R. T. Mullins and Joseph Schmid have an interesting paper trying to construct an argument against classical theism as a "model of God", called "The aloneness argument against classical theism". Unfortunately this is not a good start; classical theism is not a 'model of God'. I understand that, for reasons of habit, philosophers of a certain kind of analytic background like referring to everything as a 'model', but (a) classical theism is as much about what can be known and said about God as it is about God, and, more immediately to the point, (b) it is a family of philosophical positions, which should not be confused either in whole or in part with a model, and (c) it is, even more immediately to the point, a family whose core commitments have as one of their implications that every possible model of God we could construct, however well-founded, is inadequate. In any case, I wouldn't press the matter so sharply except that I'm quite certain that misconstruing as a model what is in fact a family of philosophical positions that implies the inadequacy of models is a reason for several of their more serious mistakes in developing the argument.
Their intent is to argue for an inconsistency in divine simplicity, divine freedom, and omniscience, so they begin with a definition of divine simplicity drawn from a couple of articles:
Doctrine of Divine Simplicity (DDS): There is no metaphysical or physical composition in God, such that: (i) there is no distinction in God between substance/attribute, essence/existence, form/matter, act/potency, genus/ differentia, agent/action, and essence/accident; and (ii) all of God’s intrinsic features are identical not only to each other but to God Himself.
OK, so already this is not promising. It's not that this is absolutely wrong -- this is indeed one doctrine of divine simplicity you could have, and you might have it if you were in one branch of the classical theism family -- but, as can be seen by the fact that Augustine, Aquinas, Scotus, Gregory Palamas, and a host of others who accept divine simplicity would reject this definition of it, we are already having red flags indicating that this supposed refutation might be one of those 'refutations' that prove the untenability of a very specific formulation of a marginal or even mongrel fringe version of what they are supposed to be refuting.
With regard to (i), this is a very weirdly formulated list. You would expect not "substance/attribute" but "substance/accident". I suppose (given things that are later said) that "essence/accident" is actually about essential and accidental properties rather than essence and accident as such, as it's odd to think of essence and accident in composition at all. The others come up in discussions of composition, so I suppose this is just an assortment of different kinds of composition, although I don't know what compositions are in view with the substance/attribute and essence/accident. But it's nonstandard to think of composition as primarily a matter of distinctions; it's primarily a matter of potentiality, or potency. (This is why agent/action is a potentially controversial one, depending on exactly how you conceive of action in this context.)
With regard to (ii), I have through long and endless aeons pointed out that trying to define the doctrine of divine simplicity in terms of identity is a weird analytic quirk that comes from over-interpreting discussions influenced by Latin, in which identitas means not 'identity' specifically but any kind of sameness at all. Rather ominously for their argument (although not surprisingly), they don't have any account of how to distinguish the intrinsic from the extrinsic. They also want to distinguish between things that are "wholly extrinsic" and "partly extrinsic", but their characterization of the former is incoherent. Their definitions are:
Roughly, S has F wholly extrinsically provided that the proposition ‘S has F’ is true solely in virtue of something outside S. S has F partly extrinsically provided that the proposition ‘S has F’ is true partly in virtue of something outside S and partly in virtue of S itself.
However, we can only say that anything pertains to S at all "partly in virtue of S itself"; this is literally built into the logical structure: It's a contradiction to say that "S has F" is not true partly in virtue of S itself, because its truth depends on S having F somehow, and that is going to depend on S and its 'intrinsic' features. You can't have the truth of a proposition not in any way depending on the subject of the proposition.
They also give definitions of divine freedom and divine omniscience, which are less problematic (in part because more vague), although we'll see in a minute that there is a worry about the first:
Divine Creative Freedom: God is free to create or not create the non-God world, where the non-God world is anything with positive ontological status distinct from God
Divine Omniscience: Necessarily, God knows everything that exists, obtains, and is true.
But we're already getting another red warning flag here, in that there is a lot of defining going on. That would not necessarily be a problem, particularly given that Mullins and Schmid do refer at most of these points to people who can be put into the classical theism family; but their attempt to tie this whole definitional complex to classical theism is pretty cursory and patchwork. That would also not be a problem if we were dealing with a particular model of something; but, as noted above, classical theism is not a particular model but a family of philosophical positions.
To this, they add the proposition that God could be alone, in the specific sense that "Possibly, God exists without a non-God world" or "there is a possible world in which God is alone." This sudden bursting of possible worlds onto the scene raises another warning flag. This premise is stated two different ways using two different concepts of "world". In "a non-God world" the "world" is not a possible world in the sense of the way the actual world can be (which is how "possible world" would usually be understood here), because it is incomplete. A possible world in this sense is effectively one list of all the compossibles (by some method of assigning them). Mixing and matching two completely different definitions of 'world' is not something you do in a well-constructed argument, and we are going to have to watch each use of it very very carefully. Really what this set of claims is describing is that God is necessary, and "the non-God world" is not; thus the next step, which maddeningly uses both senses:
Contingency of Creation: There is a possible world in which God exists alone, and there are possible worlds in which God exists with a world of non-God things.
Why not just say, "God the Creator necessarily exists, the created world could have not existed"? I don't really know, unless it's to drag possible worlds into the mix.
There is a kind of problem we are slowly circling around. Possible worlds are a logical apparatus. A possible world is a logical object associatable with a list of truth-valued propositions (or answered yes/no questions, if you prefer) and having a certain set of relations to other similar logical objects. Despite the name, in itself there is nothing about this that requires that our lists identify any kind of possibility or world. You can use these logical objects to model not possibilities but moments in time or regions in space or kinds of actions, or whatever else you please, as long as you keep the essential logical features. You can use them to model not worlds but organizations, people, regions of the world, or whatever else you please, as long as you can characterize these things in lists of truth-valued propositions or yes/no questions and they allow for the relevant logical relations. When we are talking metaphysics, we usually give possible worlds the interpretation 'ways the actual world can be'. (This is intuitive, but a bit unfortunate in that we have a third sense of 'world' being assumed, if Mullins and Schmid understand 'possible worlds' in the standard metaphysical way.) Each list is chosen to be a distinct representation of a 'way the actual world can be'. This is sufficient if we are doing modal metaphysics at a very abstract and generic level.
However, problems arise in situations in which we can start asking, "What is meant by 'the actual world' in 'way the actual world can be'?" Remember, this is not set by the logical apparatus at all -- it is being assigned as a part of the interpretation of it. For instance, to say "There is a possible world in which God is alone" is quite clearly false if "actual world" means the actual world we live in -- the actual world we live in is not one in which God is alone, so 'God is alone' will never show up as true in any of the ways it can be. So we're not talking about a way the actual world we live in can be. What's more, given the way this is being framed, the only thing that is stable here is God. So 'possible world' has to be a 'way the actual world can be' entirely and only in the sense of 'way God can be'. We can entirely do this, since possible worlds are a logical object and we give them interpretations; nothing prevents us from treating possible worlds as ways God can be, assuming we can make sense of that enough to conceive of them in terms of lists of truth-valued propositions. But we're going to be faced with the question of how we are determining these lists that in principle completely describe a way God exists. (Actually we can't do so at all unless God, understood the relevant way, actually exists, which is awkward for an argument intended to prove that He can't actually exist in that way. Mullins and Schmid, I take it, are arguing ad hominem in the Lockean rather than fallacy-theory sense of 'arguing on their opponent's principles'. The problem is that very few classical theists frame their position using possible world semantics -- only a very narrow group of analytic philosophers do this, in fact. Once again, we see that a very bold claim about classical theism in general -- a globe- and century-spanning family of positions -- ends up being parochially about a narrow group of a few hundred mostly English-speaking academics in the late twentieth and early twenty-first centuries who adhere to a particular technical vocabulary.)
In any case, Mullins and Schmid note that it follows from this that it is necessary that there be one contingent truth. Yet another red warning flag: Mullins and Schmid in their argument use 'contingent' for four completely different things that get called contingent: the divine choice to create, since God is free to create or not (they need to do this to argue that claims that the world is actually suppositionally necessary are not relevant); the world (in the sense of 'non-God world'), which can exist or not; features (in the sense of some features that are 'contingently possessed'), which can be had or not; and now contingent truths, which are actually true propositions that could have been false. It's obvious why these would all be called 'contingent' in some way; they are also obviously not the same kind of contingency.
With all of these preliminaries out of the way, and a few others, we get the argument:
1. God’s knowledge is either wholly intrinsic to God, wholly extrinsic to God, or intrinsic to God in some respects but extrinsic to God in others.
2. God’s knowledge is (i) wholly extrinsic to God or (ii) intrinsic to God in some respects but extrinsic to God in others only if God doesn’t exist alone.
3. Possibly, God exists alone.
4. So, possibly, God’s knowledge is wholly intrinsic. (1-3)
5 Necessarily, God contingently has some knowledge.
6. So, possibly, God contingently has wholly intrinsic knowledge. (4,5)
7. Whatever is wholly intrinsic to S is either an essential feature of S or an accident of S.
8. Nothing God contingently has can be an essential feature of God.
9. So, possibly, God has an accident. (6-8)
10. If DDS is true, it is not possible that God has an accident.
11. So, DDS is false. (9,10)
When we look at what our preliminaries allow us to do with this, the answer is not much. We don't have an account of intrinsic/extrinsic, and the account of 'wholly extrinsic' was incoherent, so the distinction between 'extrinsic' and 'intrinsic' here can only really mean something like 'when we are considering God and something else' and 'when we are considering God alone'. But even this is not very helpful. If God knows that a flower exists, is this 'intrinsic' or 'extrinsic'. Well, obviously God's knowing this is in some sense 'intrinsic' to God, in that it is God's knowing, but it's obviously 'extrinsic' in the sense that existing flowers are not God, and thus in that sense 'extrinsic' to the divine nature. But God is also not a merely possible flower, so the same thing would be the case if the flower were merely possible. So in every world God's knowledge is 'intrinsic' to God in the sense that God naturally knows, but in every world, even the alone world, the knowledge is extrinsic in the sense that what is known is, by definition, what is not God. What we are calling 'God's knowledge of x' is just an x-based way of referring to God, and thus is intrinsic insofar as it refers; but x is not God.
In every 'possible world' God knows every possible non-God world. That is to say, it is necessarily true that God knows even what is merely possible. If we were really looking at possible worlds, it seems the natural thing to do would be to say that God's knowledge is the same in every possible world, because in every possible world, God knows the full descriptions of every possible world. In every possible world God knows every possible world. Remember, aloneness means that we are really talking only about 'ways God can be'. But, by omniscience, in every way God can be, God knows every possible thing that can possibly be and everything He would know in knowing it to be. What sense does it have to say that this somehow changes between 'the alone [possible] world' and any other? It doesn't have any. But it's precisely what Mullins and Schmid have to assume; as they put it, God's knowledge varies across possible worlds. But in fact, in every possible world, God knows all the possible worlds, including what God knows in every single one. There is no variation here; God knows every possibility regardless what possibilities you assume.
Ah, but see, here we have the problem. Mullins and Schmid are making the mistake that people make with possible worlds: they are assuming that the actual world is a possible world, as indeed, they must in order to link up creative freedom (which is about the actual world, namely, how the non-God part relates to the actual God) with all this possible world stuff by which they characterize aloneness. As I have pointed out many times, the actual world is not a possible world, not at least in the sense of possible world semantics. Possible world semantics can't in fact characterize the difference between the actual and the non-actual at all; the closest it can get is distinguishing this possible world from that. If we assume that any possible world is the actual world, we have already assumed that there is only one possible world -- because we have identified the actual world with one way the actual world can be. If we are only talking possible worlds, for every possible way the actual world can be, God knows everything that can possibly be known about it.
If we're going to call it 'intrinsic' in one way God can be, it's intrinsic in every way God can be. If we're going to call it 'extrinsic' in the non-alone possible worlds, it's not any different in the alone one. And we could call it either, because we don't actually have an account of intrinsic/extrinsic precise enough to make precise differentiations between individual possible worlds -- which is an extreme degree of precision, but necessary in order to distinguish out the difference between one possible world and every other possible world. (We would, in fact, have to have it precise enough that we could pinpoint the problem down to a single, completely unambiguous, yes/no question.) In lots of situations, this wouldn't be a problem. If you are making a picture frame, you just need to be precise enough, and you can designate a big black dot as your 'point' and a very clearly visible pencil mark as your 'line'; but if you're dealing with the properties of one particular infinitesimal geometrical point as opposed to every other, you need a way to pin down what point you're talking about that lets you specify features it has that no other point does. A grease pencil is just not going to do. If you are talking about a single possible world, like 'the alone world', out of infinite possible worlds, and contrasting it to those other possible worlds, the features you are talking about need to be precisely characterized enough that you can pinpoint that single possible world. But Mullins and Schmid give us a grease pencil, and it's not going to cut it.
This is a problem even before we get to a question that Mullins and Schmid don't consider, which is whether you can adequately capture every divine possibility in a set of lists of truth-valued propositions. This is not a quibble; there is in fact good reason to think (and classical theists generally have said things that at least suggest it) that divine omniscience (and, even if we are not talking about God, "everything that exists, obtains, and is true") cannot be adequately described in any set of lists. But if that's the case, possible world semantics is inadequate for characterizing divine omniscience; and it would seem by analogous arguments to be inadequate for fully characterizing everything that is possible to God. 'Possible worlds' in the sense of possible world semantics are not things 'out there'; they are logical objects related to lists of propositions mapped to truth values (or, as I've said before, yes/no questions mapped to yes/no answers), and in possible worlds metaphysics, we are using those lists to model possible ways the actual can be. But it follows necessarily from this that if there are any possibilities that cannot be adequately described by lists of truth-valued propositions, possible world semantics cannot 'see' them, and if there are any possibilities that cannot be distinguished entirely by their lists of truth-valued propositions, possible worlds semantics cannot distinguish them.
There are other problems. (7) is false; besides essential features and accidents there are properties, modes, transcendental relations. Lots of things, really, depending on the background metaphysics. There are certain analytic schemes that try to divide everything up into essential features and accidental features; I suppose some analytic classical theists could be really hardcore into that dichotomy for some reason. Regardless, we see again that this bold refutation of classical theism is really, if anything, an argument raising a problem for some Harvey AnalyticGuy's attempt to translate it into a very specific metaphysically vocabulary and, apparently, a model.