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Last updated 17 July 2000
- Nicholas Beale 8 Nov 98 I thought this was reasonably well-known, but it seems that it's not, so I have put it on the web at http://www.starcourse.org/lucas.htm. Any comments?
- Steven Carr 9 Nov 98 The argument is that it is impossible to produce a totally deterministic model of human thought processes, or at least of those few human beings who are able to prove Godel's theorem without looking it up in a book.
How very true. Could you tell me if it is possible to produce a totally deterministic model of the weather which will predict the behaviour of the weather with complete accuracy?
If people do not behave in a deterministic manner, are they behaving in a random manner?
Do you consider that people are not behaving randomly and are also not behaving deterministically? Do you believe people do things for no cause whatsoever? If people are not doing things for no cause whatsoever, are they doing things because there is some cause for their actions?
Is it morally important that people make decisions at random, rather than making decisions predictable by looking at what the moral thing to do is in any situation?
If we were able to produce a moral system of calculus which could predict what a morally good being would do in any situation (perhaps we could call it the WWJD system) would it be morally vital that people did not obey the WWJD rules? Would it be much better if they acted at random rather than obeying the WWJD rules?- Odessa Elliott 9 Nov 98 I finally had a chance to check out your upload of the Lucas Theorem - thanks for posting the two items.
Several years ago, I heard a lecture by the head of the Computer Science dept. at Vassar College, USA, in which he spoke of some of the most recent studies in his speciality, Artificial Intelligence.
He was speaking to non-computer scientists and so gave a "homey" example of what was in the works. He told us to imagine we had customized computers around the house, to help with various tasks; and that the computer by our bedside was not only an alarm clock, but also a weather sensor.
"Good morning! It's a half-hour earlier than usual, but you will want to know that some 8 inches of snow fell over night, so you will have to dig out the walkway and driveway, if you want to get to work on time." Owner of this computer groans loudly. Pause.
Computer's voice comes on again, but softly and soothingly: "Of course, you really don't have to get to the office on time. I'll call your secretary and say there was a blizzard."
The professor's basic point: computers don't design and program themselves. Even with all the zillion-line instructions that permit computers to play chess, 'tis still the mind of homo sapiens that wrote all the zillions of lines (esp. the "If then..." statements).
As for "cutting edge" research into brain cell physiology, structure, and function, scientists have not determined the location of the cells that control most physical functions, much less thought.
No, indeed, the computer is not 'meat.'- Steven Carr 9 Nov 98 The article on Lucas Theorem mentions the further work of Professor Roger Penrose FRS on these ideas. He is an atheist, is he not? At least, I know for a fact that he is a humanist.
- Steven Carr 21 July 99 think I understand this now!
The idea is that if we have a machine which is simulating the mind of Lucas, then we can construct a sentence such as 'Lucas cannot , in all consistency, prove that this statement cannot be proved true.'
I can prove this sentence is true. You can. Almost everybody else can, but the machine cannot (Lucas theorem is true after all!) The only question is Can Lucas prove that that statement is true (ie can Lucas prove that that statement cannot be proved true) If he cannot, then the machine is accurately simulating the mind of Lucas.
- Nicholas 21 July 99 Nearly ... but the sentence is "[Machine] cannot..." not "Lucas cannot..." and Lucas is in no different a position than any other logician.
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