Origins and text
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 in modern editions, chapter X has also been published separately, both as a separate book and in collections.
In Hume's December 1737 letter to Henry Home, in addition to describing how he went about "castrating" his Treatise so as to "give as little offence" to the religious, 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 out 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.
Some writers, such as R.F. Holland, have 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 claimed 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" 
- Antony Flew, introduction to Of Miracles, p.3
- 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, p. 5–6.
- Hume, An Enquiry concerning Human Understanding X, i, 86
- op. cit., X, i, 90n
- op. cit., X, i, 90
- loc. cit.
- op. cit. X, ii, 93
- op. cit. X, ii, 94
- Holland, p.43
- George Campbell, A dissertation on miracles, p. 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. 569–570.
- David Hume Of Miracles (introduction by Antony Flew). La Salle, Illinois: Open Court Classic, 1985. ISBN 0-912050-72-1
- David Hume 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
- Johnson, D. (1999). Hume, Holism, and Miracles. Cornell University Press, Ithaca.
- George Campbell A Dissertation on Miracles. 1762. Reissued New York and London: Garland Publishing, Inc., 1983. ISBN 0-8240-5403-2
- John Earman Hume's Abject Failure. Oxford: Oxford University Press, 2000. ISBN 0-19-512737-4
- Robert J. Fogelin A Defense of Hume on Miracles. Princeton: Princeton University Press, 2003. ISBN 0-691-11430-7
- R.F. Holland "The Miraculous". In American Philosophical Quarterly 2, 1965: pp 43–51 (reprinted in Swinburne)
- Richard Swinburne [ed.] Miracles. London: Collier Macmillan Publishers, 1989. ISBN 0-02-418731-3 (contains "Of Miracles")