The following description of Newcomb's Paradox is quoted from the book, Labyrinths of Reason by William Poundstone.
More information on the Newcomb's Paradox can be found at Dr. Craig's "DIVINE FOREKNOWLEDGE AND NEWCOMB'S PARADOX" and Dr. Kiekeben's "Newcomb's Paradox". If that just whets your appetite or you become really confused, then you might one to look at one or more books on the subject. The one that I recommend is: Paradoxes of Rationality and Cooperation, Edited by Richmond Campbell and Lanning Sowden, UBC Press, 1985.
Newcomb's ParadoxNewcomb's paradox goes like this: A psychic claims to have the ability to predict your thoughts and actions days in advance. Like most psychics, he does not claim total accuracy. He is right about 90 percent of the time. You have agreed to take part in an unusual test of the psychic's powers. A TV news program has provided the facilities and put up a large sum of money; all you have to do is abide by the conditions of the experiment. On a table in front of you are two boxes: A and B.
Box A contains a thousand-dollar bill. Box B either contains a million dollars or is empty. You cannot see inside it. Of your own free will (if there is such a thing), you must choose either to take box B only or to take both boxes. Those are the only options. The catch is this: Twenty-four hours ago, the psychic predicted what you would choose. He decided whether to put the million dollars in box B. If he predicted that you would take only box B, he put the million dollars in it. If he foresaw your taking both boxes, he left box B empty.
Personally, you don't care whether the psychic's powers are proven or discredited. Your only motive is leaving the experiment with as much money as possible. You are not so wealthy that money means nothing. The thousand dollars in box A is a lot of money to you. The million dollars is a fortune.
The conditions of the test have been and will be enforced scrupulously. You need entertain no doubts that box A contains the $1,000. Box B can contain only $1 million or nothing at all, based on the psychic's prediction. No one is trying to trick you on that score. A trusted friend was present at the time the psychic made his prediction, and made sure he obeyed the rules about putting the money in the boxes.
Just as certainly, you will be prevented from circumventing the rules. Armed guards will prevent nihilist acts like not taking any box. Nor can you cheat the psychic by basing your decision on something other than your own mental processes. You can't decide on the basis of a coin toss or whether the number of shares traded that day is odd or even. You have to analyze the situation and decide on the most profitable of the two options. Of course, the psychic has anticipated your analysis. What should you do-take both boxes or just B?
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