[1] "Non-spatial" is a difficult quality to define. If an entity has no presence, how can it exist throughout space? If the God implied in Western theism is indeed a non-spatial soul, as H&R attest (3.1, p.39), for that God to be omnipresent poses some difficulties. While theoretically conceivable, plausibility is another matter...
Citing two early attempts to reconcile this, H&R offer St. Augustine's solution that all of space is in(side) God- a convenient answer but, to quote our professor, "nonliteral". A number of centuries later Thomas Aquinas suggests that "since God has knowledge of what exists at every place, God can metaphorically be said to be “present” at every place, even though he is literally nowhere" (41). Well... "nonliteral" and "metaphorical" are not exactly synonyms of "plausible", are they?
When we conceive of space, it is important to remember that most of it is empty already. Believe it or not, the space inside of atoms, between the nucleus and the orbiting electrons, is on a similar scale to our solar system, with the sun and its planets. Physicists have stated, for example, that if all the empty space inside the Empire State Building's atoms were eliminated, that structure would be about the size of a grain of sand. We take it for granted that we, and our surrounding objects in the environment, are all solid- and for practical applications this is true. (We don't hit someone's "empty" head with an "empty" baseball bat without consequences). But nevertheless, all these solid frameworks we exist within are mostly empty space.
I think I should note at this point that this isn't an attempt to skirt the issues presented in The Divine Attributes. But since this is a discussion, where we can comment and express our opinions on the topics, there are times when I want to lean toward the latter half of the term "meta-physics". The physics of an omnipresent God have to be considered. St. Augustine was a progressive thinker for his era, but a millenium-plus later we realize that the universe can't just be conveniently deemed to be "inside" of God. I'm suggesting that the contrary might be more accurate- that God is inside everything else. He is all that empty space. And thus God can be everywhere, yet nowhere, by that definition.
If "wholly negative" can be defined as having no positive occupation of space (i.e. having no particles or anything else we would consider as matter) then a non-spatial God fits that description. Again, in geometry, we accept certain non-spatial concepts- the mathematical point, and, by extension, the line and the plane. None of these have any mass, because the points they're composed of are infinitesimally small. A geometric line or plane has no physical existence; these are only concepts. Yet they have an irrefutable reality in the proofs of various mathematical laws. Perhaps God is that math...
Individuation? Why not- a line has individual points, a plane has individual lines, and a solid of course has individual planes. If humans have souls which are non-spatial, then it follows that each soul has its own identity, at least while it is linked to our physical bodies. Just as there are billions of individual fish in the ocean, our souls might be individual parts of the cosmic ocean of souls- God. What separates one soul from another? Would we, as non-spatial souls, be able to recognize the soul of a dead loved one, and communicate with it, while keeping our separate identities and memories? There's no doubt a wish within many of us that this would be the case- but dare we interpret such a wish as Descartes might have- that the conception and the desire for this individuation "make it so?" And if it turns out not to be that way, and instead we all melt into the soul of God (or perish the thought, that there's no God or soul anyway) will we know the difference, or care? I think not. (Therefore I am not?- hats off to Rene) If there's no individuation, there will be no "you" and "me" to miss.
I can't pretend to grasp all the subtleties of this particular chapter on "Incorporeality", as it's very heady stuff. I can only give my take on it. I feel a sense of identity within myself- something that is not linked to my body or to my age. There's something seemingly non-spatial that is "me", and that I have been aware of since I was a young child. At times it even seems to communicate with me, from somewhere outside of my mind or body. (Dreams have always seemed like a window into that realm... like those where you experience what seems like a whole lifetime in one session). That's my conception of a soul. It may just be a chemically-induced illusion caused by the various elixirs my glands produce, or it might be something yet undefined that will last forever. So far, that "me" has persisted for over 50 years, which I think qualifies as a "principle of identity over time". If a non-spatial soul is the cause, then this identity through time is indeed coherent, whether I understand the mechanics or not.
[2] As our text demonstrates, the classical attack on "intelligibility" and "causal interaction" between souls and bodies is both controversial (among philosophers at least) and very divided- H&R cite two factions that couldn't be more different. The idealists say that physical substances are impossible; that it's all in our minds (a la the Matrix?). The materialists on the other hand believe that souls are impossible. So obviously, both of those camps don't believe there is any interaction, because it takes two to tango...
Here is what I found to be one of the most telling statements, when H&R offer "Here we remain neutral on the issue of whether souls, or even bodies, actually exist, an issue that cannot be settled by reason alone" (41). But what follows is 27 pages of extremely meticulous reasoning and probing into where philosophy stands on the issue of the soul, complete with passages that read like algebra. It's very impressive, the amount of mental energy expended by philosophers on every twist and turn conceivable. But are the "answers" anything more than well-thought out opinions? No... to date, nobody has proven or disproven God, or the soul. It is indeed a neutral state of affairs.
I am new to this philosophy game, at least on the levels that it goes into here- I've thought quite a bit about God, and souls, and other metaphysical topics in my lifetime. I have no clear answers. But maybe as an outsider I can see the forest while the more intense philosopher is too preoccupied with specific trees. I keep seeing statements like "Suppose that a physical state, P1, is produced by a soul-state, S1, and that if S1 were to fail to exist, then there would be a true conjunction of a physical law, L, and physical initial conditions which implies that P1 fails to exist (58)... and think to myself "wow- what the hell does that mean?"
It wasn't until the subject of physical laws (specifically conservation of energy) arose that I felt like there was something I could stay afloat on in this chapter. I really admire H&R's finding there- that a form of energy from outside our physical world could increase energy within that closed system without violating physics. With a fairly decent grasp of that concept, I can say that the argument from others that God/souls would violate physical laws is not cogent. And it's a few points scored for the possibility of God within my own mind.
[3] I don't see a conflict with souls having parts, nor with God having parts. Let's suppose that I have a soul, for the sake of argument. It has no substance, but it has a connection with me. This implies that my soul, at the very least, had a beginning- that it wasn't around before I was conceived/born. And if we take Western theism at its word, there are good souls and bad souls; some will be rewarded, some punished. As an infant, would my soul have been capable of bad thoughts? If not, what changed in it over the years? How can an entity change if it has no parts?
Here's another angle- let's say that the idea of me is a non-spatial substance. Suppose that two of my friends are talking about me, thinking about me- in a fleeting sort of way I exist there, as a concept, between them. Certainly that concept has varying parts- my various traits, faults, quirks, etc. That is a "bundle of qualities" that can't be denied- all the more when you get to the much grander notion of God, who literally billions of people have thoughts about. God might be an infinite bundle of qualities- any and all that could ever exist or ever will.
I can sort of grasp the "divine simplicity" of a God. "He" is the emptiness in which all the particles, tropes, notions, etc. exist. But is there a difference between emptiness and infinity? Not much, I'm thinking. The ocean makes for a good analogy- let's say that God is the water (the emptiness) and that everything else in the ocean is the universe (from atoms to molecules, simple organisms to humans, right on up the scale to the stars and galaxies). That water (God) must be there for it all to be suspended in.