tag:blogger.com,1999:blog-3891434218564545511.post1230549181431026028..comments2024-03-27T20:37:09.185-05:00Comments on Alexander Pruss's Blog: Objective probabilitiesAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-3891434218564545511.post-62618943971535856002009-05-09T16:42:00.000-05:002009-05-09T16:42:00.000-05:00How about we choose a maximal set of worlds with t...How about we choose a maximal set of worlds with the properties that (a) every possible proposition expressible in L is true at some world in the set, and (b) for every world in the set there is a sentence that is true at precisely that world? I guess we need a postulate that a maximal such set exists.<br /><br />Of course, the maximal set need not be unique. So we may need to allow some indeterminacy in the probabilities. Perhaps then we replace restrictive normative claims like "x should believe p only if p has probability at least q" with quantified claims like "x should believe p only if for every maximal set of worlds, p has probability at least q relative to that set", and permissive normative claims use existential quantification.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-63117611093993938212009-05-09T15:15:00.000-05:002009-05-09T15:15:00.000-05:00I recall us talking about this in less formal term...I recall us talking about this in less formal terms before. I still have to try to get my head fully around 6, but the two things which first struck me to ask were whether there is a problem about *what* set of worlds W is and whether you are open to any charges of smuggling in a principle of Indifference into 6--"equal likelihood." I ask the latter question not because it seems to me that it does, but only because, as a friend of Indifference, I have noticed that its foes accuse people of smuggling it in all the time, and seem to believe that all attempts at objective probability are bound to smuggle it in somewhere.<br /><br />Regarding the former worry, I worry that relativising to non-maximal sets of worlds will be open to the same objections as raised against Carnap for relativising to languages. And of course there are the usual problems with maximal sets.<br /><br />I don't say these problems can't be addressed satisfactorally, only that they are what struck me on first read, based on the kinds of objections I regularly encounter in the literature and in conversation.Trent Doughertyhttps://www.blogger.com/profile/01419566472393605963noreply@blogger.com