The Aloneness Argument

Why do Schmid and Mullins think that the conjunction of those four theses is inconsistent? They helpfully summarize the Aloneness Argument as follows:

The idea is this. In the possible scenario in which God exists but creates nothing, there's nothing there for God to be related to. And since there is nothing external to God for God to be related to, God's knowledge couldn't be extrinsic. So his knowledge that he is alone in such a world is intrinsic. Moreover, it is contingent, since there are other possible situations (e.g. the actual situation) in which he does not know that he is alone. Such a contingent, intrinsic thing is an accident, so God possibly has an accident. And that contradicts the doctrine of divine simplicity.Footnote ¹

Here is their formal presentation:

1. 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. 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. 3. Possibly, God exists alone.

4. 4. So, possibly, God's knowledge is wholly intrinsic. (1–3)

5. 5. Necessarily, God contingently has some knowledge.

6. 6. So, possibly, God contingently has wholly intrinsic knowledge. (4–5)

7. 7. Whatever is wholly intrinsic to S is either an essential feature of S or an accident of S.

8. 8. Nothing God contingently has can be an essential feature of God.

9. 9. So, possibly, God has an accident. (6–8)

10. 10. If DDS is true, it is not possible that God has an accident.

11. 11. So, DDS is false. (9–10)

What ought one think of this argument? Premise 1 gives a seemingly exhaustive characterization of the ways God's knowledge might be. Premise 2 turns on an account of extrinsicality on which God's knowledge could be wholly or partly extrinsic only if God doesn't exist alone. Premise 3 is a premise admitted by classical theists, since they hold that there is a possible world in which God doesn't create anything and that in such a world nothing besides God would exist. From 1–3 it follows that, possibly, God's knowledge is wholly intrinsic, line 4. Premise 5 maintains that necessarily God contingently has some knowledge, on grounds that it is a contingent truth whether God is alone or not, and classical theists will hold that, necessarily, God knows that truth whichever it happens to be. From 4–5 the authors derive 6, that possibly, God contingently has wholly intrinsic knowledge – a possibility that would be realized in a world in which God is alone, given that God's knowledge in such a world couldn't be extrinsic, as premise 2 contends. Premise 7 presents exhaustive options for whatever is wholly intrinsic to a subject – it must either be an essential feature of S or an accident of S. But, as premise 8 contends, nothing God contingently has can be an essential feature of God. From which the authors derive at 9 that possibly God has an accident. But God's possibly having an accident conflicts with DDS, as premise 10 notes. And, thus, the conclusion at line 11: DDS is false.Footnote ²

Our reply

In our judgment, a significant problem with the foregoing argument can be found in premise 2 or premise 5, depending on how those premises are interpreted. Premise 2 turns on an account of the intrinsic/extrinsic distinction. Premise 5 makes a claim about God's contingently having some knowledge. The exact meaning of these premises is unclear, however. To appreciate the problem, consider that Schmid and Mullins talk about both ‘features’ and ‘predications’ in their article and make claims about what is needed for either one of these to be ‘extrinsic’. They don't define ‘predication’, but, presumably, they are assuming a standard meaning according to which a predication is an act or instance of asserting something, of affirming or denying a predicate of some subject. They use ‘feature’ in a very broad sense, seemingly equivalent to the way some philosophers use the word ‘entity’:

Given this broad sense of ‘feature’, we take it that not only things like colours, sizes, powers, or dispositions would be features, but also dogs, cats, human persons, or even the divine substance, insofar as these are positive ontological items.

Now consider how Schmid and Mullins characterize the intrinsic/extrinsic distinction for predications and features. In particular, consider what they take to be required for a predication or a feature to be extrinsic:

Notice that, on Schmid and Mullins’ accounting, both extrinsic predications and extrinsic features require that there be something outside the subject S of the predication or feature to which S relationally stands. They argue this with respect to extrinsic features in the above quotation. But the same point follows for the same reason for extrinsic predications, given the way they define them. For an extrinsic predication requires ‘something outside S to which S relationally stands’ (Reference Schmid and Mullinsibid., 2). But ‘without something outside S, there would be nothing to which S could relationally stand’ (Reference Schmid and Mullinsibid., 5). So, for extrinsic predications to be true, on their account, something distinct from the subject of the predication must exist. Thus, on their accounting, the predication ‘God knows P’ could not be partly or wholly extrinsic, unless there were something outside God to which God relationally stands. Nor could God's knowledge that P, understood as a feature, be an extrinsic feature unless there were something outside God to which God was related. It is this requirement on extrinsicality that underlies, and is offered as support for, premise 2 of their argument.

A question, however, concerns whether references to ‘God's knowledge’ in the premises of the argument mean to be talking about predications or features. In other words, is ‘God's knowledge’ shorthand for the predication ‘God knows such and such’ (whatever it happens to be) or is ‘God's knowledge’ some positive ontological item identical to or belonging to God? Whichever it is, consistency will need to be maintained in order for the inferences of the argument to be valid and avoid equivocation. It looks as if the inference at 9, ‘Possibly, God has an accident’, requires that line 6, from which it is inferred, be interpreted as talking about God's knowledge as a feature. But line 6, understood to be talking about a feature, won't follow from 4 and 5 unless God's knowledge in those lines is taken to refer to features as well, and so on up the rest of the argument.

We maintain that the Aloneness Argument fails either way ‘God's knowledge’ is interpreted across the argument. If it is interpreted as a feature, then premise 5 would be rejected by proponents of classical theism and, moreover, results in the argument's having contradictory premises. If it is interpreted as a predication, then premise 2 rests on an account of the requirements for extrinsic predication that is almost certainly false or, at the very least, not something to which any philosopher need feel committed.

God's knowledge interpreted as a feature vitiates premise 5

Premise 5 states ‘Necessarily, God contingently has some knowledge.’ If we read this premise as claiming that the predication ‘God knows some contingent truth’ is necessarily true, then the classical theist has no quarrel with it. Whether God is alone or whether other things besides God exist is a contingent matter according to the classical theist. And the classical theist believes that in every world God knows whether or not he is alone.

If, however, we read premise 5 as meaning ‘Necessarily, God contingently has some feature (his knowledge feature)’, not only would the classical theist reject the premise, but it would result in the Aloneness Argument having contradictory premises – for, on this reading, premise 5 would contradict premise 3. To appreciate this problem, consider again that a feature, for Schmid and Mullins, is anything with positive ontological status. Thus, on the feature interpretation, premise 5 is saying that, in every possible world, God contingently has some entity with positive ontological status. This entity cannot be God himself. For, in no world does God have God himself contingently. Instead, in every world, there would have to be some additional thing or other to be contingently had, something distinct from God. But then we have straightforwardly contradicted premise 3 of the Aloneness Argument, which says that ‘Possibly, God exists alone.’Footnote ³

Put another way: assume the feature interpretation of the argument and the uncontroversial claim that it is false that God has God contingently. Now suppose that Premise 5 is true. If Premise 5 is true, then, by the feature interpretation, in all worlds, God has some feature (a knowledge feature) contingently. In no world is that feature God himself. So in all worlds there is some entity, something with positive ontological status, other than God. Now, if in all worlds there is some entity other than God with positive ontological status, then premise 3 is false – it is not possible for God to exist alone.

Given the presupposition that Classical Theism includes the Aloneness of God thesis (that is, premise 3), and given that premise 3 implies the falsity of premise 5 on the feature reading of that premise (by contraposition on our previous conclusion that premise 5 implies the falsity of premise 3), no classical theist should accept premise 5 on the feature reading. But in addition, given that on the feature interpretation premise 5 is true only if premise 3 is false, no one at all should accept the soundness of the Aloneness Argument on the feature reading of premise 5. We conclude, then, that not only classical theists but everyone should reject the soundness of the Aloneness Argument when read according to the feature interpretation.

We also note that the support Schmid and Mullins offer for premise 5 does not, in any case, support reading ‘knowledge’ in that premise as referring to a contingent feature God has. Here's what they say by way of support just above the presentation of their formal argument:

All that those premises entitle Schmid and Mullins to is a reading of the conclusion ‘In every world, God contingently has some knowledge’ on which that means ‘In every world, God knows some contingent truth.’ In other words, it supports a ‘predication reading’ of premise 5, not a ‘feature reading’.Footnote ⁴

God's knowledge interpreted as a predication vitiates premise 2

But if we interpret ‘God's knowledge’ to be talking about predications across the argument, then we run into a different problem.Footnote ⁵ Premise 2 states: ‘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.’ But the demand on which the predication interpretation of this premise rests – that an extrinsic predication requires something outside the subject of that predication to which that subject relationally stands – is too strong. On our preferred view of extrinsic predications, they do not require an additional thing out there. Predications can be extrinsic based on whether or not the thing stands in relation to some further thing. Indeed, this is how Matthews Grant, one of the opponents that Schmid and Mullins consider, puts it. When writing of his extrinsic view of God's knowledge, Grant notes that ‘an extrinsic predication of the form “S is F” is true, not solely in virtue of what is intrinsic to S, but rather at least in part in virtue of S's relations or lack of relations to other things’.Footnote ⁶ If we understand extrinsic predications in this sense, call it the whether-or-not sense, then it does not follow from God's being alone that knowledge predications concerning God are intrinsic. For the disjunction – the whether or not – allows a way for a predication to be extrinsic even if there is nothing there to which God stands in a relation. ‘God knows that he is alone’ would be true, in part, because of God's lack of relations to other things.

Is the whether-or-not account of extrinsic predications a live option? Nothing that Schmid and Mullins have said settles the question. Nor do they consider the whether-or-not option and reject it or argue in favour of their account of the intrinsic/extrinsic distinction. As such, it seems to us that a reader is free to accept all four of the theses in the allegedly inconsistent tetrad but reject the unsupported view of extrinsicality as the real problem. Given that the classical theist is free to accept the whether-or-not view of extrinsicality, the classical theist can reject premise 2 of their argument, on the predication interpretation.

Nevertheless, one might wonder whether there is independent reason for affirming the whether-or-not view over their view. We think that there is. We will argue this by way of the authorities the authors themselves employ, and by way of unsavoury implications of their view of the distinction.

Consider the first reason to see the whether-or-not view as a tenable option: the reason from the authorities the authors rely on. Surprisingly, the single work that the authors cite in the body of their article when presenting their analysis of extrinsicality, David Lewis's On the Plurality of Worlds, on the very page they cite, defines intrinsic and extrinsic properties as follows: ‘We distinguish intrinsic properties, which things have in virtue of the way they themselves are, from extrinsic properties, which they have in virtue of relations or lack of relations to other things’ (Lewis (Reference Lewis1986), 61; emphasis added). Lewis's text makes no mention of Schmid and Mullins's preferred view of the distinction, the view that undergirds Premise 2 of their argument, upon which ‘extrinsic’ requires something outside the subject.Footnote ⁷

Second, consider the ontological implications of Schmid and Mullins's understanding of what is required for an extrinsic predication. The view that Schmid and Mullins put forward is too ontologically committal. It requires substantial ontological commitments, commitments that many will find unpalatable. We do not argue here that the entities that their distinction commits one to don't really exist. Or that one ought not believe in them. Rather, we argue that, whether or not they exist, they should not be a commitment of employing the distinction between intrinsic and extrinsic predications.

Consider the writing of this article. It was written during the pandemic, when children were still distance learning. At least one of the authors of this article wrote portions in a home office, continually visited by little humans in various states of need, drama, emotional stability, etc. At some precious moments of uninterrupted cognition, the author was alone. At many others, the author was accompanied by small humans, their noises, and their odours. Now consider the predications, ‘the author is alone’ and ‘the author is accompanied’. These are exemplary extrinsic predications.Footnote ⁸ They are true of the author depending upon what others are doing. The author is related to a small human when accompanied. According to Schmid and Mullins, the predication ‘the author is alone’ can only be extrinsic if the author is related to something then, too. But what relevant thing is the author related to when alone? Must we posit some entity with positive ontological status such as the absence of small humans in the office to which the author is related in order for ‘the author is alone’ to count as an extrinsic predication? That seems a steep entry fee just to be able to recognize the predication as extrinsic. It is an unnecessary fee given that the ‘whether or not’ characterization allows us to recognize the predication as extrinsic based on the author's lack of relations to any small humans in the office.

Or consider the extrinsic predication that the authors of this article are unsurrounded by zebras. Why must we posit a thing in relation to which each author stands in virtue of which this predication is true of each of us? The intrinsic/extrinsic distinction does not hoist such a commitment upon one who employs it. If there were such a thing, what would it be? Not any particular, far-off zebra or its locational feature, insofar as that zebra could keep its location and we could be surrounded by other zebras. Not all the currently actually existing zebras and their locational features – for all those zebras could remain where they are, and God could create a dozen more zebras in our immediate vicinity. Our being unsurrounded by zebras, it turns out, isn't explained by our current spatial relations to any actual zebras, insofar as we could keep those very same relations to those very same things and yet become surrounded by zebras. What is the thing, then, to which an author of this article is related, such that the extrinsic unsurrounded predication is true of the author? In Schmid and Mullins’ own words, letting the author be ‘S’, what is the ‘something outside S to which S relationally stands’ (Schmid and Mullins (Reference Schmid and Mullins2021), 2)?

Whatever that extra thing is, it must be a thing that would no longer exist if God popped four zebras into the author's home office. Perhaps one could reify lacks or absences, such that they have some positive reality.Footnote ⁹ Then each of us could stand in relation to a Zebra absence in virtue of which it is true to predicate of us that we are ‘unsurrounded by zebras’. Or perhaps there is a totality state of affairs that includes everything that exists and precludes anything not in it.Footnote ¹⁰ Then that totality state of affairs would make it true that no zebra is near either of us, and we could stand in relation to that thing. Such commitments are not insignificant. Like Lewis, we see no reason to require commitment to such things in order to draw the intrinsic/extrinsic distinction.

The whether-or-not view of extrinsic predications is a live option, accepted by relevant authorities and without the steep ontological costs of Schmid and Mullins's preferred account. On the whether-or-not view, contrary to the predication reading of premise 2, ‘God knows that he is alone’ could be an extrinsic predication, despite the fact that in an alone world there is nothing to which God relationally stands. The whether-or-not view of extrinsic predications asks whether the predication ‘God knows he is alone’ is true at least in part in virtue of God's relations or lack of relations to other things. Here, the answer is plainly yes – it is at least in part due to God's not being related to anything else as creator that ‘God knows that he is alone’ is true. A proponent of the whether-or-not view can, therefore, reject premise 2 of the Aloneness Argument on the predicate interpretation.

In a footnote, Schmid and Mullins offer a rejoinder to an objection, a rejoinder which might be viewed as a secondary justification for the claim that God's knowledge must be intrinsic to God.Footnote ¹¹ They write:

This line of thought concerning failures and absences will come into more scrutiny later when we discuss an objection that Schmid and Mullins consider to their Aloneness Argument. But for now, notice that the whether-or-not view does not require thinking of God's knowledge as a failure. The whether-or-not view of extrinsic predications says that it is at least in part due to God's not being related to anything else as creator that the truth ‘God knows that he is alone’ is true. As such, the predication is extrinsic, and we've made no mention at all of failures on God's part. So even if Schmid and Mullins are correct that we ought not to think of God's contingent knowledge as a failure on God's part, their being correct on this point is no problem for the whether-or-not view.

A reason to think that a simple God would know that he is alone

The foregoing considerations give us reason to reject the Aloneness Argument. Depending on whether ‘God's knowledge’ is interpreted in terms of features or in terms of predications across the argument, either premise 5 results in the argument's having contradictory premises (in addition to being a premise that classical theists would deny) or premise 2 is false. At this point, we have done the argumentative work we set out to do. We realize, though, that some readers may want something more positive about how it is that a simple God could know he is alone without such knowledge requiring God's having an accidental feature. So, in this section, we will give some reason to believe that a simple God could know that he is alone in an alone world. We want to emphasize, though, that even if the reader finds this section ultimately unsatisfactory, this wouldn't show anything faulty with our foregoing assessment of the Aloneness Argument.

The procedure will be as follows. We will propose a small number of assumptions (12–15 below) that are endorsed widely by theists, and from which it follows that God would know that he is alone in an alone world. We will then note that none of these assumptions obviously implies that God has an intrinsic contingent state or accidental feature in any possible world. To be clear, we are not here attempting to demonstrate that the assumptions in question are consistent with God's not having such a state or feature in any world. But we note that they do not imply such a state or feature on accounts of God's knowledge and action that have been defended by proponents of divine simplicity. And here is a point of dialectical significance – neither the Aloneness Argument nor any of its premises shows that any of these assumptions implies that God has such a state or feature. Thus, for all the Aloneness Argument tells us, the assumptions from which it follows that God would know that he is alone in an alone world are consistent with divine simplicity. We do not claim that this proposal is the only way to explain a simple God's knowledge that he is alone in an alone world.

How, then, could God know the contingent truth that he is alone without that implying some intrinsic, contingent state in God, an accident?

Consider the following four claims:

1. 12. In all possible worlds, nothing besides God can exist unless he creates something.Footnote ¹²

2. 13. In all possible worlds, God knows all necessary truths.

3. 14. In all possible worlds, God knows the full extent of his activity.

4. 15. In all possible worlds, God knows what follows immediately from other truths he knows.

From 12 and 13 it follows that

1. 16. In an alone world, God knows that nothing besides him can exist unless he creates something.

From 14, it follows that

1. 17. In an alone world, God knows that his activity does not include creating something.

But given 15–17, God would know that he is alone – that nothing besides him exists. For that nothing besides him exists follows immediately from the truth that his activity does not include creating something (which he knows) and the truth that nothing besides him can exist unless he creates something (which he also knows).

None of assumptions 12–15 obviously implies a contingent state in God, an accident: 12 is a necessary truth and 13 doesn't imply a contingent state, since all the truths in question are necessary. So, neither 12 nor 13 would seem to imply that God has any contingent states or accidents in any world.

Assumption 14 may seem the assumption out of 12–15 most likely to imply a contingent state in God. But it is by no means obvious that it does. In any possible world, God is either alone or he isn't. Now, on the proposal offered here, what the full extent of God's activity consists in will differ depending on whether God is alone. Consider, first, a world in which God does not create anything and therefore is alone. A proponent of divine simplicity could say that, in such a world, the full extent of God's activity consists entirely in the divine substance, which does not include God's creating anything. God would know the full extent of this activity – that it included, for example, God knowing and loving himself, and that it did not include creating anything, even though it did include God knowing that he has the power to create. No contingent state of God is obviously required here. Nothing in the Aloneness Argument requires the proponent of divine simplicity to think, for instance, that there is some positive contingent choice that God makes – the choice not to create – that resides in God as a contingent accident. Rather, knowing that he could create, God would know, given 14, that he is not in fact creating, that creating is not included in what he is doing, in that activity that consists in the divine substance.

Consider, on the other hand, worlds in which God brings about contingent objects and is therefore not alone. A proponent of divine simplicity could maintain that, in these worlds, the full extent of God's activity does not consist in the divine substance. Rather, God's bringing about contingent objects and knowing that he is bringing them about might consist in relations to items extrinsic to God, as proponents of divine simplicity have proposed.Footnote ¹³ On these proposals, God's knowledge of the contingent objects does not require any contingent states in God himself. Since, then, God's knowing the full extent of his activity in both alone and non-alone worlds does not obviously imply a contingent state in God, neither does assumption 14 obviously imply such a state.

What, finally, about assumption 15? If 13 and 14 do not imply contingent states or accidents in God, neither would it seem does 15. For, if knowledge of the truths from which another truth immediately follows does not require divine accidents, then knowledge of the immediately following truth wouldn't seem to require them either.

As far as we can tell, neither the Aloneness Argument itself nor any of the premises of the argument show that any of 12–15 requires a contingent state in God.Footnote ¹⁴ And, as we've seen, it follows from 12–15 that God would know that he is alone in an alone world. Again, God would know that he is alone because he would know that nothing besides him can exist unless he creates something, and he would know that he is not creating anything. And none of this would obviously require that God have any intrinsic contingent states or accidents.

We acknowledge that Schmid and Mullins wish to challenge the account of God's knowledge of contingent things (in non-alone worlds) that understands them to be relations to the contingent objects known, relations that do not involve any intrinsic contingent states in God – indeed, they include some challenges to this effect in their article. We don't find these challenges compelling, as we will explain briefly in the following section. But these challenges are not the main point or main interest of their article, anyway. The main interest of the Aloneness Argument – at least why it interests us and why we think it advances the discussion – is that it presents an argument against classical theism that is supposed to hold even if one were to accept that God's knowledge of contingent objects in non-alone worlds consists of relations to those objects. As Schmid and Mullins put it, ‘Grant's extrinsic strategy of locating (some of) God's knowledge (relationally) outside God . . . will not work in the alone world’ (Schmid and Mullins (Reference Schmid and Mullins2021), 5). While we don't find their arguments against Grant's sort of account for God's non-alone contingent knowledge compelling, we realize that critiquing such an account was not the central purpose of their article. Nor is the central purpose of ours responding to such critiques.

We turn, finally, to an important remaining question. What does the foregoing proposal for how a simple God might know that he is alone mean for the question of whether God's knowledge that he is alone is intrinsic or extrinsic? Answering this question requires distinguishing

1. (a) The act by which God knows that he is alone

and

1. (b) The predication: ‘God knows that he is alone.’

Now, on the foregoing proposal, (a), the act by which God knows that he is alone is intrinsic to God since that act is simply the divine substance itself. But (b), the predication ‘God knows that he is alone’ is extrinsic according to the whether-or-not view of extrinsicality since its truth value depends on whether or not God is related to other things. Its truth value depends on whether or not God is related to other things because (i) God knows that he is alone in virtue of knowing that his activity does not include bringing anything about and (ii) God's activity does not include bringing anything about because God stands in no causal relation to anything, which is what his activity of bringing something about would consist in, were he performing it.

For a similar reason that (a), the act by which God knows that he is alone, is intrinsic, so also is it necessary. That act is simply the divine substance itself, and since the divine substance is necessary, so also is the act by which God knows that he is alone in an alone world. But (b), the predication ‘God knows that he is alone’ is contingent or contingently true. It is true in some worlds but not in others, depending on whether God's total activity includes those relations to objects outside himself which constitute his causing and knowing them in worlds in which he is not alone. Notice that we have not committed to anything both intrinsic and contingent.Footnote ¹⁵

Objections and replies

Among a number of objections that Schmid and Mullins consider to the Aloneness Argument, the first is most relevant to our objection insofar as it challenges their account of extrinsicality underlying premise 2, which account we also challenged. Their discussion of the objection also affords opportunity to consider some issues that relate to our positive proposal for how a simple God might know that he is alone in an alone world, which is why we delayed consideration of these replies until after the presentation of our positive proposal. We will first summarize the objection they envision, and then discuss their three replies to the objection.

According to the objection they envision, the proper understanding of extrinsicality does not require, as the Aloneness Argument does, that a feature is extrinsic or partially extrinsic only if there is something outside the subject to which the subject relationally stands. Rather, according to the objection, the proper test of extrinsicality is this: a feature F is extrinsic to a subject S if and only if S can be deprived of F solely by changing things wholly other than (and outside) S. The objection, then, is that God can lose the property of knowing that he is alone just by something outside God beginning to exist. Thus, according to this envisioned objection, God's knowledge that he is alone is not intrinsic; it is extrinsic, even though there is no other thing outside God in that world. Premise 2 of the Aloneness Argument, then, is false.

Schmid and Mullins's first reply to this objection tries to show that, contrary to this objection, God's knowledge that he is alone is intrinsic, after all. To effect this reply, they distinguish between positive and negative extrinsic properties. After considering some possible counterexamples to their own analysis of extrinsicality, Schmid and Mullins write

What does the ‘negative’ in Lewis's ‘negative extrinsic properties’ mean? As Schmid and Mullins spell it out, it means that the properties report something of the subject of the property – in particular, they report an absence, a lack, or a failure of that subject. But, Schmid and Mullins claim, God's knowing this or that is no absence, lack, or failure. ‘God's knowledge is not a negative property/feature reporting some absence, failure, or lack of God's. In regard to divine knowledge, we are talking about some positive reality that God has or possesses’ (ibid., 7–8). So, while negative extrinsics like being alone might not require some further thing, God's knowing that he is alone isn't a negative extrinsic. Thus, the test for extrinsicality that the objection provides is not relevant to their argument; the objection fails.

What to make of this reply? There are at least three things to say concerning it. First, they again misunderstand Lewis's view. Second, once Lewis's view is properly understood, God's knowledge that he is alone is, by Lewis's definition, negative and extrinsic, contrary to what they claim. Third, this reply to their envisioned objection doesn't bear on our objection to the Aloneness Argument.Footnote ¹⁶

First, consider Lewis's distinction between positive and negative extrinsic properties. On the way Schmid and Mullins spell it out, Lewis's ‘negative extrinsic properties’ name a lack, absence, or failure in the thing that has them. But this is not how Lewis understands them. A negative extrinsic property, for Lewis, is a property that implies that the thing does not coexist with some wholly distinct contingent object.

On the way to his analysis of the terms ‘negative extrinsic property’ and ‘positive extrinsic property’, Lewis defines two other properties, being accompanied and being lonely:

Using these stipulated definitions, he goes on to define positive and negative extrinsic properties. Here's what Lewis actually says:

Again, for Lewis, a negative extrinsic property is a property that implies that the thing does not coexist with some wholly distinct contingent object. Lewis nowhere in that article or elsewhere that we can find defines a negative extrinsic property, as Schmid and Mullins do, to be a property that reports an absence, failure, or lack of the entity in question. Nor do the other authors that Schmid and Mullins cite.

Second point. Once we understand Lewis's distinction properly, we can ask whether God's knowledge that he is alone counts as a negative or positive extrinsic property.Footnote ¹⁷ Schmid and Mullins claim, as we have seen, that God's knowledge is not a negative extrinsic property on the Lewisian view they attempt to offer. But, on the contrary, it is negative and extrinsic on the analysis that Lewis gives. After all, having the property of knowing that one is alone implies loneliness.Footnote ¹⁸ For knowledge implies truth, thus God's knowing he is alone implies that he is, in fact, alone. As such, since the knowledge implies loneliness on God's part, the knowledge does count as a negative extrinsic property, contrary to what Schmid and Mullins claim, and contrary to premise 2 of the Aloneness Argument, which implies that God's knowledge that he is alone could not be extrinsic.

A referee suggests that, Lewis's actual views notwithstanding, Schmid and Mullins's first reply to their envisioned objection about extrinsicality can be put as follows:

1. 18. If God's contingent knowledge in the alone world is extrinsic, then it either consists in some failure/absence/lack of a relation to some disjoint thing, or else it consists in a relation to some disjoint thing.

2. 19. God's contingent knowledge in the alone world does not consist in a relation to something else.

3. 20. God's contingent knowledge in the alone world does not consist in some failure/absence/lack.

4. 21. So, God's contingent knowledge in the alone world is not extrinsic. (from 18–20)

Notice that, if ‘God's contingent knowledge’ means that positive item in virtue of which God knows that he is alone, then a proponent of our positive proposal from the previous section agrees with the conclusion, 21; for, on that proposal, the act by which God knows that he is alone is the divine substance, which is intrinsic, not extrinsic. Of course, on that proposal, whether God knows that he is alone by virtue of the divine substance depends on whether or not God is doing anything other than the activity that is the divine substance. If he were doing something other than the divine substance, this activity would consist in relations to items outside God. Thus, whether or not God knows that he is alone depends on whether or not God has or lacks relations to other things. Those conditions for whether or not ‘God knows that he is alone’ is true don't, to our ear, translate to the claim that God's knowledge that he is alone ‘consists in’ some failure, absence, or lack. But if someone insists that they do so translate, then we would reject premise 20, given that reading of the premise.

At any rate, here is our third point regarding Schmid and Mullins's first reply to their envisioned objection about extrinsicality. We don't see that their distinction between positive and negative extrinsic properties has any bearing on our main response to the Aloneness Argument. Our objection was that a ‘feature reading’ of ‘God's knowledge’ would result in the Aloneness Argument's having contradictory premises and to premise 5's being rejected by the classical theist. On the other hand, a ‘predication reading’ of God's knowledge across the argument would render premise 2 false; an extrinsic predication does not require that there be something outside the subject of predication to which that subject relationally stands. Schmid and Mullins’ first reply to their envisioned objection about extrinsicality wouldn't seem to gainsay these points.

Let us turn, then, to Schmid and Mullins's second reply to the flawed notion of extrinsicality objection. This second reply doesn't really bear on our concerns about premises 2 and 5, but it does suggest a variation on the Aloneness Argument which we set out here, filling in a few gaps to make the argument more explicit. The argument begins with a premise about a scenario the classical theist thinks possible – a scenario on which God did not create and therefore knows that he is alone – and by a series of premises derives a conclusion that the classical theist thinks impossible – that God is not simple.

1. 22. God's knowledge that he is alone has some reality (premise).

2. 23. If God's knowledge that he is alone has some reality, then if God is simple, then God's knowledge that he is alone is identical to God (premise).

3. 24. So, if God is simple, then God's knowledge that he is alone is identical to God (from 22–23).

4. 25. If God's knowledge that he is alone is identical to God, then God's knowledge that he is alone is necessary (premise).

5. 26. God's knowledge that he is alone is not necessary (premise).

6. 27. Therefore, God is not simple. (from 24–26)

The support given for premise 23 of this argument is that, for any x in an alone world, if

We maintain that this version of the Aloneness Argument also fails. To see why, consider that such phrases as ‘S's knowledge’ or ‘S's belief’ are often ambiguous, since they can be used to refer both to S's act/state of knowing or believing, and to that which S knows or believes. But the act/state by which S knows or believes some truth is not identical to that truth, nor need it have the same modality. For example, 2 + 2 = 4 is a necessary truth, but Mary's act/state of knowing or believing it is contingent.

Once we distinguish between ‘God's knowledge that he is alone’ understood as the act by which God knows and ‘God's knowledge that he is alone’ understood as the truth known, we can see how a classical theist may respond to this variation of the Aloneness Argument. ‘God's knowledge that he is alone’ when taken to refer to the act by which God knows that he is alone is identical to God and exists necessarily. But that which God knows – namely, that he is alone – is contingent; that is, the truth known is contingently true. We have already seen above how God could know the contingent truth that he is alone by the activity to which he is identical, which exists necessarily. The act by which God knows that he is alone is intrinsic and necessary; the truth known is contingent, and the predication ‘God knows that he is alone’ extrinsic, according to the whether-or not-view of extrinsicality.

With the foregoing distinctions in mind, we can see that Premise 23 of this version of the Aloneness Argument is true only if ‘God's knowledge that he is alone’ refers to God's act by which he knows that he is alone. Given that 23 is true only if ‘God's knowledge that he is alone’ refers to God's act by which he knows, then that must be the meaning of the phrase throughout the rest of the argument if equivocation is to be avoided. But premise 26 is true only if ‘God's knowledge that he is alone’ refers, not to God's act, but to what God knows – ‘that he is alone’ – which truth is contingent. Thus, either premise 23 or 26 is false (which one depending on what we mean by ‘God's knowledge that he is alone’) or the argument uses the same phrase to mean different things, in which case it commits the fallacy of equivocation. Either way, the argument is unsound.

Schmid and Mullins's third reply to the envisioned objection about extrinsicality also does not bear on our concerns about premise 2 or 5 of the Aloneness Argument. The various points made in their third reply are not really even focused on the Aloneness Argument, per se, but rather consist in a quick battery of objections to the claim that God's knowledge could vary (say, across worlds) without God varying himself. Because these are really different and much broader objections than the Aloneness Argument, we will treat of them only briefly. Our remarks will indicate, even if briefly, why we don't find compelling Schmid and Mullins's arguments against identifying God's contingent action and knowledge in non-alone worlds with relations to extrinsic contingent objects, as assumed by our positive proposal and discussed in the previous section.

First, the authors claim that God can know P only if he has justification for believing P and that God's justification must consist at least partly in intrinsic features of God that would be different were God's knowledge different. In indicating what they mean by justification, all the authors say is that “surely it is partly constitutive of S's having justification that S is internally consciously aware of one or more reasons upon which S bases S's belief’ (Reference Schmid and Mullinsibid.). Their argument seems to be that God's varying knowledge requires varying justification which requires varying awareness of different reasons for believing different things, which varying awareness requires variation in God himself.

Two points by way of brief reply. First, it is far from obvious that in order for a belief to be justified it must be based on reasons; thus, many accounts of justification or warrant allow for various types of properly basic belief, grounded, for example, in things like direct awareness. Second, it assumes something that proponents of divine simplicity who endorse extrinsic models of divine knowing cannot accept when it insists without further argument that God's direct awareness of creatures must be in virtue of intrinsic features of God that would not exist were God knowing no or different creatures.

In a second point, Schmid and Mullins reject the proposal that God's beliefs might just be relations to propositions, understood as abstract platonic objects existing independently of God's knowing, and that these beliefs might vary across worlds without any intrinsic variation in God. The authors maintain that this proposal suffers from a grounding problem: ‘In virtue of what does God stand in the believing relation in some worlds but not in others’ (Reference Schmid and Mullinsibid., 9)? And, without intrinsic differences in God, the authors wonder how we can ‘delineate a belief relation from other relations to propositions in which God stands’ (Reference Schmid and Mullinsibid.)

These points are, we admit, potentially interesting objections to extrinsic models of divine knowing, and we acknowledge that Schmid and Mullins are only floating them here; the main purpose of their article is not to develop such objections in detail. That said, we do not find the objections as presented to be successful against extrinsic models of divine knowing or believing. It isn't clear to us why, for example, the species of a relation must be derived from counterfactually varying intrinsic features of the relata. In response to the question, in virtue of what does God stand in a believing relation to a given proposition in some worlds but not others, Schmid and Mullins reference Grant, who has attempted to answer the grounding question by noting that God's very essence, since God is essentially omniscient, is such that God believes whatever propositions are true in a given world; there is, therefore, no need for intrinsic accidents to do the grounding. Schmid and Mullins reply that Grant's response is unconvincing because

Here we think it is helpful to clarify the dialectical context of Grant's proposed solution to the grounding problem. Grant had cited a number of authors who have proposed that human beliefs and other cognitive states, like perception, are relations. He then considers a grounding objection to this account of human beliefs, raised by Frank Jackson, to the effect that without intrinsic states in the human believer, we can't explain why the believer believes some propositions and not others. To which Grant responds by showing that, given divine omniscience, this grounding problem does not arise in the case of God. Moreover, Grant notes that his solution to this grounding problem satisfies Jackson's own account of what it is for a relation to be internally grounded. The question about grounding that Grant takes up, then, was not about how God could be omniscient in the first place without varying intrinsic states. And simply to assert that God can't be omniscient without such states is to beg the question against extrinsic models of divine cognition. What Schmid and Mullins need to show is that varying intrinsic states are required for divine omniscience, in particular, for God's knowledge of contingent truths. We don't see that they've shown that.

A final objection from Schmid and Mullins holds that ‘(i) truths are such that God desires to know them, and (ii) one cannot change S's desires merely by altering things wholly outside of and apart from S’ (Reference Schmid and Mullinsibid.). We find the initial premise of this objection puzzling. The object of desire is normally taken to be something the desirer does not yet possess. For God to desire to know some truth, then, would imply that God does not yet know it. With other classical theists, we deny that there are truths that God does not know. Perhaps Schmid and Mullins mean that God desires to know the truth, whatever that may be, whether God knows it already or not. Similarly, we might desire health even when we are healthy.Footnote ¹⁹ If that's the case, then it isn't clear that God's desire does have to change across worlds when altering things apart from him. In any world, that desire – the desire to know the truth – will be had by God.

In any case, none of these replies considered in this section touch on our concern about premise 2 or 5 of the Aloneness Argument. We conclude that these replies proffered by Schmid and Mullins do not show our objection to the Aloneness Argument to be faulty.