Magic, In Tiers

I have long thought about magic. What it is, what it isn't, how it may or must not work.  Some months ago, perhaps even a year in my past, I came up with this system of ranking magic.  I haven't come up with a final name for it yet, but for now, it's "The Tiers of Magic."  The principle is that there are three basic levels of magic, and all possible magical systems fit into one of these three. I both believe that every account of magic in the real world fits into one of these systems, and would probably overtly use these categories overtly if I ever get around to writing my own fantasy story.

First things first though; we need a definition. Going to Merriam-Webster, I found a few definitions. I prefer to use 2a of the noun form, which is as follows: "an extraordinary power or influence seemingly from a supernatural source." This works nicely for my purposes. Not too vague, not too narrow. Now, on to my categories.

FIRST MAGIC
Also called "Deep Magic" or sometimes "True Magic"
This is the magic that supersedes the natural laws to which we have become accustomed.  Most fantasy magic fits into this category. I also believe that miracles and dark magic in the real world fit into this: miracles because that's what the laws are for, dark magic because no power can break those rules.  Many of my Christian Brethren take offense at the idea of calling miracles "magic," but I have always felt that Miracles are, strictly speaking, the ultimate example of true magic. The reason I call this "Deep Magic" is because of a passage in The Lion, the Witch, and the Wardrobe, where the White Witch calls on the magic that made the world to demand blood, and Aslan *spoilers* calls on the deeper magic from before the world was made to redeem it.
The idea behind deep magic is that you appeal to higher laws. For example, the law of man says that you can't crush another man's head. The law of gravity says, "yes you can, you just need a big enough rock and a roof from which to drop it." This does not mean there won't be consequences in the lower laws (you'll still go to prison for head-smashery). It just means that the lower laws don't control the higher laws.  Here is an abridged hierarchy of laws: Laws of Man are inferior to Inherent Moral Laws are inferior to* Physical Laws are inferior to Logical Laws are inferior to (or perhaps the same as) the Nature of God. Nothing can truly defy God's nature: you can only rebel against it, just as jumping in the air doesn't break the law of gravity.
For atheists, skeptics, and the like, this category is entirely fictional. But I am not at all an atheist, hardly a skeptic (in the philosophical sense), and very little like either of them.

*Note, this is a hierarchy of influence, not of quality.  I consider moral law to be superior in quality to the Physical and Logical Laws.

SECOND MAGIC
Also called "Science," "Illusion," or "Prestidigitation," along with a host of other names
This is the magic that abides by the natural laws, and seeks to go no further. It exploits little-known quirks of perception and reality to dupe and amaze.  For those who think "science is just magic, sufficiently explained," I concede to you the Second Magic.  It is my least favorite system, when used on its own.  It saddens me.  It feels like a cheat when someone shows you something wonderful, and then you find out there's very little wonder in it at all. And in fiction, save perhaps Science-Fiction, it has no place. We are forced to live in a world where no one accepts real magic: why would you create a world that is the same in this way? Still, this is the magic most people see. It's the awe of a meal cooked in under a minute in a small box without the use of fire, and the spectacle of pulling a quarter out of a child's ear. Some might call these things two different categories, but I do not. If science is a type of magic, it is nothing more than a trick, and I will say no more on the subject at this time.

THIRD MAGIC
Also called "Chaos Magic," "Dark Magic," or "Zeroth Magic"
This is the magic that seeks to break all the rules. As I've already said, I group real dark magic into the category of First Magic, but many fantasy writers, in describing evil magic, talk about an unbound force that obeys nothing and is beholden to no rules.  This is ludicrous. If such a thing existed, the universe would not, as it could simply move through creation and undo it. What's more, it would be uncontrollable, so I honestly can't fathom why anyone would even want to use it, as they could never direct it.  Still, it seems very compatible with the aims of an evil wizard, does it not?  This is a category that is often used, but I do not think should exist, even in a fantasy world, because I prefer worlds that are internally consistent, and I do not see how any world where the Third Magic is real could be so.
As for why I call it both "Third Magic" and "Zeroth Magic," is that there are two ways to order the magics. The one I prefer is in order of power.  First Magic is most powerful because it need not obey the standard laws of physics. Second Magic can do amazing things, but not that. Third Magic, I do not acknowledge as possible, and therefore it can accomplish nothing. It would, however, be possible to group the magical types according to how many rules they follow, in which case this last magic follows none, and therefore is prior even to First Magic. The term "zeroth," I found in the wikipedia article about Asimov's Three Laws, and the less-well-known Zeroth Law.

I heartily invite comments on how to improve my system for fantasy writing purposes, or serious discussions of the real-world ideas I expressed. I will not honor inflammatory or insulting remarks in regards to my beliefs regarding miracles, magic, or God, however.