Zach and Anonymous commented on my last post on the paradox of the unexpected hanging. While their thinking is interesting, I doubt that they are on the right track toward a solution. Let me present an alternative version of the paradox (also drawn from Martin Gardner's article) and challenge them to see if their attempt at a solution applies to this form.
So a man is presented with ten boxes, each one numbered and all empty except for one, which contains an egg. He is told to open each box in sequence. He is also told that he will not know before opening the box that contains the egg that it contains the egg. So once again, the same reasoning applies. The egg cannot be in box 10 because if the man opens box 9 without having discovered the egg, he will know that it is in box 10. Elimination of the other boxes proceeds as before.
Maybe this less sinister and more basic formulation of the paradox will help in their search for a solution.
Tuesday, November 3, 2009
The Paradox of the Unexpected Hanging, Part II
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2 comments:
You are saying that it is a paradox because he is told that he will not know if the egg is in the box or not. That statement is not a contradiction. It has an aspect of falsity (He will know it is in the last box if it is in the last box), but there is not the aspect of truth in the statement. As he opens more boxes, the probability of finding the egg increases: f(b)= 1/(10-b), where 'b' is the number of boxes he opens. This is a true statement. The statement 'he will not know before opening the box that contains the egg that it contains the egg' is simply false. Rather, 'he will not know before opening A BOX IF it contains the egg OR NOT.'
Dear Julianknight,
The contradiction is that an argument seems to lead to the conclusion that no matter what box the egg is in, the man must know before he opens the box that the egg is in that box, but in reality it is possible for him to be surprised. The conclusion of the argument contradicts what we know to be true from reality. In that regard, it is like Zeno's paradoxes, which appear to show that motion and change are impossible, a result that contradicts what we know from perception.
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