bd-from-kg

Tercel:

Since you hate long posts, here’s a reasonably short one. I want to expand on HRG’s comments on your “PHI-field” analogy, since I think that this analogy really does clarify some key issues regarding the relationship (if any) between a “religious context” and a violation of natural laws.

First, unlike your “atheist scientist”, if I were going to test the “DEI” hypothesis the first thing I’d do is to ask you what results would constitute falsification. If you were to reply that your faith is so strong that no results whatever could in principle falsify it, I’d lose interest immediately, since it isn’t a scientific hypothesis at all. On the other hand, if you were to specify what results would convince you that it was false, I might (if I had the time, patience, and resources) run the necessary experiments and see what happens. Under no circumstances would I take it upon myself to decide what conditions constituted falsification of your hypothesis.

Second, HRG’s point here is highly relevant: How do I tell the PHI-field is on?

If the answer is that there is a way to tell (independently of the outcome) whether the PHI-field is turned on, the next questions are: (i) What percentage of the time do you expect the field to be turned on? and (ii) What percentage of the time do you expect M to occur when the field is turned on? (I need only order-of-magnitude estimates, so that I can design a testing regime.) If the answers are such that a testing regime is feasible, I then prepare to run the experiment and start testing for the PHI-field. If I never observe a PHI-field even after, say, a hundred times as many tests as should have been needed according to your estimates, I conclude that your hypothesis is falsified. If I do get the PHI-field occasionally, I run the experiment on those occasions. If I don’t observe M after 100 times as many trials as should have been needed according to your estimates, I again conclude that your hypothesis is falsified. If M does occur in a significant number of cases (but doesn’t occur in an equal number of trials when the field is off) I conclude that there is a correlation between the PHI-field and the M results. But it still doesn’t follow that M is being caused by the PHI-field; for example, they may both be effects of something else. So I try to systematically eliminate any other factors that I wasn’t testing for but may be responsible for the correlation. If I don’t find any, I (provisionally) accept your hypothesis.

Another possibility is that the PHI-field can’t be detected ahead of time but it’s possible to determine (independently of whether N or M occurred) whether it was present after the fact. That complicates things, but the same kind of procedure as described above can still be followed, except that we have to run the experiment a lot more times (since we can’t wait until the PHI-field is on).

But if the answer to the original question is that there’s no way to tell, independently of the outcome, whether the PHI-field is on, there is no meaningful hypothesis to test. The only meaningful claim is that occasionally M will occur. All that I can do is to run the experiment lots of times and see what happens. How many times? Well, it’s your hypothesis, so again I’ll ask you what percentage of the time you expect M to occur and base the number of tries on that. But it’s important to emphasize that in this case, even if M occurs on occasion, this will not tend in any way to confirm your hypothesis that M has some relationship to the presence of a PHI-field.

Now relating all this back to the original question of the relationship between the presence of a religious context and the occurrence of violations of natural law, we see that to make any such hypothesis meaningful three questions have to be answered:

(1) How do we determine whether there is or is not a “religious context” present on a given occasion independently of whether a violation of natural laws occurs?

(2) On what percentage of occasions would you estimate a religious context is present?

(3) On what percentage of occasions when a religious context is present would you expect a miracle to occur?

Rough, order-of-magnitude answers to (2) and (3) are acceptable, but the first question must be answered with reasonable precision if we are to have a meaningful hypothesis.

Quite aside from the PHI-field analogy, answers to (2) and (3) are required to evaluate your argument from a Bayesian perspective.

Are you prepared to answer these questions, or are you just going to dance around them?

P.S.: I've already had to use the term "violation of natural laws" over a dozen times when "miracle" would have worked fine were it not for your nonstandard definition of "miracle". (And it really is nonstandard; I just chose not to expend a lot of verbiage on the point.) But this is getting tiresome. Would you like to propose a term for a violation of natural law that does not necessarily occur in a "religious context"?

[ February 26, 2002: Message edited by: bd-from-kg ]</p>

bd-from-kg

Tercel:

In this post I’m going to focus on your comments about Hume’s argument, especially those in your latest post.

I had said:

You replied:

True. He was only, say, 99.9999% sure that they were false. What’s your point?

Wrong on both counts. I discussed this before in my Feb 20 post; why are you wasting our time repeating things that have already been answered?

Hmm. A rational person might reason as follows: “Hume rejected the Jansenist claims on grounds that I would have thought insufficient. But it turns out that he was right. Perhaps my judgment that his grounds for rejecting them were insufficient was faulty. Perhaps I should rethink my standards for evaluating such evidence.” But not you. Your opinions in such matters are impervious to evidence. You remain just as convinced as ever that your standards for evaluating such evidence are right and the other fellow’s wrong even if his conclusions turn out to be right and yours wrong. So convinced, in fact, that you call the guy who was right “stupid” and confidently attribute his being correct to pure luck.

So who’s the presuppositionalist now?

This is correct except for the word “specific”. Practically all actual empirical reasoning is embedded in a great mass of “background knowledge” which is based on a huge amount of empirical evidence not directly related to the question at hand. For example, if we learn that Jones was 3,000 miles away ten minutes before the crime took place, we immediately conclude that he didn’t do it because we know something about how fast people can get from one place to another.

This is a double misinterpretation. First, he doesn’t say that personal testimony could never, in principle, be sufficient to establish a miracle, but only that there has, as a matter of fact, never been personal testimony sufficient to establish one. Second, and more important in the context of whether his argument is a priori, his argument is that we call something a miracle precisely because, as a matter of fact, it violates regularities in the course of nature that have been firmly established by past experience. Thus to call something a miracle is by definition to say that there is a strong a posteriori argument against it. To call this an a priori argument is an abuse of language.

Another way to look at this is that Hume is pointing out that one can construct a concrete a posteriori case against any alleged violation of natural laws by simply asking the claimant what justification he has for believing that the event is really a violation of natural laws. If he cannot produce enough evidence to justify calling it a violation, the claim is invalid on its face. But if he can, he has established a strong evidential (i.e., a posteriori) case against the alleged violation.

So far so good.

That is to say, he doesn’t bother to investigate this particular case thoroughly, because he has already established that the results are a foregone conclusion: given the general nature of the evidence (i.e., testimony from religious fanatics), P(B|A) / P(B|~A) is not going to be anywhere near as large as P(~A) / P(A). Since P(B|A) and P(~A) are very close to 1, this is essentially saying that the probability that the witnesses are either lying or misremembering or misinterpreting what they saw is much, much higher than the prior probability that the alleged events really occurred. There’s really little point in doing a detailed study to determine whether the former probability is larger than the latter by a factor of a million or whether the ratio is more like a billion.

Have you gone off the deep end? Your complaint, in essence, is that Hume doesn’t prove that past experience is a guide to what’s likely to happen and what isn’t. Of course he doesn’t! Hume is famous for his demonstration that there is no way to prove, on the basis of either logic or experience, that past experience is a guide to the future. You can hardly expect him to produce an argument that he has demonstrated to be impossible in principle. However, back in the real world, only the totally insane question using past experience to judge what’s likely to happen, or what’s most likely to have happened . Those of us who are still at least somewhat grounded in reality are reasonably confident that the sun is going to rise in the east tomorrow morning, for no better reason than that the sun has risen in the east every morning from time immemorial. If someone claims that the sun rose in the west one morning we are naturally going to demand far better evidence than if he claims that it was cloudy that day. This doesn’t involve any deep philosophical insights; it doesn’t require a course in epistemology. It’s simple common sense.

Also, this complaint is bizarre coming from someone who claims to understand Bayes’ Theorem. The gist of this theorem is that the likelihood that a hypothesis is true must be judged on the basis of the direct evidence for it (i.e., P(B|A) / P(B|~A)) combined with past experience (which is of course what is used to estimate P(A) / P(~A)). If you have no problem with Bayes’ Theorem (which, as you say, you’ve invoked yourself a number of times) how can you have a problem with Hume’s methodology here?

Now you quote Hume as saying:

And you comment:

The whole paragraph that begins with this question represents a total misunderstanding of Hume’s argument here. Once again the point can be stated very simply in terms of Bayes’ Theorem. In order for P(A|B) to be greater than P(~A|B), P(B|A) / P(B|~A) must be greater than P(~A) / P(A). If P(A) is very small, the latter ratio is very large, so a person claiming that A has occurred bears a high evidentiary burden.

Then why are you stubbornly determined to misconstrue Hume’s argument when it can so easily be understood in terms of Bayes’ Theorem? It looks to me as though you are simply determined to misunderstand it because, as soon as you understand it correctly, you can hardly avoid seeing that it demolishes your whole position.

Either the point is that you think this is what I’m doing, in which case it’s an ad hominem argument, or you’re referring to some other folks, in which case it’s irrelevant. Let’s stick to the point, which is what evidence would justify rational belief in miracles.

I’ll pass over the rest of your post, at least for now, since it relates to the issue of the relationship between a “religious context” and the prior likelihood of a violation of natural laws rather than Hume’s argument. No doubt the “religious context” business will be the subject of later posts.