Gutting argues that Dawkins is not justified in assuming as a premise that God is complex, and that God's complexity requires explanation. There is some brief mention that Dawkins addressed arguments by Richard Swinburne but did not address the serious thinkers on divine simplicity. I'm glad to know that Swinburne can be excluded from the club of serious thinkers. Even so, according to Gutting, Dawkins cannot assume that God is complex, and so Dawkins's argument, that God must require at least as much explanation as the complexity of the universe that God is posited to explain, fails. Gutt enjoins Dawkins to review the serious thoughts from this article in the Stanford Encyclopedia of Philosophy on divine simplicity.
As a first pass at divine simplicity, we might claim that God is a simple, non-physical substance and so is simple in that sense. God might have complex thoughts that occur in a substance that has no parts and so no possibility of complex relations among its parts. How this thinking might occur without any interaction of cognitive systems is all very mysterious. And immaterial substances are highly problematic entities. We have no way of verifying or falsifying claims about them. Why think, for example, that God is constituted by only one immaterial stuff rather than two? Why think that God's immaterial stuff is the same stuff from one day to the next? What does it even mean to say that immaterial stuff is the same or different? Immaterial stuff is so mysterious that it is hard to see how there could be any such substance, divine or not. These problems with the concept of a simple, immaterial substance are probably insuperable. But let's move on.
Even if God does not have parts, God is still informationally complex in the Shannon-sense that representing God's knowledge and potential behavior--assuming that God created and designed the universe and considered all possible alternatives in doing so--would require an enormous, indeed infinite, number of bits. I believe some theists will say that this is a mistaken view of God's knowledge of the world. God, it might be said, does not represent anything but knows it directly in a non-representational way. I cannot make sense of this if God considers alternative possibilities in creating the universe. Merely possible objects cannot be their own representation. So, how God's informational complexity is instantiated in God's supposedly simple substance is another significant mystery.
All this suggests that Dawkins is right that God is complex--and if not, there is no way to understand what God is and so there could be no reason to believe that God exists. Even so, it would not follow that God's existence and complexity must be explained by reference to anything outside God's own nature. A better alternative for theists is not to argue that God is informationally simple but to argue that God, or God's complexity, can be explained by God's own nature or concept. That is a key assumption of the cosmological argument and evaluation of such a claim goes far beyond my discussion here. However, the idea of divine simplicity discussed in the Stanford Encyclopedia of Philosophy is altogether more bizarre and probably incoherent if not logically inconsistent.
The author of the SEP piece William F. Vallicella suggests another notion of divine simplicity. This notion is that God is not a thing that has properties but is those properties, or, as Vallicella writes,
Besides lacking spatial and temporal parts, God is free of matter/form composition, potency/act composition, and existence/essence composition. There is also no real distinction between God as subject of his attributes and his attributes.
There is no distinct stuff that makes up God and the properties that God has. There is no distinction between God's nature, the properties God "has", and God's existence. God is God's properties; for God, our ordinary conception of objects as things with properties does not apply.
What could motivate such a strange and seemingly incoherent doctrine? One central consideration derives from the Anselmian definition of God as maximally perfect, as that than which no greater can be conceived. A God who was less than maximally perfect would not be an absolute reality and appropriate object of worship. A God who was less than ultimate and absolute would be an idol. Now an absolute reality must be a se, from itself, and so not dependent on anything distinct from itself for either its nature or its existence. If God had properties in the way creatures have them, however, he would be distinct from them and so dependent on them. This is the case whether one thinks of a property of x as a constituent of x, or as an entity external to x to which x is tied by the asymmetrical relation (or nonrelational tie) of instantiation. If the properties of x are constituents or ontological (proper) parts of x, then x will depend on them in the same way that any whole composed of parts depends on its parts. But if x is tied to its properties by the asymmetrical relation of instantiation, it is still the case that x will depend on them: if x is F in virtue of x's instantiation of F-ness, then F-ness is a logically prior condition of x's being F. In sum, the divine aseity would seem to require that God be rather have his attributes.
Translation: if God is "composed" of a stuff that has properties, then God would depend on that stuff and those properties in order to exist. The immaterial stuff and the divine properties would be more basic than God. But God cannot depend on anything; nothing can be more fundamental than God. So, God must not be "composed" in this way.
The author defends this view of God against the charge that it is incoherent or logically inconsistent. This is an extremely low bar, but I do not think he meets it. Or, he might meet it in the very weak sense that it might be logically possible for 2 + 2 not to equal 4. That is, if I were completely mistaken about everything I think I know about numbers, then this might somehow be logically consistent even though I could have no idea what such a claim could even mean. In this case, it might be logically possible that God be identical to God's (singular) property if I somehow was completely wrong about everything I think I know about what objects are, what God is supposed to be and what properties are.
It is at least as plausible a conclusion of the previous argument that God does not exist. Since everything that exists is "composed" in this way of substance with properties, and if God cannot be so composed, then God does not exist. Unfortunately, as nice as it would be to have such a simple argument against the existence of God, I think the assumptions of this argument are incorrect.
Do things depend for their existence on the properties and underlying stuff that "composes" them? I don't think so. First, it's not plausible that anything depends for its existence on its properties. On the Aristotelian conception, properties depend on their instantiations (the things that have them). Bob would exist whether he was tall or short. Bob does not depend on his tallness in order to exist. Possibly things have essential properties, but it's hard to see how even then the thing would depend on its properties. How could Bob depend for his existence on his humanity? Aristotle supposes that properties depend on their instances, so humanity as a property would not exist without humans to instantiate that property. Even if we do not accept Aristotle's view, it is bizarre to suggest that Bob depends for his existence on his humanity (even if Bob could not exist without being human).
It is more plausible that God's existence might depend on the stuff that makes God up. For example, we might think that humans are constituted by physical stuff that could exist even if those humans did not exist. In that case, the stuff that makes us up is more basic than we are. But this is not the sense of "constitution" Vallicella mentions.
We should not think the matter that constitutes things is more fundamental than the thing itself when we get to the most basic stuff. Humans might depend on the organs and cells that make them up, and those cells and organs might depend on the molecules and atoms that make them up. But it is a fundamentally different situation when we get to the basic constituents of the world, quarks, say. If we ever reach bottom, there will not be a stuff more basic which constitutes that bottom level. And in that case, it does not make much sense to say that a quark depends on the matter that constitutes the quark. There is no other matter (or energy) there besides the quark; there just is the quark. The quark is not "constituted" by matter and properties in any sense that makes this matter and these properties more basic. It may still be correct to say that the quark is matter with properties, but it does not follow from this that the matter of the quark exists more fundamentally than the quark and the quarkiness of it is a property that also preexists (one might say) the quark itself. This "pincushion" model of reality in which a thing is undifferentiated matter with properties imposed on it to give it structure--especially one in which the pins and the pincushion are more fundamental than the thing itself--takes us from the realm of common sense (i.e. things have properties) to the realm of highly problematic metaphysics. If I am right about this, and God is a simple substance, then there's no more basic stuff that constitutes God, and so God does not depend on God's properties and undifferentiated stuff. Vallicella continues:
A central threat to coherence is the question of how a thing could be identical to its properties. Alvin Plantinga (1980, p. 47) maintains that if God is identical to his properties, then he is a property, and they are a single property, in which case God is a single property. Given that properties are abstract entities, and abstracta are causally inert, then God is abstract and causally inert — which is of course inconsistent with the core tenet of classical theism according to which God is the personal creator and sustainer of every contingent being. No abstract object is a person or a causal agent. No abstract object can be omniscient, or indeed know anything at all. More fundamentally, no abstract object can be identical to any concrete object.
Vallicella is making a very clever move here without it being at all obvious what he's doing. This is a form of the strawman fallacy, one I call the fallacy of Spurious Specificity. This fallacy occurs when one takes only one specific idea or argument, rather than the broader set of such ideas or arguments of which it is a subset, and counters only that narrower idea. Plantinga and those arguing for the view of facts as abstract objects are not the only ones who might object to the doctrine that God is identical to God's property, and so you cannot undermine objections to the doctrine by rejecting Plantinga's view. And you cannot reasonably pretend that this debate is a matter of some obscure, debatable program of one particular philosopher. The problem with divine simplicity is not exhausted by Plantinga's argument that it entails that God is abstract. Vallicella comes close to the problem by saying that "More fundamentally, no abstract object can be identical to any concrete object."
The problem with Vallicella's account of divine simplicity is basic and obvious. It does not even make sense that a thing, being or entity, an individual object, is identical to a property. Properties are features or characteristics of things. A property cannot itself be a thing. Let's consider why philosophers even talk about properties; properties are things that are shared by multiple objects; they account for sameness or similarity of individual things. There are lots of different accounts of properties, whether they must be abstract, or whether we can understand properties completely as sets of individuals (or sets of actual and possible individuals). A theory of properties that did not somehow account for similarities among objects would not be a theory of properties at all. But the reason we talk about them in the first place is because we need to account for how two things can share something in common, how, for example, two things can both be red. If there is some property, redness, that they each have, then we have an explanation for why they are both red and how the statement "John McCain's angry visage is the same color as a ripe tomato," is true. That means that nothing can do the job of a property if it cannot, in some sense, be shared among individual things or instances of that property.
God, an individual thing, cannot be shared, exemplified, instantiated or otherwise exist in more than one thing. The reason we call them "individual things" is that they cannot be shared by other individuals (not in this sense, anyway). You might say that God is everything (in which case we are all part of the individual object that is God), or you can say that God is omnipresent (in which case that individual thing pervades the universe like a particularly invasive gas), but you cannot say that anything is an instance of God. Even God is not an instance of God but is identical to God. Even if there were only one red thing in the universe, redness would not, could not, be that thing. Redness would be a property with a unique instance, but it just makes no sense to say that being red could be identical to a red thing. (Even for the nominalist about properties, the unit set is distinct from its element.) What I'm saying is that individual, distinct, enumerable objects cannot at the same time be characteristics or qualities that can be shared by distinct individuals.
In short, the only way to understand God as a property is to throw out everything that properties are for and understand properties in your own unique way. This is a bit like saying, "Well, in your ordinary language 2 + 2 = 4, but in my vernacular, '4' refers to a rabbit's rectum, not a number, so on my way of understanding '4', 2 + 2 is not equal to 4." Fine, you can change talk of properties in this way if you want to, but when you do so, you have given up any possibility of making sensical claims that anyone else can accept.
My argument here might be little more than an incredulous stare: how can a thing be a property or a property be a thing? Those are mutually exclusive ontic categories (types of being). Properties can be shared by individuals, and individuals can exemplify properties, but neither can be identical to the other.
In sum, to say that God is the property Godness (say), is nonsensical; it contradicts everything we understand about the nature of properties. This whole construct of divine simplicity is misguided. Even though there are lots of issues philosophers discuss that he should take seriously, in this case, Dawkins has no obligation to evaluate such a bizarre theory. Gutting may as well have demanded that Dawkins, if he denies the existence of angels, must have a complete theory of angelic nature--including their pin-head-dancing proclivities--before denying their existence. Some theist arguments are too arcane, bizarre, wrong-headed or incoherent to be seriously entertained outside academia. The claim that God is identical to God's singular property is one such claim.
Plantinga, A., 1980, Does God Have a Nature?, Milwaukee: Marquette University Press.