St. Thomas’s article on divine simplicity as such has three parts. Articles 1-4 deal with ontological simplicity, articles 5 and 6 deal with logical simplicity,* and a. 7 is a general proof against composition in God.
For our purposes here we’ll take Article Five as the climax to the whole question, with its central argument concluding to
Therefore it is plain that God is not in a genus as if He were a species. From this it is also plain that He has no genus nor difference, nor can there be any definition of Him; nor, save through His effects, a demonstration of Him: for a definition is from genus and difference; and the mean of a demonstration is a definition.
The conclusion arises from an argument in the previous article, and applies more broadly than even mere genus and difference, but to anything common to God and another. It’s worth taking the whole argument from the beginning.
1.) If there is anything in a thing different from what is essential to it, then it is either caused by essence or by something else.
2.) God exists.
3.) Therefore, if God’s essence and existence are different, either (a) the essence causes it to exist, or (b) God is caused to exist by another.
4.) But a thing can cause something only if it exists, and so no essence – divine or otherwise – could cause itself to exist; and God cannot be caused to exist by another.
5.) So essence and existence do not differ in God.
6.) In order to place something in a genus, we need to identify many existent things that share something essential in common.
7.) Therefore things in a genus have an essence in common and an existence not common, and so differ in essence and existence.
8.) Therefore God cannot be in a genus.
Notice that the argument makes it impossible to locate God in any category – we cannot start with some general field of things and then narrow it down till we find a quality that sets it apart as divine. And while the transcendentals are not in a genus, the argument still applies to them so far as they are taken as describing something essential or intrinsic to many different things. If we call God good or thing or other or powerful or dignified we cannot be taking these as predicates, i.e. as things said of many or communicable. The “good” we say of God is in fact as proper to him as a personal name.
This utter uniqueness of divine predicates has been gestured at for a long time in the convention of capitalizing the word “God”, which seems to be best understood philosophically as an attempt to capture the incommunicability of the divine name. Said another way, while the name of the divinity is the name of a sort of thing or nature, capitalizing it gives the word the sense of having the incommunicability of a proper name. That said, the capitalization always threatened to overshadow the formal sense of the word as a nature, and this seems to be how many people take it – i.e. “God” is word is like “Socrates” and not like “animal”. I don’t even mind the convention adopted both by Hitchens and N.T. Wright of reverting to the lower case “god” to refer to even God himself, since this does at least capture the truth that the word is a name for a sort of thing. Ultimately, though, this just trades what the word “god” can’t capture for what the word “God” can’t capture. What we are trying to do is beyond any convention of capitalization or naming. What counts is the the interior recognition that both our divinity’s name and the predicates said of him substantively are both predicates and as unique to him as proper names. As predicates, they are open to the various sorts of analyses that we can perform on predicates (like correlation by univocity and analogy) and as proper names they are utterly incommunicable. Since we have no category of names that transcends these two sorts of names, we are left to see God as he who is unspeakable, as both hidden and revealed by the names said of him.
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*Article 6 denies that God is composed of substance and accident, but for an Aristotelian these start off as logical distinctions, being introduced in the Categories and which are essentially defined through predication.
Just Thomism 
JSPflug said,
February 7, 2015 at 7:57 pm
While reading your argument I found myself considering different—most likely non-Thomistic—ways of understanding concepts (“simplicity,” “essense,” “composition,” “existence,” “name” and “good”) you mention therein. I don’t mean to sound dismissive of your particular use of these concepts, but by the end of your post I asked myself the following question: what is the “good news” about the ultimate conclusion of this argument? If I were to pin myself down to rigid Thomistic understandings of these concepts, so that your conclusion necessarily follows from the premises, how would this meaningfully engage me in my faith and my life in general? It is primarily in this way that I found your argument lacking. This isn’t to say I don’t want to have a better understanding of Thomism, and it does not mean that I am afraid to follow an argument to some hard truth, but such thoughts do give me hesitancy in commiting to a strict Thomistic philosophical perspective.
One thing is for certain: the conclusion of the argument you present here comes no where close to the inspirational force of Jesus’s words: “Now eternal life is this: that they may know you, the only true God, and Jesus Christ, whom you have sent.” (Jn 17:3). This is may be trivial because what you present is a “philosophical” argument and not revelation, but it in no way leads me to really “befriend Wisdom.” Perhaps it is for similar reasons that at the end of his life Aquinas considered all his earlier writing, and gave up current writing projects, as “so much straw” compared to the knowledge he gained in a mystical encounter with God.
None of this is to say, however, that I don’t enjoy having my mind’s perspective broadened by your intellectual take on such matters. Thank you.