David Hume on 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; that lead cannot, of itself, remain suspended in the air; that fire consumes wood, and is extinguished by water; 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? 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. There must, therefore, be a uniform experience against every miraculous event, otherwise the event would not merit that appellation....

The plain consequence is (and it is a general maxim worthy of our attention), 'That no testimony is sufficient to establish 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....' 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. I weigh the one miracle against the other; and according to the superiority, which I discover, I pronounce my decision, and always reject the greater miracle. 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.

In the foregoing reasoning we have supposed, that the testimony, upon which a miracle is founded, may possibly amount to an entire proof, and that the falsehood of that testimony would be a real prodigy: But it is easy to shew, that we have been a great deal too liberal in our concession, and that there never was a miraculous event established on so full an evidence.

From David Hume, An Enquiry Concerning Human Understanding, L. A. Selby Bigge, ed. (Oxford: Clarendon Press, 1902), pp. 114-16.
Commentary
Some may feel that David Hume is hairsplitting, but his central argument is interesting. He holds that to believe a miracle exists, we must believe testimony or evidence as to its truth; but there will always be a stronger reason to believe the testimony or evidence is flawed.

To expand, even if I see something with my own eyes, I do not know for sure it is true: I do not always recognise things correctly even in everyday life; I may be hallucinating through illness, tiredness or drugs; it may be a fraud. And if I have to rely on the testimony of others, the strength of the evidence I have is even weaker, since you can add communication flaws and deliberate lying or deception to the fact that they may be mistaken. Is it more likely that I am deceived, of which I admit the possibility, or that some natural law I hold to be certain is false? Surely the former.

Most of us would hold as a self-evident truth the fact that it is possible for a miracle to happen and for us to acknowledge it as a miracle. But would we really? Would we look for a scientific explanation, or accept that it is a miracle against natural laws (assuming a miracle is by definition something against natural laws)? Would we seek deception, rational reasons we could be mistaken? Are only certain people ever susceptible to believing in miracles? Does it require a credulity, an openness, a belief that rationality is not always the best way to approach the world?

(One criticism is that Hume is disputing our epistemological grounds for believing in a miracle, rather than the question of whether miracles can exist. However, Hume was an empiricist, who believed the evidence of our senses is the only way we can understand the world, and therefore to talk of miracles existing without evidence is as ridiculous as to talk of invisible pink unicorns. And since his concern was largely the argument of the existence of God based on miracles, this approach of Hume's has force.)

David Hume was a clear and unwavering atheist. He sought to demolish what he saw as the superstitions of religious belief. Elsewhere he attacked the main arguments for the existence of God (the ontological argument, the argument from design and the argument from first cause) on the basis that even if these are true they prove nothing about the nature of God, other than that It is an entity capable of creating a universe (no morality, scriptures, etc.) In modern terms, even if we accept God created the Big Bang, that proves nothing else than that something created the Big Bang and we choose to call it God.

The argument against miracles is complementary to that claim, since miracles justify the existence of God on a small scale to individual people in the same way that the ontological argument and other philosophical arguments seem to prove the existence of God in the philosophy class. The latter attacks philosophers; attacking miracles attacks the ordinary believer who may believe they have witnessed something extraordinary. In either case, Hume says, you have no grounds to believe in any religion.

Afterword
It may be argued that Hume is guilty of circular reasoning, by defining a miracle as something which is irrational to believe and then claiming it is irrational to believe in miracles. However, Hume's definition does not depend on his conclusion: if we define a miracle as something which goes against what we believe are certain natural laws, or something far less probable than anything in our natural experience (which includes being tricked and mistaken), there is nothing circular about his argument.

But following from this, we can take Hume's argument as a criticism of the concept of miracles in general, based question of what is the definition of a miracle. If we define that a miracle is something against current natural laws, and expect to prove any miracles exist, we will fail, since many things against past scientific laws are now wholly lawful; and rather than declaring it a miracle, we can formulate a new scientific law.

And if we define it is against all scientific laws both now and in future, there is no way of proving this assertation. We are left with a definition based on probability or believability, which Hume can attack with ease. By this linguistic version of the argument, there is no definition of miracle which allows us to claim miracles exist. (And claiming "A miracle is an act of God" gets you nowhere, unless you can catch God in the act.)