From Asimov's The Robots of Dawn ch. 4 (sect. 16):
Fastolfe sighed. "I'm sure Daneel told you what I have maintained at the inquiry--but you want to hear it from my own lips."
"That is right, Dr. Fastolfe."
"Well, then, no one committed the crime. It was a spontaneous event in the positronic flow along the brain paths that set up the mental freeze-out in Jander."
"Is that likely?"
"No, it is not. It is extremely unlikely--but if I did not do it, then that is the only thing that can have happened."
"Might it not be argued that there is a greater chance that you are lying than that a spontaneous mental freeze-out took place?"
"Many do so argue. But I happen to know that I did not do it and that leaves only the spontaneous event as a possibility."
"And you have had me brought here to demonstrate--to prove--that the spontaneous event did, in fact, take place?"
"But how does one go about proving the spontaneous event? Only by proving it, it seems, can I save you, Earth, and myself."
"In order of increasing importance, Mr. Baley?"
Baley looked annoyed. "Well, then, you, me, and Earth."
"I'm afraid," said Fastolfe, "that after considerable thought, I have come to the conclusion that there is no way of obtaining such a proof."
(This is all from p. 83 of the Bantam edition (April 1994).)
What immediately struck me about this passage, which I read over the weekend was the parallel to the early modern discussion of miracles. The basic story is this: Elijah Baley has been called to the planet Aurora to solve a case of roboticide, in which the robot Jander was sent into a "mental freeze-out," i.e., was mentally shut down. Dr. Fastolfe's enemies, and in particular Dr. Amadiro, have whispered about that Dr. Fastolfe did it for political purposes. Dr. Fastolfe maintains his innocence and insists (everyone agrees) that only he, the most eminent living roboticist, would have the ability to shut down Jander intentionally, and that, since he knows he did not do it, it must have occurred spontaneously despite the enormous improbability of doing so. Baley eventually discovers another possibility. (I'll let you read the book to find out - it is, on re-reading, easily the best of Asimov's Elijah Baley novels.)
If we think in terms of miracles rather than spontaneous events, the parallel is this:
* Dr. Amadiro is David Hume, who argues that we can only believe (on testimony, at least) the occurrence of a miracle if it is more improbable that the person who is informing us of the miracle is deceived or dishonest than that the event itself occurred. This, you will notice from the passage above, is much like the campaign against Fastolfe.
* Some have argued that while no miracles occurred, since the standard causes have been eliminated, nothing but a spontaneous event can remain. (Fastolfe.)
* Both these positions agree on a lot of their assumptions. Others, however, like Lady Mary Shepherd, take the Baley solution to the problem of miracles and try to introduce a sort of causal reasoning other than that allowed by the first two into the consideration of the probabilities. Their conclusion: there can be a causal circumstance other than the standard ones that allows for the existence of a genuine miracle.
The parallel is only loose, and wouldn't exist at all, except that Hume puts so much emphasis on probability alone, and so has difficulty distinguishing miracles and spontaneous events in the first place (for which he is roundly criticized by Campbell and Shepherd).
How would one go about proving that a spontaneous event has occurred? This is, I think, a question that could only be answered if we had a clear idea of the 'metaphysical status' of spontaneity (i.e., when we talk about 'spontaneous events' what does this signify about the real world?). And this is a difficult problem. It bears some thought....