Gödelsoft - the ultimate expert system.
HEAD OF MARKETING: Introducing Gödelsoft - the ultimate expert system. All the mathematical, logical and algorithmic expertise of one of the world's greatest mathematicians has been copied from his brain and uploaded to CD. This software can solve all the mathematical, logical and programming problems that Professor Gödel himself can solve . And it is guaranteed to be totally infallible. So all you software houses out there can fire those overpaid programmers and save yourselves a fortune.
Cheers and rapturous applause from audience.
HEAD OF MARKETING: And here with us we have Professor Gödel in person. He's still in full command of all his mathematical abilities because the neuroimaging technology we used to extract the knowledge from his brain employs a non-destructive reading scan. Now Professor, I'd like you to ask Gödelsoft the most difficult question you can think of...
PROF GÖDEL: Gödelsoft will never say that this sentence is true. Is this true or false?
Gödelsoft goes catatonic. The computer locks up. The audience grows restless, starts muttering, and eventually drifts away to the bar.
So what went wrong?
If Gödelsoft were to output the statement that the sentence is true, it would have made the sentence false. This it cannot do, because being the ultimate infallible logic processor it cannot produce false statements.
If Gödelsoft were to state that the sentence is false, it can only do so after issuing the statement that the sentence is true, which is of course false.
Consequently Gödelsoft can do nothing.
Therefore we and Professor Gödel know that the statement 'Gödelsoft will never say that this sentence is true' is in fact true. Which means that Professor Gödel knows more than his entire knowledge uploaded onto a machine. So Professor Gödel's mind can do something that the Gödel emulator cannot do. Hence Professor Gödel's mind is something more than a machine.
The knower's entire body of knowledge, even when implemented on the most powerful computer, is not functionally equivalent to the knower's mind. Gödel's mathematical knowledge can only exist as objects which must have algorithmic form, whereas Gödel's mind is clear and formless and has the power to know those objects. A similar argument applies to qualia, where the total of all the incoming information is not the same as what is known. Likewise, Buddhist philosophers would argue that the 'mother of all algorithms', which must exist in every programmer's mind, is itself not an algorithm - see the section on artificial intelligence.
Minds, Machines and Mathematics - David J. Chalmers
- Sean Robsville
If we regard Buddhism as a combination of a philosophy, psychology and religion, then how much mileage can we get from the first two aspects before we have to start invoking religious faith?
Christian versus Buddhist worldviews