tag:blogger.com,1999:blog-5944248932558389199.post3781561691050820820..comments2024-02-15T19:40:29.872-08:00Comments on neopolitan's philosophical blog: Marilyn's Six Gamesneopolitanhttp://www.blogger.com/profile/02501854905476808648noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-5944248932558389199.post-6482377600954906072015-03-14T09:03:50.827-07:002015-03-14T09:03:50.827-07:00It does not boil down to the belief in ontic struc...It does not boil down to the belief in ontic structural realism. I could be an ontic structural realist and still hold that using proper empirical methods and mathematical descriptions, we would be able to describe the relationship between the goat and the door such that we could say which door the goat was behind, 100%. Of course this would be breaking the rules imposed by the Monty Hall situation, which limits our knowledge. But a complete description of the situation, even under a structuralist viewpoint, would not yield probabilities such as 2/3 or 1/2. <br /><br />-BAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5944248932558389199.post-32608273499952885742015-03-11T21:46:10.029-07:002015-03-11T21:46:10.029-07:00Anonymous I guess that boils down to whether you t...Anonymous I guess that boils down to whether you take ontic structural realism seriously or not. I do.<br /><br />Something to throw a spanner in the works here, is that in Monty Fall the contestants chances are NOT 50/50. T hey only become 50/50 if Monty can fall on the door with a car and not only the goat door. Here is a paper which outlines the issue;https://www.ffri.hr/phil/casopis/abstracts/9_2_3.pdf<br /><br />And simulations confirm this.KaySennoreply@blogger.comtag:blogger.com,1999:blog-5944248932558389199.post-91322652472395188122015-03-11T10:16:14.611-07:002015-03-11T10:16:14.611-07:00I think that you misrepresent probability when you...I think that you misrepresent probability when you speak of information "in the world" versus information in the mind. Quantum mechanics aside, in the world, the goat is completely behind one of the doors, 100%. The only reason that we come to a probability of 2/3 and so on is because we have limited information. If we had a viewpoint "from the world," we would know which door the goat was behind, collapsing the probability to 100%. But, as you suggest, in the reverse Monty, the opening of the door adds no new information to our point of view, and so the probability remains at 2/3.<br />But probability is entirely dependent upon the information we have, not upon the information "in the world."<br /><br />-BAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-5944248932558389199.post-87638729989585323192015-03-07T16:37:15.537-08:002015-03-07T16:37:15.537-08:00So I put the question up as to why we intuitively ...So I put the question up as to why we intuitively fail in the MHP in an analytical philosophy group. The conclusion I reached was that we fail to shift perspective from ourselves to the other side where the two doors after a choice should be treated as 1 item giving a 2/3 probability on the other side.KaySennoreply@blogger.comtag:blogger.com,1999:blog-5944248932558389199.post-11838748652376249472015-03-07T15:36:37.735-08:002015-03-07T15:36:37.735-08:00You've identified an intensely irritating typo...You've identified an intensely irritating typo (subsequently fixed). It's not really English, in so much as it's grammatically incorrect and it should read "However, prior events do not always affect the present."<br /><br />Note that the structure as written was ambiguous, so I disagree that it was not true for events that are not independent - that would only be the case if I had written "prior events always do not affect the present" - which is not a true statement, because there are prior events that do affect the present. Mathematical formalism might be significantly more important to you than for me because you have a higher tolerance for grammatically incorrect and thus ambiguous phrasing in English. And don't get me started on "All oils are not the same". If you think that this is a fine and dandy sentence, then please consider "All people who call themselves mathematicians are not intelligent". <br /><br />That all said, and correcting what you wrote to account for the typo, you are saying that it is true that not all prior events affect the present (because independent event ones don't affect each other - including simultaneous events, if that was your point) but in this case we don't have independent events, therefore conditional probability. Agreed, but I do think that there is something else going on in there - as exemplified by the dice and the Monty Falls variant.<br /><br />I went back to see who it was who said that conditional probability didn't apply, it was a user called <a href="http://www.reddit.com/r/math/comments/2wd66m/the_reverse_monty_hall_problem_and_conditional/coprwxl" rel="nofollow">/u/chrox,</a> and it was only that one person. For some reason, this took on a much larger significance than it should have, but I do note that no-one corrected the user and I interpreted some of the later comments as saying "you, neopolitan, only think that conditional probability applies because you don't understand conditional probability", which of course led to irritation that when you, Mathematician, suggested that I read up on it. I know that conditional probability applies, which you now confirm, but I was being told by a few people (I thought) that it didn't. It was an example of "tunnel vision", I suspect.neopolitanhttps://www.blogger.com/profile/02501854905476808648noreply@blogger.comtag:blogger.com,1999:blog-5944248932558389199.post-77777536155706268442015-03-07T14:36:55.900-08:002015-03-07T14:36:55.900-08:00One philosophical problem us mere humans face is t...One philosophical problem us mere humans face is that mathematics is able to describe reality where ordinary language fails. Specifically I am referring to QM. The Monty Hall problem may just give us a glance into what is our cognition doing wrong.KaySennoreply@blogger.comtag:blogger.com,1999:blog-5944248932558389199.post-54580349831034014072015-03-07T14:27:45.907-08:002015-03-07T14:27:45.907-08:00It is interesting that intuitively we believe that...It is interesting that intuitively we believe that when a door is eliminated that a new state of affairs is created where we now have 50/50 chance of having the car behind our door. Logically it makes no sense to think this because after the contestant picked a door, no matter what, there was a goat remaining behind one of the other two doors, so eliminating a goat makes no difference at all to the original position. Logically, nothing at all has changed by knowing which of the two remaining door has a goat, yet for some reason we think it has. The information has not changed in the world, but information has changed in the brain because now we know something additional; which other door has the goat. It is a mistake in thinking that what we know has consequences in the world.KaySennoreply@blogger.comtag:blogger.com,1999:blog-5944248932558389199.post-35741133441723962522015-03-07T10:18:18.943-08:002015-03-07T10:18:18.943-08:00I know that you are already convinced that your ar...I know that you are already convinced that your argument is wrong (and that I said that I wouldn't post anymore), but it seems important to emphasize where exactly I think you were fundamentally wrong (not only for you but for other readers as well). <br /><br />This sentence is the key to your misunderstanding :<br /><br />> However, prior events do always not affect the present.<br /><br />First, this is an english sentence, not a mathematical one. The reason formalism and proofs are useful is to avoid using these kind of "obvious" statements that are, in fact, not logically correct. <br /><br />As I already said, this sentence is perfectly true for independent events. Like in your "tossing a fair coin and getting seven heads in a row" argument. The eighth throw is independent from the first seven ones, so that the probability for the eight throw being heads is 1/2, whatever were the first seven results. The definition of independence is almost exactly saying that the past does not affect the present (it's even more general than that, but anyway ...)<br /><br /><br />But then, your sentence is not true anymore for events that are not independent ! That's exactly why conditional probabilities are introduced !! Otherwise, if your sentence were always true, the definition of conditional probability would be completely useless. (By the way, you kept repeating that someone said that conditional probability did not apply to this scenario. I don't know who said that, but it is nonsense. You can "apply" conditional probabilities to all the situations you want ! And especially here you have to do it) <br /><br />So, the opening of the red door is not independent from the other variables of the game (placement of cars, choice by the contestant). Hence, to compute the wanted likelihood of winning by staying, you use the formula for conditional probability : the probability that (the car is behind the Green door knowing that the contestant chose Red&Green and the host opened Red), is equal to the probability that (all of these three events take place (1/9)) divided by the probability that (the contestant chose Red&Green and the host opened Red (1/6)).<br /><br />A priori, there is no reason to believe that this computation could be simplified ! (and even then, it is often better to do the computation with all possible details if you want to be sure that you are not oversimplifying). So you just compute the answer, and you find P = (1/9)/(1/6) = 2/3.Mathematiciannoreply@blogger.com