Why Roger Penrose thinks computers can't
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Why Roger Penrose thinks computers can't
1–10 of 37 posts
Re: Why Roger Penrose thinks computers can't
#2Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html
Re: Why Roger Penrose thinks computers can't
#3because he's wrong and confused
Re: Why Roger Penrose thinks computers can't
#4Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html
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Re: Why Roger Penrose thinks computers can't
#5Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html
'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...
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! "
Re: Why Roger Penrose thinks computers can't
#6Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html
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?
Re: Why Roger Penrose thinks computers can't
#7Penrose and his book have been debunked. http://www.mth.kcl.ac.uk/~llandau/Homepage/Math/penrose.html
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 syst…
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?
Re: Why Roger Penrose thinks computers can't
#8Earlier quoted context omitted.
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 syst…
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?
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.
Re: Why Roger Penrose thinks computers can't
#9"The question of whether a computer can think is no more interesting than the question of whether a submarine can swim."
E. Dijkstra
Re: Why Roger Penrose thinks computers can't
#10He's a Platonist, so he believes in the existence of a real world that is neither material nor mental.
His central claim that conscious acts are in some sense noncomputational is prima facie false.
And his concrete solution to problem collects together several other very difficult problems and essentially says, solve one, solve them all. (Great news for his publishers btw.)
For those reasons, it's hard to take seriously because it's outrageously speculative.