tag:blogger.com,1999:blog-3891434218564545511.post5995838106356352459..comments2017-09-22T02:22:36.140-05:00Comments on Alexander Pruss's Blog: Probabilities and Boolean operationsAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-3891434218564545511.post-7938840076032358032017-09-18T13:51:28.734-05:002017-09-18T13:51:28.734-05:00I wasn't aware of this problem.I wasn't aware of this problem.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-62607371216285345872017-09-15T15:00:20.621-05:002017-09-15T15:00:20.621-05:00So-called ‘Dilation’ is a standard problem for int...So-called ‘Dilation’ is a standard problem for interval theories.<br /><br />Suppose, in the above setup, that you will be told after the event whether the coin landed heads or tails, but not whether A occurred. Before the event you will give A the sharp probability of 1/2. After the event, if you learn H, you will give A the interval probability of [0,1]. The same if you learn T. Either way, more evidence makes you less confident. And how does this relate to the Reflection Principle?<br /><br />I’m not sure what to make of this. It is discussed in the literature.IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-40505343934137837562017-09-14T15:34:54.646-05:002017-09-14T15:34:54.646-05:00That is a good point, and one that I had missed. I...That is a good point, and one that I had missed. It could apply equally to epistemic probabilities. I may think that C has an objective probability, but have no idea what it is. Or I may have no idea at all about the probability of C, and no interest in it. All that matters is that C is independent of coin flip.IanShttps://www.blogger.com/profile/00111583711680190175noreply@blogger.com