Thinking about it a bit more, it seems like their argument lets us generate a strange argument about geometry. Say that one space is the union of a sequence of other spaces. If these other spaces have the feature that most points in them are near the boundary, then the union must also have this feature. This argument ignores the question of whether the union even has a boundary, and they seem to claim that it lets us infer that the union does have a boundary. Which is obviously false in many cases.
So their semantics for probability must be messed up.
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timeasmymeasure
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Date: 2010-09-29 11:34 pm (UTC)So their semantics for probability must be messed up.