Lowe's modal ontological argument

According to Lowe, the most perspicacious formulation of the modal ontological argument for a modern audience exploits Alvin Plantinga's way of presenting it, making use of the language of possible worlds and modern modal logic.Footnote ² There are differences between Lowe's and Plantinga's versions of the argument, but I do not discern any clear improvements (or weakenings) in the former as compared to the latter. The differences between them are not thus worthy of mention.Footnote ³ Here is Lowe's formulation of the argument:

1. (1) God is, by definition, a maximally great being and thus a being whose existence is necessary rather than merely contingent.

2. (2) God, so defined, could exist; in other words, he does exist in some possible world.

3. (3) Suppose that w is a possible world in which God, so defined, exists: then it is true in w, at least, that God exists there and, being God, exists there as a necessary being.

4. (4) But a necessary being is one which, by definition, exists in every possible world if it exists in any possible world.

5. (5) Hence, the God who exists as a necessary being in w is a being that exists in every possible world, including this, the actual world.

6. (6) Therefore, God exists in the actual world; he actually exists.

Let us grant that the conclusion follows from premises (1) and (2); the acceptability of the conclusion then depends on the acceptability of the premises. Premise (1) says that God is, by definition, a necessary being; a being who, if it exists, exists in every possible world. Why think so? Ultimately, Lowe holds, like many philosophers of religion, that God's necessity is entailed by the Anselmian definition of God as a maximally great being or a perfect being. The claim is that a maximally great being could not just happen to exist, but it has to exist no matter what. In other words, a maximally great being cannot be a contingent being, but it has to be a necessary being.Footnote ⁴

There are, of course, several objections to premise (1). One critique Lowe discusses is the Kantian complaint that existence – whether contingent or necessary, one must add – is not a predicate. According to this critique, it is an error to suppose that ‘exists’, as opposed to, say, ‘is red’ or ‘is round’, attributes some property to an object or objects. In modern philosophy, this complaint has been made in terms of first-order predicate logic.

In the language of predicate logic, existence is expressed by the existential quantifier, ‘∃’, which is taken to be a second-level predicate: it is used to predicate a second-level property of instantiation of first-level properties. Thus, contrary to the Kantian complaint, on this view that which expresses existence, namely, the existential quantifier, is a special kind of predicate. However, a consequence of this view is that the existential quantifier is not a first-level predicate: it does not predicate a property of any object or objects. This is in line with the Kantian complaint. For example, on this view, ‘cats exist’, formalized as ‘(∃x) Cat(x)’, is just to say in logician's jargon that the property of cathood has at least one instance. While things are a bit different vis-à-vis propositions including singular terms such as ‘God’, the same point still applies. As the standard way of translating singular propositions of the form ‘s exists’ is ‘(∃x) x = s’,Footnote ⁵ on this view, then, ‘God exists’ is just to say that the property of being identical with God has an instance – and presumably it has an instance necessarily, if we want to speak of necessary existence here.

All of this allegedly bears upon the acceptability of premise (1). For, on the face of it, the premise treats necessary existence as being one of the divine first-level properties, along with such supposed divine first-level properties as omnipotence, omniscience, and moral perfection. However, according to the critique at hand, this is to make a logical error of treating a second-level property as a first-level property.Footnote ⁶ Consequently, assuming that the modal ontological argument's soundness depends on making this logical error, the argument is a failure.

In response, Lowe holds that nothing in the formulation of the modal ontological argument implies that existence or necessary existence must be a first-level property. In fact, we do not have to presume any particular view of what it is or is not.Footnote ⁷ Lowe says several things here. First, logic's account of existence is actually rather counterintuitive and hard to understand. It seems that it does not explain existence but needs to be explained by that notion. For is not a property F having an instance just to say that an object exists that possesses F? Second, there is much to be said in favour of the view that existence is a primitive notion. However, Lowe does not say just what there is to be said for this view. Third, maybe existence is not a property at all. We should not reify existence, that is, treat it as an entity of any kind, like a property. For entities exist or can exist. Do we seriously want to say that existence exists or can exist? Lowe concludes that the Kantian objection is just a red herring with no real bearing on the modal ontological argument's soundness.Footnote ⁸

Clearly, Lowe's case against the Kantian critique is far from substantial. All of his points are more or less opening proposals, and he does not give us a positive account of existence. In this connection, one might note that, when it comes to God, claiming along with Lowe that necessary existence is not a divine property can be supported by the thesis of divine simplicity. According to this view, God has no composition, but he is identical to his properties, which, in turn, are identical to each other. But if so, it is a mistake to take God to be a being that literally has distinct properties, including the alleged property of necessary existence. Whether divine simplicity is a thesis that should be accepted is a question I do not try to address here.Footnote ⁹

So much for premise (1) of the modal ontological argument. Let us assume that we can make sense of what the premise says in a way that does not affect the argument's soundness. We are more interested in the argument's premise (2) and how Lowe defends it. Premise (2) claims that it is possible for God, a maximally great being, to exist, that is, there is a possible world in which God exists. This is not an innocent modal claim. If the recent literature on modal epistemology teaches us anything, it is that it is far from obvious whether we are justified in accepting such extraordinary modal claims as ‘possibly, I exist and nothing material exists’, ‘the laws of nature are necessary’, and, of course, ‘possibly, God exists’.Footnote ¹⁰ At any rate, such modal claims call for a detailed justification. In view of that, let us consider how Lowe seeks to support the possibility of God's existence.

Lowe on the possibility of God's existence

Lowe's case for the possibility of God's existence can be concisely put as follows: All we need for rational acceptance of God's possibility is to grasp God's essence, that is, to understand the real definition of God; to understand what God is or would be like. In fact, we do not even need to fully understand what God is or would be like, which is fine, since this is probably beyond the capacities of finite intelligences like ours. Instead, we just need to understand that, at the very least, God is a maximally great being. We can accomplish this task. Hence, God's existence is possible.Footnote ¹¹ This is how the case goes short and sweet. But it clearly calls for unpacking. Lowe is here assuming his neo-Aristotelian essence-based account of modal knowledge according to which the source of all modal knowledge is in our knowledge of essences. Let us first describe what the account says of knowledge of essences and then how that bears upon modal knowledge. The central features go as follows.

The essence of an entity is revealed by its real definition, which is a proposition that tells us what the entity is or would be like.Footnote ¹² Real definitions must be distinguished from verbal definitions, which are typically stipulative or conventional in character, allowing us to substitute one word for another, as, for example, ‘bachelor’ may be defined as ‘unmarried man’.Footnote ¹³ Essences should not be considered as entities, because that would lead to an infinite regress: if essences were entities and if all entities have essences, then essences would also have to have essences, and so on ad infinitum.Footnote ¹⁴

We come to know propositions that express real definitions by understanding them; we can understand what an entity is or would be like. The sort of understanding at issue is not any kind of mysterious rational insight concerning some ethereal things – essences are not entities – but an intellectual ability we must already be acknowledged to possess, that is, the ability to understand some propositions.Footnote ¹⁵

Understanding real definitions is an a priori process. The conception of a priori in use here is atypical, however. A priori processes are not independent of empirical elements, but they proceed in a cyclical manner by altering stages of a priori and a posteriori inquiry.Footnote ¹⁶ On this account (or so it seems to me), a posteriori elements play more than just the typical enabling role in a priori processes. This means that, as a priori processes include a posteriori elements and the latter are visibly fallible, the former must be fallible, too. The essence-based account of modal knowledge is thus a fallibilist one.Footnote ¹⁷

We can understand the real definitions not only of existing entities, but of non-existent ones, too, such as mermaids and unicorns, perhaps.Footnote ¹⁸ As a matter of fact, we can in general know the real definitions of things antecedently to knowing whether they exist (think about some kind of aliens, for example). This is the thesis that ‘essence epistemically precedes existence’. For it is hard to see how we could find out that an entity exists before knowing what it is whose existence we have supposedly discovered.Footnote ¹⁹

Thus far we have discussed knowledge of essences. However, the main claim of Lowe's essence-based account of modal knowledge is that the source of all modal knowledge is in knowledge of essences; knowledge of essences entails modal knowledge. How does this happen? Here the claim is that necessary truths are grounded in essential truths, that is, a necessary truth is either an essential truth or obtains in virtue of essential truths (but not vice versaFootnote ²⁰). Thus, we can derive necessary truths from essential truths. How does this help us in discerning what is possible? Certainly, if p is an essential and hence necessary truth, it follows that p is also a possible truth. But this is not a very exciting piece of knowledge of possibility.

As I see it, Lowe is not fully explicit on the question of how knowledge of essences yields knowledge of possibilities. However, his answer can be deduced from what has been already said. In the beginning of this section, we noted that understanding God's real definition in Lowe's view suffices for rational acceptance of God's possibility. Now this inference is ill-advised and groundless, unless something like the following general formula is assumed: one is justified in accepting the possibility of an entity E just in case one understands the real definition p of E. So, something like this must be Lowe's view of how knowledge of essences entails knowledge of possibilities. As regards our case, Lowe of course holds that we do understand, at least partially, the real definition of God, and hence, assuming the stated general formula, we are justified in accepting God's possibility. But if so and if, as I assume, everything else in the modal ontological argument is in order, the conclusion to be drawn is that God exists.

So far so good. But now it is time to raise objections. My chief claim is that Lowe's modal epistemology fails; his defence of the modal ontological argument's premise (2) is unsuccessful. I have two complaints. I call them ‘the modified “perfect island” objection’ and ‘the conflicting possibilities objection’. Both of these refer to the concern that Lowe's modal epistemology is too permissive: it justifies possibility claims that question the acceptability of premise (2) and the underlying modal epistemology, in general. My critique is not directed at the validity of Lowe's formulation of the modal ontological argument or its other key premise, namely, premise (1). Quite the opposite: I make use of modal ontological argumentation in my critique.

Before discussing the objections, let me briefly mention one further potential critique that can be directed against Lowe's essence-based account of modal knowledge. One might call into question Lowe's claim that essential truths entail modal truths and hence that understanding the real definition of an entity justifies one in accepting the entity's possibility.Footnote ²¹ For why should we think that essential truths entail modal truths? Although Lowe does not really argue for this entailment, it seems hard to cast doubt on it. Still, for those who are sceptical on this point, I can only refer to the fact that there is a widespread acceptance of a close connection between essence and modality. For example, Kit Fine notes that in the recent analytic philosophy it has been a commonplace to reduce even essential truths to modal truths (neither Fine nor Lowe accept this reducibility-thesis, though).Footnote ²² I shall assume that essential truths entail modal truths. I focus on different problems in my critique.

The modified ‘perfect island’ objection

Anselm's contemporary monk Gaunilo challenged Anselm's ontological argument on the grounds that it allows one to define into existence pretty much any sufficiently perfect thing one wants, the upshot then being that there must be something wrong with the argument, though it may be hard to say just where the flaw is.Footnote ²³ My claim is that, when put forward with a suitable example, this critique applies to Lowe's defence of the modal ontological argument. Moreover, in this case it is not hard to say where the flaw is. For it can be located in Lowe's modal epistemology being too permissive: when conjoined with modal ontological argumentation, it permits us to define into existence beings which we do not want to have in the domain of existing things. But let us start with an example that is not entirely convincing.

Consider Gaunilo's example: a perfect island. Let us try to define such an island into existence by applying Lowe's views. What we need, first, is a real definition of a perfect island, which tells us what such an island would be like. A perfect island is in all respects flawless: it has excellent beaches, streams, tree stands, flora, species, and so on. Furthermore, it is surely greater for the island that it does not just happen to exist, but that it exists no matter what, that is, that it is a necessarily existing island. By virtue of this description we can claim that we understand, at least partially, the real definition of a perfect island. As per Lowe's essence-based account of modal knowledge, it follows that it is possible for a perfect island to exist.

Now we can put forward a modal ontological argument for the existence of a perfect island; by the argument, we conclude that such an island exists. But this is an outright absurdity. No sane person accepts the existence of a perfect island on these grounds. But if so, there is also something wrong with Lowe's defence of the modal ontological argument for God's existence. More precisely, as I grant the validity of the modal ontological argument, the error is to be located in Lowe's modal epistemology: it is too permissive; besides the possibility of God's existence it justifies the possibility of a necessarily existing perfect island.

In this form, the objection has not gone unnoticed by Lowe. He maintains that it is ‘clearly spurious and unfair’ on the following grounds. When one talks about a perfect island, one is talking about a certain material being with certain humanly pleasing features in the highest degree. Such a being must be a contingent being, since all material beings are by their nature contingent beings. This means that one cannot via modal ontological argumentation infer that a perfect island exists from the mere fact that it is possible for such an island to exist. By contrast, Lowe holds, similar reasoning does not apply to God, who, in virtue of being maximally great by nature, has necessary existence.Footnote ²⁴ Clearly, an assumption here is that not all non-material beings have to be contingent by their nature, God being an example of such a being.

Lowe's rejoinder is open to discussion. First of all, one may try to query its claim that all material beings are contingent beings by their nature. For example, Graham Oppy maintains that it is plausible naturalistic metaphysical speculation that natural reality as a material being could not have failed to exist, that is, that it is a necessary material being.Footnote ²⁵ However, no matter how one explicates this view, I have no clue how it could be used to support the claim the stated ‘perfect island’ objection needs, namely, that such material beings as a perfect island could be necessary beings. So, this is not an especially promising way to reinforce the objection.

What about the alleged necessity of natural reality? Does it as such have some relevance to the discussion at hand? Maybe it does. But instead of elaborating this idea, I opt for a different approach: let us leave material beings aside and change our example to a non-material being. For even if one could not define unwanted material beings into existence via Lowe's modal epistemology plus modal ontological argumentation, it is still open to argue that that can be done with respect to suitable kinds of non-material beings. This should be sufficient to cast doubt on Lowe's essence-based account of modal knowledge.

Lowe has noted a related worry. While it does not concern Lowe's modal epistemology so much as the modal ontological argument, in general, it is worth discussing here. The worry is that given that the modal ontological argument for the existence of a maximally great being is successful, are we really entitled to suppose that there could be only one maximally great being? In Lowe's view, it is not easy to find a simple and compelling answer to the provable uniqueness of God. Even so, he claims that if this were the only weakness in the argument, it would still be a remarkably important argument. I disagree. For the weakness, if true, just shows the absurdity of the modal ontological argument. No sane person accepts the existence of a plausibly infinite amount of perfect beings on these grounds.

However, the worry that, by the modal ontological argument, we have to conclude that there are many perfect beings is not inevitable. For let us just introduce uniqueness to the definition of a maximally great being. While this may look like an ad hoc move, it is not, in fact, a made-up claim that a maximally great being must be unique. To take but one example, Peter van Inwagen argues that uniqueness is a feature that a maximally great being would have to have, as it adds to a being's greatness.Footnote ²⁶ Perhaps this is true. Here is my simple defence of the uniqueness of a maximally great being: we value unique and rare things more than commonplace things that are great in number. On the supposition that our value judgement is here correct, the right conclusion to draw is that uniqueness is a great-making property. That the modal ontological argument supports the existence of many perfect beings looks like a groundless worry.

But be that as it may, I believe that we can make a case for the claim that Lowe's modal epistemology plus modal ontological argumentation permits us to define into existence such non-material beings that make one doubt the cogency of Lowe's modal epistemology. I call this the modified ‘perfect island’ objection. Plausible candidates here are non-material beings, who, like God, are necessary but otherwise have some major or minor deficiencies or negative features.Footnote ²⁷ Let us consider as an example a maximally evil being, a perfect demon. Such a being is, I say, very much like God in being a non-material person and having power and knowledge to the highest degree, but, instead of being morally perfect, it is immorally perfect; it only does what is bad. Furthermore, I do not see any reason to suppose that a maximally evil being must be a contingent being by its nature. But then it is a necessary being. For necessary existence is a feature a maximally evil being would have: it is more evil to wreak havoc no matter what were the case than just to happen to do that.

Given the above description, we can reason, in accordance with Lowe's essence-based account of modal knowledge, that we understand, at least partially, the real definition of a maximally evil being, and hence a maximally evil being is possible. By presenting a modal ontological argument for the existence of a maximally evil being, we conclude that such a being exists. But this is just absurd, and the same must then go for Lowe's defence of the modal ontological argument for God's existence. More precisely, the fault is in Lowe's modal epistemology being too permissive: on top of God's possibility, it justifies the possibility of a necessarily existing evil being – and no doubt a host of other similar necessary beings turn out to be possible.

I surmise that Lowe would reply to the objection as follows. Defining such beings as a perfect demon into existence is acceptable only if one thought that definitions are, in Lowe's words, ‘arbitrary concoctions of the human mind’. Some definitions might be like that, and it would be dangerous to suppose that they could have positive existential implications. Presumably, Lowe would count the definition of a maximally evil being as an arbitrary definition, whereas, he says, ‘very arguably, the definition of God is far from being an arbitrary concoction of the human mind, any more than the definition of a circle is’.Footnote ²⁸ This potential rejoinder introduces a further problem, however.

For who is to say that the definition of God as a perfect being is a non-arbitrary, real definition, whereas other similar and controversial definitions, such as the definition of a perfect demon, are just arbitrary definitions? Here Lowe is silent. He does not offer any criteria to distinguish between arbitrary and non-arbitrary definitions. But then we have no compelling reasons to accept his claim that the definition of God is a real definition and that God is thus a possible being. On this point, Lowe's modal epistemology is incomplete. On the other hand, if we grant that we are dealing with a real definition here, it is hard to see why the definition of a perfect demon – along with the definition of a mermaid or a unicorn – would not also count as a real definition. But if so, the modified ‘perfect island’ objection is still valid, and Lowe's essence-based account of modal knowledge fails.

The conflicting possibilities objection

This objection also refers to the concern that Lowe's modal epistemology is too permissive. More precisely, it justifies possibilities that actually rule each other out in the sense that if one is possible, the other is not. No cogent theory of modal knowledge should yield such results. In order to grasp this objection, let us start with supposing that Lowe is right. Consequently, by the essence-based account of modal knowledge, the possibility of God is justified, and the modal ontological argument for God's existence is sound. As a result, God exists, and not just in the actual world but in every possible world.

That God exists in every possible world has major consequences for the domain of possibility. For it entails that everything that is incompatible with the existence and nature of God is impossible. Consider, for example, gratuitous evil, that is, roughly, evil that does not promote some greater good or prevent some greater evil. In all probability, there is no possible world in which God allows gratuitous evil to occur; hence, gratuitous evil is impossible. Incidentally, this, if accurate, means that the so-called modal problem of evil is a failure, as its key premise is that, possibly, gratuitous evil exists.Footnote ²⁹

However, I do not want to focus on gratuitous evil here but on beings whose existence is incompatible with God's existence. The aforementioned perfect demon is no doubt such a being, but here I decide on a different example. So, consider the numerous deities of Hinduism, and Ganesha in particular. Ganesha is the deity who in Hindu iconography is often depicted with an elephant's head and a big belly. He is typically taken to be the son of deities Shiva and Parvati, and his task in the Hindu pantheon is to place and remove obstacles. Assume that, as a created being, Ganesha is contingent by his nature. Further, let us grant that there is no possible world in which God would allow Ganesha to exist. Consequently, granted that necessary God exists, Ganesha is an impossible being. (If you disagree with the consequent, just replace Ganesha with some contingent being X you think fulfils the condition ‘there is no possible world in which God allows X to exist’.)

But now, given Lowe's essence-based account of modal knowledge, we have a problem. For whatever our opinion on Ganesha is, we have to admit that we understand, at least partially, the real definition of him (or, rather, some variant of Ganesha, as there are quite a few incompatible descriptions of what he is or would be). Thus, in line with the essence-based account of modal knowledge, we are justified in accepting Ganesha's possibility. But this goes against our previous result that Ganesha is an impossible being.

The upshot here is that Lowe's essence-based account of modal knowledge is too permissive: it permits us to infer possibilities that actually rule each other out in the sense that if one is possible, the other is not. Lowe's account entitles us to suppose that both God and Ganesha are possible beings, whereas, in fact, if one is possible, the other is impossible. This is as such an undesirable feature in any theory of modal knowledge and makes one question Lowe's account. But we can also say the following.

Since ‘possibly, Ganesha exists’ is justified on the grounds of Lowe's essence-based account, it is a rebutting defeater to similarly justified ‘possibly, God exists’ (and, of course, vice versa). As a rebutting defeater, ‘possibly, Ganesha exists’ precludes the rational acceptance of ‘possibly, God exists’ (and vice versa). Given Lowe's modal epistemology, the only rational response is to suspend judgement on the possibility of God's (and Ganesha's) existence. Thus, contrary to Lowe's claims, his essence-based account of modal knowledge does not entitle us to suppose that God's existence is possible. So, Lowe's defence of the modal ontological argument's crucial possibility claim fails.