[1] Stated as simply as possible, St. Anselm's self-existent being concept translates to "God is God because he is God." Not because we can conceptualize God, nor because any words or thoughts can define God- (those are qualities, and a self-existent being transcends its attributes). We're all familiar with the phrase "it is what it is"... well, there you go. I feel as if I'm on familiar, zen-like ground here. But much like a zen koan, it's utterly unintelligible.
Nothing can be self-existent except, perhaps, nothing. (No-thing). Whatever the universe was, before it was. If there is a God, then there's a reason for that to be the case. So we can philosophize about it; so, as Descartes did, we can conceive it. Otherwise, what's the point? Why are we here on Earth, surrounded by all this astounding immensity of the known universe? In other words, if there's a God that created all of this, then it follows that it all defines God. Not a self-existent, but an omni-existent God.
The idea that a God and its essence are two different things- it depends on how you perceive it. We humans, for example; in one sense we're just a mass of flesh and bones and fluids. But we're a lot more than that, aren't we... don't our qualities count in the sum total of our existence, and define what we are? History remembers some of us long after the body is gone.
As for brute facts (which I interpret as facts that we cannot explain but which nevertheless exist), I like the spin put on that by H&R when they offer "even supposing that one has conceded the possibility of brute facts, it remains true that one ought to explain as much as one can" (92). Philosophy in a nutshell, right there. If God chooses to exist "just because" then I suppose we have to live with it, but I think we all suspect there's a little more method to all this madness.
[2] Hume's basic argument is that for anything that exists, it follows that the contrary must also be true- that it can cease to exist, or not exist. And if this is true, then there can be no entity that must necessarily exist, including God. It's a point for the atheists, in this "game" of proving God's reality. But the game continues...
This chapter and most everything else encountered so far in The Divine Attributes has (for the first time in my fairly lengthy adult life) exposed me to just how intricate and mind-bending the field of philosophy is. Some of our authors' theorems are extremely well constructed (some I can even understand!); but am I alone in feeling sometimes that it becomes "much ado about nothing"? I mean, I realize that all these questions are vital for humanity (at least an important segment of it) and how it conceptualizes its place in the grand scheme. But is the debate ever winnable, or is the process itself all we can count on?
As long as we think in dualities (right/wrong, here/there, true/false...) there will always be contention among us. And maybe that's just the way it is. Some believe in God, some don't. Maybe that's why I've been a humble follower of zen buddhism for a few decades now, because in zen, the goal is to see through the dualities. God might be both material and immaterial, and exist both within and outside of time. God may even exist and not-exist simultaneously. Impossible? From our viewpoint, yes. But I dare say we don't know all the rules yet.
The believer in God (the theist) can respond to Hume and other skeptics by countering in that spirit- that just because we can't prove the necessity of being doesn't mean it can't occur.
[3] Conceptualist model- In this thought experiment (and at least three of the four are just that), our universe, and any possible other worlds, are all mental constructions; entities exist because we can think of them, or imagine them. It was famously the means that Rene Descartes used to confirm the existence of a supreme being- because he could conceive of such, then the same must exist. The only advantage I see here is that it makes it very convenient to believe whatever one wants to. But logically, we can also imagine events and situations that are paradoxes, and therefore impossible. I can imagine time travel, but I can't perform it.
Combinatorial model- Our actual world is the collection of everything that exists. Sounds reasonable enough. But it also allows for an infinity of alternate universes, where different events occur, or different choices were made. Maybe, if a few years ago, I had decided to take a left turn instead of a right on a given street, there would have been an accident in which I died. Maybe that universe, and countless others exist where little choices had big consequences. And that's just for me- now imagine everyone and everything else and all the possibilities. Intriguing to think about, but how would we ever know? An infinity in just one universe is more than long enough to experience- how could we experience an infinity of infinities?
Abstract worlds model- Everything is an abstract construct, a collection of all the propositions that are true (such as "hydrogen and oxygen atoms can combine to form water" or "carbon and water can mix to form life"). Again, this allows for alternate universes where one or more propositions are false- but how would they work? Maybe there's universes out there with no life in them. Would God still exist, and if so, why?
Concrete worlds model- The most accessible model for most of us here in the real world: the universe is an isolated collection of concrete entities. This one universe is all we can know, even given the theoretical existence of infinite others. But they too would be made of real, concrete particles that follow similar laws as our own. Even given this seemingly logical model, reading the main paragraph that H&R devote to it on page 83 shows how amazingly convoluted this most rational of the four models can be to define.