There are some really terrible ways to define "miracle". Some of the worst definitions are "something that violates the laws of nature" or "a low probability event". Aside from the blatant biases embedded in these definitions, they are poor definitions in the sense that it is difficult to apply them to label real world events. Laws of nature as understood by whom? Is quantum tunneling a miracle to Isaac Newton? If we discovered a magnetic monopole would that be a miracle? If we say "laws of nature as they actually are", then how is anyone to know what those are and apply them today, with our limited scientific knowledge? Similarly, if we define "miracle" as "a low probability event", probability according to what model and what background information?
Defining "miracle" as an "unusual act of God" still runs into the problem of how to define "unusual". But we are getting closer. We must be very careful of what we mean by "unusual". Does God have two separate modes of operation? Does the fact that he sometimes needs to resort to miracles mean that he is inconsistent or that he needed to make an exception to his usual laws? This is the kind of error we may fall into with the wrong meaning of "unusual".
Here, then, is my definition: A miracle is an event which reveals more of God to humans. Alternatively (and equivalently), miracles are events which causes humans to learn new things about God. Let's now apply this definition to some examples:
Is quantum tunneling a miracle to Isaac Newton? Yes. Quantum tunneling reveals more about the universe to Newton, and therefore reveals more about the universe's Creator to him. It would continue to be a miracle for Newton until he fully understood the phenomena (by learning quantum mechanics), at which point the phenomenon would cease to be a miracle, to be subsumed by the deeper miracle of the revelation of new laws of nature.
Is quantum tunneling a miracle to a modern physicist? No. The phenomenon itself is understood and therefore we get no new information about the universe and its Creator by observing it. But even to the modern physicist, the deeper miracle of the revelation of the laws of nature would remain. Note that miracles are specific to individual persons - What is a miracle for one person is not to another.
However, sometimes an event is a miracle is for everyone - that is, it is something new and unexpected to the entire human race. The discovery of a magnetic monopole would be such a miracle, because nobody currently knows for certain that they exist. Now, this would be a minor miracle, because it doesn't tell us a whole lot about God. It would be a relatively minor modification to our current understanding of physics, which only partly inform us about God. So it would be a small miracle, but for everyone.
Is a solar eclipse a miracle? To an astronomer, no. This is like the case of quantum tunneling to a physicist. How about for someone ignorant of astronomy? Possibly, if the ignorant person actually learns more about God as a result. He may think, "I didn't know that the Creator allowed things like that to happen!" in which case it's a miracle. Or he may think "The sky dog is eating the heat ball", in which case it's not. Note that whether something is a miracle for a person depends on their interpretation of it. This is why Jesus did not perform miracles among people who lacked faith. In extreme cases, such persons would choose to learn nothing of God even if a dead man were to come back to life. As C.S. Lewis said in his book "Miracle", one must first settle the philosophical question in favor of allowing for miracles, otherwise nothing will convince you.
A sunset can be a very small miracle if you allow it to teach you that God is beautiful, faithful, and glorious. But not every sunset will be a miracle - only the ones that you actually learn new things from.
A scientist should not consider any phenomenon that they can physically explain as a physical miracle: they can, however, still appreciate the miracle in a sunset. Any new, unknown phenomena (which we'll always be discovering more of) would be a miracle to them, as it teaches that God is a little bit bigger, a little bit cleverer, than they previously understood.
But the superior miracle granted to the scientist is the revelation of the laws of nature. It is a miracle that explains many other miracles of less knowledgeable individuals. It is a grand miracle, as it reveals a great deal about who God is. It is a universal miracle, in that discovering an additional law of nature is news to everyone in the world.
"But", you may say, "at this point, have we not gotten far away from a simple understanding of what a miracle is? You can define the word however you'd like, but what good is it if it's different from everyone else's understanding of the word?" Good point. I will now show how my definition coincides with the normal understanding of "miracle", in the sense of it being an unusual, surprising event attributed to God.
The reason that miracles are unusual, surprising, and rare is because these we do not learn anything new from information we already have. In order to learn more about God we must be confronted with an event that is beyond what our current understanding of God can explain. If the event is more unusual, then my understanding of God changes more, so I learn more, and therefore it is a greater miracle. I already know that God created the world so that gravity causes things to fall. Therefore observing something falling is not a miracle. If, after much petition in prayer, something did NOT fall according to gravity, that would be a miracle because I would have learned something new about God - that either God created the laws of physics to be different than what I know, or that God somehow works strangely altogether. This is surprising and unusual to me because it is not how I expected God to act. Note, however, that this is a statement about MY ignorance of God, not about how God works usually or unusually or inconsistently or violates his own rules.
Say you witnessed God raising someone from the dead. This would be a miracle on several levels, but on the question of science, it would be a miracle to you because you do not know how God could have done it. It would teach you new things about God because it is different than what you expected of him. But again, this is a reflection of YOUR lack of knowledge, not a statement about how God breaks the laws of nature or is inconsistent. If you do in fact believe this event happened (which is a separate question), the proper thing to do is to confess your ignorance and learn more about God and the world he created, rather than simply claiming that it is impossible based on your limited current scientific knowledge.
I have explained how my definition accounts for the rarity and unexpectedness of miracles. It also explains why the frequency of miracles decrease as time goes on. In world history, in a particular nation or people's history, and in an individual's life, there are fewer miracles with the passage of time, because when we are ignorant there is much to learn, but later there are fewer (but deeper) things to learn about God which explains the earlier miracles. My definition also explains why God does not do miracles on demand: because that would teach us the wrong thing about God, namely that we could control him. My definition explains why God rarely if ever breaks the laws of nature, choosing rather to do his miracles through the laws of nature: to teach us that God is the Creator who made these laws, not a magic genie who must work against them. It furthermore explains why God does not miraculously answer every prayer: because miracles are for teaching us more about God, not for making our lives easier. He does sometimes answer miraculously, but only to teach us that he cares for us on a far deeper level.
I've mentioned how miracles happen in different levels. Higher level miracles explain the lower level miracles, and deeper truths we learn about God explain the shallower truths. There are no miracles at the highest level: If we could somehow understand God completely through one last final miracle, we'd find that there are no exceptions or surprises or inconsistencies in God, for God is perfectly logical and consistent in himself. All the lower level miracles would be contained and explained in the last miracle to give a complete picture of God.
We can see this happening on smaller miracles: a miraculous healing is miraculous at the medical care level, but perhaps not miraculous at the chemical level or a physics level. That is to say, if we could understand how God works in all the movement of all the particles at the physics or chemistry level (which we of course cannot), then there would be nothing unusual going on and no new information to learn by saying that the person was healed. The catching of many fish is miraculous in the life of a fisherman, but I presume nothing miraculous happened at the biological or deeper levels. David defeating Goliath is said to be a miracle, and it was for king Saul and his army. But on a spiritual level? Goliath went against David with spears and swords, and David opposed him in the name of the God of Israel, whom Goliath had defied. How could Goliath have ever had a chance?
The last, deepest, greatest miracle is the Incarnation. It is a miracle at the level of the nature of God himself. It reveals to us everything about God. "Anyone who has seen me has seen the Father". It is the miracle that explains all other miracles.
You may next want to read:
For Christmas: the Incarnation
Answering objections: science as evidence for Christianity against atheism
Another post, from the table of contents