Date: Mon, 30 Aug 1999 14:21:32 -0600 (MDT) Subject: BHA: RE: In which kind of world is probability theory useful?Marsh, thank you for your additional examples. I did try to go the reductionist route: instead of postulating the existence of irreducibly probabilistic generative mechanisms, I tried to see how far one gets explaining random outcomes by leakages from other layers of reality in a stratified world. You gave convincing examples that this is not always the case: quantum mechanics is apparently irreducibly probabilistic, and also thermodynamics cannot be reduced to the mechanics of lots of molecules, since the laws of mechanics are reversible in time, but those of thermodynamics are not. I doubt that quantum mechanics can be seen in part as epistemic uncertainty. One such interpretation, according to which there are "hidden variables" which we don't know about, can be refuted by the a simple mathematical theorem which shows that even pure states in quantum mechanics, which are not mixtures of other states, are subject to Heisenberg's uncertainty relation, according to which either location or impulse can be sharp, but not both. Hans E. --- from list bhaskar-AT-lists.village.virginia.edu ---