Put simply, Hume argues not only that miracles violate the laws of nature, but that when a miracle is reported it is always more likely that the reporter is either malign or mistaken ("that this person should either deceive or be deceived") than that the miracle is true. For obvious reasons, the latter and highly provocative part of the argument has infuriated some Christians, especially given the reference to the Resurrection in the following quote.
When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened.... If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till then, can he pretend to command my belief or opinion.
See the picture box below for the quote in its wider context.
Origins and text
Hume did not publish his views on miracles in his early, 1739, Treatise, and the sections on miracles were often omitted in early editions of his 1748 Enquiry.
For instance, in the 19th-century edition of Hume's Enquiry (in Sir John Lubbock's series, "One Hundred Books"), sections X and XI were omitted, appearing in an Appendix with the misleading explanation that they were normally left out of popular editions. Although the two sections appear in the full text of the Enquiry in modern editions, chapter X has also been published separately, both as a separate book and in collections.
In his December 1737 letter to his friend and relative Henry Home, Lord Kames, Hume set out his reasons for omitting the sections on miracles in the earlier Treatise. He described how he went about "castrating" the Treatise so as to "give as little offence" to the religious as possible. He added that he had considered publishing the argument against miracles—as well as other anti-theistic arguments—as part of the Treatise, but decided against it so as to not offend the religious sensibilities of readers.
Hume starts by telling the reader that he believes that he has "discovered an argument ... which, if just, will, with the wise and learned, be an everlasting check to all kinds of superstitious delusion".
Hume first explains the principle of evidence: the only way that we can judge between two empirical claims is by weighing the evidence. The degree to which we believe one claim over another is proportional to the degree by which the evidence for one outweighs the evidence for the other. The weight of evidence is a function of such factors as the reliability, manner, and number of witnesses.
Now, a miracle is defined as "a transgression of a law of nature by a particular volition of the Deity, or by the interposition of some invisible agent." Laws of nature, however, are established by "a firm and unalterable experience"; they rest upon the exceptionless testimony of countless people in different places and times.
Nothing is esteemed a miracle, if it ever happen in the common course of nature. It is no miracle that a man, seemingly in good health, should die on a sudden: because such a kind of death, though more unusual than any other, has yet been frequently observed to happen. But it is a miracle, that a dead man should come to life; because that has never been observed in any age or country.
As the evidence for a miracle is always limited, as miracles are single events, occurring at particular times and places, the evidence for the miracle will always be outweighed by the evidence against – the evidence for the law of which the miracle is supposed to be a transgression.
There are, however, two ways in which this argument might be neutralised. First, if the number of witnesses of the miracle be greater than the number of witnesses of the operation of the law, and secondly, if a witness be 100% reliable (for then no amount of contrary testimony will be enough to outweigh that person's account). Hume therefore lays out, in the second part of section X, a number of reasons that we have for never holding this condition to have been met. He first claims that no miracle has in fact had enough witnesses of sufficient honesty, intelligence, and education. He goes on to list the ways in which human beings lack complete reliability:
- People are very prone to accept the unusual and incredible, which excite agreeable passions of surprise and wonder.
- Those with strong religious beliefs are often prepared to give evidence that they know is false, "with the best intentions in the world, for the sake of promoting so holy a cause".
- People are often too credulous when faced with such witnesses, whose apparent honesty and eloquence (together with the psychological effects of the marvellous described earlier) may overcome normal scepticism.
- Miracle stories tend to have their origins in "ignorant and barbarous nations" – either elsewhere in the world or in a civilised nation's past. The history of every culture displays a pattern of development from a wealth of supernatural events – "[p]rodigies, omens, oracles, judgements"– which steadily decreases over time, as the culture grows in knowledge and understanding of the world.
Hume ends with an argument that is relevant to what has gone before, but which introduces a new theme: the argument from miracles. He points out that many different religions have their own miracle stories. Given that there is no reason to accept some of them but not others (aside from a prejudice in favour of one religion), then we must hold all religions to have been proved true – but given the fact that religions contradict each other, this cannot be the case.
R. F. Holland has argued that Hume's definition of "miracle" need not be accepted, and that an event need not violate a natural law in order to be accounted miraculous. It has been argued by critics such as the Presbyterian minister George Campbell, that Hume's argument is circular. That is, he rests his case against belief in miracles upon the claim that laws of nature are supported by exceptionless testimony, but testimony can only be accounted exceptionless if we discount the occurrence of miracles. The philosopher John Earman has recently argued that Hume's argument is "largely unoriginal and chiefly without merit where it is original", citing Hume's lack of understanding of the probability calculus as a major source of error. J. P. Moreland and William Lane Craig agree with Earman's basic assessment and have critiqued Hume's argument against being able to identify miracles by stating that Hume's theory "fails to take into account all the probabilities involved" and "he incorrectly assumes that miracles are intrinsically highly improbable" 
C. S. Lewis, in his book Miracles: A Preliminary Study, argues that Hume begins by begging the question. He says that his initial proposition - that laws of nature cannot be broken - is effectively the same question as 'Do miracles occur?'.
- Hume 1748/2000, 86-87
- Hume 1748/2000, 89
- For the nineteenth century controversy over Hume's argument, see for instance Frederick Burwick, 'Coleridge and DeQuincey on Miracles', Christianity and Literature, Vol.39, No.4, 1980, pp.387ff.
- Hume 1748/2000, 89
- Antony Flew, introduction to Of Miracles, p. 3
- E.C. Mossner, The Life of David Hume, p.58.
- John P. Wright, "The Treatise: Composition, Reception, and Response" ch. 1 in The Blackwell Guide to Hume's Treatise ed. Saul Traiger, 2006, ISBN 9781405115094, pp. 5–6.
- Hume 1975, An Enquiry concerning Human Understanding X, i, 86
- Hume 1975, X, i, 90n
- Hume 1975, X, i, 90
- Hume 1975, X, i, 90
- Hume 1975, X, ii, 93
- Hume 1975, X, ii, 94
- Hume 1975, X, i, 90
- Holland, p. 43
- George Campbell, A dissertation on miracles, pp. 31–32, London: T. Tegg, 1824 
- Earman, Hume's Abject Failure, Preface.
- Moreland, J. P.; Craig, William Lane (2003). Philosophical Foundations for a Christian Worldview. Downers Grove, IL: InterVarsity Press Academic. pp. 569–70. ISBN 0-830-82694-7.
- Burwick, Frederick. 'Coleridge and DeQuincey on Miracles', Christianity and Literature, Vol.39, No.4, 1980, pp.387ff..
- Campbell, George. A Dissertation on Miracles. 1762. Reissued New York and London: Garland Publishing, Inc., 1983. ISBN 0-8240-5403-2
- Earman, John. Hume's Abject Failure. Oxford: Oxford University Press, 2000. ISBN 0-19-512737-4
- Fogelin, Robert J.. A Defense of Hume on Miracles. Princeton: Princeton University Press, 2003. ISBN 0-691-11430-7
- Holland, R.F.. "The Miraculous". In American Philosophical Quarterly 2, 1965: pp. 43–51 (reprinted in Richard Swinburne below)
- Hume, David. Of Miracles (introduction by Antony Flew). La Salle, Illinois: Open Court Classic, 1985. ISBN 0-912050-72-1
- Hume, David. Enquiries concerning Human Understanding and concerning the Principles of Morals (introduction by L.A. Selby-Bigge); third edition (revised and with notes by P.H. Nidditch). Oxford: Clarendon Press, 1975. ISBN 0-19-824536-X
- Hume, David, 1748 et seq., An Enquiry Concerning Human Understanding, Tom L. Beauchamp (ed.), New York: Oxford University Press, 2000.
- Johnson, D. (1999). Hume, Holism, and Miracles. Cornell University Press, Ithaca.
- E.C. Mossner, The Life of David Hume, Oxford, O.U.P., 1980.
- Swinburne, Richard [ed.] Miracles. London: Collier Macmillan Publishers, 1989. ISBN 0-02-418731-3 (contains "Of Miracles")
- "Hume on Miracles" – part of the Stanford Encyclopedia article by Paul Russell and Anders Kraal
- "Of Miracles" – full text as part of the Leeds Electronic Texts Centre's on-line edition of the Enquiry concerning Human Understanding
- "Miracles" – dialogue by Peter J. King
- "Hume On Miracles" – commentary by Rev Dr Wally Shaw