## Friday, August 5, 2011

### Hume and the confirmability of miracles

While discussing the McGrews' Bayesian analysis of the Resurrection (CCRJ), I frequently mentioned that the McGrews and myself were not attempting to derive odds on the Resurrection. Rather, we were focusing on the Bayes factor - aka the likelihood ratio - which if you recall, is the number by which the prior odds ratio p(thing')/p(other thing') is multiplied to yield the posterior odds ratio q(thing')/q(other thing'). So at the very minimum, one needs to estimate what the prior odds should be in order to derive the final odds. Since neither of our approaches were sufficiently general to capture a truly cumulative Bayes factor, even this may be inadequate, but since the factor I derived - 106 - was calibrated given generous textual assumptions in favor of the Resurrection, we may be able to tentatively estimate an upper bound on reasonable posterior odds using that factor if we have an upper bound on reasonable priors. If that upper bound is less than 10-6, we may conclude that the Resurrection probably did not occur, i.e. 0.5>q(R).

I opine that barring other arguments in the context of a natural theology, such an upper bound exists. That is, the Resurrection can not reasonably be confirmed from the textual record alone with respect to convincing background knowledge which is shared by skeptics and Christians alike. But I am interested in Hume's more general thesis, which is that miracles by their nature can not reasonably be confirmed. The details of an analysis of the Resurrection are merely an instance of a more general unconfirmability argument.

I pause to obviate a potential objection: I am fully aware that the proper interpretation of Hume's Enquiry concerning Human Understanding, especially Of Miracles, is a hotly disputed topic. I am attributing an unconfirmability argument to Hume; I doubt he can be convincingly interpreted as not making such an argument. But I am not here interested in any historical exoneration or conviction of Hume of philosophical crimes. Rather, I want to work with his apparent argument by recasting it in formal terms, propose that it is inadequate, and attempt to shape a more satisfactory unconfirmability argument.

I am neither discussing nor proposing a definition-dependent impossibility argument, e.g., "A miracle is the violation of mathematical, divine, immutable, eternal laws. By the very exposition itself, a miracle is a contradiction in terms: a law cannot at the same time be immutable and violated." Rather, I am interested in miracles loosely defined as particular exceptions to otherwise exceptionless laws or regularities of nature. In this context, the regularities of importance are putative laws, and their importance is epistemic, not ontological. Whether or not a putative law is true is largely irrelevant: what matters is how well-supported it is.

The proper definition of a miracle is also in dispute. As regards this item, I follow Tim and Lydia McGrew in treating the Resurrection as a paradigm (CCRJ, p.4). As I will explain in the course of this discussion, working with paradigm cases like the Resurrection is all that should be required. Failures of consensus on miracles are relevant to Hume's argument, but they will not prove necessary to reject his conclusion. Which is roughly as follows:

Hume's Argument: There cannot exist evidence E for a miracle M such that

$\beta=\frac{p(E|M)}{p(E|\sim M)}>\left[\frac{p(M)}{p(\sim M)}\right]^{-1}$.

With conditionalization, this is equivalent to stating that the posterior odds on a miracle can never be greater than 1/2.1

The initial prospects of this statement are rather dim. As is commonly pointed out, there are no a priori boundaries on the size of Bayes factors: no matter how small the prior odds on a miracle, there exist finite Bayes factors which can overcome them. Similarly, disputes concerning the definition of a miracle make it impossible to have confidence in such a general statement.

I would also add that we should not be overly interested in such an argument as employed to justify ignoring any potential evidence for miracles. The debate is worthwhile. As I have noted in a slightly different context:
It is very often said, by e.g. PZ Myers and Massimo Pigliucci, that one cannot evidence Christianity or gods because they are not coherent hypotheses. More needs to be said about this, but I would at least suggest the following: if the evidence for the Resurrection really is extremely convincing to reasonable people on the assumption of coherency, we should take an attitude similar to that which I think we take to science: some conceptual fuzziness is to be tolerated, barring flat contradiction, where overwhelming evidence for an aspect of a theory is available. Were I to find the evidence for the Resurrection convincing, I know I would be working very diligently to craft a coherent Christian philosophy to accommodate it. So to me, the coherency difficulty is in many ways secondary, unless that difficulty is so severe that one cannot even begin to discuss relevant evidence. I think we usually manage to do so. Wouldn't you agree?
The argument also conflicts with the empirical, tentative nature of skeptical inquiry. I think we should wish to avoid such categorical statements.
The temptation to fashion such an argument is understandable. But it should be resisted. Any epistemology that does not allow for the possibility that evidence, whether from eyewitness testimony or from some other source, can establish the credibility of a UFO landing, a walking on water, or a resurrection is inadequate. (Earman, p.4)
As Earman also notes, there are events which, were they to occur, surely amount to convincing evidence for a miracle claim:
Suppose, for the sake of illustration, that there is a well developed theology based on the existence of a god called Emuh. who promises an afterlife in return for certain religious observances in this life. Suppose that this theology predicts that on such-and-such a day Emuh will send a sign in the sky. And suppose that on the appointed day, the clouds over America clearly spell out in English the words “Believe in Emuh and you will have everlasting life,” while the same message is spelled out in French over France, in Deutsch over Germany, etc. Then even though these cloud formations may not contravene any of the general principles taken at the time in question to be laws of nature and, indeed, may be explicable in terms of those principles, it would not be untoward to take these extraordinary occurrences to be support for Emuh theology. (p.11)
So Hume's argument, were it valid and coherent, would prove too much. It also ignores the effect of evidence for a theology and its implications for the proposed miracle claim. Were the gloating fiction of LaHaye's Left Behind series to be actualized, it would confirm the Resurrection. I am unsure as to how or why someone would seriously argue otherwise, even if the various details of Christian theology are unclear.

I will not second another common objection: I do not think that Hume's argument, interpreted as I have interpreted it, would destroy the possibility of overturning laws in science. His "straight rule of induction" is problematic in this context (Earman, pp.31-2), but laws are not to my knowledge overturned in the way that a putative miracle claim would overturn them.

Take the Conservation of Mass. Did measurements of nuclear reactions overturn a uniform experience? No, because what changed was not the article where uniform experience applied, but where a novelty was being analyzed. If for example I react 50 grams of sodium with 70 grams of chlorine gas to form salt (NaCl) at approximately standard temperature and pressure and measure a net change in mass of 20 grams, I or my instruments screwed up. Mass is still conserved within significant margins of instrumental error for ordinary' chemical reactions. The implications of such experience have not been contradicted, but superseded. With miracles, where the putative law needs to otherwise be intact for theological reasons, no such consideration applies. We are not talking supercessions or the overturning of laws as done in the sciences; we are talking about flat-out, singular violations of an otherwise sound natural order. We are talking about an experiment incapable of replication. Were mass conservation to always hold, and the only exception were to occur in one apparently sound experiment, we should have discounted the experiment as flawed if replication failed.

I judge Hume's argument to be a failure and its conclusion to be unsound. But this need not be the end of the story. We may yet build a better monument by clearing away the noisy rubble of Hume's rhetoric and picking out the useful pieces. That will be the subject of my next post.

1. This interpretation, though disputed, has a lot of support, perhaps apart from the target threshold 0.5>q(M). Were Hume making an impossibility argument, it is odd that he should emphasize the relative strength of evidences (p.169) and the uncertainty of the relevant propositions (pp.169-70); that he discusses evidence at all would also be strange. In addition to his use of probabilistic terminology, he also casts his argument in terms of degrees-of-confidence: "Some events are found, in all countries and all ages, to have been constantly conjoined together: Others are found to have been more variable, and sometimes to disappoint our expectations; so that, in our reasonings concerning matter of fact, there are all imaginable degrees of assurance, from the highest certainty to the lowest species of moral evidence." And he continues famously: "A wise man, therefore, proportions his belief to the evidence. In such conclusions as are founded on an infallible experience, he expects the event with the last degree of assurance, and regards his past experience as a full proof of the future existence of that event" (p.170).

With terms like infallible' and proof' in play, I think that Hume may be interpreted as arguing for a prior probability of zero for miracles, or perhaps an infinitesimal probability (p.171). But I do not think that such a prior is convincing to all - or many - concerned, and it is therefore useless. Many Bayesians accept - here the terminology is unfortunate - the principle of regularity, which states that all possibilities have probability greater than 0, assuming that those possibilities are uncertain and assigned any probability whatever. In any case, we are presumably inviting Christians to the discussion, so we must at least assume that non-zero priors are in play.

There are other ambiguities, and I am lead to second Earman's hostile conclusion (p.20):
I defy the reader to give a short, simple, and accurate summary of the argumentation in "Of Miracles." What on first reading appears to be a seamless argument is actually a collection of considerations that sometimes mesh and sometimes don't. It will take much work to tease out the components of Hume's argument and to evaluate the soundness of individual components and the effectiveness of the entire package.
Immediately after bringing up proofs' of experience, Hume dives right back into emphasizing the fallibility of evidence, particularly witness testimony (EPHU, p.171). There are other deficiencies in his presentation. After defining miracles as putative exceptions to uniformly evidenced laws, he states the following:
There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appelation. And as a uniform experience amounts to a proof, there is here a direct and full proof, from the nature of the fact, against the existence of any miracle; nor can such a proof be destroyed, or the miracle rendered credible, but by an opposite proof, which is superior. (p.173)
With this stringency, the mere proposal of evidence for an event disqualifies that event's being a miracle, as experience is no longer uniformly against it. And then, the presentation of additional evidence should leave an opening. I'll stick with the Bayesian interpretation because it is the only plausible interpretation to be found.