tag:blogger.com,1999:blog-3891434218564545511.post8398000585610175140..comments2021-05-15T08:44:54.382-05:00Comments on Alexander Pruss's Blog: An approach to the Sleeping Beauty problemAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3891434218564545511.post-49042133365155705192014-03-10T01:13:26.008-05:002014-03-10T01:13:26.008-05:00Are you missing out on a great skin and hair care ...Are you missing out on a great skin and hair care solution? Then Argan oil is the perfect personal care product for you. <a href="http://www.puradoroil.com/" rel="nofollow">Organic Argan Oil</a> can supply pure argan oil for you.Helen Evanshttps://www.blogger.com/profile/06732540681774111328noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-64568020416803390342013-05-21T22:40:59.509-05:002013-05-21T22:40:59.509-05:00This comment has been removed by the author.f|35hhttps://www.blogger.com/profile/17034266507564709709noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-72256717347148580912008-02-22T11:17:00.000-06:002008-02-22T11:17:00.000-06:00Here's an argument that 1/3 is the credence in my ...Here's an argument that 1/3 is the credence in my Experiment 2. In Sleeping Beauty cases, the only two plausible credences are 1/2 and 1/3. Now, let's suppose you are in Experiment 2. You wake up. Before you open your eyes, however, you think about your credence. It's clearly 1/2. You open your eyes and see a red flag. Clearly this is evidence--you might have seen a white flag instead. It would be absurd to say that your credence should remain the same upon seeing the red flag. <BR/><BR/>Here's a more rigorous argument. If you were to see a white flag after opening your eyes, that would change your credence in heads to 1. But:<BR/><BR/>Theorem: If P(H|E)=1 and 0 < P(E) and 0 < P(H), then P(H|~E)< P(H).<BR/><BR/>So, not seeing a white flag after opening the eyes must decrease your credence (since 0 < P(white flag) and 0 < P(heads)).<BR/><BR/>Hence, after seeing the white flag, one's credence has to be less than 1/2.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-678582688925671352008-02-18T07:47:00.000-06:002008-02-18T07:47:00.000-06:00Hi Alexander,I think the problem with this puzzle ...Hi Alexander,<BR/><BR/>I think the problem with this puzzle is the ambiguity over what the sleeper is trying to do. Here are two versions of the problem using money:<BR/><BR/>Version 1 - A fair coin is flipped on Sunday, without you seeing the result, and then you go to sleep.<BR/>Tails: You get woken up Monday and Tuesday and each time you are given one pound. Your memory is erased each time, and you don't know whether it's Monday or Tuesday when you wake up.<BR/>Heads: You get woken up Monday and you are given one pound.<BR/><BR/>Version 2 - A fair coin is flipped on Sunday, without you seeing the result, and then you go to sleep.<BR/>Tails: You get woken up Monday and Tuesday and each time you are asked if the coin came up heads or tails; if you get it right you get a pound, if not, you get nothing. Your memory is erased each time, and you don't know whether it's Monday or Tuesday when you wake up.<BR/>Heads: You get woken up Monday and you are asked if the coin came up heads or tails; if you get it right you get a pound, if not, you get nothing.<BR/><BR/>In version 1 you get the money whatever you say. The probability you should assign to the coin being tails is the same as the probability you should assign to you winning one pound instead of two. This is clearly 1/2.<BR/><BR/>In version 2 you only get the money if you utter a truth. In this case it is clearly preferable to say it was tails because that will get you more money, but it won't change the probability.<BR/><BR/>In the original problem, when you are woken up you should assign a probability of 1/2 to both heads and tails. However, if you wish tomake more true utterances that you should always say tails.Anonymousnoreply@blogger.com