tag:blogger.com,1999:blog-9451012.post114115515978534694..comments2023-05-20T07:50:15.676-04:00Comments on Running with a pencil: Just flip a coinDianahttp://www.blogger.com/profile/07847331467246659997noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-9451012.post-1141256902283909552006-03-01T18:48:00.000-05:002006-03-01T18:48:00.000-05:00Thank you for your carefully considered comment. I...Thank you for your carefully considered comment. I really appreciate it. I didn't realize that so many philosophers were working on this.<BR/><BR/>One thing I didn't mention is that the key thing here is that the original 50% -- "if I flip this coin, what are the probability it will be heads?" -- is based on long-run probability. <BR/><BR/>So you're right, the basic question of what the statement means is an important one. Usually, it means the long-run probability: If I flipped this coin many times, what is the fraction of the time it would come up heads? The long-run probability has no applicability, though, to something that has already occurred.<BR/><BR/>Philosophers may be working on the theoretical aspects, but I think mathematicians are done with it. Of course, this isn't really a question of mathematics, but of statistics. It has to do with whether you believe in <A HREF="http://en.wikipedia.org/wiki/Bayesian_probability" REL="nofollow">Bayesian probability</A>, which is a frequentist framework, or not.<BR/><BR/>If I run into Professor Gerrard, I might just ask him about this. Thanks for the reference.Dianahttps://www.blogger.com/profile/07847331467246659997noreply@blogger.comtag:blogger.com,1999:blog-9451012.post-1141250927615342652006-03-01T17:08:00.000-05:002006-03-01T17:08:00.000-05:00You're touching on an area of analytic philosophy ...You're touching on an area of analytic philosophy that legions of philosophers are working on. (Well, probably a couple dozen, but given the number of philosophers, that qualifies as "legions".)<BR/><BR/>The basic question is "What does the statement 'X has a p% chance of happening' mean?"<BR/><BR/>Does it say something about the results of an implied experiment? (such as flipping a coin?) - this would be an OBJECTIVE interpretation of probabilistic statements.<BR/><BR/>But the problem with that is that we use probabilistic statements in many situations when experiments are impossible or even nonsensical.<BR/><BR/>Perhaps instead a probabilistic statement says something about the speaker's confidence in the statement? - this would be a SUBJECTIVE interpretation of probabilistic statements.<BR/><BR/>There are of course problems with this way of thinking also, since the probability of a coin turning up heads doesn't depend on what I think!<BR/><BR/>Really interested? This comment comes pretty close to exhausting what I know about this subject. Talk to Prof. Gerrard, who isn't an expert on this either, but i'm sure knows more than me.Anonymousnoreply@blogger.com