Okay, in the next few posts that I manage to make I'm hoping to deal with some major religious...things. Too vague? I can't really come up with an all-encompassing term to describe them. The idea of free will, the argument that the universe is fine-tuned (for...something...), the various implications that using naturalism/empiricism/whatever means that you are excluding "other types of explanations," and, in this post, the idea of miracles. If you can come up with a clear categorical term for these, feel free to mention it. Otherwise "things" seems sufficient.
So, what is a miracle? A very rough definition you could use (or that I will effectively be using here) is "anything that could serve as proof of something supernatural at work". So here are some basic categories: prophecy, exceptional good fortune, obvious violation of natural law, and personal revelation. I'll elaborate on each separately.
As a general rule of thumb, something probably shouldn't be considered a miracle or supernatural if there is an adequate natural explanation for it. What one considers an adequate natural explanation or simply just desperate handwaving is, I suppose, a personal perspective. It is sometimes a hard distinction. Other times, not so much.
Prophecy: Accurate predictions of the future. Of course, one may need to qualify this a bit. Predicting that there will be war in the future, that a given person will die, or that the sun will rise tomorrow, even if accurate, should not be considered prophetic. Why? Because these things can be concluded inductively, since war, death, and sunrises have effectively been constants in the course of human existence. In other words, they are obvious.
Other things can mar one's ability to declare something to obviously be prophecy. The alleged prophecy being only mentioned or recorded after the event that it predicts is one thing that makes the claims questionable. Another is an excess of metaphor, symbolism, and references to vague (or commonplace) events as indicators of when the predicted occurrence will happen. A good acid test for a prophecy is to determine whether there is only a select few events that it could possibly be referring to, and if that event could have been predicted before it actually occurred using the prophecy.
Most recorded prophecies suffer from vagueness and overuse of symbols to allow you to interpret the prophecy as possibly predicting an event after it has already occurred by imposing your knowledge of the completed event on those symbols, filling them with meanings after the fact.
So, in order to get a good prophecy with the possibility of being supernatural in origin (rather than being merely psychologically exploitative poetry or predictions from Captain Obvious), one should make it clear what you are predicting. Literal language, details that could not be easily guessed, and a specific time frame (and, ideally, location) where it is supposed to occur are necessary. "A king draped in a mantle of darkness will descend upon the land of the lost sheep, and blood will rain from the sky" as a prediction for a war is bad. As is "something bad will happen on October 6th" or "a building will fall in Canada". In the first example, if you don't take it literally, you can make it mean anything you want with the basic format "bad authority hurts helpless things". The second is too vague to predict anything, and the fact that it does not limit itself geographically virtually guarantees accuracy (also not mentioning a year is helpful). The third is probably the best prediction, save for one key problem: no time frame at all (well, and not a lot of detail). With such a prophecy you are just perpetually waiting until the prediction is finally, inevitably confirmed, because there is no way that you can ever be wrong.
One final problem with prophecies: the self-fulfilling kind. If a certain prediction relies on human behavior and the humans involved are well aware of the prediction, they may go out of their way to bring it about (or to prevent it from happening, I suppose). I personally would put the re-establishing of Israel as a country in this category, as an example.
If you can avoid all of these pitfalls, then there are just two possibilities left: the predictor has supernatural knowledge or it was a lucky guess. Determining the probability of guessing such a thing correctly is pretty much all you have left to do, and at that point you can comfortably assume that there is something weird at work. I'll reference the implications of "proving" the supernatural using such methods at the end.
Exceptional good luck: This is one is purely weighing probability. A few examples of this (that are often the sole things the word "miracle" is used to describe in real life) are spontaneously recovering from an illness or disability (cancer, blindness, paralysis) and surviving a catastrophe (fire,plane crash, getting shot). Other similar things are getting money at just right time, and other fortuitous coincidences. The only conditions in which I would personally deem spontaneous recovery a miracle is when it is not only unlikely, but when it is seen as near impossible and there is no known biological mechanisms involved that would help explain how it occurred. The same is at play for survival, but more often than not, the cases of surviving a catastrophe are obviously not miracles. It is just probability at work. 99 people die in a plane crash and one survives is not evidence of a miracle, but just of that one who did survive being a somehow more ideal position during the crash. Only if there was a clear violation of the laws of physics or something to that effect does such "luck" become possibly supernatural. As for coincidences, it is very hard to say. The improbable is not necessarily impossible, and countless improbable things happen everyday. Determining whether something is serendipity or simply just a happy consequence of chance is nearly impossible to do, and frankly, as a result, I think it is very hard to use such things as evidence either way.
Obvious violation of natural law: For a few minutes in downtown Detroit, gravity pulls you up. The sun suddenly vanishes from a clear sky. A river turns into blood and is chemically verified as such. The girl down the street turns into salt. A city vanishes from the map when it is decimated by a single massive beam of light. In short, this kind of miracle is the most impressive, and involves things working one way for the rest of recorded human existence, and then suddenly something completely unprecedented and unexplainable happens. There are still some problems though.
First off, a violation of natural law that occurs predictably and in a repeated manner is not a violation of natural law but simply an indication that the natural laws as we have formulated them are in error.
Second, if there is no concrete evidence of the event occurring and only eyewitness testimony, it is actually more probable that the event was a case of hallucinations, mass hysteria, or an elaborate lie. The probability of this being the case decreases with the number of first hand accounts, however.
Finally, an unprecedented or unexplained event does not necessarily mean that it was supernatural in origin. In other words, it may be that attributing the event to divine agency is God of the gaps thinking and that there may be unknown natural mechanisms behind it that have yet to be thoroughly explored or understood. This applies to all miracles, so in a way miracles aren't as much proof of the supernatural as "unknowns" that may be supernatural. Furthermore, such unknowns tell us no more about the nature of the supernatural or about any other things involved in the supernatural. The miracles themselves are the full extent of the supernatural that we could possibly be aware of.
With all that said, there are certainly situations which you couldn't be blamed for taking an incredibly improbable event that is currently unexplained by science (and, ideally, contradictory to it). These are violations of natural law that you personally witness and experience. The reasoning for this is given in the description of the "personal revelation" category below.
Personal revelation: Something common with most of the categories above is that they mostly rely on weighing the chances of an event happening and deeming it unlikely to occur and therefore more likely supernatural (the threshold for this, of course, being debatable). Another is that they mostly rely on second-hand accounts. Personal revelation is different, in that it is based on you directly getting a message in some manner from a clearly non-natural source. You see an angel, or hear the voice of God in your head.
Key point: other people's personal revelations are irrelevant. You have no idea about the nature of it. It could have been a dream, a hallucination, a completely misremembered mundane event, something they saw on T.V. and received as a false memory of their own life, or they could be outright lying to you. You have no idea whether this is the case for them because you did experience it yourself. Only having a personal revelation yourself serves as anything more than anecdotal evidence for the purpose of convincing yourself about the veracity of a miracle. You will be able to know that you are not lying or dreaming, and you have one other key benefit over other people.
You need to assume that you are sane.
In order to function at all, people need to assume that they are not themselves completely insane unless given adequate external evidence that they indeed are (i.e. clear accounts by others about how your perceptions contradict reality). As a general rule of thumb, though, if your personal revelation would pit you against the well-being of other people...you are either insane or just got a revelation from something/someone who is not worth obeying. Other than those cases, getting a personal revelation yourself is more than an adequate to believe in the supernatural, even if it isn't necessarily logical for a strict use of the word.
As mentioned before, even if you do come across an actual miracle, it could only prove the supernatural in so far as the miracle itself (i.e. the only aspect of the supernatural that is proven to exist is the miracle in question). And, also as mentioned before, it is very hard to prove that something is a miracle as much as simply disprove that it occurred by (known) natural processes. This is essentially what the saying "extraordinary claims require extraordinary evidence" alludes to: the fact that a miracle would have to almost pull off a miracle in order to even be considered a miracle. This level of difficulty is often taken as the fault of the mode of naturalistic logic that makes it almost impossible for a miracle to be proven, suggesting that it is an almost deliberate attempt to exclude such things as even a possibility. I will try to address that basic concept in a later post.
Thank you for your time [staggers off stage]