Two arguments below will be deductive, and they come straight from my book. The third argument will be inductive, and I will show that it is inconclusive.
As per my methodology, the existence of God is proved by discovering, one adequate and unique argument after another, God's attributes or the meaning of the term "God." Moreover, unless God is shown to differ from creatures substantially, we gain nothing, since this God might as well be considered to be part of the universe.
1. Why does our universe obey laws rather than exhibit prime matter style chaos? "Laws of nature" are of course abstractions made by humans; nevertheless, the obvious orderliness of the world may point to something. This is an intuitive argument to the effect that at the beginning of every human project, there are raw materials and human labor that transforms them into something useful, virtuous, or pleasant. Similarly, it stands to reason that in the beginning of the universe, there was chaos which was later on ordered. The pure potency of prime matter is an ideal building block, because one is not constrained by any pre-existing form in shaping prime matter into whatever he desires. It grants absolute freedom to the maker to fashion out of such matter anything he likes.
Why do all things obey laws? Another argument that answers the question "Why is there something rather than nothing?" reveals that the universe was created out of nothing. What informed the universe with laws? If object A gave the law to matter, then if A itself is law-bound, then the problem remains. "What ordered A?" we are liable to ask. We cannot go to infinity; hence, the ultimate first cause of the order of the universe itself obeys no laws at all. But there are only two sorts of things that obey no laws at all: one is pure chaos, and the other is absolutely simple; pure potency and pure act. But the chaos of the former does not generate order. We must acknowledge this simple thing that is free to such a perfect degree to be the cause of order of the universe and to be God.
This argument proves deductively that the cause of the universe, whatever it is, is not restricted in its operation by any intricacies of its own nature. There are no "laws of the divine nature" (as there are laws of the nature of atoms, cats, and humans) that are prior to God which determine, condition, and thereby limit His functioning.
2. Now the inductive argument from the same. William Dembski has developed the notion of specified complexity (SC) which, when applied to physical mechanical systems (and in particular to biological structures, such as molecular robots within cells), permits and even makes inevitable a rational inference to intelligent design.
It may be possible to ascribe SC to the universe as a whole: not to any self-contained arrangement of material parts within it, but to its natural laws. I include the laws studied by both natural and social sciences, both, say, physics and economics.
There are then two questions. (1) Can we adopt the premise that the universe exhibits specified complexity? And (2) given that premise, can we conclude that if the universe was created, then whatever created it must be an intelligent thing?
One difference is that ID in biology studies "grace" which mingles with works of nature, such as perhaps evolution. But the design argument for God's existence deals not with post-creation grace that perfects nature but with the original divine act of creation of nature itself.
The second difference is that specified complexity for Dembski regards clever and sophisticated structure of working machines, be they tractors or bacterial flagella, i.e., complexity of something concrete. The SC of natural laws is abstract complexity, such as the complexity of the axiomatic-deductive math that models natural laws.
Despite these differences, I think the answer to (1) is yes.
However, the positive answer to (2) does not follow. Design inference in biology depends on the limited amount of computational resources in nature. And earth, despite the considerable length of its history, is certainly sufficiently finite.
With the universe, we cannot be sure of that. For all we know, there may be a googolplex (though not an infinitude) of other worlds, randomly generated, so that, although the vast majority are chaotic, ours just happened to be lucky to be ordered and intelligible.
The previous deductive argument cannot be ruined in this manner. Whatever X generated our world, as well as all the other ordered worlds out of the googolplex of all attempts either obeys its own laws or does not. If X is meaninglessly chaotic, then it cannot produce order in its effect. At the very least, X must be precisely tuned to reliably give birth to universes. If X is law-bound and rational, then the question of what made it so remains. The conclusion as before is that the first cause is efficiently free.
As a result, the deductive argument succeeds, and the inductive argument fails, at giving us a slice of God.
3. This argument may be called the problem of particularity: why is the world this and not something else? All chaotic worlds are identical to each other, all equally boring; but each orderly world is uniquely interesting, and again there is an infinitude of possible ordered worlds, so they cannot all exist. How did this particular world manage to obtain its highly peculiar reality out of an infinite number of its possible brethren?
I refer you to my book for a full explication of the consequences of this strange situation.