Some of the comments have asked whether miracles can be violation of laws of nature as well as demonstrations of purpose. For example, could Jesus have made the extra loaves and fishes out of nothing (ex nihilo) or was he only able to foreknow that everyone had stashed food in their sleeves?

My argument was that "laws of nature" are a useful fiction. There are only regularities that we as scientists and physicists, suppose / postulate / hypothesize to represent an underlying reality. That is why scientists are often called "naive realists" by philosophers, because they think of the "laws" as a one-to-one map from deep reality to their bench-top experiment. This assumption works most of the time, but it can be very disconcerting when it doesn't. Usually it means that something is wrong with the experiment, but occasionally it means something is wrong with the theory.

For 300 years, a sort of Newtonian, materialist, mechanical view of the universe worked remarkably well to explain physics and astronomy experiments. Then came quantum mechanics, and the whole system stopped working. Just for fun, Einstein's relativity also threw a monkey wrench into the business by making it a non-intuitive reality, though physicists have gotten used to relativity better than QM.

So what happened to naive realism?

The dirty secret is that it is still taught in physics classes from high school through college and graduate school. We then treat QM as if it is the exception to the rule, and has to be learned separately. No one wants to undermine the materialist philosophy of methodological naturalism that undergirds both naive realism and Darwinism. That would be too disorienting. It's a useful fiction, sort of like the "frictionless forces" we teach in freshman physics classes.

But since we know it is a fiction, how do we get to the truth?

The truth is as much a religious and philosophical statement as it is scientific. The whole reason Newton could come up with his famous 3 laws and turn the universe into a machine, is because he relied on the medieval monks who defined momentum, conservation laws, and forces. And the medieval monks could do this, because they believed in an unchanging God. The Greeks had made enormous strides in science, but ultimately failed because they didn't have an unchanging God. Ditto for the Chinese and the Babylonians. Islam is a different story, but shows the error on the other extreme, that an arbitrary and capricious god is just as detrimental to science as a pantheon of bickering gods.

So if we have an unchanging God whose attributes are regular and rational, then we can have a universe that displays "laws", but laws which are extensions of God's personality. God could have the sun rise in the west tomorrow if He wanted to, but He doesn't. This is because of His character. But on the other hand, He can heal my aunt of cancer if He wants, and He may very well chose to do so, for He is a personal God, an approachable God, as well as an infinitely just and unchangeable God.

It is precisely those twin characteristics of person and perfection that make Science possible. It also means that miracles are neither "violations of laws", nor "arbitrary acts of power". Rather, they are personal choices of an approachable, infinite God. Or to use seminary language, they are the revelatory immanence of the transcendent divinity.

This is why there is no qualitative difference between the sun rising in the east every morning, and the Red Sea parting for the Israelites. They are equally personal acts of the infinite God. The only difference is quantitative, that the Sun has been rising daily for all of recorded history, whereas the Red Sea only parted once that we know of. Thus there are a continuum of God's acts, a gray scale between the repeated "law" and the surprising one-off "miracle" of God's actions.

And as far as Science is concerned, there is no contradiction finding reasons for both. Some repeated events are still completely mysterious to Science, just as some singular events are easily explained away. The difficulty for Science is not the inductive step of finding a generalizable "law", but rather the step of identifying a philosophical connection to "deeper reality".  That is why the highly repeatable and often measured QM effects are still seen as "mysterious" to physicists, whereas the singular origin of the first life on Earth is thought to be "understood".

But having said that there is a continuum between law and miracle, I still do not mean that one can't tell the difference. We are constantly having to make split second decisions about probability. When I was young, I drove with a 1% chance of causing an accident. I reckoned it to be small enough to not matter. After 3 accidents in my 17th year, I lowered the threshold. It will never be 0% until I stop driving, but now I don't assume that the lady on the cell phone with the turn signal blinking will actually turn in the intersection, and I leave some space to maneuver if she starts heading my direction. In the same way, we spend our lives recalculating probabilities, learning the difference between law and miracle.

My daughters used to ask me "Does God answer prayer?" and I replied "Of course."
"But how do we know when God is speaking?" they asked. "You will learn." I said, "For he said, 'My sheep know my voice.'"

And that is what distinguishing miracles is all about.