My friend Bill is going to be revising his entry on Divine Simplicity at the Stanford Encyclopedia of Philosophy, and he recently posted a bleg asking for sources of the most recent discussion. At his request and with his agreement, here are a few of my own thoughts on the matter. Perhaps they may assist in him in the organization of the revised version of the entry. I will provide a couple notes on the topic of the doctrine of divine simplicity. This is a very long post, so I will split it.
1. Why divine simplicity?
Why should anyone believe as esoteric an exhibit of theological-philosophical arcana as the doctrine of divine simplicity? There are a number of ways to go about proving the point. They are all related to the notion that God is a metaphysical Absolute whose mode of being is utterly unique. Whereas all other beings are relative, dependent, contingent, caused, God must be absolute, independent, necessary, and uncaused. Why should that be so? At the end of the day, the argument is that anything whose existence is characterized by the former set of attributes is a kind of existential anomaly: nothing within it explains the fact of its existence, and its existence is most definitely a phenomenon which needs some kind of explaining, if the universe is going to have a semblance of intelligibility; ultimately there must therefore be something which is not characterized in any of those ways, something the existence of which is entirely from itself, in a way. Now if this thing were a composite of parts, its existence would be explained by the unity of its parts, and it would need something outside of it to cause its existence; therefore the absolute cannot composite in any way, since this is a generally valid principle of all forms of composite being: compositions need composers.
That is one way to go about motivating the doctrine. There is a lot which may sound controversial to the contemporary analytic philosopher who has not been trained in the classical metaphysical tradition, that kind of Platonism and Aristotelianism and everything in between that characterized the thought of such luminaries as Plato, Aristotle, Plotinus, Aquinas, etc. None of what I have said is controversial within that tradition, and that tradition is the one in which the doctrine of divine simplicity must be understood. I don't take objections to the coherence of the doctrine of divine simplicity very seriously, because they inevitably arise from a failure to appreciate the specific metaphysic which motivates the doctrine in the first place. In this way, objections to the coherence of divine simplicity are an exercise in begging the question.
Here's the way I argue for and understand divine simplicity. (Before I begin, get all such notions of properties as abstract, causally inert universals in Plato's heaven out of your head, as well as the notion that individual concrete existents are ontologically structureless "blobs" -- an impossibility, anyway.)
In the first place, I start from a critical presupposition of the intelligibility of the world. If the world is intelligible, if we may know it, then the structures of understanding in our mind must "map on" to actual ontological structure in the world. That means that the structures of substance-accident, subject-predicate, essence-existence, etc., by which alone we may understand a thing at all and have any kind of knowledge of it -- these structures must be real, they must have real correlates in the thing itself. If there is no such structure in the thing, then we don't know the thing by imposing that structure on it or by attempting to understand it through the terms and logic of that structure.
Now we find that these various categories of understanding (which also have correlated categories or modes of being) are such that they do not need to be unified in the order we find them. For instance, we find that there is nothing about the substance 'apple' and the accident 'red' that necessitates that an apple is red; some apples are not red, and some red things are not apples. More interestingly, we find that there is a distinction between essence and existence: our concept of 'cat' is one thing on its own, and my concept of Alley Cat, my pet cat, is another thing; Alley Cat is an individualized existent instance of the concept cat.
From this contingency I infer a real contingency. To the extent that I have knowledge of cats, apples, red, etc., I can see that there is nothing about my cat that requires that she exist. Previously she didn't exist; one day she too will pass (though I should hope it's a long while till then). In fact the contingency of the unity of my concepts is precisely grounded in the contingency of the real world: at times an apple is green, then later it becomes red, then later it goes out of existence; this tells me that its accidents (at least some of them) are contingently had, and that ultimately its existence is contingently had as well.
Now take some concrete existent thing, such as my cat. The unity of the components of my concept of my cat is a contingent one; it is a unity only because I unite these concepts myself, as an agent with unifying power exterior to the concept, and if I didn't do this, the individual components of the concept themselves would never be unified into a concept of an existing thing. In the same way, the ontological components which form my cat are contingently united to one another, so that she exists. It must be by something outside of her. Now unless we are not going to explain anything at all and be set off on a vicious regress, there must be some ultimate cause of the existence of all such beings which is itself not composite in the relevant ways. Since it was ontological composition that necessitated the positing of a cause, that cause (in order for it to do its prescribed explanatory and metaphysical work) cannot be of the same sort as its effects, such as to require for itself an explanation.
Therefore the cause of the existence of all intelligible (and therefore composite) reality must itself not be composite in any way. It also follows from this that it is not intelligible; it is not knowable. We can't understand it through the structures of form-matter or substance-accident or anything of the sort, since it is not a being of sort. It is something altogether otherwise from intelligible reality. If anything it is super-intelligible, it is beyond understanding. It obviously is not nothing, since it is the cause of everything else, but in a critical way it is beyond something; it is a sort of overabundant infinite existence. Quod omnes dicunt deum.
2. Theological language and revelation
Obviously this implies a certain view of theological language and revelation. Perhaps we could consider three approaches to theological language:
a. The kataphatic univocal view. On this view, we must describe divine simplicity as the doctrine that "God is identical to his properties," "God is his goodness and his justice," etc. Thus we import certain concepts (such as 'property') into our language of God and speak of him as if we are actually describing his being. We are speaking κατὰ φύσιν, according to his real nature. This view is hopeless, to my mind, since the statements we might attempt to describe God with are clearly (e.g., "goodness", "power" not synonymous and oftentimes just lead to contradiction. Not only that, if God is unintelligible per the above argumentation, and if God is never an object of ordinary experience to which we apply the standard categories of thought/being (as he can't be, per the above argumentation), we have no reason to suppose that those terms are adequate to the task. Why should we describe God in those terms? Why should God be just, and good, and powerful, etc., if we take these to be descriptions of his intrinsic being?
b. The kataphatic analogical view. On this view, we make affirmations about God's intrinsic being, but they are of an analogical sort. God is something like what we mean by goodness, though the term may not match up entirely; it may not be entirely adequate in describing God's goodness.
c. The apophatic view. On this view we do not make actual statements about God's intrinsic being. We may make negative statements (e.g., God is not a substance-accident composite), and we may make statements about the relation between things and God as their cause (e.g., God is just because he realizes just states of affairs in response to evils or injustices). But we do not say anything or know anything about God's intrinsic being.
I prefer to avoid the problems of the coherence of the doctrine of divine simplicity by taking the apophatic view of theological language. But then how can we engage in the act of theology, if we do not make statements about God's intrinsic being? In fact, how can we even relate to this God, how can we come into contact with him?
I understand theology to be intimately connected with revelation. The Christian tradition affirms that the texts of the Bible (and perhaps also the tradition of the church established after the apostles) are inspired, that they provide for us a way of approaching and thinking about God and speaking about him that is approved by him in a way. To my mind theology is more about the training and development of the religious mind than about accurate description of God; it is more about giving you a way of approach him and thinking about him. So theology teaches us to pray, for instance, as a way in which we can seek to come into contact with God. Likewise Jesus teaches us to pray to God as Father, because this orients our relationship to him in a way that insisting on a title like Lord or Deity might not.
There is more to be said, but this is a start.