THE ONTOLOGICAL ARGUMENT

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1 36 THE ONTOLOGICAL ARGUMENT E. J. Lowe The ontological argument is an a priori argument for God s existence which was first formulated in the eleventh century by St Anselm, was famously defended by René Descartes in the seventeenth century, and still has important modern advocates, such as Alvin Plantinga. It has also had equally famous critics, such as Immanuel Kant in the eighteenth century and Gottlob Frege and Bertrand Russell in the nineteenth to twentieth centuries. To say that the argument is an a priori one is just to say that it is a deductive argument from premises whose truth is deemed to be knowable without recourse to empirical evidence of any kind. The argument has received many different formulations in the course of its long history, but St Anselm s original version in his Proslogion of 1077/8 (chs. 2 and 3: see Charlesworth 1965) can be reconstructed in something like the following way: 1 God is, by definition, a being than which none greater can be conceived. 2 A being than which none greater can be conceived exists at least in the mind. 3 It is greater to exist in reality than to exist only in the mind. 4 Therefore, God a being than which none greater can be conceived exists not only in the mind but also in reality. The premises here need some elucidation. Premise (1) is supposed to be a conceptual truth. It tells us that the concept of God is the concept of a greatest possible being a being so great that it is impossible to conceive of a greater being, or, in other words, a being of maximal greatness. This is a plausible claim, certainly concerning the traditional Christian conception of God as a being who is omnipotent, omniscient, omnibenevolent, and the creator of all things. Even so, the idea of maximal greatness may appear a little puzzling to the modern mind, because it seems to imply that there are degrees of being, as though being lies on a scale with a maximum at one end and a minimum at the other. And yet modern philosophers tend to assume that being is simply an all-or-nothing affair: either something exists, or it does not, and exists means exactly the same as it applies to any sort of entity.

2 E. J. LOWE However, this modern view is not incontrovertible, and for many centuries philosophers have thought differently about existence. In particular, traditional metaphysics, with its roots in the thought of Aristotle and his medieval followers, the Scholastics, holds that entities belonging to different ontological categories do not all exist in exactly the same way. For example, it holds that entities in the category of substance have a more basic kind of existence than entities in the category of quality or mode, because entities of the latter sort depend for their existence on substances, whereas the reverse is not the case (see Lowe 1998: ch. 6). Thus it would be said that the shape and color of an individual substance of an individual animal, let us say, such as a horse depend for their existence on that individual, precisely because they are essentially its qualities and so cannot exist separately from it. But it would also be said that even within the most fundamental category of substance, there are degrees of being, because there are degrees of existential dependence. Consider, for instance, something such as a pile or heap of rocks. This is clearly an individual thing or substance, rather than a quality or mode of any such thing. Even so, the pile evidently depends for its existence on the individual rocks that make it up whereas they do not, conversely, depend for their existence on it. In that sense, the pile is a more dependent being than is any of the rocks that compose it. However, the rocks in turn depend for their existence on other things, most obviously the various mineral particles of which they themselves are composed. It would seem that all material substances are, very plausibly, dependent beings in this sense, even if some should turn out to be simple substances, not composed of anything further. For it seems that they are all contingent beings, where a contingent being is one that does not exist of necessity. Consider, for example, a single elementary particle of physics, such as a certain individual electron, e, which is, according to current physical theory, not composed of anything more fundamental. Surely, e might not have existed at all. But could e have been the only thing to exist? We might think that we can imagine a world in which all that exists is this single electron, e. But, in fact, modern physics would repudiate this idea as nonsensical. Electrons are not really to be thought of as being particles in a commonsense way, but are, rather, best thought of as quantized states of a space-permeating field; and according to this way of thinking of them, it really makes no sense to envisage one of them as having an existence that is wholly independent of anything else. However, even though it makes no sense to think of an electron, or indeed any material substance, as having such a wholly independent existence, we clearly can make sense of the idea of a being that does have such an existence: a being that depends for its existence, in any sense whatever, on absolutely nothing other than itself. This, indeed, would seem to be the core of the idea of a maximally great being. Without presuming that such a being does exist, we can surely affirm that such a being could exist. And this, in effect, is what premise (2) of the argument is affirming. So let us turn to that premise. Premise (2) states that A being than which none greater can be conceived exists at least in the mind. In other words, we can coherently think of there existing such a being, one which has an absolutely independent existence. A corollary seems to be, 392

3 THE ONTOLOGICAL ARGUMENT as I have just remarked, that such a being could exist: it has at least possible existence, even if it does not actually exist. The reference to the mind in premise (2) suggests that something of a purely psychological nature is being affirmed by it, but this is misleading. The ontological argument is not supposed to be about our powers of thought or imagination, but about whether a being of a certain kind could and indeed does exist. Understood in this way, premise (2) seems to be fairly compelling. That being so, the cogency of the ontological argument in its present formulation turns on the status of premise (3), which affirms that It is greater to exist in reality than to exist only in the mind. This premise, too, needs some unpacking. The idea behind it can be cashed out in the following way. I have already said that it seems plausible to suppose, in line with premise (2), that a maximally great being could exist. But suppose that such a being is a merely possible being, that is to say, a being that could exist, but does not actually exist, and therefore does not exist of necessity. To suppose this is to suppose that a maximally great being could be a contingent being. However, expressed this way, the supposition looks decidedly suspect. For we have already seen that it is very plausible to suppose that all contingent beings are, in one way or another, dependent beings, and hence not maximally great, in the sense of having an absolutely independent existence. In other words, a supposedly maximally great being that did not exist of necessity and so also in actuality ( in reality ) would not really be a maximally great being. This, in effect, is what premise (3) can be construed as saying. Of course, this is not the only possible way of construing (3): it could be construed instead as saying, merely, that anything that actually exists is, for that reason alone, a greater being than anything that does not actually exist but merely could exist. Indeed, that is what (3) more literally seems to be saying. But understood in that way (3) is not at all plausible. Clearly, given that we are now interpreting the notion of degrees of being in terms of degrees of existential dependency, it is rather implausible to contend that no merely possible being is less dependent in nature than any actually existent being. Consider, for instance, some merely possible material substance, such as an individual horse that might have existed but does not in fact exist, and contrast this with an actually existing quality or mode of an actually existing horse. Surely, the actually existing quality is an entity that is more of a dependent being in its nature than is the merely possible horse: for the latter is (or would be) a substance whereas the former is merely a quality, and all qualities are subordinate to substances in their degree of dependency. Of course, if one thought of possible existence as being a lesser (because, presumably, more dependent) kind of existence than actual existence, then indeed one might suppose that even the most dependent actually existing entity is less dependent than the least dependent merely possible entity. But that way of thinking is very arguably confused. To say that something could exist ( has possible existence ) is, plausibly, not to assign to it a kind of existence, but merely to qualify or modify, in a certain manner, a claim concerning the existence of that thing. For example, when I say that the golden mountain could exist, I am not assigning to it a shadowy sort of existence: indeed, I am not affirming that it does exist at all, in any sense whatever. 393

4 E. J. LOWE Rather, I am retreating from any such existence claim to a weaker claim: one that is entailed by, but does not entail, the claim that it exists. Let me now try to reformulate the ontological argument, as it was set out earlier, with the foregoing elucidations in mind. It now comes out as follows: 1* God is, by definition, a maximally great being that is, a being that is absolutely independent of anything else for its existence. 2* A maximally great being could exist. 3* A maximally great being could not have merely possible existence it would have to exist of necessity and so also in actuality. 4* Therefore, God a maximally great being does actually exist. Is this a sound argument? That is to say, are its premises true and does its conclusion follow deductively from those premises? On the face of it, it would seem so. Of course, one might have doubts as to whether the being whose existence is affirmed in the conclusion, (4*), must have all of the various divine attributes traditionally assigned to God, such as omniscience and omnibenevolence. But let s set aside that difficulty for present purposes. Even without assuming that the argument establishes the existence of the traditional Christian God in this sense, it is a remarkable enough argument. Before I proceed, let me say something concerning Descartes s version of the ontological argument, which appears in his Fifth Meditation of 1641 (see Descartes 1984). Although Descartes did not formulate the argument in anything much like the way that Anselm did, he did formulate it in a way that seems reasonably close to the version that I have just presented above. Descartes maintained that, because God is by definition a perfect being, eternal and necessary existence belongs to the nature or essence of God, just as, for example, having internal angles whose sum is equal to that of two right angles belongs to the nature of a Euclidean triangle. From this Descartes inferred that God must indeed exist, just as we may infer, with regard to any (Euclidean) triangle, that its internal angles add up to two right angles. He anticipated the objection that, in the case of a triangle, we can only infer from the nature of the triangle that its internal angles have this sum on the supposition that the triangle does indeed exist, and thus that, likewise, we can only infer from the nature of God that God exists, on the supposition that he exists thereby making the ontological argument implicitly circular. But Descartes rejected this objection as spurious, apparently with good reason. For a triangle is only a contingent being: it is something which, given its nature, could fail to exist, and which consequently only has any properties at all on the supposition that it does exist; for, or so it would clearly seem, a nonexistent thing cannot actually possess any properties. But what is being claimed concerning God is that he is, by nature, a necessary being; one whose essence includes its existence. This is a good point to consider some of the other well-known objections to the ontological argument in its various formulations. One of the oldest is the perfect island objection that is due to the monk Gaunilo, an early critic of Anselm to whom Anselm himself replied. The idea is this. The ontological argument looks suspiciously 394

5 THE ONTOLOGICAL ARGUMENT like a formula to define into existence pretty well anything we like. Consider the perfect island. This would not only have, let us say, exactly the right amount of sun and shady palm trees, cool running streams of fresh water, delightful breezes, green pastures, and so forth, but also, of course, it would exist: for it is surely more perfect ( greater ) to exist in reality than merely to exist in the mind. Who would not rate an existent island of the above description more highly than a merely imagined island of that description? But it is plainly absurd, wishful thinking to suppose, on these grounds, that such an island really does exist. The same, it will be said, applies to the ontological argument: it is merely an exercise in wishful thinking. However, the objection is clearly spurious and unfair. When we talk about God as being, by nature, a perfect or maximally great being, we are using these terms in a quite specific technical sense, to imply that God is, by definition, a being whose existence is absolutely independent of anything else. By contrast, in talking of a perfect island, we are talking about a purely contingent being of a certain kind for all islands, being material objects, are by their nature contingent beings which has certain humanly pleasing features in the highest possible degree. Clearly, from the mere fact that such an island could exist, we cannot infer that it does exist. But the whole point about God, according to the ontological argument, is that he is conceived and coherently can be conceived to be a being who, in virtue of being maximally great by nature, has necessary existence and who consequently does exist. But perhaps the best-known objection of all to the ontological argument an objection that is commonly thought to deal it the killer blow is the Kantian objection that existence is not a predicate (Kantian because it first appears in Kant s Critique of Pure Reason of 1781; see Kant 1933: 500 7). This objection is usually cashed out in the following way. It is an error, or so it is claimed, to suppose that the verb exist functions, as many other verbs and verb phrases do for example, the verbs run and eat and the verb phrases is red and is square to attribute some special property to an object or objects. Accordingly, when we list the properties of anything, we should certainly not include existence among them. As one of the original critics Pierre Gassendi of Descartes s version of the ontological argument urged, existence is not so much a property of any thing as it is that without which something cannot have any properties. And as Kant himself put it, the notion of existence adds nothing to the concept of a thing: to conceive of an existent table of a certain color, shape, size, and weight is no different from merely conceiving of a table with just those properties. After all, if the concept of an existent F were different from that simply of an F, then it seems that I could not conceive of an F and bring just such a thing into existence: for what I would bring into existence would have to be an existent F; and this, allegedly, is not precisely the sort of thing that I was conceiving of when I was merely conceiving of an F. But that is surely absurd: I can, surely, conceive of an (as yet nonexistent) table and bring exactly such a thing into existence. In modern times, in the hands of such logicians as Frege and Russell, this sort of point has been made in terms of the proper way to translate talk about existence into the formal language of first-order predicate logic, namely, by means of the so-called existential quantifier, (see, e.g., Frege 1953: par. 53 and Russell 1919: 203). In this 395

6 E. J. LOWE language, Dogs exist, for instance, is translated as ( x)(x is a dog), which can be re-expressed in logician s English as There is something, x, such that x is a dog. According to the Frege Russell view of existence, There is something, x, such that x... is, technically speaking, a second-level predicate, used not to predicate a property of any object or objects, but rather to predicate a rather special second-level property of first-level properties where a first-level property is a property that can be had by objects, such as redness or squareness. Thus, on this view, to say that dogs exist is just to say that the first-level property of doghood, or being a dog, has the second-level property of having at least one instance, that is, of being possessed by at least one object. Of course, Dogs exist is a general proposition, as opposed to the singular proposition God exists. However, there is a standard way of translating a singular proposition of the form a exists, where a is a singular term (such as a proper name), into the formal language of first-order predicate logic; namely, as ( x)(x 5 a), that is, in logician s English, as There is something, x, such that x is identical with a. So, on this view, to say that God exists is just to say that the property of being identical with God has at least one (and, of course, only one) instance. But how is all this, even supposing that it is correct, supposed to bear upon the ontological argument? Well, it does so in the following way. In one version of the ontological argument (one that is very close to Descartes s), it may be expressed thus: 5 God is, by definition, a perfect being and thus a being that possesses all the divine perfections. 6 One of the divine perfections is eternal and necessary existence. 7 Hence, God possesses eternal and necessary existence and so, a fortiori, possesses existence. 8 Therefore, God exists. The error in the argument is then supposed to be that it treats eternal and necessary existence, and thus also existence simpliciter, as being one of the divine attributes or properties, alongside such properties as omniscience, omnipotence, and omnibenevolence. But, according to the Frege Russell account of existence, existence is not a first-level property a property of objects but only a second-level property: it is a property of first-level properties. Thus, on this view, what we affirm, effectively, when we affirm that God exists is that all of the divine attributes are in fact instantiated, indeed, that collectively they are uniquely instantiated, by just one object. But we cannot regard eternal and necessary existence as one of these attributes, because to do so is to make a logical error: the error of treating a second-level property as if it were a first-level property. Hence, there is no sound logical argument from a definition of God as a perfect being, together with a list of the divine perfections, to the conclusion that God does in fact exist. We can no more define God into existence than we can define anything into existence. However, it may be objected that nothing in the foregoing formulation of the ontological argument implies that either existence or eternal and necessary existence 396

7 THE ONTOLOGICAL ARGUMENT is a first-level property. For nothing in that formulation of the argument presumes that a divine perfection must be a divine attribute or property, in the way that omniscience or omnipotence are. It is true that line (7) speaks of God possessing eternal and necessary existence, and indeed of possessing existence. But it needn t be presumed that possession in this sense has to be thought of as a relation between an object and a first-level property. In short, it is far from clear that the Frege Russell account of existence does anything to undermine the ontological argument if it is carefully and appropriately formulated. Furthermore, it is in any case very much open to question whether Frege and Russell were in fact correct in their account of existence (see McGinn 2000: ch. 2). On the face of it, their account is really rather counterintuitive and not altogether easy to comprehend. Suppose, with Frege and Russell, we take the statement Dogs exist to be expressing the proposition that the property of doghood has at least one instance. What, exactly, are we to understand by the notion of a (first-level) property s having at least one instance? Isn t this really just to say that at least one object exists that possesses the property in question? In other words, isn t it the case that the logician s notion of a property s having at least one instance, far from serving to explain the notion of existence, needs to be explained by appeal to that very notion? There is much to be said in favor of the view that the notion of existence is a basic or primitive one, which cannot be explained in terms of any more fundamental notion or notions. This is not to say that we should regard existence as being a firstlevel property. Maybe we shouldn t regard it as a property at all. After all, properties themselves are entities that do, or at least can, exist: but do we seriously and literally want to say that existence itself exists? Very arguably, we should not reify existence, that is, treat it as being, itself, an entity of any kind. But, in any case as I have already indicated in formulating the ontological argument, we do not have to presume a particular view regarding what existence is, or is not. Contrary to the followers of Frege and Russell, we do not need to presume that it is a first-level property. Indeed, we do not need to presume that existence itself is anything at all, in the sense of being an entity belonging to some specific ontological category. The Frege Russell objection and the Kantian objection from which it descends is just a red herring with no real bearing on the soundness of the ontological argument. As for the charge that the ontological argument illicitly attempts to define God into existence, perhaps we should reflect on the following fact. No one objects to the claim that the nonexistence of certain things follows from their definition: that, for example, the nonexistence of squircles follows from the definition of a squircle as a plane figure that is both square and circular. If definitions can have implications regarding nonexistence, why should they not have implications regarding existence too? The worry might be that, if we allowed this, a priori existence claims would be just too easy to make. But why should that be supposed? Only if one thought that definitions are just arbitrary concoctions of the human mind. Some definitions might be like that, perhaps and it would certainly be dangerous to suppose that these could have positive existential implications. But, 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. 397

8 E. J. LOWE We need to distinguish, in this context, between real definitions and purely verbal definitions (see Fine 1994). A purely verbal definition is typically stipulative or conventional in character, consisting in a rule which allows us to substitute one word or phrase for another, as, for example, bachelor may be defined as unmarried man. A real definition, by contrast, attempts to characterize, as perspicuously as possible, the nature or essence of some actual or possible being. Essence is simply a word standardly used to translate a phrase of Aristotle s whose more literal translation is something like the what it is to be or the what it would be to be. Thus, a characterization of the essence of a geometrical figure, such as a circle, is a perspicuous way of saying what it is, or would be, for something to be a circle. Here is one such way, standardly found in textbooks of geometry: to be a circle is to be a closed line all of the points in which are equidistant from another given point (the centre of the circle). Here is another: to be a circle is to be the locus or path of a point moving continuously at a fixed distance around another point. These real definitions tell us what circles are or, at least, would be. Similarly, a real definition of God tells us what God is or would be. But according to Anselm, Descartes, and other adherents of the ontological argument, the real definition of God is distinctive and remarkable, in that it tells us that what God is or would be is something that could not fail to exist. And that, in their view, is why we are rationally compelled to conclude that, indeed, he does exist. All we need to come to this conclusion rationally is to grasp the real definition of God, that is, understand what God is or would be. Actually, we do not even need to fully grasp what God is or would be which is just as well, since this is probably beyond the capabilities of finite intelligences like ours but just to grasp that, at the very least, he is or would be a maximally great being. This is why Anselm, quoting the biblical text (Ps. 14: 1; 53: 1), remarks that The fool has said in his heart that God does not exist. His point would seem to be this. Either the Fool does grasp, to a sufficient extent, the real definition of God, but nonetheless denies that God exists, in which case he is indeed a fool, for he thereby displays a failure of rationality. Or else the Fool does not grasp, to a sufficient extent, the real definition of God, in which case he is likewise a fool; he thinks that he understands what he is saying in denying that God exists and that he is justified in that denial, but does not really understand it and so is not really justified, so that in this case too he displays a failure of rationality. If, as I am suggesting, the ontological argument is a sound one, how can we formulate it most perspicuously for a modern audience? Here we may usefully draw upon Alvin Plantinga s way of presenting the argument (Plantinga 1974: ch. 10), using the language of possible worlds and modern modal logic: the logic of possibility and necessity. Here is how it may be done along these lines. 9 God is, by definition, a maximally great being and thus a being whose existence is necessary rather than merely contingent. 10 God, so defined, could exist; in other words, he does exist in some possible world. 11 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. 398

9 THE ONTOLOGICAL ARGUMENT 12 But a necessary being is one which, by definition, exists in every possible world if it exists in any possible world. 13 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. 14 Therefore, God exists in the actual world; he actually exists. There are, of course, various queries that one could raise about this version of the argument. Are we, for example, really entitled to suppose that God, so defined, could exist that he exists in at least some possible world? Might it not be the case that the real definition of God harbors some deep-seated contradiction, rendering his existence impossible? Perhaps so: after all, we should not be dogmatic in matters of fundamental metaphysics, but should always be prepared to acknowledge, if need be, the fallibility of our rational intellects. On the other hand, there does not appear to be any such contradiction; so the burden of proof surely lies with the opponent of the ontological argument to try to show that there is. Although we should not be dogmatic, neither should we be unduly skeptical. We should put trust in our rational capacities unless and until we find good reason to doubt them; and even then, of course, we cannot abandon trust in them altogether, for we must at least be confident that we have indeed found a good reason to doubt them. Another worry might be this: are we really entitled to suppose that, even if there could be a maximally great being a being that depended on absolutely nothing else for its existence there could be only one such being? This is a worry about the provable uniqueness of God. To this worry it is less easy to find a simple and compelling answer. Even so, if this were the only weakness in the ontological argument, it would still be a remarkably important argument. Finally, what are we to say in answer to those let us call them the metaphysical nihilists who claim that there might have been nothing rather than something? If they are correct, then, of course, God cannot possibly exist. But then, doesn t this mean that the burden of proof lies with the metaphysical nihilists to show that God a maximally great being cannot possibly exist? For unless they can show this, what entitles them to be so confident that, indeed, nothing at all need have existed that there might have been absolutely nothing? See also Immanuel Kant (Chapter 16), Eternity (Chapter 31), Goodness (Chapter 33), The cosmological argument (Chapter 37), Problems with the concept of God (Chapter 43). References Charlesworth, M. J. (1965) St Anselm s Proslogion, Oxford: Clarendon Press. Descartes, R. (1984) [1641] The Philosophical Writings of Descartes, Vol. II, trans. J. Cottingham, R. Stoothoof and D. Murdoch, Cambridge: Cambridge University Press. Fine, K. (1994) Essence and modality, in J. E. Tomberlin (ed.) Philosophical Perspectives, 8: Logic and Language, Atascadero, CA: Ridgeview Publishing. 399

10 E. J. LOWE Frege, G. (1953) The Foundations of Arithmetic [Die Grundlagen der Arithmetik, 1884], trans. J. L. Austin, 2nd edn, Oxford: Blackwell. Kant, I. (1933) [1781] Critique of Pure Reason, trans. N. K. Smith, corrected edn, London: Macmillan. Lowe, E. J. (1998) The Possibility of Metaphysics: Substance, Identity, and Time, Oxford: Clarendon Press. McGinn, C. (2000) Logical Properties: Identity, Existence, Predication, Necessity, Truth, Oxford: Clarendon Press. Plantinga, A. (1974) The Nature of Necessity, Oxford: Clarendon Press. Russell, B. (1919) Introduction to Mathematical Philosophy, London: Allen & Unwin. Further reading Millican, P. (2004) The one fatal flaw in Anselm s argument, Mind 113: (An overview of Anselm s version of the ontological argument and the many objections that have been raised against it.) Nolan, L. (2005) The Ontological Argument as an exercise in Cartesian therapy, Canadian Journal of Philosophy 35: (A well-informed and original interpretation of Descartes s conception of the purpose of the ontological argument.) 400

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