[QUOTE=enigm4tic]
how so, the third computer still has to solve an infinitely recurring problem, I don’t see how it can do so any better than the computer that’s directly attempting to solve the problem. I fail to see how using a third computer to solve an infinite problem makes it less infinite
[/QUOTE]
Computer B can look at Computer A together with Joe-Bob, and predict, “Computer A will go into a recursive loop and will be unable to make a prediciton. Joe-Bob, having seen no prediction either way, will do the following: X”
Do you want to let Joe-Bob see Computer B’s reports? No problem. Computer B will now no longer to make reports, but some computer D could look at all of this and come up with a report.
Your argument doesn’t show that the will is non-deterministic. Rather, it shows that a given computer can not predict the actions of a person if that person is allowed to see that computer’s reports.
Think of the following situation. You have a marble rolling, you have a person, and you have a weight. You have a table, and on the table are two squares. The person is instructed, “If you believe the marble will continue rolling to the edge of the table, put the weight on square A. If you believe otherwise, put it on square B.” The catch is, square A is directly in the path of the marble: putting a weight on it will block the marble, preventing it from rolling to the edge of the table.
You see where that’s going, I’m sure. We don’t want to attribute magical non-deterministic powers to the marble on the basis of the fact that the person with the weight can not successfully express his prediction given the constraints he has been saddled with, do we? Of course not. What we say, as third person observers, is that the person in the scenario has been rendered unable to successfully deliver any prediction. We also know the ball will continue on its determined way and roll to the edge of the table.
Of course, the person can say “I refuse to place a weight, since by doing so I would falsify whatever prediction I would thereby make.” But that is for the person to refuse to enter causally into the marble’s trajectory. The machine in your thought experiment is stipulated to be such that if it does make a prediction, then it does enter into the person’s causal trajectory.
I believe there is probably a connection to be made here between the kind of situation we’re looking at on the one hand, and incompleteness in mathematics and logic. But I am not sure, and maybe I shouldn’t have begin to crack open that can of worms. But the parallel would be: Just because a system can’t prove such and such theorem about itself, doesn’t mean the theorem isn’t true and proveable by some other system. Similarly, just because a person’s actions can’t be predicted by one particular system, doesn’t mean it couldn’t be predicted by some other system.
-FrL-