{"id":221,"date":"2007-01-17T22:54:00","date_gmt":"2007-01-18T02:54:00","guid":{"rendered":"http:\/\/alanrhoda.net\/wordpress\/?p=221"},"modified":"2007-01-17T22:54:00","modified_gmt":"2007-01-18T02:54:00","slug":"from-the-mail-on-miracles","status":"publish","type":"post","link":"http:\/\/alanrhoda.net\/wordpress\/2007\/01\/from-the-mail-on-miracles\/","title":{"rendered":"From the Mail: On Miracles"},"content":{"rendered":"

I received the following reply to an earlier blog post<\/a> concerning whether it was possible<\/span> for someone to rationally believe in the miraculous.<\/p>\n

Dear Alan,<\/p>\n

I am a Czech grad student in philosophy who wants to write a dissertation concerning contemporary analytical philosophy of religion, mainly the evidence for the resurrection of Jesus Christ. I am interested especially in R. Swinburne and W. L. Craig. Your post about Ehrman is very useful, so I will try to ask you for an advice.<\/p>\n

Currently, I have, say, a problem with an argument against miraculous events in Jordan Howard Sobel\u2019s Logic and Theism (2004, Cambridge UP).<\/p>\n

There is, in Sobel, pp. 332f., a proof of a Bayesian proposition which Sobel calls Hume\u2019s Theorem. It concerns conditions of the establisment of an event by a testimony and, in adapted notation, reads as follows: [(P(tM) > 0) and (P(M\/tM) > 0.5] only if [P(M) > P(tM and not-M)]. P: probability; M: an event occurs; tM: a testimony for M occurs.<\/span><\/p><\/blockquote>\n

Nice to make your acquaintance, Vlastimil. I’ve not yet had the chance to read Sobel’s book, so I’m relying on your summary. My first question is why Sobel presents “Hume’s Theorem” (HT) as<\/p>\n

(HT) <\/span>[(P(tM) > 0) and (P(M\/tM) > 0.5] only if [P(M) > P(tM and not-M)]<\/span><\/p><\/blockquote>\n

and not as<\/p>\n

(HT*) <\/span>P(M\/tM) > 0.5 only if [<\/span>(P(tM) > 0) and <\/span>P(M) > P(tM and not-M)]<\/span><\/p><\/blockquote>\n

<\/span>In other words, why put P(M\/tM) > 0 on the LHS of the “only if” rather than on the RHS? It may not matter much, but (HT*) seems much more natural to me.<\/p>\n

Now, if M is a miraculous event, P(M) is, according to Sobel, ALWAYS extremely small: nearly 0. Why? It seems Sobel gets the value of P(M) as the [ratio] of miraculous events of certain kind on the one hand [versus] of all events of this kind on the other. E.g., sum of human-water-walking-events \/ sum of human-water-walking-events + sum of human-disability-of-water-walking-events; or sum of the resurrected people \/ sum of those people who died. <\/span><\/p><\/blockquote>\n

So Sobel is relying on a simple ratio definition of probability (# of cases of a specified type \/ total # of cases). I can see why he would. Not only is that how Hume would do it, and not only does it make the probability estimations more straightforward, but it also easily gets him his desired conclusion, namely, that P(M) be very low. And if P(M) is inevitably really small, then it’s going to be very hard to satisfy (HT) because P(M) will very rarely, if ever, be greater than P(tM and not-M).<\/p>\n

But why think that the simple ratio definition of probability is the appropriate <\/span>conception of probability to apply here. Offhand, it seems to me that an epistemic definition of probability (e.g., betting quotients) makes more sense. Isn’t P(M\/tM) supposed to be an epistemic <\/span>probability. Isn’t it supposed to measure the degree of rational credence<\/span> of M given tM? And obviously we should apply the same conception of probability on both sides of (HT). So if P(M\/tM) is read as an epistemic probability, then so should P(M), and now it’s not at all clear that P(M) must invariably be low. In fact, depending on one’s background beliefs, P(M) may in some cases be moderately high, or at least high enough to beat out P(tM and not-M).<\/p>\n

For this reason, I’m not much impressed with Sobel’s argument. By appealing to additional background beliefs here I am essentially endorsing a version of your (b) proposal, namely, that P(M) needs to be assessed in the light of one’s total relevant evidence, not simply in the light of past event-type ratios, as Sobel wants to do. But the relativization of P(M) to background beliefs means that whether P(M\/tM) turns out to be greater than 0.5 may vary from person to person. In relation to the background beliefs of someone like Sobel, I suspect that P(M) is effectively zero, such that no amount of testimony could even in principle qualify a miracle-report as worthy of credence for him.<\/p>\n

PS. The lottery example in your Appendix does a really good job of showing why a simple ratio definition of probability is the wrong one to use. Unsurprisingly, Sobel responds to the problem by tacitly shifting to an epistemic notion of probability when he appeals to the background assumption that “in common circumstances, nothwistanding the antecedent improbability, we should believe [a] report according to how we consider the reporter to be.”<\/p>\n","protected":false},"excerpt":{"rendered":"

I received the following reply to an earlier blog post concerning whether it was possible for someone to rationally believe in the miraculous. Dear Alan, I am a Czech grad student in philosophy who wants to write a dissertation concerning contemporary analytical philosophy of religion, mainly the evidence for the resurrection of Jesus Christ. I\u2026 Read More »<\/a><\/span><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-221","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/221","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/comments?post=221"}],"version-history":[{"count":0,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/posts\/221\/revisions"}],"wp:attachment":[{"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/media?parent=221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/categories?post=221"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/alanrhoda.net\/wordpress\/wp-json\/wp\/v2\/tags?post=221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}