19/06/08 18:37:36.38 e2T0R87W.net
>>298
つづき
Bas van Fraassen has produced a compelling paradox arising from this principle.2 Here I’ll quote Aidan Lyon’s discussion in his 2010 paper “Philosophy of Probability” (published as a chapter in Philosophies of the Sciences: A Guide):
Consider a factory that produces cubic boxes with edge lengths anywhere between (but not including) 0 and 1 meter,
and consider two possible events:
(a) the next box has an edge length between 0 and 1/2 meters or
(b) it has an edge length between 1/2 and 1 meters.
Given these considerations, there is no reason to think either (a) or (b) is more likely than the other,
so by the Principle of Indifference we ought to assign them equal probability: 1/2 each.
Now consider the following four events:
(i) the next box has a face area between 0 and 1/4 square meters;
(ii) it has a face area between 1/4 and 1/2 square meters;
(iii) it has a face area between 1/2 and 3/4 square meters;
or
(iv) it has a face area between 3/4 and 1 square meters.
It seems we have no reason to suppose any of these four events to be more probable than any other, so by the Principle of Indifference we ought to assign them all equal probability: 1/4 each.
But this is in conflict with our earlier assignment, for (a) and (i) are different descriptions of the same event (a length of 1/2 meters corresponds to an area of 1/4 square meters).
So the probability assignment that the Principle of Indifference tells us to assign depends on how we describe the box factory: we get one assignment for the “side length” description, and another for the “face area” description.
(引用終り)