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Here's a summary of his conclusion about induction.

Thus not only our reason fails us in the discovery of the ultimate connexion of causes and effects, but even after experience has inform'd us of their constant conjunction, 'tis impossible for us to satisfy ourselves by our reason, why we shou'd extend that experience beyond those particular instances… . We suppose, but are never able to prove, that there must be a resemblance betwixt those objects, of which we have had experience, and those which lie beyond the reach of our discovery. A Treatise of Human Nature 1.3.6.11, 1739-40

... and a summary of his argument against miracles.

…. A miracle is a violation of the laws of nature; and as a firm and unalterable experience has established these laws, the proof against a miracle, from the very nature of the fact, is as entire as any argument from experience can possibly be imagined. Why is it more than probable, that all men must die;….; unless it be, that these events are found agreeable to the laws of nature, and there is required a violation of these laws, or in other words, a miracle to prevent them? …. It is no miracle that a man, seemingly in good health, should die on a sudden…. . But it is a miracle, 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 appellation. 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;…. An Enquiry Concerning Human Understanding 1.10.1.90, 1748

I don't see how these views can be reconciled.

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    "Even after experience has inform'd us of their constant conjunction, 'tis impossible for us to satisfy ourselves by our reason... 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". Reason cannot be satisfied with just about anything, but experience provides an argument against miracles "as entire as any argument from experience can possibly be". What is there in need of reconciliation?
    – Conifold
    Commented Oct 31, 2022 at 20:23
  • @Ludwig V. I agree. Hume should have explained this. Is there any passage where he does so? Commented Oct 31, 2022 at 21:04
  • This is an excellent question. Given Hume's views on empirical knowledge, his views on miracles degenerates into the observation that people are led by their mental faculties to expect miracles to be impossible--which is, of course, exactly what makes it a miracle. Commented Nov 1, 2022 at 3:37
  • @conifold Yes, but in his discussion of induction (though I realize that he never uses that term), he is very clear about what proofs experience can and cannot provide. Hume assumes that our experience to date does not provide support for miracles. But that does not prove anything about miracles in the future. But that is exactly what he is trying to persuade us of in this passage. True, he is talking about probabilities here, but his argument applies to any probability of miracles that we find in our past experience. Full disclosure - I think Hume's miracles argument is a very persuasive.
    – Ludwig V
    Commented Nov 1, 2022 at 8:12
  • @David Gudeman Thanks for the compliment. You comment is an interesting move, but I'm not clear what conclusion you might draw from it.
    – Ludwig V
    Commented Nov 1, 2022 at 9:54

2 Answers 2

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I'll give a modern take on reconciling them that I can't promise is rooted in anything Hume himself clarified for the benefit of any reader who might critique him as you have.

On the one hand, Hume argues he can't know of natural laws; on the other hand, he takes them for granted in critiquing miracles. You could just as easily chastise him elsewhere because, on the one hand, he argues he can't know of causation, but on the other hand he takes it for granted in critiquing free will. (His argument against knowledge of causation is completely different from the one against inductively derived natural laws; it's worth a read.)

To both of these objections, we can present an answer called epistemic contextualism. The basic idea is there are multiple types of knowledge. Consider skeptical syllogisms of the form

P1. I don't know not-h

P2. If I don't know not-h, I don't know p

C. I don't know p

Now let's admit "know" may be ambiguous:

P1. I don't A-know not-h

P2. If I don't B-know not-h, I don't C-know p

C. I don't D-know p

This syllogism is only valid if A is B and C is D, and how plausible P2 is depends on the choices of B, C, and may even require B to be C. This is how you can respond to people who say "you don't know you have hands because you don't know you're not a brain in a vat". You don't have were-it-otherwise-I'd-notice knowledge you're not a brain in a vat, but you have I-can-see-them knowledge of your hands, which is typically all you care about.

Now onto Hume. On the one hand, he argues against the possibility of having one particular kind of very demanding knowledge of something. For instance, his argument against induction is basically that we have neither a priori nor non-circular a posteriori knowledge that the unexperienced will be like the experienced. You "know" it will in a cheaper sense, such as that expectation having predictive and explanatory power, concordance, and so on. But, for whatever reason, Hume takes it as read, even if only by psychological compunction, that natural laws exist in the middle of his anti-miracles argument. Insofar as he "knows" of the laws, they have certain implications.

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  • Well, if I've understood right, you would say that Hume A-knows that natural laws are predictive and B-knows that they are not. Yes? It could work provided it is clear which sense of "know" he is using. Do we get to have an opinion about whether it is appropriate for him to switch contexts? If we do, I would suggest that in this case, it is not. Either way, it makes it difficult to assess arguments.
    – Ludwig V
    Commented Nov 1, 2022 at 11:08
  • @LudwigV There's no one proposition he both knows to be true and knows to be false, even with "knowledge" having multiple senses. Ironically, "predictive" may have a context-dependent meaning in your confusion as well. You must distinguish laws being predictive in the sense Nature obeys them so their predictions are accurate from their being predictive in the sense we know such predictions will be accurate, which subdivides based on the sense of knowledge. (By the way, your use of A and B is reversed relative to my answer.)
    – J.G.
    Commented Nov 1, 2022 at 11:26
  • @ J.G. I'm sorry my last reply was so confusing. I think Hume and I are interested in how we can make predictions and know that they are true. Hume does identify a kind of psychological compulsion which he calls custom or habit, but doesn't confuse that with proof. He gives a kind of justification by saying that these predictions are useful. However, he doesn't offer any proof of that, which leaves me nowhere.
    – Ludwig V
    Commented Nov 2, 2022 at 13:01
  • @LudwigV If your question is how his stances can be reconciled in modern terms, we can claim he only refuted one kind of knowledge claim for natural laws but not another. If your question is how Hume would have reconciled them, my guess is he didn't mind arguments with premises which had his confidence but which he would admit he couldn't know were true. The modern option is obviously more satisfying. (Hume does the same thing, by the way, with ethics: he's famous for the is-ought gap, but he also advocated specific ethics, including conservatism.)
    – J.G.
    Commented Nov 2, 2022 at 13:05
  • @J. G. It's beginning to look as if there are a number of inconsistencies in Hume's work. This one, between causation and free will and yours in ethics. H'm. But this epistemic contextualism has me confused. He refuted the claim to prove knowledge of natural laws a priori. Are you suggesting our psychological compulsion to believe them is a knowledge claim? That seems odd.
    – Ludwig V
    Commented Nov 2, 2022 at 13:13
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We are encouraged to answer our own questions and to share our research. So I would like to share my thoughts on the question after the very helpful discussion of it.

When I asked the question, I quoted from A Treatise of Human Nature. In this answer, I have restricted myself to An Enquiry Concerning Human Understanding because one can expect the Enquiry to be self-consistent and there is no need to get involved in assessing the differences between the two for the purposes of the question.

Hume's project

Hume summarizes his project in the final section of the book (Section 12 Of the Academical or Sceptical Philosophy). It is to identify the proper scope of human knowledge and get rid whatever is useless. This means we should “commit to the flames” any volume of divinity or school metaphysics that does not contain either "abstract discussion of mathematics (quantity or number)" or "of matter of fact and existence".

Which seems clear enough, if a bit radical. Divinity and metaphysics are condemned because they try to extend the scope of human reason beyond what it can do. It gives rise to excessive scepticism and vacuous ideas with no basis in experience. Some divinity gets a pass because “It has a foundation in reason, so far as it is supported by experience.” “But” he continues “its best and most solid foundation is faith and divine revelation.” (Section 12.3). However, his critique of reason does allow for a role for reason, with limitations.

He explains the project in a different way in the body of the section, where he distinguishes between Pyrrhonism or excessive scepticism and what he calls mitigated scepticism.

Excessive scepticism is the philosophical scepticism we are familiar with from Descartes and Berkeley. Hume believes that it is difficult, if not impossible, to refute. His main objection is that no lasting good can come of it, and he prescribes “action, and employment, and the occupations of common life” as a cure. This respect for common life shows at several points in his philosophy.

Mitigated scepticism is characterized in two ways. Part of proper thinking, he says, is “a degree of doubt, and caution, and modesty …, in all kinds of scrutiny and decision.” The other characterization is the result of Pyrrhonian scepticism. It is “the limitation of our enquiries to such subjects as are best adapted to the narrow capacity of human understanding.” (Section 12.3)

The problem

In Section 10.1 Of Miracles Hume offers “uniform experience” as “proof, full and entire” for his proposition that miracles are impossible. How does he get that from his argument against induction in Section 4 Sceptical Doubts Concerning the Operations of the Understanding?

Proof

In Section 4, he presses home the key point that experience in the past cannot be extended to cover experiences in the future, or indeed any experiences not yet known. In Section 5 Sceptical Solution of these Doubts he does not abandon empirical generalizations but argues that they are customs or habits, arising from the imagination, which calls up the idea of the effect when the idea of the cause is presented; he calls this the association of ideas. He argues that this is a good thing, because it is useful. He also claims (in Section 5.2) that “we find (sc. have found in the past) a pre-established harmony between the course of nature and the succession of our ideas”. All this runs up against the sceptical objection of course, but this isn’t about what is rational. It is about what we do.

In a footnote to the title of Section 6 Of Probability Hume cites Locke’s distinction between “demonstrative” and “probable” arguments; Hume objects that this means that it is only probable that everyone must die. He proposes that we classify arguments as demonstrations, proofs and probabilities. “By proofs meaning such arguments from experience as leave no room for doubt or opposition.”

So he does explain to the attentive reader how he will use the term ‘proof' in future. One might object that the aim of proof is justification of belief, while an account of the mechanism that generates belief is not, or not necessarily, a justification of belief. So it seems odd to suggest that his account of the genesis of customs or habits is a justification of them. But presenting evidence will cause belief, so the aim of proof is achieved. In practice, this will mean that “uniform experience” will amount to a proof. The ruling out of doubt or opposition is rather surprising, but it is hard to argue with the examples he offers later in the same section – “Fire has always burned, and water suffocated every human creature: The production of motion by impulse and gravity is an universal law, which has hitherto admitted of no exception.” (Section 6)

He seems in no doubt that he has succeeded in resolving the sceptical doubts, but without directly refuting excessive scepticism; that would certainly explain the odd title of Section 5 - Sceptical Solution of these Doubts. So the difference between his discussion of induction and “custom or habit” in Section 5 and his presentation of the argument against miracles in Section 10 is really just a change in emphasis and presentation.

Miracles

Hume tells us that “A miracle may be accurately defined, a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent.” (Footnote in Section 10.1) His long argument against the testimony for miracles culminates in his argument that because a miracle is defined as a violation of the laws of nature, which are established by “firm and unalterable experience”, they are impossible.

Knock-down arguments are very satisfying, but they are rare and I am suspicious of them. In my view this argument is very narrow and over-simplified. Hume does recognize some of the complications, but not all. To understand the topic a wider view is required. But that is beyond my scope.

He even applies his argument to the miracle of the resurrection of Jesus Christ and then declares that the real foundation of belief in that miracle is not reason, or even custom and experience. It is faith. He further says that faith is itself a miracle. So there is no more to be said. It seems that the real point of the section is to show, not only another limitation of reason, but also of custom and experience.

The appeal to faith is a surprise. There is no hint of it Section 4 or 5. On the other hand, it is not exactly incompatible with those Sections 4 and 5.

Hume is following the same strategy in his discussion of induction and of miracles and he is consistent in that. Start with an argument of excessive scepticism, separate what needs to be saved and what must be let go, and find an alternative justification for what needs to be saved. So the argument against causation is allowed to run its course; then an alternative foundation – experience - is found for empirical generalizations and the pre-established harmony between the course of nature and the succession of our ideas” justifies him referring to natural laws that are objectively true. In the same way, the argument against miracles is pressed to the end, at which point, faith saves at least the two miracles that are critical for him.

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  • In other words, Hume deems Pyrrhonian scepticism and scepticism about induction impractical (even though he's famous today for buoying the latter), and the latter's empirical generalizations convinces as readily as anything that should, to the detriment of alleged miracles such generalizations would contradict.
    – J.G.
    Commented Nov 26, 2022 at 14:24
  • @J.G. Yes. Complications. He does have a reputation for buoying scepticism about induction. But he thinks he has solved the problem of induction, by providing something that will do anything that a rational method would. Maybe his solution untenable, but I would like to know why. So his reputation is only half the story.
    – Ludwig V
    Commented Nov 26, 2022 at 17:44
  • @J.G. In the same way, his promotion of the argument against miracles is not what it seems. He presses the argument against some "miracles". But when it comes to the resurrection, faith rescues from his own scepticism. No wonder he thinks that faith irself is a miracle. Note that there's no room for argument about it. I think this is exactly what Wittgenstein had in mind when he wrote that philosophy is a conjuring trick.
    – Ludwig V
    Commented Nov 26, 2022 at 17:45
  • I think Wittgenstein may have been meant something else, but it's funny how a close reading can suggest Hume was a fideist while contemporaneous readers and later scholars have mulled whether he was an atheist. I think one issue here is when he says "X isn't A-resoluble but is B-resoluble" (making his ideas closer to the contextualism my answer discusses than I gave him credit for), later philosophers had their own opinions about which Xs they'll settle for being B-resoluble. So "Hume" became shorthand for "none are A-resoluble", then e.g. Russell agreed on miracles but not on induction.
    – J.G.
    Commented Nov 26, 2022 at 18:20
  • @J.G. I knew he was accused of being an atheist in his own time, but decided to read the text as it stands. But I think it is unfair to get too suspicious of people who may be conforming without enthusiasm but also without scepticism. We all do it in one way or another, in order to get along. I like your diagnosis of why orthodoxy doesn't seem to recognize what Hume was trying to do. I gather that there's a similar issue about Berkeley who also thought he was solving scepticism. No-one really pays any attention to Descartes' route out of scepticism, either.
    – Ludwig V
    Commented Nov 26, 2022 at 22:36

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