RUTH WEINTRAUB

THE CREDIBILITY OF MIRACLES

(Received in revised form 4 November 1994)

Hume (1777, section X) adduced two complementary arguments to invalidate testimony about miracles. He argued, first (pp. 115-116), that "no testimony is sufficient to a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish". In particular, we shouldn't believe that a miracle has occurred even on the strength of the testimony of wontedly reliable witnesses. He suggested, next, that there were, in fact, no well-attested miracles, because witnesses purporting to have observed a miracle have been "barbarous", credulous, and sensation- seeking.

Hume set more store by his first argument. He recognised that the second argument was contingent on historical circumstances, and thought the first enabled him to show that no testimony ever confirms the occurrence of miracles. The argument, he thought, "will be useful as long as the world endures". Its premises are:

1) The reliability of the witness (the extent to which he is informed and truthful) must be compared with the intrinsic probability of the miracle.

2) The initial probability of a miracle is always small enough to outweigh the improbability that the testimony is false (even when the witness is assumed to be reliable).

The sceptical conclusion straightforwardly follows: the posterior probability of a miracle is small, even when the witness is reliable.

Philosophical Studies 82: 359-375, 1996. �9 1996 KluwerAcademic Publishers. Printed in the Netherlands.

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The first premise of the argument can be defended (section II), and its defence suggests that Hume's argument can be applied to purported observations of miracles, as well (section III). But Hume failed to pro- vide an adequate support for his second premise (section IV). A more cogent defence can be provided for a weaker premise. The resultant argument has, consequently, a less sweeping conclusion than Hume's (section V).

II

Hume's reasoning can be presented, as has become quite customary, in Bayesian terms. This is not the only possible interpretation of Hume's argument, but it is a plausible one, and renders his reasoning perspic- uous, and the issue easier to grapple with. So let us denote by E the proposition reporting the occurrence of some event, and by TE - the proposition reporting that a witness has testified to the occurrence of E. Hume may be construed as arguing that when confronted with a testi- mony that E, i.e., upon learning the truth Of TE, one assigns a probability to E in accordance with Bayes' theorem:

P(TE/E)*P(E) P(TE/E)*P(E) P(E/TE) = P(TE) = P(TE/E)*P(E)+P(TE/,,~E)*P(,,~E)

Is this Bayesian rendition of the assimilation of testimony correct? In this section I shall argue that seeming difficulties notwithstanding, it can be vindicated.

The dependence of the testimony's credibility on the initial prob- ability of the event might seem to have devastating consequences. Information conveyed in ordinary communication is often antecedently improbable: conveying new information is, after all, an important func- tion of conversation. If that sufficed to discredit the testimony, there would "be so little trust among individuals as to make most communi- cation pointless" (Schlesinger, 1991, p. 121). Suppose a reliable witness reports that ticket 267 has won in a 10,000 ticket lottery. Should we dis- believe him because the prior probability of that ticket winning is only 1/10,000? One might initially suppose so, if one ascribes the following

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values to the probabilities in Bayes' formula:

P(E) = 1/10,000

P(TE/E) --- 0.99

P(,-~E) -- 0.9999

P(TE/~E) = 1 - P(TE/E)= 0.01

But in fact, as Schlesinger shows, the value cited above for (P(TE/,'~E) is wrong. 0.01 is the probability that the witness should lie: he reports the truth 99 times out of a 100. But he has 9999 ways of lying, and the probability that he should choose precisely number 267 is 0.01/9999. And when we use this value in the calculation, the probability that his testimony is accurate; i.e., the probability that ticket 267 has, indeed, won, turns out to be quite high - 0.99.

99/100,1/10,000 _ 99 P(E/TE)-- 99 / 1 0 0 . 1 / 1 0 , 0 0 0 + 1 / 1 0 0 . 1 / 9999.9999 /10,000 - 10---0

Our difficulties aren't over yet. Schlesinger's response doesn't quite vindicate the Bayesian rendition of the assimilation of testimony Witnesses' credibility will be significantly tarnished when there are a few alternatives available, and the one chosen is antecedently improb- able. Three examples will illustrate this claim.

The first is the taxi-cab problem (Kahneman and Tversky, 1972). 85% of a town's taxi-cabs are blue; the rest are green. A witness has identified a cab involved in an accident as green. The witness, furthermore, is known to give the correct colour in 80% of the cases, and the other colour in 20%. Many subjects estimate the likelihood that the cab involved in the accident was green as 80%. In this estimate, they ignore the initial probability of the testimony (the distribution of cab-colours), thus violating Bayes' theorem. If prior probabilities are taken into account, the posterior probability is 12/29. It seems as if the Bayesian calculation (unintuitively) engenders a reduction in the credibility of a reliable witness reporting an improbable occurrence. 1

Consider, next, a heavily-biased lottery, in which there are two tickets. Ought I to believe a witness' statement that ticket number 2

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won the lottery? Not if the prior probabilities are as follows:

P(2 won) -- 0.001

P(1 won) -- 0.999

P(witness reports that 2 won/2 won) -- 0.99

P(witness reports that 2 won/2 didn't win) --

P(witness reports that 2 won/1 won) -- 0.01

My posterior probability will be:

P(2 won/witness reports 2 won) -- o.99,o.ool 0.99.0.001-t-0.01.0.999 -- 0.09

Finally, when a disinterested and reliable informant (P(TE/E) -- 0.99) replies affirmatively to the question "Did ticket number 267 win the prize?" we ought, if we apply Bayes' formula, to disbelieve that the ticket has, indeed, won: if there are 10,000 tickets in the lottery, the posterior probability is (roughly) 0.01 (Schlesinger, 1991). To see this, no te tha t this case is different from the one discussed above, in which the witness responded to the question "Which ticket won?", and could choose from 10,000 possible replies. In the present case, the witness has only two possible responses ("Yes" and "No"), and the probabilities, consequently, are:

P(267 won) = 1/10,000

P(says yes/267 won) -- 0.99

P(says yes/267 didn't win) = 0.01

99/100.1 / 10,000 1 P(267w~ = 10--~

Isn't it implausible in the extreme (even if it happens only rarely) that the testimony of a reliable witness, having no axe to grind, should be treated with such scepticism? Testimony, surely, doesn't work that way. Don' t I believe my honest informant, even if prior to his statement I thought it quite unlikely?

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Cohen (1986, ch. 3, section 16) replies affirmatively. In defence of common-sense judgements (and contra Hume's first premise), he invokes a distinction between counterfactualisable and uncounterfactu- alisable probabilities. The latter kind of probability has no counterfactual implications, because "its range of application does not extend beyond the actual membership of its reference class" (p. 166). Thus, the relative frequency of pennies among the coins in my pocket is uncounterfactu- alisable. I would not project it on the coins in my pocket a week hence. 2 The relative frequency of blue cabs is accidental, Cohen continues, and, therefore, unprojectible. The prior probability to be used in Bayes' for- mula is 0.5, because "there is as much (or as little) stated for it as against it" (p. 167).

I will, first, criticise Cohen's positive suggestion as to how the witness' testimony is to be assimilated, and then rebut two general arguments for ignoring prior probabilities .3 Two objections can be raised against Cohen's suggestion. First, if one must project a probability, it should, of course, be counterfactualisable. Cohen's choice of 0.5 is, pre- sumably, based on the (reasonable) assumption that an individual blue cab has the same propensity to being involved in an accident as does a green one. (The wording invites a less charitable reading, according to which the principle of indifference is invoked to transmute ignorance into a projectible probability.) Propensities, of course, are projectible probabilities. But has Cohen chosen the right propensity? The popu- lation o f cabs, after all, has a greater propensity to produce blue-cab accidents than green ones. Which propensity should we project? an individual or a collective one? The latter (0.85) - if we are trying to predict the colour of a cab involved in a hypothetical accident in this town. (Projecting the former is blatantly wrong when there are no green cabs at all.)

The second objection to Cohen's proposal is that it is reasonable to suppose that one must prefer a counterfactualisable probability over an uncounterfactualisable one (when both are available) if one is reasoning about an object which is not a member of the reference class. If I know that a coin is fair, I assign probability 0.5 to the next toss landing heads, even if the relative frequency of heads so far is different. Knowledge of the coin's bias screens offthe relative frequency (Lewis, 1980). If, on the

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other hand, I must assign a (subjective) probability to heads on one of the tosses already performed (about whose outcome I am ignorant), then, surely, I ought to use the relative frequency, rather than the known bias of the coin, since an actual member of the reference class is involved; there is no projection on to a new case. Here, the uncounterfactualisable probability screens off the counterfactualisable one. (There are hybrid cases, in which the two kinds of probability must be combined: I might know the coin's bias and the relative frequency of heads among fifty out of a hundred tosses.) When people are reasoning about a taxi-cab, they are reasoning about an actual member of the reference class, and not about a hypothetical one, and shouldn't, therefore, ignore an "acci- dental" relative frequency, even when they have counterfactualisable probabilistic knowledge.

Let us, now, consider two arguments for ignoring prior probabilities. In giving more credence to a report with a greater antecedent likelihood, it might be argued (Cohen, 1981, p. 329), we are absurdly supposing that the speaker's honesty, or his eyesight are (causally) affected by the colour of the taxi-cab (or the structure of the lottery). The confusion behind this argument may be untangled by distinguishing between dif- ferent senses of the term 'reliable', as it is applied to a testimony (and, derivatively, to a witness). Reliability1 is measured by the conditional probability P(E/TE): the probability that E has happened given that the witness reports it. It is the probability I will assign to E upon hearing his testimony (and learning nothing else of relevance). Hume's argument, of course, purports to show that no testimony about miracles is reliable in this sense.

Testimony is reliable2 if both conditional probabilities, P(TE/E), P(~TE/~E), are high. The two senses are quite distinct. The witness (and the testimony) in the cab problem is reliable2 about cab-colours. He is not very reliable1. Conversely, a barometer which gives the correct reading in 90% of the cases (P(E/TO -- P(~E/,-~TE) = 0.9), and is, there- fore, reliable1 (about the weather), will not be reliable2 if nice weather is rare (P(E) -- 0.05). Most of the time, when it indicates nice weather, the weather will, in fact, be bad.

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P ( E / T E ) * P ( T E ) _ P ( E / T E ) * ( P ( T E ) _ P(TE/E) = V(E) -- P(E/TE)*P(TE ) +P(E/,.~TE ) - -

0 . 9 * 0 . 0 5 _ 9__ 0 . 9 . 0 . 0 5 + 0 . 1 . 0 . 9 5 - 2 8

With this distinction in mind, we can address Cohen's charge that in taking into account prior probabilities we are misconstruing the causal facts. The witness' relevant traits (eye-sight, honesty) causally deter- mine (combine to constitute) his reliability2: his propensity to name a blue (green) cab when there is one. The facts he reports, to be sure, causally affect his eyes (the nature of this interaction partly determines his reliability2 rate); they do not affect his eyesight. The reliabilityl of his testimony is (non-causally) determined by the prior probability of his testimony jointly with his reliabilityE-rate.

The problem seems to have been compounded. For what is the jus- tification for discriminating against the improbable testimony given by the same witness? Shouldn't we give equal credence to any testimony given by a sharp-eyed and honest witness?

The answer is affirmative provided the testimonies are relevantly similar. We are tempted to think the only relevant aspect is reliability2, ignoring (at our peril) the testimony's prior probability, and the witness' reliability1. A powerful antidote to this temptation is the appeal to the long run. For instance, only 0.09 of the witness' reports that ticket number 2 won the biased lottery will be correct in the long run. And similarly, in the taxi-cab problem, despite giving the correct colour in 80% of the cases, the witness is only correct 12/29 of the time when he identifies the cab as being green. That is, if we rely on his testimony on those occasions, we will be correct less than half of the time! 4 Similar (long-run) considerations will vindicate other, seemingly unintuitive, results of applying Bayes' law (Schlesinger, 1991, p. 124). Thus, the probability of an event can be reduced upon being reported by a trustworthy witness. If the informant is asked to name a non- winning ticket, and names number 267, the probability of ticket 267 not winning goes down from 0.9999 to 0.9! Correlatively, the probability of the complementary event (ticket number 267 winning) is raised by a disconfirming testimony! Here, again, we need only remember that in a long run of reporting that ticket 267 did not win, the witness is correct 0.9 of the time - less than the antecedent probability of that event.

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The second general argument for ignoring prior probabilities enjoins us to compare testimony with observation. If I utilise Bayes' formula to modify my subjective probability upon observing the draw (prior probabilities as above), I ought, similarly, to distrust my observation. But that, surely, does not happen. I simply trust my eyes (the light is good), and change the probability to (nearly) 1. I do not conclude that my eyes have deceived me, because (according to Bayes' law) the (posterior) probability of the ticket winning is only 0.01!

The reliability of the observer and the prior probability of his obser- vation, we are reminded, are quite distinct. We are often reliable in observing things we couldn't predict. Our observations, therefore, con- stantly override our prior probabilities: improbable things are happening and being reliably observed by us all the time. That is why observation is useful. If governed by Bayes' law, its impact would be decimated. To allow one's prior probabilities to affect one's observations to this extent, it may be claimed, is dogmatic. Recognising our ignorance and our capacity to learn from experience, we ought to confront the world with a greater preparedness to change our mind; to be open to new information.

I ought to treat my honest informant as I do my senses, the argument continues. A witness' testimony is a kind of observation. The witness functions as another sense. Of course, people aren't always reliable informants. They sometimes deceive (if only to appear interesting or amusing). But like seeing, hearing from a reliable witness is believ- ing. Both observation and testimony screen off new from antecedent probabilities.

Is this a cogent empiricist argument for ignoring prior probabilities? Not really. We are, in fact, not forced to choose between adhering to Bayes' formula and being empiricists. Bayesianism is just a formal (and very versatile) framework within which the assimilation of testimony can be represented. Substantive claims about probabilities' values will only be got out of Bayes' formula if other values are fed in. Hearing from a reliablel witness is like seeing, but that is not because testimony renders prior probabilities irrelevant, but because it may swamp them. I can quite rationally believe a medical specialist who informs me of a new (and to m e - amazing) treatment. About such matters he is very reliable2,

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and my prior probabilities embody this assumption. They sanction - via Bayes' formula - my trust. The probability that the treatment is reliable given that he recommends it is high, although the prior probability is very low.

llI

In the light of the considerations adduced with respect to testimony, we can now consider the impact of observation on our beliefs. "Testimony", Price (1811, p. 240) suggested, "is truly no more than sense at second- hand; and improbabilities . . . can have no more effect on the evidence of the one, than on the evidence of the other". Price, of course, thought that prior probabilities were irrelevant in both cases. I suggest that the analogy Price discerned ought to persuade us that prior probabilities affect the credibility of observation, as well.

Knowing that when drunk the world seems to reel, I will distrust - when d runk - my feeling that the world is reeling. To observations made in optimal conditions, on the other hand, I will give greater credence. It is only natural to suppose that Bayes' formula governs the assessment of observations, as well as that of testimony. When we observe, we con- ditionalise on a proposition reporting how things seem to us. I do not mean to suggest that such propositions are linguistically more funda- mental. Rather, once the sophisticated distinction between how things are and how they seem is introduced; once we recognise the fallibility of our senses, and theorising becomes possible about the reliability of observations to which they give rise, a more reflective stance can be adopted towards observations.

It is but a small step to realise that when observing the biased lottery, similar considerations apply. We trust our senses more than we do others' testimony. But we ought, sometimes, to distrust our eyes. The prior prob- ability of what we (think we) observe certainly affects the observation's credibility. And, of course, it becomes apparent that Hume's argument - once its second premise is defended - can be straightforwardly applied to purported observations of miracles, even if (Flew, 1986, ch. VIII) Hume intended to restrict it to testimony.

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IV

Hume's first premise is vindicated. But its defence threatens to under- mine the second one. The improbable, we have seen, can often be rationally believed. Why not the miraculous? Of course, if the prior probability of a miracle is infinitesimal (Sobel, 1987), it will be sub- stantially raised only by testimony the probability of whose falsity is itself infinitesimal. Similarly, we could render miracles unbelievable by supposing their occurrence given testimony or observation to be improb- able. Here, it is the conditional (rather than the prior) probability which enables us to be sceptics about miracles. But finding a formal frame- work within which to represent one's reluctance to believe testimony about (or observation of) a miracle must be backed by an argument as to why miracles are to be assigned an infinitesimal prior probability, and, thereby, rendered (almost) immune from confirmation. Did Hume have such an argument? Should we dismiss testimony (and observation) pertaining to miracles?

Hume nowhere used the word ' improbable' in characterising those events testimony about which he recommended be disbelieved. He dis- tinguished between events which were merely "unusual" (a healthy man dying suddenly), "extraordinary" or "marvelous", and those that were actually "miraculous". With the distinction between the unusual (improbable) and the miraculous, we can try to vindicate Hume's second premise.

That ticket number 5 won the lottery (out of 100,000 tickets) is improbable, but credible. That an elephant flew over London yesterday is incredible. Testimony about the latter ought to be given less credence. The difference does not stem from, or at least, it is not exhausted by, the prior (im)probability of the events in question, for we can suppose - without changing our attitude to the examples - the number of tickets in the lottery to be large enough so that the probability of a given ticket winning is comparable to the probability of an elephant flying. (If need be, we can suppose the number of tickets to be infinite. 5)

The first explanation that comes to mind for the difference in credi- bility is that although both events are improbable, the ticket winning is, and the elephant flying isn't, an instance of a kind of event that is very

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probable: some ticket must win. But the explanation fails. According to the probability calculus, the likelihood that some improbable event will occur in the long run converges to 1 (when the length of the run nears infinity). So the elephant flying is an instance of a kind of event that is very probable: the improbable. And we have yet to find what distinguishes it from ticket number 5 winning.

Hume thought the difference lay between events that were, and those that weren't, compatible with the laws of nature. "[I]t is a miracle", he argued, "that a dead man should come to life; because that has never been observed in any age or country. 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" (1777, p. 115, original italics). But what is this proof?.

Hume was not suggesting that the notion of a miracle was incoherent; that a law of nature - by definition - could not be violated. Miracles, he thought, were logically possible. If "a person . . , should command a sick person to be well, a healthful man to fall down dead . . . . these might justly be esteemed miracles, because they are really . . . contrary to the laws of nature" (1777, p. 115, fn.).

Hume's considerations against miracles were epistemological, rather than conceptual. But they do not seem convincing. Has "a finn and unalterable experience. . , established these laws", rendering "the proof against a miracle . .. as entire as any argument from experience can possibly be imagined" (1777, p. 114)? True, "where the past has been entirely regular and uniform, we expect the event with the greatest assur- ance, and leave no room for any contrary supposition" (1777, p. 58). But the fact that we expect past regularities to continue does not give us license to ignore the occurrence of an event which does not conform to them. If in having a "proof" of a law one is warranted in rejecting purported falsifying instances, then it is simply not true that we have "proof" of any law. The rejection of a testimony pertaining to a miracle on the ground that it conflicts with our accepted theories is dogmatic and contrary to scientific practice. It sanctions the rejection of any conflicting testimony, rendering our theories immune from refutation.

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Hume hinted at a more promising line of argument against belief in miracles. Suppose, he argued, "all authors, in all languages, agree, that from the first of January 1600, there was a total darkness over the whole earth for eight days . . , it is evident, that our present philosophers, instead of doubting the fact, ought to receive it as certain, and ought to search for the causes whence it might be derived" (1777, pp. 127-128). Perhaps Hume was reasoning as follows. Even when testimony to the apparently miraculous is so well established that it cannot reasonably be rejected, then we still do not have grounds for believing in a miracle. Rather, we have a good reason to believe that our currently held theory of the laws of nature is mistaken. To gee whether the argument is cogent, it needs to be developed further, and the distinction between the improbable and the incredible must be more closely examined. This will be done in the next section.

V

I shall now provide an account of credibility which will show Hume was mistaken in identifying the incredible with that which violates a law of nature. It will also explain why he erred: credibility and conformity to law often go together. And it will lend limited support to Hume's injunction against believing in the occurrence of miracles.

Our willingness to accept an observation (testimony) depends (at least partly) on the effect it will have on the coherence of our belief- system. Coherence requires logical and probabilistic consistency. It depends, in addition, on the extent to which component beliefs can be explained. Of course, we cannot explain everything. For instance, while fundamental laws may be used to explain, they remain unex- plained. So perhaps there is no perfectly coherent belief-system. But ceteris paribus, the more we can explain, the more coherent our beliefs will be.

For a Bayesian, the value of coherence will be reflected in the way he assigns prior probabilities. Coherent belief-systems (conjunctions of jointly coherent beliefs) will be, ceteris paribus, antecedently more probable. And everything else being equal, the probability of a theory

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conditional on some observation will be higher the better the former explains the latter. Once the observation is made, and we modify our probabilities by conditionalising on our newly acquired evidence, the theory's posterior probability will reflect its explanatory value. Thus, finding the suspect's fingerprints on the murder-weapon raises the prob- ability that he is guilty: the supposition explains the evidence, and is, therefore, rendered more credible by it.

Belief in a proposition contravening an accepted theory adversely affects coherence. For it either introduces an inconsistency, or - if we give up the theory - reduces the system's explanatory strength (the theory can no longer be invoked to explain phenomena within its domain). Explanatory coherence plays an even more prominent role in determining our (rational) attitude towards testimony (and obser- vation) pertaining to phenomena which do not violate laws of nature (telepathy, e.g.). Improbable events which can be explained are more credible than those which cannot. When confronted with testimony, we must either explain why the witness should testify falsely (whether sin- cerely or deceitfully), or alternatively, account for his testimony being true (explain the event which he reports). Hume described possible motives for lying, but in the absence of independent warrant for ascrib- ing them to the witness, the explanation is not well-confirmed. If it is the only one available, it may gain some credence; but if it is too pre- posterous (the witness is of impeccable honesty and unimaginative), we will believe an event has occurred which we cannot (as yet) explain, rather than infer the truth of the best (but very poor) explanation that we have. This explanation leaves some questions unanswered: Why did the witness lie? How could he have thought up the fantastic tale?

The same methodological principle applies to purported observa- tions. We have become used to the idea that theories are confirmed by observations they explain. With the blurring of the distinction between theory and observation comes the converse idea: that observations are made credible by theories which explain them. In assessing the veracity of an observation, one has to compare the credibility of explanations (if any) of it being true (explanations of the event purportedly observed) with explanations of it being false (one's instruments were faulty, one was dreaming, hallucinating, or being played a trick upon). If the

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latter kind of explanation is deemed ludicrous (sufficiently improba- ble or itself mysterious), the occurrence of an anomalous event will be acknowledged, and a more adequate explanation sought. We have here a principled way of rejecting the genuinely incredible, while admitting bona fide anomalies.

We can now apply our account of credibility to miracles. That a testimony (or observation) conflicts with an accepted theory does not suffice to vitiate it. Anomalies are recognised within scientific theories even before the advent of rival theories which can accommodate them. To be sure, they are less easily admitted than equally improbable obser- vations which "cohere" with an accepted theory. But if well-attested, their occurrence will be, nonetheless, credible: the supposition that the relevant observations and testimony are all false mars the coherence of our belief-system to a much greater extent. This is, indeed, what Hume had in mind when he suggested that we ought to believe in the occur- rence of eight days of darkness, our "testimony be[ing] very extensive and uniform" (1777, p. 128).

Hume suggested, further, that we "ought to search for the causes whence [this event] might be derived" (1777, p. 128). Now, one way of doing this is to view the purported miracle as a falsifying instance of the law of nature we have formulated; i.e., not a miracle at all. Striving for coherence, we ought, then, to find the true law of nature, relative to which the purported miracle will no longer be anomalous (inexplicable). But there is another way.

It is true that a miracle, by Hume's definition, contravenes the laws of nature, and cannot, ex hypothesi, be "naturally" explained. But its occurrence is susceptible to an explanation of a sort; an explanation to which Hume's definition of a miracle as "a transgression of a law of nature by a particular volition o f the Deity" (1777, p. 115, italics partly removed) points. If miracles aren't credible, it must be because the explanation is somehow deficient; because, unlike Newton's theory, for instance, the theological hypothesis doesn't engender enough of an explanatory gain to offset the decrease in simplicity and economy. The theological explanation of a miracle ("God wished it") brings with it too many new mysteries. Why does God have the desires that he does? How does he impose his will upon the world (Goldman, 1988, p. 212)?

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to say that he does it by "a simple act of will" (Alston, 1993, p. 79) is not at all explanatory.

In criticising the argument from design (1777, section XI), Hume allowed - somewhat grudgingly- the inference from the order in nature to the existence of a creator. What he objected to vehemently was the attribution to Him of qualities, such as benevolence and justice. Such attributions cannot be warranted, Hume argued, because "when we infer any particular cause from an effect, we must proportion the one to the other, and can never be allowed to ascribe to the cause any qualities, but what are exactly sufficient to produce the effect" (1777, p. 136). Consequently, we "have no reason to ascribe to these celestial beings any perfection or any attribute, but what can be found in the present world" (1777, p. 138).

Perhaps Hume's concession was rhetorical. Even were he to allow that the world had a cause, he could still "deny a providence and a future state" (1777, p. 135); i.e., the attribution to the creator of particular traits, such as justness. Hume shouldn't have allowed the inference to God's existence. Perhaps (Salmon, 1984) every explanation must be causal. But the very citing of a cause may not be very explanatory. To be told that the butler did it only explains the murder if we are also told how he managed to fake his alibi and leave the room locked from the inside. The bare theological hypothesis, reporting the existence of a creator, provides a very poor explanation of "the order, beauty, and wise arrangement of the universe" (Hume, 1777, p. 135), and is, therefore, unwarranted. But if we had a full-blown theological theory, providing a genuine explanation of miraculous occurrences, both it and the miracles which it explained would gain credibility. Of course, Hume would have admitted that a miracle could be countenanced after the theological theory was established. But this would require the provision of independent warrant for the theory. I am urging the possibility of rendering belief in God and the occurrence of miracles credible jointly and interdependently.

The methodological considerations adduced above show that we have as yet no adequate theological explanation of either natural or miraculous phenomena. Can its existence be ruled out a priori, by arguing, for instance, that we could never be warranted in accepting

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a theological hypothesis because God's wishes, which an explanation of miracles must invoke, are inscrutable? This strategy is epistemo- logically weak. For if the claim is true, it cannot be confirmed as part of a theory of divine psychology: one cannot appeal to claims about unknowable entities. The claim that God's wishes are inscrutable can only be justified on the basis of our failure to know them. It will be refuted by a successful theological theory.

An alternative strategy for ruling out a pr ior i the acceptability of theological hypotheses is to argue that any event which can be explained in divine terms can also be explained "naturally". But this behaviour- istic bias is no more tenable in divine psychology than it is in its human counterpart. Just as we prefer the mentalistic explanations common sense provides for actions to those behaviourists adduce, so we might reasonably plump for a future theological hypothesis, should it be suf- ficiently explanatory.

Hume's argument against miracles may be quite cogent if construed contingently: as the claim that we have - as o f n o w - no (testimonial or observational) warrant for believing in the occurrence of miracles. But it may not, p a c e Hume, "be useful as long as the world endures". For who knows what the future may bring in impressive testimony, compelling observations, and innovations in theology?

NOTES

i For an extensive discussion of the cab problem see Cohen's (1981) paper, and responses to it in the same issue. 2 Cohen correctly points out that the distinction between counterfactualisable and uncounterfactualisable probabilities does not mirror that between objective and subjective probabilities. An accidental relative frequency is objective but uncounter- factualisable. 3 Cohen presents the dispute as one about how prior probabilities are to be determined, rather than about their relevance. But since he claims that prior to the testimony the probability does equal the relative frequency, his chamcterisation is misleading. If the evidence changes the prior probability, its assimilation is Bayesian in a Pickwickian sense only. 4 A Corollary of the strong law of large numbers states that with probability 1, the limiting time an event E occurs is its probability.

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5 Of course, a lottery with infinitely many tickets isn't a practical possibility. It is merely intended to elicit our intuitions about the probabilities.

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Department o f Philosophy TeI-Aviv University Ramat Aviv 69978 Israel