Comments on: The Principal Principle http://antimeta.wordpress.com/2007/08/03/the-principal-principle/ A general distrust of strong metaphysical claims in mathematics and philosophy. Tue, 14 Jul 2009 21:45:18 +0000 http://wordpress.com/ hourly 1 By: rabriggs http://antimeta.wordpress.com/2007/08/03/the-principal-principle/#comment-2297 rabriggs Fri, 14 Sep 2007 15:09:40 +0000 http://antimeta.wordpress.com/2007/08/03/the-principal-principle/#comment-2297 I don't think the deterministic case is quite as bad as it seems. Suppose I believe (or suspect) that the chance of a roulette wheel's landing on red is 1/2. I then learn that the wheel is being spun by an enthusiastic croupier. I've ruled out some worlds in which the chance of the roulette wheel's landing on red is 1/2 (namely, those worlds in which its chance of landing on red is 1/2 and it is spun by an enthusiastic croupier). This does not mean that I have inadmissible information, because general propositions about the cropier's level of enthusiasm don't tell you anything about how the wheel will land, conditional on propositions about the (non-fundamental) chances. Your credence function screens the croupier-enthusiasm propositions off from the chance propositions. Ideally, the believer in non-fundamental chances should have a story about why your credence function ought to screen croupier-enthusiasm propositions off from chance propositions. Michael Strevens seems to have such a story: very abstractly, the idea is that every set of worlds where the roulette wheel lands on black can be matched with a very similar set of worlds with the same measure where the roulette wheel lands on red, and that this still holds true if you restrict yourself to worlds with enthusiastic croupiers. I don’t think the deterministic case is quite as bad as it seems. Suppose I believe (or suspect) that the chance of a roulette wheel’s landing on red is 1/2. I then learn that the wheel is being spun by an enthusiastic croupier. I’ve ruled out some worlds in which the chance of the roulette wheel’s landing on red is 1/2 (namely, those worlds in which its chance of landing on red is 1/2 and it is spun by an enthusiastic croupier). This does not mean that I have inadmissible information, because general propositions about the cropier’s level of enthusiasm don’t tell you anything about how the wheel will land, conditional on propositions about the (non-fundamental) chances. Your credence function screens the croupier-enthusiasm propositions off from the chance propositions.

Ideally, the believer in non-fundamental chances should have a story about why your credence function ought to screen croupier-enthusiasm propositions off from chance propositions. Michael Strevens seems to have such a story: very abstractly, the idea is that every set of worlds where the roulette wheel lands on black can be matched with a very similar set of worlds with the same measure where the roulette wheel lands on red, and that this still holds true if you restrict yourself to worlds with enthusiastic croupiers.

]]> By: Sridhar http://antimeta.wordpress.com/2007/08/03/the-principal-principle/#comment-1925 Sridhar Fri, 03 Aug 2007 21:17:12 +0000 http://antimeta.wordpress.com/2007/08/03/the-principal-principle/#comment-1925 In terms of the first view, one needn't restrict it in a temporally asymmetric way. Just as there may be no fact of the matter about future chancy events, the same could hold of past chancy events as well; the status of "Tomorrow's coin flip will come up heads" could be entirely analogous to the status of "The bit which was written on this paper until being erased yesterday (with all traces of its particular value removed) was a 1". For that matter, there may be no fact of the matter about present chancy events either (say, "The bit which is written on the paper locked away right now in this box..."). The chanciness of an event could be entirely orthogonal to its temporal status, the attribution of "there is a fact of the matter" status to propositions occurring on some unrelated (or, at least, not necessarily related) basis. In terms of the first view, one needn’t restrict it in a temporally asymmetric way. Just as there may be no fact of the matter about future chancy events, the same could hold of past chancy events as well; the status of “Tomorrow’s coin flip will come up heads” could be entirely analogous to the status of “The bit which was written on this paper until being erased yesterday (with all traces of its particular value removed) was a 1″.

For that matter, there may be no fact of the matter about present chancy events either (say, “The bit which is written on the paper locked away right now in this box…”). The chanciness of an event could be entirely orthogonal to its temporal status, the attribution of “there is a fact of the matter” status to propositions occurring on some unrelated (or, at least, not necessarily related) basis.

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