tag:blogger.com,1999:blog-3891434218564545511.post5692041313727147764..comments2024-03-27T20:37:09.185-05:00Comments on Alexander Pruss's Blog: Counting and chanceAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-3891434218564545511.post-10511625756089295112018-01-09T14:54:43.024-06:002018-01-09T14:54:43.024-06:00You should use all the (relevant) information you ...You should use all the (relevant) information you have. If there are relevant objective chances, use them. If there aren’t, you have to either give up or resort to controversial ‘counting’ principles like Indifference. ‘Counting’ and objective chance don’t compete: ‘counting’ is the fall-back option.<br /><br />Think about the following cases. (Case A) There is a finite number N of fair, objectively chancy, 6-sided dice. An angel starts by arbitrarily choosing a die (‘your die’). The angel tells you that he will roll all the dice and note the outcomes. If there are not exactly M sixes and N - M non-sixes he will roll all the dice again. He will do this until there are exactly M sixes and N – M non-sixes. The angel tells you that he has done what he said he would. What should be your credence that your die shows six? Ans: M/N. This may look like mere ‘counting’, but actually it can be calculated from the objective chances by Bayesian conditioning. (Case B) As above, but this time the dice are biased. The angel tells you that all the dice have the same bias, but does not reveal the relevant probabilities. Again, what should be your credence that your die shows six? Answer: M/N again. (Case C) As above, but all the dice are biased differently. This time, you can’t apply Bayes. If you want to say that the answer is M/N, you will have to invoke Indifference over that angel’s choice of ‘your die’.<br /><br />It is amusing and instructive to compare these cases with similar infinite ones…IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-90505481738090934602018-01-08T12:08:49.619-06:002018-01-08T12:08:49.619-06:00Maybe SSI and SSA both fail when there are countab...Maybe SSI and SSA both fail when there are countably infinitely many people you "could have been", because there's no uniform distribution over the integers. Maybe instead of denying them, you just say you need a more general theory to deal with scenarios where the set you are drawn from has no uniform distribution.avihttps://www.blogger.com/profile/02079243100582806530noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-24600220438852708262018-01-08T10:43:37.283-06:002018-01-08T10:43:37.283-06:00That's not a resolution. That's giving up....That's not a resolution. That's giving up. :-|Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-36246232496956939302018-01-08T10:29:04.587-06:002018-01-08T10:29:04.587-06:00I thought the resolution for this was that probabi...I thought the resolution for this was that probabilities aren't sensible with infinities?avihttps://www.blogger.com/profile/02079243100582806530noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-14932605401220002822018-01-08T09:25:01.354-06:002018-01-08T09:25:01.354-06:00This comment has been removed by the author.Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.com