist take the time to write a few books refuting the reductionist approach. There certainly seems to be no room for a contrarian around those parts! Thanks for the link, but to state that it debunked anything does not seem to be correct. It was an attempted refutation by a computationalist, and Penrose answers these criticims in: http://web.archive.org/web/20080618195657/http://psyche.csse.monash.edu.au/v2/psyche-2-23-penrose.html http://web.archive.org/web/20080618195657/http://psyche.csse... I'd recommend reading the section "4. The "Bare" Gödelian Case". Two particularly relevant points! "4.5 The many arguments that computationalists and other people have presented for wriggling around Gödel's original argument have become known to me only comparatively recently: perhaps we act and perceive according to an unknowable algorithm; perhaps our mathematical understanding is intrinsically unsound; perhaps we could know the algorithms according to which we understand mathematics, but are incapable of knowing the actual roles that these algorithms play. All right, these are logical possibilities. But are they really plausible explanations? 4.6 For those who are wedded to computationalism, explanations of this nature may indeed seem plausible. But why should we be wedded to computationalism? I do not know why so many people seem to be. Yet, some apparently hold to such a view with almost religious fervour. (Indeed, they may often resort to unreasonable rudeness when they feel this position to be threatened!) Perhaps computationalism can indeed explain the facts of human mentality - but perhaps it cannot. It is a matter for dispassionate discussion, and certainly not for abuse! "
- spot 16y ago
  Did you see where he admits he's wrong? "these are logical possibilities". IE, Penrose made a logical argument, and he didn't cover all the cases. Maybe this one is clearer: http://www.nytimes.com/books/97/04/27/nnp/17540.html http://www.nytimes.com/books/97/04/27/nnp/17540.html
- shasta 16y ago
  "refuting the reductionist approach" is pretty strong language for describing an argument that's been debunked
yequalsx 16y ago
I haven't read the entire article you linked to. Can you elaborate on something? Godel's Incompleteness Theorem (in essence) said that the first order Peano axioms for the integers was not strong enough to prove all statement in the second order Peano axioms. My understanding is that mathematicians wanted a computable system that would be strong enough to prove all true statements encompassed by the second order system. Godel showed this can't be done. No computable system can be strong enough to prove all true statements in the second order system. Given that humans can prove statements that are true in a system that can't be reducible to a computable set of axioms how can computer intelligence ever equal human intelligence? Human intelligence must be fundamentally not a computable system. What's wrong with this reasoning?
- wlievens 16y ago
  Could you elaborate on "... given that humans can prove statements that are true in a system that can't be reducible to a computable set of axioms ..."? Perhaps with an example?
  - yequalsx 16y ago
    From Wikipedia: The true but unprovable statement referred to by the theorem is often referred to as “the Gödel sentence” for the theory. It is not unique; there are infinitely many statements in the language of the theory that share the property of being true but unprovable.
    - xlpz 16y ago
      How does that prove in any way that the human mind can find all true statements in Mathematics and thus go beyond the limits of computability? Do you have any proof of this? Also, do you have any proof that the human mind is in fact consistent (meaning it can't possibly reach A and ~A at the same time)?
      - yequalsx 16y ago
        I'm not claiming that humans can discover all true statements in mathematics. I'm saying the Incompleteness Theorem demonstrates that such a task is not computable and in the proof of the theorem a statement that can't be proven in a computable system is proved. So....can a computer ever reach the same level of reasoning? I'm skeptical.

by spot 16y ago

Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html

deleted 16y ago

[deleted]

justsee 16y ago

'have been debunked' - quite an emotionally laden phrase to introduce what is in fact an opposing view by another mathematician don't you think? The hostility the Strong AI camp have for Penrose's views is fascinating - it must be infuriating to have such a respected mathematician and physicist take the time to write a few books refuting the reductionist approach. There certainly seems to be no room for a contrarian around those parts! Thanks for the link, but to state that it debunked anything does not seem to be correct. It was an attempted refutation by a computationalist, and Penrose answers these criticims in: http://web.archive.org/web/20080618195657/http://psyche.csse.monash.edu.au/v2/psyche-2-23-penrose.html http://web.archive.org/web/20080618195657/http://psyche.csse... I'd recommend reading the section "4. The "Bare" Gödelian Case". Two particularly relevant points! "4.5 The many arguments that computationalists and other people have presented for wriggling around Gödel's original argument have become known to me only comparatively recently: perhaps we act and perceive according to an unknowable algorithm; perhaps our mathematical understanding is intrinsically unsound; perhaps we could know the algorithms according to which we understand mathematics, but are incapable of knowing the actual roles that these algorithms play. All right, these are logical possibilities. But are they really plausible explanations? 4.6 For those who are wedded to computationalism, explanations of this nature may indeed seem plausible. But why should we be wedded to computationalism? I do not know why so many people seem to be. Yet, some apparently hold to such a view with almost religious fervour. (Indeed, they may often resort to unreasonable rudeness when they feel this position to be threatened!) Perhaps computationalism can indeed explain the facts of human mentality - but perhaps it cannot. It is a matter for dispassionate discussion, and certainly not for abuse! "

spot 16y ago
Did you see where he admits he's wrong? "these are logical possibilities". IE, Penrose made a logical argument, and he didn't cover all the cases. Maybe this one is clearer: http://www.nytimes.com/books/97/04/27/nnp/17540.html http://www.nytimes.com/books/97/04/27/nnp/17540.html
shasta 16y ago
"refuting the reductionist approach" is pretty strong language for describing an argument that's been debunked

yequalsx 16y ago

I haven't read the entire article you linked to. Can you elaborate on something? Godel's Incompleteness Theorem (in essence) said that the first order Peano axioms for the integers was not strong enough to prove all statement in the second order Peano axioms. My understanding is that mathematicians wanted a computable system that would be strong enough to prove all true statements encompassed by the second order system. Godel showed this can't be done. No computable system can be strong enough to prove all true statements in the second order system. Given that humans can prove statements that are true in a system that can't be reducible to a computable set of axioms how can computer intelligence ever equal human intelligence? Human intelligence must be fundamentally not a computable system. What's wrong with this reasoning?

wlievens 16y ago
Could you elaborate on "... given that humans can prove statements that are true in a system that can't be reducible to a computable set of axioms ..."? Perhaps with an example?
- yequalsx 16y ago
  From Wikipedia: The true but unprovable statement referred to by the theorem is often referred to as “the Gödel sentence” for the theory. It is not unique; there are infinitely many statements in the language of the theory that share the property of being true but unprovable.
  - xlpz 16y ago
    How does that prove in any way that the human mind can find all true statements in Mathematics and thus go beyond the limits of computability? Do you have any proof of this? Also, do you have any proof that the human mind is in fact consistent (meaning it can't possibly reach A and ~A at the same time)?
    - yequalsx 16y ago
      I'm not claiming that humans can discover all true statements in mathematics. I'm saying the Incompleteness Theorem demonstrates that such a task is not computable and in the proof of the theorem a statement that can't be proven in a computable system is proved. So....can a computer ever reach the same level of reasoning? I'm skeptical.