tag:blogger.com,1999:blog-4856596194106820549.post4879028905676623083..comments2022-08-22T19:56:26.776-05:00Comments on Ben Wallis’s counter-apologetics blog: Robin Collins' restricted principle of indifferenceBen Wallishttp://www.blogger.com/profile/00131358613835119782noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-4856596194106820549.post-56916500996676728422014-12-15T14:38:55.308-06:002014-12-15T14:38:55.308-06:00If I knew absolutely nothing about a coin (because...If I knew absolutely nothing about a coin (because it was, say, designed by space aliens) I'd consider that the probability of its landing heads is represented by the interval [0;1]. <br /><br />Most (albeit not all) SINGLE-VALUED Bayesians reason like this: <br /><br />1) If the relative frequency of heads is roughly 0.50 I consider it is as likely to land heads as tails. <br /><br />2)If I know absolutely nothing about this coin then I know it is as likely to land heads as odds. <br /><br />I think this is magical thinking in its purest form. I am not alone in that assessment.<br /><br />The late great philosopher of science Wesley Salmon (who was himself a Bayesian) wrote what follows. “Knowledge of probabilities is concrete knowledge about occurrences; otherwise it is uselfess for prediction and action. According to the principle of indifference, this kind of knowledge can result immediately from our ignorance of reasons to regard one occurrence as more probable as another. This is epistemological magic. Of course, there are ways of transforming ignorance into knowledge – by further investigation and the accumulation of more information. It is the same with all “magic”: to get the rabbit out of the hat you first have to put him in. The principle of indifference tries to perform “real magic”. “<br /><br />Colin believe that our utter ignorance allows us to make very precise predictions. <br /><br />It is disheartening that he doesn't seem to even realize the problem. <br /><br />I know it's an old post but I'd be delighted to learn your take on what I've just written. <br /><br />Cheers. :-)Marchttps://www.blogger.com/profile/07109994971710733825noreply@blogger.comtag:blogger.com,1999:blog-4856596194106820549.post-23001437058597280632011-12-29T09:19:07.534-06:002011-12-29T09:19:07.534-06:00Ok, so I see how you arrive at a contradiction:
LP...Ok, so I see how you arrive at a contradiction:<br />LPU given NSU is possible.<br />LPU given NSU is impossible.<br /><br />But now I'm not sure how you see this as a problem. If the range of possible universes is large but finite, P(LPU|NSU) will be small but greater then zero. If the range is infinite, the probability is zero. So our judgement of the probability will depend on whether we think the range of possible universes in infinite or finite. But we need not hold both at the same time, so no one is forced to accept the two contradictory statements.<br />All Collins needs for his argument is for the P(LPU|NSU) to be much smaller then P(LPU|T). Whether the value is a small non-zero number or just zero, it would still confirm theism over naturalism.brian_ghttps://www.blogger.com/profile/12019153272635659263noreply@blogger.comtag:blogger.com,1999:blog-4856596194106820549.post-11494261417438153222011-12-28T12:19:43.811-06:002011-12-28T12:19:43.811-06:00brian_g,
Well the entire argument (4)-(6) as well...brian_g,<br /><br />Well the entire argument (4)-(6) as well as the discussion thereof takes place under the NSU assumption. So in (4) the bit about "given NSU" should be interpreted as a parenthetical, i.e. given NSU,<br /><br />(4) the probability of LPU is zero,<br /><br />and given NSU,<br /><br />(5) LPU is impossible.<br /><br />and given NSU,<br /><br />(6) there are possible values of the parameter space for which LPU is possible.<br /><br />But this means that given NSU, LPU is possible. Contradiction.<br /><br />--BenBen Wallishttps://www.blogger.com/profile/00131358613835119782noreply@blogger.comtag:blogger.com,1999:blog-4856596194106820549.post-26686228264020791852011-12-28T12:03:17.445-06:002011-12-28T12:03:17.445-06:00Sorry, I messed up your numbering. I added premis...Sorry, I messed up your numbering. I added premise (6) and you already had a premise (6).brian_ghttps://www.blogger.com/profile/12019153272635659263noreply@blogger.comtag:blogger.com,1999:blog-4856596194106820549.post-90560073975958623942011-12-28T12:01:37.708-06:002011-12-28T12:01:37.708-06:00Thanks for the quick reply. Although, I'm not...Thanks for the quick reply. Although, I'm not sure I understand. Consider your argument:<br /><br />(3) If the probability of X is zero, then X is impossible.<br /><br />But notice that on Collins' view, given the aforementioned epistemic conditions,<br /><br />(4) the probability of LPU given NSU is zero.<br /><br />From (3) and (4) it follows that<br /><br />(5) LPU is impossible.<br /><br /><br />But (5) doesn't follow from (3) and (4). What follows from (3) and (4) is <br /><br />(6) LPU given NSU is impossible.<br /><br />In order to get (5) we need the additional premise that NSU is correct. So it seems we're back to the same problem I mentioned before. So I'm guess I'm not sure we're understanding each other.brian_ghttps://www.blogger.com/profile/12019153272635659263noreply@blogger.comtag:blogger.com,1999:blog-4856596194106820549.post-71098638576773393292011-12-28T11:42:22.845-06:002011-12-28T11:42:22.845-06:00Hi brian_g, glad to see you!
I'm sorry if I w...Hi brian_g, glad to see you!<br /><br />I'm sorry if I wasn't clear about the zero paradox, but the apparent contradiction I find is different from the one you're critiquing. The one you have is as follows:<br /><br />(1) On Collins' view and under appropriate epistemic conditions where the LPU range of a constant is finite (but nonzero) and the EI region is infinite, LPU has probability zero given NSU.<br />(2) But here we are, so obviously the probability was not zero!<br /><br />But this isn't the contradiction I'm trying to reach. Indeed you correctly analyze it as only showing that NSU is false.<br /><br />Instead, we needn't "look ahead" to see what actually happens. It's quite sufficient just to analyze the relationship between POSSIBILITY and PROBABILITY. My argument proceeds from the premise that<br /><br />(3) If the probability of X is zero, then X is impossible.<br /><br />But notice that on Collins' view, given the aforementioned epistemic conditions,<br /><br />(4) the probability of LPU given NSU is zero.<br /><br />From (3) and (4) it follows that<br /><br />(5) LPU is impossible.<br /><br />But wait! Recall that part of the "appropriate epistemic conditions" defined above is that the LPU range is nonzero. That means<br /><br />(6) there are possible values of the parameter space for which LPU is possible.<br /><br />Hence LPU is possible, a contradiction.<br /><br />--BenBen Wallishttps://www.blogger.com/profile/00131358613835119782noreply@blogger.comtag:blogger.com,1999:blog-4856596194106820549.post-56260567366362264292011-12-28T10:58:05.104-06:002011-12-28T10:58:05.104-06:00I believe you made a mistake in the Zero Paradox a...I believe you made a mistake in the Zero Paradox and the Continuity Paradox. I think the mistake is essentially the same so I'll only address what you say in under the Continuity Paradox. You said:<br /><br />"Suppose now that at some point we learn about the whole parameter space (which has infinite measure). According to Collins, we should then decide that LPU has probability zero. In other words, we must again be certain that LPU is false, even though we know that there is a positive-measure range of LPU values for the parameters."<br /><br />So basically if there is a finite range of life permitting values and an infinite range of non-life permitting values, we should assign LPU a probability of zero. But of course we're here, so it cannot be zero. But this is incorrect. Under these circumstances we should assign a LPU given naturalism a zero probability. The theistic hypothesis isn't suggesting that every value be given an equal probability. Given theism, we would expect a very narrow range of universes to be preferable to God. You can dispute this point, but this would be a very different objection, then the one you mention. This objection would just be that God and chance are indistinguishable, which would make the point your making here irrelevance. <br />Assuming that we can distinguish between God and chance, if the probability of LPU given naturalism is zero, and we know that we exist, then naturalism should be rejected as false. This would hardly be problematic for Collins' thesis. Collins seems to be giving naturalism a more fair hearing by granting that naturalism has a small, but non-zero probability of generating a life permitting universe.brian_ghttps://www.blogger.com/profile/12019153272635659263noreply@blogger.comtag:blogger.com,1999:blog-4856596194106820549.post-41404116854941679672011-12-15T00:34:27.942-06:002011-12-15T00:34:27.942-06:00Hey Ben, so I found your blog, and I thought I'...Hey Ben, so I found your blog, and I thought I'd say hi. Cool layout. Maybe I should have a 'recent comments' section featuring prominently like you do.....<br /><br />MikeAnonymoushttps://www.blogger.com/profile/09302939516532864508noreply@blogger.com