|
|
Joined: Sep 2000
Posts: 4,757
Carpal Tunnel
|
Carpal Tunnel
Joined: Sep 2000
Posts: 4,757 |
an exceptionally clear exposition of Godel's Incompleteness Theorem, Godel's Proof by Ernest Nagel
I gave this a try. Never finished it though.
|
|
|
|
|
Joined: Mar 2000
Posts: 1,004
old hand
|
|
old hand
Joined: Mar 2000
Posts: 1,004 |
an exceptionally clear exposition of Godel's Incompleteness Theorem, Godel's Proof by Ernest Nagel
I gave this a try. Never finished it though.
Penrose, in The Emperor's new mind does a good job of explaining the incompleteness theorem (in my opinion), though he is a bit unsound when it comes to his theory of mind (again my opinion). And Douglas Hofstader does brilliantly in Godel, Escher, Bach: An eternal golden braid, though again, some of what he says about the mind is a bit dated (yes, the field has moved on considerably in twenty or so years).
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
an exceptionally clear exposition of Godel's Incompleteness Theorem, Godel's Proof by Ernest Nagel
I gave this a try. Never finished it though.
Penrose: The Emperor's new mind... Douglas Hofstader: Godel, Escher, Bach: An eternal golden braid
I have the Hofstader tucked away somewhere in my efficient filing system. It is the source of my present incomplete understanding. I shall endeavour to find it and I will scope out the Penrose.
My present understanding is basically that any system of thought can produce statements like "this statement is a lie" and that, while these statements can be resolved by building some metasystem that includes the offending system as a subset, that metasystem will also be capable of generating similar statements. I take this to mean that we are not infinitely intelligent.
PS
According to Ænigma the book is Douglas Hog: Godfather, Escherichia, Bach: An eternal golden braid
PPS
I love Ænigma's correction of her own name.
|
|
|
|
|
Joined: Mar 2000
Posts: 1,004
old hand
|
|
old hand
Joined: Mar 2000
Posts: 1,004 |
My present understanding is basically that any system of thought can produce statements like "this statement is a lie" and that, while these statements can be resolved by building some metasystem that includes the offending system as a subset, that metasystem will also be capable of generating similar statements.
In essence, yes.
I take this to mean that we are not infinitely intelligent.
Here I take exception. Godel showed, in principle, that even an 'infinitely intelligent' being (whatever that may be) could not utilise a logic system that was both consistent and complete (consistent in not giving rise to inherent falshoods - paradox's, complete in being able to prove every true statement within the system itself). It is not a limitation on intelligence, but upon the notion of logic, or reason, itself.
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
It is not a limitation on intelligence, but upon the notion of logic, or reason, itself.
I suppose I think that if we were infinitely intelligent, or, better, we had some facility that was superior to intelligence (which I think is highly overrated), we would have something better than logic or reason to work with.
Just this Fool's slant on things.
|
|
|
|
|
Joined: Apr 2000
Posts: 10,542
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Apr 2000
Posts: 10,542 |
>According to Ænigma the book is Douglas Hog: Godfather, Escherichia, Bach: An eternal golden braid
escherichia?? that's a new level of enteric weirdness.
|
|
|
|
|
Joined: Dec 2000
Posts: 13,803
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Dec 2000
Posts: 13,803 |
escherichia?? that's a new level of enteric weirdness.
It's an enigma wrapped in a sausage skin stuffed into a turkey
|
|
|
|
|
Joined: Jul 2000
Posts: 1,094
old hand
|
|
old hand
Joined: Jul 2000
Posts: 1,094 |
I suppose I think that if we were infinitely intelligent, or, better, we had some facility that was superior to intelligence (which I think is highly overrated), we would have something better than logic or reason to work with.
There's always creativity. It seems to me that all jobs either require analytical intelligence or creativity, and usually some mix of both. Then there are the mind-numbingly robotic jobs like bean counting.
Then again, isn't creativity just a different type of intelligence?
|
|
|
|
|
Joined: Nov 2000
Posts: 3,146
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Nov 2000
Posts: 3,146 |
Is it so important to posit infinite intelligence? I read somewhere, and can't find any argument with, the idea that paradoxes are almost always due to incomplete information and that all apparent paradoxes are, by extrapolation, a product of ignorance.
This definition may have been overtaken either by better information - or infinite intelligence, of course!
The idiot also known as Capfka ...
|
|
|
|
|
Joined: Sep 2000
Posts: 4,757
Carpal Tunnel
|
|
Carpal Tunnel
Joined: Sep 2000
Posts: 4,757 |
the idea that paradoxes are almost always due to incomplete information
I think this theory is based on incomplete information.
|
|
|
|
Forums16
Topics13,915
Posts229,845
Members9,197
| |
Most Online3,341
Dec 9th, 2011
|
|
|
0 members (),
611
guests, and
3
robots. |
|
Key:
Admin,
Global Mod,
Mod
|
|
|
|
