Being is an act in which the beings (that is existing things) participate. There are only two basic aspects of this act. Either a thing exists or it does not (meaning it is just a concept in the mind). If something does not exist in actuality, there are only two options as to why: either the right circumstances just didn't happen to come together to produce them, or, the concept itself is contradictory. The latter case one can think of square circles, or in the former, pinks unicorns. A Pink unicorn could exist if there just happened to be such things, the concept itself is not too contradictory (aside from dependending upon a fictional mythos which contradicts the laws of physics--that is also within the same category because the laws of physics could have been different). If a thing does exist it is either necessary or contingent, meaning either it cannot fail to exist without contradiction, or, its existence depends upon some higher cause, and thus it could fail to exist but just doesn't. So the two basic categories are Necessity and contingency
Now they can be subdivided but if we consider them in their most basic form there are only two categories into which they can fall (and no I'm not arguing that this proves God, but it is a good way to start thinking about him). Those two being: 1) Necessity; 2) contingency. And of each of these there are also two subdivisions. For necessity there is either arbitrary or impossibility. An arbitrary necessity has no logical reason for being, an impossibility is logically incoherent and cannot exist and cannot come to exist. Examples: Arbitrary necessity as I said in my post a 1962 Rambler as the ultimate origin of the universe. Impossibility, square circles. In the contingency category there is exiting contingency and non-existing. the former; everything we see in the world; the latter; purple dolphins, pink unicorns. Some of these categories could be subdivided; but these four represent the basic options. These are the primary categories in thinking about being and any others flow out of subdividing these.These are the four basic options. You can try to think up more of them, but there aren't any more basic, and their validity is just a matter of logic. Think about it.
Impossible Non existent (contingent)
This is all very logical, and anyone who tries to cliam that it is arbitrary is merely lashing out to deny anything that they fear might prove the existence of God. But these modes of being, in and of themselves, do not prove the existence for God. For that we need the arguments, but before we can turn to them there is one more crucial concept which must be dealt with:
An "arbitrary necessity is a contingency that has been placed in the position of a necessity, merely to furnish an answer to a problem. This is an impossibility, since contingencies cannot be necessities. Arbitrary necessities are logical impossibilities just as square circles are impossibilities. Many skeptics argue that we can't know if certain things are the case or not, this requires empirical knowledge. It may require empirical knowledge to be totally sure, but we can be fairly certain since we know that logical contradictions are truly contradictory and thus, impossible.
An example of an arbitrary necessity is the notion of the Quantum vacuum beyond time creating an endless stream of space/time "bubbles." There may be such an endless stream, but if so, it is not mere that it "just happens to be there." There must be some source, origin, or reason for its existence, since space/time bubbles are contingent (they have beginings) and thus they cannot be placed in the position of necessities.
Arbitrary necessities are no more logical than saying that the universe was caused by a 1958 Studebaker Golden Hawk, that just happened to always be beyond time. This would be a totally arbitrary solution, and while we do not have absolute proof without empirical knowledge, why should we believe it? All of these arguments about the assumptions that we should make. We should make the most logical assumptions that we know how to make. Arbitrary necessities are not logical.
Is Necessity necessary?
Skeptics often argue two things against this view: 1) that it is assuming God in the premise of the argument; 2) that the notion of necessity and contingency is invalid and thus only empirical knowledge serves to offer "proof" as to the nature of the universe. Both of these arguments are illogical and both are based upon misconceptions. The first is ill-conceived because the skeptic misunderstands what is being said. Most skeptics assume one is saying that the nature of the world indicates that it is necessary that there be a God. This is not what is being said. Or they assume it means that a necessary being is one that must exist because the world could not exist without it. The concept has nothing to do with the nature of the world. Rather, it is saying that the concept of God is that of necessary being, because the concept of God is such that God cannot cease to exist or fail to exist without contradiction. In other words, God is eternal and is not created by anything else.
At this point many atheists will says "How can you know that?" But it is not a matter of empirical knowledge, but of the concept itself. The concept of God is that of an eternal non-created being, whether God really exists or not. To that extent than, God cannot be contingent and must be necessary (logically necessary). That is the premise of the argument and it does not require any empirical knowledge. This is also the answer to the second argument, that the arguments don't assume that God already exists before the argument begins, but that the concept is that of necessary being. The point, than is to prove that such being is the nature of the case. We don't start with the asumption that God exists, but that if God exists, God must be necessary. With that premis as a given,which is a logical assumption given the nature of the concept, we go to reason from that point to the existence of such "a being." This means that God is, if God exists, necessary and cannot be contingent. Even if that distinction doesn't lend itself to direct proof of God, it is a very important distinction, because it is useful for understanding the nature of God and helps with many different arguments.