tag:blogger.com,1999:blog-3891434218564545511.post5069731772617530160..comments2024-03-28T13:23:50.623-05:00Comments on Alexander Pruss's Blog: Probabilities of propositions and beliefsAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-3891434218564545511.post-87650813825426878192010-10-02T04:17:42.016-05:002010-10-02T04:17:42.016-05:00There may be other problems with (1) too, e.g. do ...There may be other problems with (1) too, e.g. do you mean by 'belief' to include beliefs that we never express or even explicitly hold? Suppose you walk into a busy room, see someone and start up a conversation. Do you believe that the roof is there? You probably didn't notice that it was, but let us say that you did believe that it was there.<br /><br />Then such beliefs form an infinite set, and the notion of randomness becomes messy. E.g. for each true belief there are lots of false ones. Furthermore, even with beliefs expressible in few words that may well be true. We are of course careful in what we say, but therefore I think that the plausibility of (1) may rely on an implicit confusion of the beliefs we are likely to express with the beliefs that we actually hold.<br /><br />For just one example, I see a green tree and so I believe that it's green. But at the same time I believe that it's that colour sensation I have, that I call 'green', that is out there, the colour of the tree. And the latter is false, I think (I've been thinking about this recently, in my <a href="http://enigmanically.blogspot.com/2010/09/putting-green-back-in-greenery.html" rel="nofollow">Putting the green back in the greenery</a>:) Now, I also believe that that's a false belief, but that just makes my total belief-set inconsistent.<br /><br />I try to address that problem when I say things, by being careful in my expressions, but the problem of perception is so innate that I can hardly make it go away just by knowing that there is a problem. And of course, if our belief-sets are inconsistent, then there are a lot of false propositions that we would be inclined to agree with (more than we would think). So in short, I suspect that denying (1) is not necessarily overly pessimistic.Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-36664090026064208592010-09-30T12:59:44.273-05:002010-09-30T12:59:44.273-05:00The fact that someone ever believed p is evidence ...The fact that someone ever believed p is evidence for p. I hadn't thought about stopping. We want to distinguish between forgetting and changing one's mind. Forgetting shouldn't affect the evidence. But if she changes her mind, that cancels out the initial evidence if she moves from belief to suspension of judgment, and makes for evidence for the negation if she moves from belief to disbelief.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-83933835073518550632010-09-30T11:41:04.377-05:002010-09-30T11:41:04.377-05:00Here's a few thoughts.
1. It looks like we ca...Here's a few thoughts.<br /><br />1. It looks like we can weaken your (1) quite a bit without damaging your conclusion, provided that the probability in (1) is still higher than the probability in (3). That means the argument is relatively robust.<br /><br />2. If someone believes p, your argument says that I now have evidence for p. But suppose the person stops believing p. It looks like I may have lost my evidence for p (or at least the contribution to that evidence from the person's former belief in p). This seems strange. <br /><br />To avoid this, maybe (1) doesn't have to be about present beliefs, but also about past or future beliefs. This might introduce too much instability.<br /><br />We could also revise (1) to concern what could or would be believed. This is a common move in the epistemology of disagreement, I think-- what matters can't just be the actual distribution of opinion, otherwise part of your evidence for theism would vanish if all the theists vanished.<br /><br />If we make this change, though, it's not as clear that (1) would be true, even on a weakened version. (1) wouldn't be true in evil demon worlds, for example.<br /><br />3. I wonder if there are reference class issues here. You argued that p's being believed raises the subjective probability of p, and that this means that there is now evidence for p. I wonder if the claim about evidence depends on restricting the reference class for the subjective probabilities to something like "positions you might take on Q," where Q is a question you might answer by believing p. <br /><br />Here's why this might matter: even if a randomly chosen believed proposition is at least as likely true as false, it doesn't follow that a randomly chosen believed proposition about the ontology of possible worlds, or the simplicity of God, is at least as likely true as false, since the reference classes are different.Matthttps://www.blogger.com/profile/01562649776374771198noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-33094561468177602442010-09-30T11:37:30.248-05:002010-09-30T11:37:30.248-05:00This comment has been removed by the author.Matthttps://www.blogger.com/profile/01562649776374771198noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-34278959151103640872010-09-30T11:10:01.855-05:002010-09-30T11:10:01.855-05:00People are naturally credulous, of course, not lea...People are naturally credulous, of course, not least because we are naturally inclined to be honest most of the time, and tend to be epistemically adequate. But we don't usually think about it; and is it not precisely when we have cause to think about it that the mere fact that someone holds a belief is <i>insignificant</i> evidence for its truth? (Nevertheless I like your post, which seems to me to be a neat argument for an important epistemological principle:)Martin Cookehttps://www.blogger.com/profile/11425491938517935179noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-87577668150744482982010-09-30T09:46:25.642-05:002010-09-30T09:46:25.642-05:00There are infinitely many propositions, so one can...There are infinitely many propositions, so one can group them in various ways. One way will group p with ~p, and so the numbers will be equal. But there are other ways of grouping, too.<br /><br />What I do is I randomly generate propositions. This random process favors shorter propositions (just as our belief processes do). So it favors p over ~p. And that leads to the result.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-10027109147641128132010-09-30T09:18:00.483-05:002010-09-30T09:18:00.483-05:00Surely there is a problem in the math?
I rememb...Surely there is a problem in the math? <br /><br />I remember a conversation with my logic prof in grad school. My intuitive sense was that there were more ways to be wrong than right. He pointed out that for every p there is a ~p, so there are just as many true propositions as false ones.<br /><br />Why doesn't that same fact apply here?Heath Whitehttps://www.blogger.com/profile/13535886546816778688noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-842867345780835352010-09-30T07:43:07.130-05:002010-09-30T07:43:07.130-05:00A little bit of fiddling shows that as long as we ...A little bit of fiddling shows that as long as we have at least two basic predicates, the random recursion that I use to generate sentences has probability 1 of converging.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.com