Hume defines a miracle as an event that (a) is caused by God (directly, or indirectly through an ‘invisible agent’) and (b) ‘violates’ (or ‘transgresses’) a law of nature (76, 77). This is his answer to the semantic question. Hume then employs this definition in an argument that concludes that it is never reasonable to believe that a miracle has occurred. This is his answer to the epistemological question.
discussion of premise 1
Though Hume would probably say that the epistemological principle stated in premise 1 applies to all beliefs, what he has in mind here is its application to beliefs about ‘matters of fact’ (as opposed to beliefs about ‘relations of ideas’). A matter of fact concerns the way the world actually is, and a relation of ideas has to do with the connections between our concepts. For instance, a matter of fact is that Hume was a bachelor all his life, and a relation of ideas is that all bachelors are unmarried men. Hume's focus on beliefs about matters of fact in his argument concerning miracles is appropriate, because if miracles occur, their occurrence is a matter of fact about the way the world is. Notice that given Hume's definition of a miracle, stated above, premise 3 of his argument is a relation of ideas (a claim about the content of our concept of a miracle) rather than a matter of fact.
According to Hume, ‘experience is our only guide in reasoning concerning matters of fact’ (73). So Hume assumes that all our beliefs about matters of fact are empirical beliefs. Empirical beliefs are beliefs that are based on our experiences of the world rather than beliefs that are grounded in our rational grasp of the relationships between our concepts. Furthermore, the types of empirical beliefs Hume discusses in this context include both beliefs about particular occurrences (i.e., events) and beliefs concerning generalizations about the relationships between types of events. An example of an event is the coming back down of something you've just thrown up in the air. An example of a generalization about types of events is the statement that everything that goes up comes down. That is, this general claim is that the type of event that involves something going up is always conjoined with (followed by) the type of event of that thing coming back down again.
As Hume's examples show, the evidence for some of our particular beliefs about events will often include general beliefs about relationships between types of events. For instance, our evidence for our particular belief that the bread we are about to eat will nourish us is our general belief, based on our past experience, that ‘all bread nourishes us’. Hume points out that, though some types of events are invariably conjoined with other types of events (as in the case of bread and nourishment), other event-type combinations are variable. Hume's example of a person reasoning about a case of this latter sort is of ‘one, who in our climate, should expect better weather in any week of June than in one of December’ (73). People with such expectations have occasionally been mistaken, because though this generalization about the weather in Great Britain is usually true, it is sometimes false.
We are now in a position to appreciate why it is that Hume says that reasonable people will proportion their beliefs to the strength of the evidence they have for them. In some cases our experience is that two different types of events have been constantly conjoined without a single exception. This is the case with the types of events of eating bread and being nourished. Hume thinks that in such cases reasonable people will have the highest degree of assurance that the bread they are about to eat will nourish them. In Hume's view, believing with this maximal degree of confidence is appropriate because the evidence of experience in this case provides a proof of the particular belief in question. That is, since experience has shown that eating bread is uniformly associated with being nourished, we have the strongest possible experiential evidence that the bread we are about to eat will nourish us.1 Thus, it is reasonable to have the strongest degree of confidence that our expectation is true.
However, in cases in which our experience is not uniform but variable, as it is with weather conditions, the evidence provided by our experience is weaker, and so does not constitute a proof that a given unobserved weather condition in a certain place and during a certain month will be similar to the observed weather conditions at that place and during that month in previous years. In such cases the evidence only supports a particular expectation with some degree of probability or other, short of complete proof (where the degree of probability depends on the frequency with which the types of events in question occur together). Hume points out that reasonable people are more cautious in their expectations when their evidence makes the expected outcome only probable rather than certain, and their degree of caution is correlated with the relative strength of their evidence.
discussion of premise 2
Premise 2 of Hume's argument is about laws of nature. Hume construes laws of nature as contingently true universal generalizations (though this is not his terminology).2 A universal generalization is a statement of the form ‘All As are Bs’. In the case of laws of nature, the ‘A’ and ‘B’ are placeholders for types of events. A universal generalization is contingently true if and only if it is actually but not necessarily true (in the logical or metaphysical sense) that every A is also a B. In the discussion of premise 1 above, the claim that all instances of eating bread are cases of being nourished would qualify as a law of nature in Hume's sense, whereas the claim about weather in Great Britain would not. To say that a universal generalization relating types of events is true is to say that the two types of events it relates are uniformly, invariably, and constantly conjoined. If there is just one instance of an event of type A not also being an event of type B, then the universal generalization that all As are Bs is false. So if it is true (and a matter of fact) that all As are Bs, then according to Hume, it is a law of nature that all As are Bs. If instead there is at least one A that is not a B, then it is not true, and so not a law of nature that all As are Bs.
To say that a law of nature of the form ‘all As are Bs’ has been violated is simply to say that there has actually been an A that was not a B.3 So the law that if you eat bread you will be nourished would be violated if there were just one instance of someone eating bread and not being nourished. Thus, if a law of nature of the form all As are Bs is unviolated, it is a true universal generalization, and if it is violated, then it is true instead that some As are not Bs and so false that all As are Bs. Consequently, for every statement that expresses a law of nature in Hume's sense (as I interpret him), there is a corresponding statement that expresses a state of affairs that would be a violation of that law, and these pairs of statements are logical contradictories. That is, a natural law statement is true if and only if the statement expressing its (possible) violation is false. For instance, it is true that all bread nourishes if and only if it is not the case that there is some bread that does not nourish.
Since natural law statements and statements expressing their violation are contradictories, evidence for one will be evidence against the other. If we have reason to believe that it is a law of nature that all As are Bs, then we thereby have reason to believe that there is no violation of this law, and if we have reason to believe that some As are not Bs, then we have reason to believe that there is no law that all As are Bs.4 What should we do if we have evidence for the claim that all As are Bs and evidence for the claim that some As are not Bs (and so that not all As are Bs)? Since reasonable people will proportion their beliefs to the evidence they have for them, what we should do in such a case depends on whether the evidence for the law is stronger than the evidence against the law or vice versa. If the evidence both pro and con is equally weighty, then we should suspend belief. But Hume says (and this is premise 2), that every law of nature is such that the evidence that it has never been violated is stronger than the evidence that it has been violated. So Hume believes that reasonable people will never believe that a law of nature has been violated. What kinds of evidence do we have for laws of nature and for their alleged violations, and how much of each of these types of evidence do we have?
Since both natural law statements and statements of the alleged violation of a natural law fall into the category of ‘matters of fact’, the kind of evidence required to support each type of statement is experience. However, though the type of experiential evidence necessary to justify both types of claims is perception or observation at the foundational level, on Hume's account of laws of nature these universal generalizations require inductive support as well. With respect to event types A and B, we are justified in believing that all As are Bs if and only if we have observed a sufficient number of As being conjoined with Bs (and no As that fail to be Bs). The type of experiential evidence adequate to justify a claim that an alleged law of nature of the form ‘all As are Bs’ has been violated is instead a single observation on someone's part of some A that is not a B. Now Hume appears to assume that no one among his readers will have access to such perceptual evidence; he discusses only cases in which we have access to testimonial evidence – evidence provided by someone else who claims to have witnessed a miracle. So the type of evidence that supports natural law claims is inductive and the kind that supports natural law violation claims is observational or testimonial.
Why does Hume think that the inductive evidence that supports a natural law claim is always stronger than the (observational or) testimonial evidence that supports the claim that this natural law has been violated? Well, he states that the laws of nature have been established by ‘a firm and unalterable experience’ and that, since ‘a miracle is a violation of the laws of nature . . . the proof against a miracle . . . is as entire as any argument from experience can possibly be imagined’ (76). He also says that there must ‘be a uniform experience against every miraculous event’ (77).5 What is this experiential evidence for the laws of nature (as Hume conceives them) that is ‘firm’, ‘unalterable’, and ‘uniform’ (and therefore constant, invariable, and exceptionless)? Though Hume does not answer this question in any detail, it seems clear that he has in mind the collective experiences of human beings throughout history. Hume implies that it is a law of nature that dead people stay dead. He does so on the grounds that a dead person's coming to life ‘has never been observed, in any age or country’ (77). So Hume implicitly assumes that the universal generalizations that constitute the laws of nature have been established and proven to be true (and thus unviolated) on the basis of human experience in every time and place.
But what about those human beings who provide testimonial evidence that they have observed a violation or falsification of one of these universal generalizations? What, for instance, about the claims of over 500 people to have seen Jesus of Nazareth alive again after his death (Holy Bible, I Corinthians 15.3–8)? If their claims are true, then Hume is wrong to say that a dead person's coming to life ‘has never been observed in any age or country’ (77). Hume is willing to grant the possibility that someone's testimony could establish that there has been a violation of a law of nature. But in order for this to happen, the falsehood of the testimony must be ‘more miraculous’ (and thus less probable) than the alleged miracle for which the testimony is evidence (77). What this seems to boil down to when expressed more simply is that it must be more likely that the person who claims to have witnessed a miracle is telling the truth than that this person is either lying or deceived.
Hume gives two reasons for thinking that, in spite of this theoretical possibility, it can never be established or proven on the basis of testimony that there has been a violation of a law of nature. The first reason is that, even if it should be more likely that a person reporting a violation of natural law is telling the truth than lying or deceived, the strength of this testimonial evidence must be diminished by the strength of the counterevidence – which is the evidence for the claim (in the form of general human experience) that the law of nature in question has not been violated after all. So the best we can hope for is probability rather than proof. The second reason Hume gives for his claim that there cannot be testimonial proof of a natural law violation is that there has never been testimonial evidence of sufficient strength to support the conclusion that alleged eyewitnesses to miracles are more likely telling the truth than lying or deceived. It follows that testimony has never proven nor even made probable a miracle claim. Hume devotes most of Part II of ‘Of Miracles’ (78–90) to his defense of this allegation, but space limitations preclude further discussion of it here.6
discussion of premise 3
In ‘Of Miracles’, Hume does not defend his definition of ‘miracle’ by means of argument, and he does not suggest the possibility that there are any alternative ways to understand the concept. Nor does he provide a justification of or a competitor for his analysis of the concept of natural law, which is included in his definition of ‘miracle’. However, in earlier sections of the Enquiry, Hume argues that natural laws are nothing but descriptions of general causal relationships between events. He then contends that these causal principles are nothing but statements of the constant conjunction of similar events from which we infer effects from causes and vice versa (54–5). As an empiricist, he is skeptical about the existence of unexperienced forces or causal powers in objects or necessary connections between events (39–53). This explains why it is appropriate to say (as articulated above) that he views natural causal laws simply as contingent universal generalizations of the form ‘All As are Bs’ and violations of these laws (miracles) as cases in which there is an A that is a not a B. These universal generalizations are simply summaries of our discoveries of ‘the constant conjunction of similar events’ (As and Bs).7
Since we never discover a force or power that necessitates a connection between As and Bs (e.g., eating bread and being nourished), our only basis for confirming that there is a constant conjunction between them is our repeated experience of their joint occurrence, and the more experience of this sort we have, the stronger our evidence for the truth of the generalization. As we have seen, Hume assumes that the more experiential evidence we acquire that confirms such generalizations, the more experiential evidence we possess that disconfirms counter-claims (violations, miracles).