The Eastern Orthodox are fond of distinguishing God’s essence from his energies. God essence is his essential features, while his energies are the things that emanate from his essence. God’s essence is thought to be mysterious, while his energies are the things we can become acquainted with.
The way I think of it is that his essence is his most essential feature while his energies are the things that weakly emerge from it. God has one simple property essentially, but that property explains and entails other properties, just like most fundamentally in the world there are just atoms, but from those, things like fire and cars emerge. I do not know if this is the traditional distinction. I have not done much reading on the topic. But I came across a discussion of the distinction recently and it seemed to provide a nice way to develop a nice theistic model.
This can be analogized to the following: suppose one has a view according to which all possible conscious experience exists. What is fundamental would be unlimited consciousness, yet from that, particular consciousnesses would emerge. Or if one is essentially unlimited love, then care for particular people would be entailed by their essence.
A common objection to theism’s simplicity involves claiming that God depends on his features. It’s all very well to say that perfection is simple, but perfection requires various other features—unlimited power, knowledge, and goodness. Thus, perfection is not a simple property—it’s a bit like claiming that a set composed of an ant, a gorilla, and a book is simple, on the grounds that it’s just one set.
There are various ways to respond to this. One of them is to say that simplicity is determined by something like shortest description one can provide of a thing that fully captures its qualities. To fully describe such a set, in detail, would require describing all the things in the set, meaning it wouldn’t be simpler. In contrast, to describe God, one only needs to invoke one fundamental property—goodness—in unlimited degrees.
But it’s not so clear if this works. While God doesn’t have parts, if you derive a bunch of features from one simple description, that might be cheating. Not sure.
Yet ideally, the path to establishing that theism is very simple won’t hinge on just one contentious view of simplicity that feels like it might be cheating. If there are a few different ways one can establish the simplicity of theism, then that makes it more plausible that theism is simple. Fortunately, I think we have four ways. The first I described before.
The second is the one carried out by Swinburne. It says that God is just what an unlimited agent would be. Agents are perfectly ordinary things which we take to be fine explanations. If you ask “why is the chair there,” the answer “because John moved it there to facilitate the ritual to turn his foes into dolphins,” is a perfectly fine answer. Agents consistently have knowledge, power, and will, yet theism just posits those in unlimited quantities.
Third, also in the vein of Swinburne’s arguments, theism can be derived from limitless power. If something has limitless power, it must have a will, for only a will can make the choices to bring about a state of affairs. It also must be omniscient, for it would have the ability to know all things. It would also have to be omnipotent obviously. And if Parfit is right (which he usually is) having perfect rationality would result in moral perfection.
Fourth, and this is the route I’m most sympathetic to, perhaps we can make use of the essence/energies distinction. God’s essence is unlimited perfection. From this his energies—omniscience, omnipotence, etc—weakly emerge. Omnipotence is to God’s essential nature what heat is to moving atoms—it emerges weekly from that.
If this is true then God is fundamentally simple. His attributes are all explained by his more fundamental character. And while I’m not super sure that this is coherent, it’s not obvious that it isn’t. This means theism will have a non-insignificant prior, on the grounds that it might just be the simplest theory, positing one property, that we have independent reason to expect to be unlimited, in infinite quantities. It has no parts, nor additional assumptions, beyond boundless, unlimited perfection.
A few thoughts, mostly similar to ones I left in a comment a few days ago. First, it may be true that "unlimited agent" may be a simpler concept than any specific limited agent, but FWIW it should be noted that "agent" is already smuggling in a decent amount of complexity, at least if it's referring to a mind that has desires, plans and decisions.
Second, it's not clear why (say) moral perfection is something an unlimited agent would have, if we're being moral realists and building that into our concept of God. Why is moral perfection less limited than complete moral indifference, or being perfectly evil? In fact, it's not really clear that the concept "limit" as you're wielding it is really all that simple, itself; maybe, like "perfection," it's (IMO) implicitly tying together a bunch of unrelated things, or maybe it actually depends on the notion of minimal description length in some way.
Third, "limitless agency" or "limitless knowledge" or "limitless power" or any of those things might be simple, but under-specific. For example, if there's more than one way to have limitless power or the like (e.g., deities that can preserve anything versus deities that can destroy anything), then "limitless power" doesn't completely characterize God or God's powers, and so that description fails to capture God's full complexity, much like the relatively simple description "is based on manifolds" fails to capture the complexity of general relativity.
"Suppose one has a view according to which all possible conscious experience exists. What is fundamental would be unlimited consciousness, yet from that, particular consciousnesses would emerge."
What do you think about a version of berkeley idealism? The idea that what is fundamental is a necessary mind, God's mind, from which all contingent minds and contingent ideas emerge.
Combine Berkeley's principle "to be is to be perceived" and combine it with Platonism. If abstract objects can be perceived, then there are just too many objects such as sets or numbers to be perceived by any limited mind. But an unlimited mind perceives all abstract objects and all concrete objects.