[1]  Per Hoffman and Rosenkrantz (H&R) from Chapter Two's introductory paragraphs, the three senses of substance are:

     "(i) Aristotle’s primary ousia, (ii) a quantity of material stuff of some kind, and (iii) an individual thing such as an inanimate physical object, a living organism, or a nonphysical soul" (23).

     Ousia is a Greek term that apparently loses much of its meaning in translation, but H&R recommend "basic entity", which Aristotle regarded first as a "living thing", and later amended to "form". It's a bit unclear to me how (i) differs from (iii) which also includes "living organism", but our task here ultimately is defining the substance that a God might be made from, so no need to over analyze this minor inconsistency. My general impression is that the three types of substance are (1) living organisms, (2) inanimate objects, and (3) non-physical souls/energy fields.

     I've always thought of the concrete/abstract distinction as fairly clear-cut, such as H&R's concrete=observable and abstract= nonobservable definition. But here in the world of philosophy, it's beginning to sink in to me- nothing is ever really clear-cut! (It reminds me of former President Bill Clinton's infamous statement during his failed impeachment proceedings: "It depends on what your definition of "is" is).

     There's a second way of looking at it which is also simple enough: concrete=physical and abstract=non-physical. But it's H&R's third distinction where things get interesting (and confusing). There are two schools in philosophy, realism and nominalism, which differ on whether abstract entities even exist; the latter accepts only the concrete. From there, things get too complicated to avoid writing too long a post here... but maybe I can touch on them in parts [2] and [3].

     The significance of deeming God as concrete and substantial? In a nutshell (per H&R), it allows Him to have feelings and intentions, and to perform actions. That's what the text says, but I'll have to admit that I'm not yet convinced by that argument, perhaps due to my philosophical naivete.

     If God is the ultimate entity, it seems to me that He can assume any form, concrete or abstract, or any combination of the two; even some category of essence that we humans are not aware of yet. Physicists hypothesize that most of the universe is dark matter. (There's also a similar theoretical substance known as anti-matter). Chances are, we haven't even scratched the surface of how many distinctions of substance are out there...

@Amy Olsen:

The idea of a "single instance over an interval of time" (from our prompt) is confusing to me... what is a "single instance"? Is it a very small quantity of time (like a geometric point), or a certain segment of time?

     I also found the idea of Absences being entities very odd, yet interesting. But the lack of something is indeed an entity that can be felt, and sometimes very strongly- say if someone stole your car, or you lost a loved one.

     One other thing strikes me as peculiar, in Western theism and religion in general. The idea of a God being worthy of worship and praise. I know it's a long-standing tradition to worship God; I think of Psalms from the Bible, and the many hymns. But much like prayer, wouldn't we agree that the worship is all for our benefit? It just seems a little less than God-like, and in fact arrogant (more of a human trait) for a supreme being to demand praise.

[2]  A concrete entity, in philosophy, isn't necessarily as solid a substance as the term implies. (Compared to what the same phrase might mean to a sculptor, for example). Although it seems counter-intuitive, a soul can be a concrete entity, and in The Divine Attributes, H & R contend that God is such a phenomenon. This is due to the premise that God has mental qualities (such as compassion) and that only a concrete being can possess such.

     I don't quite grasp that line of reasoning... (but what do I know?) Why something as ethereal (and unproven, I might add) as a soul must be a concrete entity, and furthermore that it thus follows that God must be a soul- I'm not there yet. I feel like a "stranger in a strange land" here among the philosophers, where the premises of arguments are presented as facts, yet have little hard evidence to support them.

     But back on track. It makes sense to me that a concrete entity would stand (exist?) in space, as well as time (temporally). Where else would it be? I suppose there could be a non-space where non-entities go about non-existing, correct? I'm not being flippant- we know that negative numbers exist. If infinity is possible, then so is "nothing". If God exists, and the universe is infinite, and anything that can ever happen eventually does- then God must have an opposite; an anti-God. (And my train of thought has now derailed).

     Ontological categories are philosophy's equivalent of the taxonomy we use in biology- where it goes kingdom/phylum/order... etc., each subsequent category being more specific. We humans are in the animal kingdom, and on it goes (vertebrate, mammal, etc.) until we get to our distinct species.

     In ontology, where we delineate categories of "existence", the broadest category, Level A, is "Entity". Level B subdivides entities into "Abstract" and "Concrete" entities. And so, Level C is the next division, where we get categories on the abstract side such as "properties", "relations" and "sets"; and on the concrete side we have "events", "places", and "times". (There are many more Level C categories, the few given are just examples). The distinctions between concrete and abstract ontological qualities are, in my opinion, practically self-explanatory: concrete categories are those we can experience more directly, while the abstract are more conceptual.

     Below is an ontological chart, of sorts. Not exactly the same categories or subject as our text, but it's a decent example of the process itself.

[3]  It's no problem to understand the autonomy, or independence, of particular objects/substances. Set two apples on a table, and there's three distinct autonomous objects in that set- each apple, and the table they're on. They are not a singular entity known as "appletable"...there's this apple, that apple, and the table. Simple, right?

     Ontologically, they are just parts of bigger categories. The two apples are a part of the bigger category "all apples that exist now"; the even larger "all apples that have ever existed and ever will exist"; and the increasingly larger categories such as all "fruits", "plants", "organisms". The same goes for the table- you can come up with your own categories there...

     And of course, within those two apples and the table are also smaller categories- pulp, seeds, stems, skin.... wood, varnish, nails... and so on, decreasingly so until we get to molecules, atoms, and even tinier particles.

    I've cited these examples of the obvious for the sake of contrast: how could there possibly be a substance that exists without any other substance? The various Level C categories are in two major divisions- concrete and abstract. Most of the concrete types (events, places, times...) cannot exist independently, can they? There's no single event, for example (with the possible exception of the Big Bang, in only that infinitesimally small moment that it occurred, triggering all other events since).

     So let's consider the abstract ones. "Property", the condition of something (such as height, or color, etc.); this doesn't work because there has to be something that has those qualities. So property, relation, boundary, and the like cannot exist purely by themselves either.

     From what little meaning I can extract from H & R's (D1) proposal (29), this elusive totally independent substance has to be either an eternal entity (their words "having a single instance throughout an interval of time") or an entity outside of time (?) and simultaneously not share any aspects of any other Level C categories. It's a riddle to me, putting it mildly. And rather than write my way into a quagmire here, let me cut and run as succinctly as possible, if it's not already too late...

    This substance would have to be something extraordinary. Such as a God. H & R do postulate that it could exist both within and outside of time (30). All the other Level C categories listed in our prompt (property, trope, number, etc.), via the (D1) equations, cannot exist in a single instance, nor independently. An entity like the God of Western theism alone, it would seem, could satisfy this seemingly impossible state, and hence becomes a "proof" that He exists. Plausible? I think I'll wait to see how others weigh in.

@Amy Olsen:

I have a theory about the soul that relates to physics- I think there's a strong possibility that there are still various particles out there that haven't been discovered yet (such as the recently confirmed Higgs-Boson); and that there is actually a "soul-particle" that will be detected some day... Our thoughts are known to be the result of small electrical impulses within the brain. It makes sense to me that there would be a way that our thoughts survive our physical death, and linger in the universe. And they would be in the same network of God's omnipresent "soul"- perhaps all of our thoughts go into a "cloud system"- a database of experience that is constantly updating God's omniscience.