Every semester I guest speak at a local college for philosophy and religion classes. Today the question of miracles came up, and the more I argued that they did not happen the more I realized that claim is impossible to make. There are too reasons for this. (1) Even if out of all the humans that ever lived there was not one person who rose from the dead, to say rising from the dead is impossible because of this is a huge leap of statistical faith.
Kinda sorta. Inductive reasoning can never get you to perfect certainty. However, this doesn't mean we should dismiss inductive reasoning as completely worthless, especially if we're talking about "certainty for all practical purposes" instead of "perfect certainty."
Consider an example that doesn't rely on miracles or the like:
While swimming in the ocean, there is a very small but non-zero chance that the random fluctuations in salt concentration will cause an island of salt to crystallize beneath you and carry you out to sea.
This is absolutely possible: the relevant equations from physics and chemistry tell us that the probability of this is greater than zero (it's miniscule, but still greater than zero). Still, even though we can acknowledge that this is a *theoretical* possibility, we can also treat it as a *practical* impossibility. Nobody carries a waterproof bag with food and a two-way radio while swimming in the ocean "just in case".
For most purposes, I find it more useful not to ask "is there any theoretical chance that X is possible?", but instead to ask "are the chances of X greater than or less than other things that I've decided are so unlikely that they can be ignored?"
(2) In order to know if something was a miracle – a violation of natural law – you would have to know every single little thing about the universe and the could possibly happen, and determine that this absolutely could not.
That's right... and it applies to people making miracle claims as much as it does to people denying them. It may not be justified to say "miracles can't happen", but it's perfectly reasonable to say - for ANY miracle claim - that the label "miracle" is unjustified.
So faith or arrogance, neither of which I am a big fan of, I was required to use in my claim that miracles do not exist, and eventually to avoid arrogance was forced to accept the concept of “miracles” as an untouchable topic, since we may well never have enough knowledge to comment on such a thing.
But again: that goes both ways. If it's true, then it means that it can never be justified to claim that some event was a miracle.
... but in the end, I'm not sure it matters. Set aside the "miracle" aspect and miracle claims just turn into claims of the form "____ happened by an unknown mechanism." This claim still needs support for the "____ happened" part for us to accept them rationally. The "... by an unknown mechanism" part is the bit that's much harder (maybe impossible) to demonstrate, but this is really the problem of the person making the claim
Things get even crazier though. Understanding everything about our universe from a human perspective means that all the knowledge will be sense based and three dimensional, as humans interpret all the information and the universe as we experience it is third dimensional. Yet there is absolutely no reason or ability to say that is all there is. Perhaps there are Nth dimensional entities who are responsible for miracles, and even though we understand the universe as we experience it we have no way to know of these beings, therefore no ability to know if there are the cause of supposed miracles. Even if these beings came into your living room and told you all the things they know, there would still be no way of knowing whether they had the full picture or not.
We're limited, finite creatures. It's eminently reasonable that there's all sorts of stuff beyond our knowledge... or maybe even beyond our capability to know.
... but it's all beyond us, which means that it isn't available to someone trying to justify their claims.
Sure: we can't conclusively rule out the possibility that some claim that someone made by guessing just coincidentally turned out to be true. Even a stopped clock is right twice a day. But for any unsupported-but-not-completely-ruled-out claim, we can come up with some other unsupported-but-not-completely-ruled-out-claim that's incompatible with the first one. Any valid answer to the question "why should we take your claim more seriously than this other one?" is going to deal with things within human knowledge... and if there's no valid answer given, then we can disregard the claim, since its truth value is indistinguishable from that of a false claim.
There are any number of claims that are compatible with what we know of the universe but false. The mere fact that a claim is compatible with what we know of the universe is not enough reason to take it seriously. That's the point of mental exercises like Russell's Teapot and Sagan's Dragon in the Garage.