Hofstader's magnus opus Goedel, Escher, Bach.
Fret not that this will somehow prove that humans are nothing more than sophisticated computers. Kurt Godel proved otherwise in 1931 with his paper "On Formally Undecidable Propositions of Principia Mathematica and Related Systems".
Godel proved that there are things we know are true, but cannot be arrived at given a starting set of rules like a computer program.
Ernest Nagel in his 1958 book "Godel's Proof" correctly concludes this, "Godel's conclusions bear on the question whether a calculating machine can be constructed that would match the human brain in mathematical intelligence...the brain appears to embody a structure of rules of operation which is far more powerful than the structure of currently conceived artifical machines. There is no immediate prospect of replacing the human mind by robots."
Godel's proof is a killer logical problem for atheists like Hofstader who want to reduce man to nothing more than a sophisticated machine. It's mathematically proven that our thinking brains are outside the system. Hofstader trys to get around Godel's proof by suggesting that machines can change their own logical set of rules they function by. The end result is Hofstader spiriling down to nowhere in his book "Godel, Escher, Bach".
Force = Mass * Accelleration is just an assignment huh?
I founded the NASA KSC AI lab in '86, do you LisP?
CAR CDR
I would not use the mathematics of 1958 as the basis for an opinion on sophisticated computing theory. We've come a long way since then, and his objections have been proven to be obsolete in the interim, particularly in the last decade. The human mind has the same fundamental limitations as computers by all available metrics and mathematics.
I don't know what this means, but this is NOT mathematically correct. I'm not sure where you got this idea but it wasn't from a relevant field of mathematics.
Hofstader trys to get around Godel's proof by suggesting that machines can change their own logical set of rules they function by.
You must have read a different version of GEB than the rest of us. Your above statement doesn't even make sense. Lovely handle though.
It also makes an appearance in a really bizarre novel, Uncle Petros and Goldbach's Conjecture, by Apostolos Doxiadis.
No, he didn't.
What he did prove was that a sufficiently complex formal system can be either consistent, or complete, but not both at the same time.
This only "proves" that computers can't do what people can do if you're silly enough to claim that human minds are both complete (e.g. can logically solve all possible problems) *and* consistent (e.g. never self-contradictory).
If you truly believe that we are, I've got several bridges to sell you.
Since we *aren't* complete, and *aren't* consistent, there's no impediment for a computer to equal our less than perfect performance, and Godel's theorem does not apply.
Godel proved that there are things we know are true, but cannot be arrived at given a starting set of rules like a computer program.
Right -- nor can they be arrived at via logical deduction by humans, either, since logical deduction is itself a formal system.
We "know" them by taking something as a given because we choose to *believe* it to be true, not because we can prove that it is. A computer can do this as well -- accepting a proposition as a premise is easy for a computer.
Ernest Nagel in his 1958 book "Godel's Proof" correctly concludes this, "Godel's conclusions bear on the question whether a calculating machine can be constructed that would match the human brain in mathematical intelligence...the brain appears to embody a structure of rules of operation which is far more powerful than the structure of currently conceived artifical machines. There is no immediate prospect of replacing the human mind by robots."
What was correct about the "immediate prospect" of computer ability in *1958* is hardly the case now.
Godel's proof is a killer logical problem for atheists like Hofstader who want to reduce man to nothing more than a sophisticated machine.
You didn't actually *read* his book, did you? He does nothing of the sort.
It's mathematically proven that our thinking brains are outside the system.
No, it's only "mathematically proven" that our brains aren't consistent -- i.e., we don't operate on Spock-like pure logic. But then we knew that already. Humans do much of their work via intuition, leaps of faith, rules-of-thumb, believing what we wish were true, and so on.
And computer programs can be just as fuzzy-headed as humans when they're set up right. Computer programs can operate on presumption, illogical trial-and-error, etc.
Hofstader trys to get around Godel's proof by suggesting that machines can change their own logical set of rules they function by. The end result is Hofstader spiriling down to nowhere in his book "Godel, Escher, Bach".
You clearly didn't read "Godel, Escher, Bach", or if you did you didn't understand it -- nor are you really clear on what Godel did and did not say. Try again.