I continue my Sunday theology posts. You can see a map to the whole concept here. I'm figuring out the order and precise content of this series as I go.
God has the power to do anything he wants. He is "all-powerful." In theology, we say he is "omnipotent."
The idea that God is all-powerful flows directly from the idea that he created the universe out of nothing or "ex nihilo," as the Latin goes. When we say God created the universe out of nothing, we are saying something different from what ancient creation stories typically said. In those creation stories, creation is the organization of matter that already exists in a chaotic state. When Christians say that God created the universe out of nothing, we are saying he not only ordered the creation but that he created the matter of the creation itself. 
The creation is thus distinct from God. The creation is not part of God, let alone all of God.  As a previous article said, God does not need the creation, although the creation needs God. The creation is not self-sufficient, although God is.
With the discovery of relativity in the twentieth century, we are now in a better position than ever to recognize that God not only created the matter of the universe but the very space in which that matter exists. That is to say, God not only created the universe, but he created the emptiness in which the universe exists. He created space and time. This realization may help clarify aspects of God's relationship to the creation that no Christians before the 1900s would have fully understood.
If God created the world out of nothing, then it follows logically that he must have enough power to create the universe. You cannot lift a rock if you do not have enough strength to lift the rock. In the same way, God must have enough power to create a universe out of nothing, meaning that he must have all power in relation to the creation.
So God has the power to do anything in the creation that the creation can do and more. Miracles are when God does more than the creation can do. God created the universe to follow certain natural laws. On its own, the universe follows these rules. But as God, God sometimes interrupts the normal cause-effect chain of reality and breaks the rules. This is what a true miracle is, when God does something in the creation that is outside the normal cause and effect chain of events.
Indeed, one argument for the existence of a Creator is the "cosmological argument," which suggests that the existence of God makes sense in the light of cause and effect. Although we should not consider the determinations of science final or necessary for theology, science currently suggests that the universe had a beginning. But if the universe had a beginning, it makes sense to ask why it began or what caused it. The notion that God was the "first mover" or the initial cause of the universe certainly makes sense, even if it is not an absolute proof. 
The common response, "Then where did God come from?" misunderstands the argument as presented above. The idea that it makes sense for the universe to have a cause is a comment on the universe, not on its cause. Indeed, this argument directly suggests that God's essence is "outside" or "beyond" the universe. Things inside this universe seem to need causes. We have no point of reference to say whether things outside this universe do.
An even more foolish question is whether God can create a rock so big that he cannot lift it, as if the notion of all power is incoherent in itself. The word "can" in this question is used in two different ways and we might reword it to ask, "Is it possible for God to create a rock so big that he cannot lift it?" The answer is no, because God can can lift any rock. In fact, God would not be omnipotent if there were a rock he couldn't lift. It is a trick question which more or less asks whether it is possible for God not to be omnipotent. The answer is "no."
Basically, to say God is all powerful does not mean that everything is possible for God to do. Is it possible for God to fail? No. God could only fail if he chose to fail, and in that case he would have succeeded.
God has the power to do anything, because he created the universe out of nothing. So God has absolute power over every aspect of the world. He can make the universe do anything the universe can do, and he can even make the universe do things it can't do.
Next week. G4. God can do whatever he wants.
 It is not clear that the Bible itself yet understood creation out of nothing. Genesis 1:1-2 can be read grammatically and contextually as the ordering of chaotic waters and creation out of materials that were already there. Similarly, it is not agreed whether Hebrews 11:3 pictures creation out of nothing. Nevertheless, it is agreed that by the end of the second century AD, the Gnostic controversy had solidified Christian belief in creation out of nothing, and it has been part of common Christian belief ever since.
The Gnostics believed that matter was evil. An early Christian named Marcion (ca. 150) even believed that the creator God of the Old Testament was an evil being. In response to Gnosticism, Christians asserted strongly not only that the God of the Old Testament was the same God as in the New Testament but that he had created the universe out of nothing, not from pre-existing materials. Non-Christian Jews seem to have solidified their belief in creation out of nothing at the same time for the same reasons.
 The view that the world is God is called "pantheism." The view that the world is part of God is sometimes called "panentheism" today. As early as the 100s and 200s, Christians generally rejected the idea that the world was an emanation from God.
 Another argument for the existence of God is the so called "ontological argument." In its classical form, it probably doesn't make sense. Anselm in the 1000s suggested in effect that, since we can conceive of the greatest possible being, he must actually exist (in a work called Proslogion). Although the way he formulated this argument probably doesn't work, some in modern times have attempted to rehabilitate it in a different form, chiefly Alvin Plantinga, The Ontological Argument from St. Anselm to Contemporary Philosophers (Garden City, NY: Doubleday, 1965). However, it is not clear that they succeeded.