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“The Ontological Argument”
Gareth B. Matthews
St. Anselm’s Ontological Argument is certainly one of the most audacious arguments in the history of Western philosophy; it may even be the most audacious. It is also one of the most perplexing. Some philosophers have scorned it. St. Thomas Aquinas did. Others have thought they had refuted it. Immanuel Kant thought he had done that. Many philosophers have tried to ignore it. But it is difficult for a serious philosopher to ignore the claims of such a daringly elegant bit of reasoning.
Many philosophers have developed their own version of Anselm’s argument. Some of these versions are quite crude, others are very sophisticated. In the 17 th^ Century every self-respecting rationalist philosopher, including Descartes, Malebranche, Leibniz, and Spinoza, promoted some version or other of the argument. In the three subsequent centuries the argument suffered periods of almost complete neglect. But after each period of neglect, the argument has always been re-discovered, re- defended, and re-criticized.
The ontological argument is certainly not neglected today. No other argument for the existence of God – indeed, for the existence of anything! – has received such lavish attention in the last half-century as has the ontological argument. To be sure, the argument’s detractors are more numerous today than its defenders; but the detractors are not obviously more acute, ingenious, or wise than the defenders. And sometimes a vocal detractor turns into a defender, or the other way around.
Bertrand Russell reports this moment of illumination:
I remember the precise moment, one day in 1894, as I was walking along Trinity Lane, when I saw in a flash (or thought I saw) that the ontological argument in valid. I had gone out to buy a tin of tobacco; on my way back, I suddenly threw it up in the air, and exclaimed as I caught it: “Great Scott, the ontological argument is sound.” 1
Although Russell later un-convinced himself of the cogency of the argument, he retained a deep respect for what it attempts to accomplish, if not for what it succeeds in accomplishing. In his A History of Western Philosophy he offers this summary of the argument:
We define “God” as the greatest possible object of thought. Now if an object of thought does not exist, another, exactly like it, which does exist, is greater. Therefore the greatest of all objects of thought must exist, since, otherwise, another, still greater, would be possible. Therefore God exists.^2
As we shall see in what follows, Russell’s précis is not an entirely accurate reflection of Anselm’s own version of the argument. Yet it does make vivid an essential part of that version. Russell also makes clear one important reason why philosophers keep returning to the argument:
The real question is: Is there anything we can think of which, by the mere fact that we can think of it, is shown to exist outside our thought? Every philosopher would like to say yes, because a philosopher’s job is to find out things about the world by thinking rather than observing. If yes is the right answer, there is a bridge from pure though to things; if not, not. 3
Although there are many versions of the Ontological Argument, it is the original version, the one to be found in St. Anselm’s little treatise, Proslogion (also sometimes referred to by its latinized title,
Proslogium ), that I shall concentrate on here. I have two reasons for paying special attention to Anselm’s own version. One reason is simply that it is the original one. Another reason is that it is, in fact, much more interesting than most all the successor versions.
Among the many intriguing peculiarities of the original argument in Anselm is the fact that this argument for God’s existence turns up in a work that is, not an impersonal treatise on metaphysics, or theology, but rather in a sort of philosophical prayer, an “allocution,” or address, to God! It is surely paradoxical to be addressing a being whose existence one is trying to establish. It is especially paradoxical to be offering the proof as part of a petitionary prayer to that very being. There is, to be sure, no formal contradiction is saying to someone (or as if to someone), “I hereby offer a proof that you exist,” or even, “Help me construct a proof that you exist.” But such a procedure is extraordinarily odd. Indeed, the sincerity of one’s address to God seems to be undermined by the project of offering a proof of God’s existence, just as the sincerity of one’s truly needing or wanting a proof seems to undermine the genuineness of the prayer. Nor does paradox or perplexity end there. Why should God, if He does exist, even be interested in one’s proof that He exists, especially if God is omniscient? The whole enterprise seems riddled with paradox.
Still, odd as it may seem to be telling God about one’s proof of His existence, the project does have important antecedents in Western, especially in Christian, thought. For starters, there is the biblical story of the father who asks Jesus to cure his demoniac son. When Jesus tells him, “All things are possible to him who believes,” the father responds, according to the story, “I believe, help my unbelief.” ( Mark 9:23-24)
Then there is an important precursor passage early on in Augustine’s Confessions , which work is also, in its entirety, a prayer addressed to God. “Give me to understand, Lord,” Augustine writes,
whether to call on you first or to praise you, and whether to know you first or to call on you. But who calls on you who does not [yet] know you? Not knowing you he could call on another [beome] in your place. Or are you rather called on that you may be known. (1.1.1)
A reader might think it only a rhetorical flourish for Augustine to suggest that the one who prays might actually, by mistake, be calling on another being, instead of God. But it is well to remember that Augustine was a Manichean learner before he was converted to Christianity. So he could well have thought that some of his own prayers while he was a Manichean were, as it later became clear to him, simply misdirected.
Readers of Plato will recognize in Augustine’s puzzle a close relative of what has come to be called the Paradox of Inquiry, which is to be found in Plato’s dialogue, Meno , at 80de. There Plato’s interlocutor, Meno, asks how it will be possible to inquire into the nature of virtue. Either one knows already what virtue is, so that the inquiry will be a sham; or one doesn’t, in which case one will not know at what to aim the inquiry, nor will one recognize it, should one happen apon it.
The application of Plato’s paradox of inquiry to Augustine’s project of searching for God is obvious. Augustine is searching for God when he asks for God’s help in the search for Him. So, it seems, his directed search shows, by its very directedness, that it is not a genuine search for something he has not yet found. In addition to Plato’s worry about how one can direct a search without already knowing the object of the search and his worry about how one could recognize the object of the search, should one stumble on it, Augustine has another problem. It is the problem of knowing how to direct his request for assistance in his search to the right being, when the being whose assistance he is requesting in the search and the being he is searching for are one and the same.
Argument S
(1) God is something than which nothing greater can be conceived.
Therefore,
(2) God is something.
Therefore,
(3) God exists.
Argument S1 is not only simple, it is also simple-minded. Since what Anselm actually presents in Proslogion 2 is neither simple nor simple-minded, we should protect him against the accusation that his argument is, even in its barest bones, simply Argument S1. The best way to do that is to read (D) in such a way that it comes to no more than this:
(D*) To be God is, or would be, to be something than which nothing greater can be conceived.
Since (D) is somewhat cumbersome, and (D) is closer to what Anselm actually says in Proslogion 2, I shall continue to appeal to (D). But in the further use I make of (D) I shall ask that it be read in such a say that it is equivalent to (D).
There is another way in which Anselm might be charged, falsely, with begging the question. In modern standard quantificational logic there is a rule called “Existential Generalization.” This rule
allows us to infer from ‘a is F’ (i.e., ‘Fa’) that something is F (i.e., (∃x) Fx). If we add identity to first-
order quantification theory, we can infer ‘Aristotle exists’ from, say, ‘Aristotle is a philosopher.’ Thus from ‘Aristotle is a philosopher’ (Pa) we may infer ‘Someone is a philosopher and he is Aristotle’ (i.e., (
∃x)Px.x=a)), which may be simplified to ‘Someone exists who is Aristotle’ (i.e., (∃x)(x=a)).
Having seen how the rule of Existential Generalization works we may think that any statement about God – whether it is a complex statement, such as ‘God is something than which nothing greater can be conceived’ or something quite simple, such as, ‘God is wise’ – is enough to warrant the conclusion that God exists. Thus we could have this argument, which is almost as simple-minded as Argument S1:
Argument S
(1) God is a perfect being.
Therefore.
(2) Something is a perfect being and it is God.
Therefore,
(3) Something is God, i.e., God exists.
There is, moreover, nothing special about beginning with the premise that God is a perfect being. We could as well begin with any other claim about God, for example, that He is wise, thus:
Argument S
(1) God is wise.
Therefore,
(2) Something is wise and it is God.
Therefore,
(3) Something is God, i.e., God exists.
As we shall see, Anselm seems to have thought about such simple-minded arguments; he certainly has a way of making sure we don’t confuse them with his argument. Thus he distinguishes between existence in the understanding ( in intellectu ) and existence in reality (in re ). With this distinction in hand, he can agree that using a proper name, such as ‘God,’ in a statement, almost any statement, sets us up for existential generalization. But just because we understnd and accept the claim that Homer wrote the Odyssey, or that Hamlet is a prince, or that God is, say, wise, it does not follow that Homer or Hamlet or God exists in reality. All that follows is that Homer and Hamlet and God exist in the understanding. We will need something more to prove that they exist in reality.
So (D) doesn’t immediately concede what is to be proved simply because something is being said of God and it follows from the fact that God is such-and-such, say, wise, or a perfect being, or whatever, that God exists. Rather, we are going to have to pay attention to the particular “such-and-such” that (D) gives us -- that is, to what it is, or would be, to be something than which nothing greater can be conceived, to be justified in concluding that God exists in reality.
Where did Anselm get the idea that a proper noun might succeed in doing its job by picking out something in the understanding that is not anything in reality? That is, where did he get the idea that proper names can function by picking out merely imaginary, or mental, entities, rather than robust dwellers in reality? He doesn’t say. But it seems likely, when you stop to think about it, that he was drawing on a response to an ancient puzzle in philosophy. That puzzle concerns a difficulty about how we can ever succeed in making a statement that is both meaningful and true when we say something of
the form, ‘ ‘! doesn’t exist’ (where, it is understood, ‘!’ will be replaced either by a proper name, like
‘God’ or ‘Hamlet,’ or by a definite description, such as ‘the teacher of Aristotle.’ To be meaningful, it
seems, the proper name or definite description that replaces ‘!’ must succeed in picking out something.
But if ‘the Loch Ness Monster’ or ‘Shangrila’ succeeds in picking out something, then what it succeeds in picking out exists and the statement, ‘The Loch Ness Monster doesn’t exist,’ or the statement, ‘Shangrila doesn’t exist,’ will be false. If, on the other hand, the proper name (say, ‘Hamlet’) or definite description (say, ‘the teacher of Aristotle’) does not pick out any definite person or thing, then our hope of denying existence to the teacher of Aristotle, or to Hamlet, would be dashed by the fact that the putative statement we make would not be a real statement at all. Saying “Hamlet doesn’t exist” or “The teacher of Aristotle doesn’t exist” would be like saying “Blah doesn’t exist.”
We can call this puzzle about statements of the form ‘! doesn’t exist’ “the Problem of Negative
distinguishes Anselm’s form of ontological argument for God’s existence from many other forms of the argument. By insisting that the atheist must agree that God is in the understanding anyway, Anselm opens the way to prove that the atheist is assigning contradictory features to this entity that both he and the atheist have in mind. Thus, whereas Anselm himself supposes this entity in the understanding, something than which nothing greater can be conceived, exists in reality as well, the atheist supposes that this something than which nothing greater can be conceived is only a mental or imaginary entity.
We can think of Anselm’s making the atheist admit that God exists in the mind anyway as establishing a “referential peg” on which to hang his definition-like characterization of God, ‘something than which nothing greater can be conceived.’ 6 Anselm is then in position to ask whether this something in the understanding could be both
(a) something than which nothing greater can be conceived
and also
(b) something that fails to exist in reality.
His argument will try to show that assigning both (a) and (b) to this something in the understanding is absurd, and even absurd in the philosopher’s favorite sense of being self-contradictory.
Should the Fool ever have allowed Anselm to have his referential peg? Without that peg Anselm would not be in position to argue that atheism assigns incompatible features to something in the understanding. Perhaps the Fool should not have been so accommodating. What could Anselm have said to a fool who had dug in his heels and refused to admit that this something than which nothing greater can be conceived exists even in the understanding? 7
Presumably Anselm’s response would have been something along these lines:
Oh Fool, if you either claim not to understand the words, ‘something than which nothing greater can be conceived,’ or else deny that, having understood these words, you still do not have something than which nothing greater can be conceived in your mind, you will not be able to deny God’s existence.
Warming to his topic, he could have gone on in this way:
For your atheism to amount to anything, your denial of existence must be directed at God, rather than at the Abominable Snowman, or at Santa Claus, or at an old man in the sky. So, when you say, “God doesn’t exist,” you mustn’t mean “There is no man with a long white beard in the sky,” or anything of that sort. You must, in fact, have in mind something than which nothing greater can be conceivd and deny the existence of that.
We shall return in a moment to the question of whether the Fool should have allowed Anselm to have his referential peg so that he could interpret the Fool’s atheism in the way he does. But, for now, we can say that Anselm does have a good case for saying that Fool’s atheism consists in saying of something, x, that x is both (a) and (b).
Anselm’s final move in Proslogion 2 is to argue that saying of anything that it satisfies both (a) and (b) is self-contradictory. The reason is this:
(G) It is greater to exist in reality as well than to exist merely in the understanding.
We can call (G) “the great-making assumption.” Although, as we shall certainly have to admit, (G) is highly controversial, it has a certain immediate plausibility. Persons and things that exist in reality thereby have actuality, something that merely imaginary entities lack. This actuality, it seems quite plausible to say, makes them greater than their merely imagined counterparts. After all, things that exist only in the understanding are obviously dependent beings in the relatively straightforward sense that they wouldn’t have existed at all if someone hadn’t thought of them. By contrast, things that exist in reality are not in this way mind-dependent for their existence. And such mind-independence, it seems plausible to say, is a great-making property.
To see that we are now ready to conclude that God exists in reality, let’s rehearse the steps that Anselm has taken so far in Proslogion 2. We find at the beginning of the chapter a definition -style characterization of the being whose existence is to be proved, namely, God. ( You are something than which nothing greater can be conceived .) Next, we try assuming the opposite of what is to be proved, with the aim of showing that it leads to absurdity – ideally, self-contradiction. Anselm’s way of assuming the opposite is to quote “the Fool” from the Book of Psalms: There is no God. He then reasons that even the “Fool,” that is, the atheist, must have God in mind when he denies God’s existence. Thus the denial of God’s existence is to be understood as the claim that something in the mind, namely, God (that is, something than which nothing greater can be conceived ) fails to exist in reality. But now we are to see that what the Fool is claiming is self-contradictory. It is self-contradictory because it is the claim of something in the understanding that it is both
(a) something than which nothing greater can be conceived
and also
(b) something that fails to exist in reality.
But anything in the understanding that satisfies (b) will be something than which a greater can be conceived, namely, something that exists in reality. And so the atheist’s claim becomes, it seems, a claim about something in the understanding that it is both something than which nothing greater can be conceived and also something than which a greater can be conceived, which would clearly be absurd. So God exists in reality, as well as in the understanding.
Objections to the Argument in Proslogion 2
- A fairly obvious way to reject the argument in Proslogion 2 would be to deny the great- making assumption, (G). Why can’t a supremely great being be simply a figment of one’s imagination? Less grandly, why does, or would, existing in reality make something greater than it would be if it existed only in the understanding?
Norman Malcolm, who shocked many in the American philosophical community back in 1960 by defending a reconstruction of the argument he thought he found in Proslogion 3, criticized the argument in Proslogion 2 for relying on (G), which he considered a mistaken principle. Malcolm wrote:
The doctrine that existence is a perfection is remarkably queer. It makes sense and is true to say that my future house will be a better one if it is insulated than if it is not insulated; but what could it mean to say that it will be a better house if it exists than if it does not?^8
Malcolm took himself to be restating a criticism of Anselm’s argument to be found in Kant, whom he quoted thus:
more excellent than all others, rather than a perfect one:
Now if someone should tell me that there is such an island, I should easily understand what was said, in which there is no difficulty. But suppose that he went on to say, as if by logical inference: “Moreover, you cannot doubt that this island more excellent than all [other] lands, which you do not dispute is in your understanding, exists somewhere in reality. And, since it is more excellent not to be in the understanding alone, but to exist both in the understanding and in reality, for this reason it must exist [in reality].^11
Gaunilo’s lost island (or “Perfect Island,” as it is generally referred to in the literature) is clearly meant to be a parody of Anselm’s argument in Proslogion 2. With his parody of Anslem’s argument Gaunilo presents Anselm with a challenge. Although the parody does not, by itself, make clear exactly what is wrong with Anselm’s reasoning, the parody is meant to be so obviously unsatisfactory as an argument for its own conclusion that Anselm is challenged to either (a) explain why the objection one has to the parody does not apply to the ontological argument, or else (b) agree that the ontological argument is also unsatisfactory. Thus Gaunilo’s parody produces the conclusion, by reasoning alone, that some lost island exists. But surely we ought not to be able to establish facts about lost islands by merely a priori reasoning, without any empirical investigation at all. Yet if there is something wrong with the lost-island argument, there must equally, it seems, be something wrong with Anselm’s argument.
In fact, the reasoning in Gaunilo’s parody does not track exactly Anselm’s reasoning in Proslogion 2. To bring it closer into line with Anselm’s argument we should have to characterize the lost island as something than which nothing greater can be conceived. But no mere island could plausibly be thought to be something than which absolutely nothing greater, or more excellent, can be conceived. More appropriately, it might be thought to be an island than which no greater island could be conceived. Perhaps Gaunilo should have characterized his lost island that way.
If Gaunilo did characterize his lost island as an island than which no greater island can be conceived, we could reply that islands, like natural numbers, are inherently limited entities. For any specified island, it could be argued, one might conceive one that is bigger and better – perhaps one that has even more palm trees, or bigger beaches, or whatever. 12 Anselm’s characterization of God, by contrast, does not claim that God is merely an F such that no greater F can be conceived Anselm’s characterization of God is unqualifiedly superlative. God, Anselm supposes, is something than which nothing greater (period!) can be conceived. Thus one might agree that there can be no such thing as an island than which no greater island can be conceived any more than there could be such a thing as a natural number than which no greater natural number can be conceived. But that fact, by itself, does not establish that there can be no such thing as something than which nothing greater can be conceived. And so Gaunilo’s parody is just that, a parody. It does not undermine the credibility of Anselm’s argument.
- Another popular attempt at a counterexample to Anselm’s reasoning is an argument for the existence of the devil. Can’t we prove the existence of the devil, a being than which nothing more evil can be conceived, by similar reasoning? If so, again, there must be something wrong with Anselm’s reasoning.
One complication this time concerns the idea, perhaps quite plausible to us, that existing in reality ought to make an evil being even more evil, just as existing in reality makes a good, or great, being even better or greater than it would be if it were purely mental. Anselm, however, stands in the Platonic tradition, according to which the scale of being is also a scale of goodness, or greatness. That means that nonexistence would be evil. Implausible as it may seem to us, a devil that exists in the understanding, but not in reality, would actually be less good, and so more evil, than one that exists in reality.
- Perhaps the most interesting objection that can be made to Anselm’s argument in Proslogion 2 is what we might call a “meta-objection.” It concerns the way Anselm interprets the Fool’s claim, ‘There is no God.’ As we have seen, Anselm understands this claim, and, by implication, all claims of the form ‘
! doesn’t exist,’ to be claims about something in the understanding. More specifically, according to the
Anselmian, each such claim is a claim about something in the understanding that it fails to exist in reality. But, as we know from 20 th^ Century philosophy, there are other ways to understand negative existentials besides this.
Bertrand Russell suggested that when we say, “Socrates doesn’t exist,” we can be taken to have a definite description in mind to replace ‘Socrates’ -- maybe ‘the teacher of Plato.’ So perhaps ‘Socrates doesn’t exist’ means ‘The teacher of Plato doesn’t exist,’ and what that means is, perhaps, ‘Nobody fits the description, ‘the teacher of Plato.’’
If we don’t accept the idea of translating
(1) Socrates doesn’t exist
into a sentence that mentions the English phrase, ‘the teacher of Plato’ (after all, (1) doesn’t mention any English phrase), we could follow Russell’s “theory of descriptions” and translate (1) into this:
(2) It is false that that there is at least and at most one person who taught Plato.
Similarly, we could begin with the Fool’s
(3) God doesn’t exist
and use Anselm’s quasi-definition to get this:
(4) Nothing fits the description, ‘something than which nothing greater can be conceived.’
If, now, we wanted to get rid of the English phrase in (4), we might come up with this:
(5) For any given thing, in the understanding or in reality, a greater than it can be conceived.
Someone might ask how the fool could possibly know (5) to be true. But here it is well to keep in mind that the form of Anselm’s argument is a reductio. Since the Fool is simply stating, in a dramatic way, the supposition Anselm wishes to show absurd, Anselm doesn’t need to know that (5) is true, or even produce any evidence for thinking it is true. The Fool’s role is simply to state that God does not exist so that Anselm can show that the Fool’s statement leads to self-contradiction. If the Fool insists on having his statement of atheism understood as (5), he can avoid, it seems, Anselm’s claim that the Fool has contradicted himself.
Interestingly, this Russell-type response to Anselm’s argument seems to be anticipated in a comment St. Thomas Aquinas makes in his Summa contra gentiles. This comment has gone largely unnoticed in the literature. 13 Instead, commentators have focused on objections to Anselm’s argument that Aquinas makes in his other summa , the Summa theologiae. In that work Thomas says that God’s existence, though self-evident in itself, is not self-evident to us, since we do not know God’s essence. 14 But Anselm can easily accommodate that objection, since he, too, thinks we do not know God’s essence. As he argues in Proslogion 15, God is a something greater than can be conceived , that is, presumably, a being greater than can be comprehended, or fully understood. Thus we can know, Anselm thinks, that
only intelligible way of rejecting Anselm’s claim that God’s existence is necessary is to maintain that the concept of God, as a being a greater than which cannot be conceived, is self-contradictory or nonsensical. Supposing that this is false, Anselm is right to deduce God’s necessary existence from his characterization of Him as a being a greater than which cannot be conceived.^15
Leibniz had made a somewhat similar claim. He chided Descartes for not bothering to establish that the existence of God is possible. He himself provided such a proof, with the assurance that if God’s existence is possible, then it is necessary. 16
It isn’t, however, clear that Anselm understands ‘cannot be conceived not to exist’ to mean ‘necessarily exists,’ let alone ‘exists by logical necessity.’ As I have already mentioned, Anselm argues in Proslogion 15 that God, i.e., something than which nothing greater can be conceived, is a greater than can be conceived. By this claim he presumably means that God exceeds our powers of comprehension. In any case, he quite clearly does not mean that God is being greater than is logically possible (and so, presumably, a logically impossible being).^17 Nevertheless, Proslogion 3 has inspired a tradition of developing ontological-style arguments, not just to prove that God exists, or exists in reality, but to prove that God has necessary existence.
Whether or not Proslogion 3 constitutes an independent argument for God’s existence, it actually poses a threat to the cogency of Chapter 2. After all, as I have emphasized above, Proslogion 2 has the form of a reductio. In that reduction the Fool is made to state what is to be shown, by reduction, to lead to self-contradiction. But Proslogion 3 seems to conclude that, when the Fool says, “There is no God,” he cannot even make sense of what he is saying. He cannot understand what he is saying precisely because, if the reasoning of Proslogion 3 is correct, God cannot be conceived not to exist.
Anselm addresses this new threat in Chapter 4, where he asks, appropriately, “How has the Fool said in his heart what he could not conceive?” Anselm replies that there are two ways of conceiving something in the heart, that is, two ways of having something in mind. In one way, he says, a thing is conceived when the word signifying it is thought, in another, when the object itself is understood. His idea seems to be that the Fool can conceive God according to the word and so state his atheism well enough for the reductio to work, even though his atheism rules out his being able to conceive God himself as not existing..
Does this move rescue the reductio of Proslogion 2? Or does it, perhaps, further cast the intelligibility of the reasoning there in doubt. After all, Proslogion 4 seems to allow the possibility that
A1. ‘God’ doesn’t name anything
is a perfectly good way for the Fool to conceive God “according to the word” and thus to succeed in denying God’s existence. But if the Fool insists on having his atheistic claim interpreted as (A1), it’s hard to see how Anselm’s style of argumentation can show atheism self-contradictory.
Again, Anselm does seem to have a plausible reply open to him. It is a pretty uninteresting atheism, he can say, that consists in making a claim about the English word, ‘God,’ or the Latin word, ‘deus,’ namely the claim that those particular words are empty. “You are something than which nothing greater can be conceived,” Anselm says to God (or, as he supposes, to God), and then adds, “Or is there no such nature?” ( An ergo non est aliqua talis natura [?] ) For him the question of atheism should be the question of whether there exists, in reality, something than which nothing greater can be conceived. Can the Fool be coherently supposed to say these words, either without any signification or with some extraneous signification” ( aut sine ulla aut com aliqua extranea significatione ) and manage, by these
shabby means, get God in his understanding?
Before we judge Anselm uncharitably on this question, it would be well to remember that, for a whole range of a priori truths, to attempt to prove them by reductio may land us in a similar puzzle. In a discussion of reductio arguments in mathematics, Alice Ambrose and Morris Lazerowitz have this to say:
Still, there seems no escaping the question whether we are really making a supposition when we say “Suppose Goldbach’s proposition is true [that is, suppose there is an even number greater than 3 that is not the sum of two prime numbers]”, and whether we are really assuming anything when we start the proof of
the irrationality of √2 by saying”Suppose there is a rational number = √2”. In the latter case the end result
of the demonstration implies that we could not have conceived what we stated we were supposing. Are we merely going through the verbal motions of making an assumption or asking a question, without actually doing so? One can utter the words “I am in two different places simultaneously”, but are we using the words to express something we are entertaining?”^18
Ambrose and Lazerowitz suggest in their article that ‘suppose’ as it is used to introduce a statement in mathematics that is being reduced to absurdity has only an extended sense, since we can’t really suppose the impossible. Similarly, Anselm suggests that ‘conceive’ in our supposition that the Fool conceives God as not existing in reality must also be understood in an extended sense. The Fool can, so to speak, mumble inwardly the words, ‘Something than which nothing can be conceived.’ Even supposing that those word truly pick out God, when the Fool goes on to suppose that this something than which nothing greater can be conceived fails to exist in reality, he has failed to conceive God properly.
You might think that my efforts to defend Anselm have back-fired. If I have succeeded in making plausible and appropriate Anselm’s suggestion that the Fool mumbles the magic words and fails to appreciate their true signification, haven’t I removed the peg in intellectu on which Anselm needs to hang the Fool’s contradiction?
I don’t think so. Whatever the Fool comes up with to associate with the words he mumbles in his heart (“something than which nothing greater can be conceived”), when he adds that it – that thing he has in mind, whatever it is – is both (a) something than which nothing greater can be conceived and (b) something that fails to exist in reality, the Fool has, Anselm can insist, contradicted himself. And that is the genius of Anselm’s ontological argument, as he presents it in Proslogion 2.
Modal Arguments
I have already mentioned that Norman Malcolm claimed to find in Proslogion 3 a distinct ontological argument – one that would establish, not the mere existence of God, but God’s necessary existence. Let’s call any ontological argument meant to establish the necessary existence of God a “modal ontological argument.” I have also suggested one reason for being skeptical about whether the argument Malcolm claims to find in Anselm is actually there. It is that ‘cannot be conceived not to exist’ in Proslogion 3 does not mean ‘necessarily exists,’ let alone ‘exists by logical necessity.’
There are, however, other passages in Anselm one might look to for an authentically modal argument. Robert Adams offers a very interesting reconstruction of an Anselmian text as a modal ontological argument. 19 But Adams looks for this proof, not to Proslogion 3, but rather to this rather turgid passage from the first chapter of Anselm’s reply to Gaunilo:
For no one who denies or doubts that there exists something than which a greater cannot be conceived denies or doubts that if it did exist, its nonexistence, either in reality or in the understanding, would be impossible. For otherwise it would not be that than which a greater cannot be conceived. But as to whatever
On the other hand, Lewis’s modal realism leads him to deny that what we think of as the actual world has any special character, and so it leads him to reject this crucial premise of the ontological argument as he reconstructs it: “There is an understandable being x, such that for no world w and being y does the greatness of y in w exceed the greatness of x in the actual world.” Here is part of Lewis’s reasoning:
Think of the ontological arguer in some dismally mediocre world—there are such ontological arguers— arguing that his world alone is actual, hence special, hence a fitting place of greatest greatness, hence a world wherein something exists than which no greater can be conceived to exist. He is wrong to argue thus. So are we.” 24
Alvin Plantinga, who has offered one of the recently most discussed modal arguments for God’s existence, begins his chapter on “God and Necessity” in The Nature of Necessity 25 with a full quotation of Proslogion 2. Plantinga then turns what he considers to be the core of Anselm’s reasoning into talk of logically possible worlds and, after a number of intermediate steps, finally ends up with the following, as we might say “stripped-down” version of the argument:
Where ‘unsurpassable greatness’ is equivalent to ‘maximal excellence in every possible world,’
(42) There is a possible world in which unsurpassable greatness is exemplified.
(43) The proposition a thing has unsurpassable greatness if and only if it has maximal
excellence in every possible world is necessarily true.
(44) The proposition whatever has maximal excellence is omnipotent, omniscient, and morally
perfect is necessarily true.
[Therefore]
(45) Possesses unsurpassable greatness is instantiated in every world. 26
The interested reader is invited to read Chapter 10 of Plantinga’s classic work to see in detail how Plantinga motivates his movement from the text of Proslogion 2 to the “stripped-down argument” above. In the end Plantinga concedes, however, that this argument, for all its merits, “is not a successful piece of natural theology.” The reason is, he says, that there are many properties , possibly instantiated, whose instantiation is incompatible with maximal greatness. So we need to know whether there is indeed a possible world in which maximal excellence in every possible world is exemplified, that is, whether it is possible that God, so understood, exists.
Peter van Inwagen has a somewhat different criticism of Plantinga’s argument, and, indeed, of all ontological arguments for the existence of God. Even a minimal ontological argument, he insists, must presuppose that the property of existing at every possible world is compatible with the property of being a concrete entity, that is, something “we can see, hear, be cut or burned by, love, hate, worship, make, mend, trust in, fear, [or] covet.” 27 Van Inwagen maintains, not only that we don’t, in fact, know whether the property of necessary existence is compatible with the property of being a concrete entity, but that we cannot know whether they are compatible. If we cannot know whether the existence of God, as traditionally conceived, is thus even possible, then, it seems, any ontological argument will fail.
Graham Oppy has recently published a masterful summary and critical assessment 28 of the huge body of recent literature on Anselm’s original argument, and the many related arguments it has inspired.
Oppy’s impressive work gives remarkable testimony to the high level of logical, philosophical, and scholarly understanding that has gone into recent discussion of Anselmian-types of reasoning concerning knowledge of the existence of God. From his book we learn in rich detail that modern counterparts to Anselm’s Fool, on whose behalf Gaunilo first wrote, have become, if not wise fools, certainly very sophisticated ones.
Selected Literature on the Ontological Argument (since 1960)
Adams, Robert Merrihew [1971], “The Logical Structure of Anselm’s Argument,” Philosophical Review 80, 28-54. _____ , ______ ________ [1994], Leibniz: Determinist, Theist, Idealist , New York: Oxford. Barnes, Jonathan [1972], The Ontological Argument , London: Macmillan. Barth, Karl [1960], Anselm; Fides Quaerens Intellectum , I. Robertson, trans., London: Macmillan. Berg, Jan [1961], “An Examination of the Ontological Proof,” Theoria 27, 99-106. Bouwsma, O.K. [1984], “Anselm’s Argument,” in J. L. Croft and Ronald E. Hustwit, eds., Without Proof or Evidence: Essays of O.K. Bouwsma , Lincoln: University of Nebraska Press, 40-72. Brecher, Robert [1985], Anselm’s Argument: The Logic of Divine Existence , Brookfield, VT: Gower. Cargile, James [1975], “The Ontological Argument,” Philosophy 50, 69-80. Chandler, Hugh [1993], “Some Ontological Arguments,” Faith and Philosophy 10, 18-32. Charlesworth, M. J. [1965], St. Anselm’s Proslogion , Oxford: Oxford University Press. Coburn, Robert [1963], “Professor Malcolm on God,” Australasian Journal of Philosophy 41, 143-62. Devine, Philip [1975], “The Perfect Island, the Devil, and Existent Unicorns,” American Philosophical Quarterly 12, 255-60. Dicker, Georges [1988], “A Refutation of Rowe’s Critique of Anselm’s Argument,” Faith and Philosophy 5, 193-202. Fitch, Frederick [1963], “The Perfection of Perfection,” Monist 47, 466-71. Gale, Richard [1991], “Ontological Arguments,” On the Nature and Existence of God , Cambridge: Cambridge University Press,201-31. Gregory, Donald R. [1984], “On Behalf of the Second-Rate Philosopher: A Defence of the Gaunilo Strategy Against the Ontological Argument,” History of Philosophy Quarterly 1, 49-60. Grim, Patrick [1982], “In Behalf of ‘In Behalf of the Fool,’” International Journal for the Philosophy of Religion 13, 33-42. Hartshorne, Charles [1962], The Logic of Perfection , La Salle, IL: Open Court. __________, _______ (1965), Anselm’s Discovery , La Salle, IL: Open Court. Hick, John, and Arthur McGill [1967]. eds., The Many-Faced Argument: Recent Studies on the Ontological Argument for the Existence of God, New York: Macmillan. Hintikka, Jaakko [1969], “On the Logic of the Ontological Argument,” in Models for Modalities , Dordrecht: Reidel, 45-54. Hopkins, Jasper [1972], “Ontological Argument,” in A Companion to the Study of St. Anselm , Minneapolis: University of Minnesota Press, 67-78. _______, ______ [1978], “On Understanding and Preunderstanding St. Anselm,” New
Philosophy of Religion 6, 102-10. Read,Stephen [1981], “Reflections on Anselm and Gaunilo,” International Philosophical Quarterly 21, 437-38. Richman, Robert [1976], “A serious Look at the Ontological Argument,” Ratio 18, 85-89. Rowe, William [1976], “The Ontological Argument and Question-Begging,” International Journal for Philosophy of Religion 7, 425-32. Rowe, William [1989], “The Ontological Argument,” in Joel Feinberg, ed., Reason and ResponsibilityReason and Responsibility, 7 th^ ed., Belmont, CA: Wadsworth, 8-17. Steinitz, Yuval [1994], “Necessary Beings,” American Philosophical Quarterly 30, 505-9. Stone, J. [1989], “Anselm’s Proof,” Philosophical Studies 57, 79-94. Tapscott, Bangs L. [1971], “Plantinga Properties and the Ontological Argument,” Philosophy and Phenomenological Research 31, 604-5. van Inwagen, Peter [1977], “Ontological Arguments,” Nous 11, 375-95; reprinted in Williams, C.J.F. [1981], What is Existence? Oxford: Oxford University Press. _______, _____ [1993], “Russelm,” Philosophical quarterly 43, 496-99. Zemach, Eddy [1993], “Existence and Non-Existents,” Erkenntnis 39, 145-66.
Gareth B. Matthews
University of Massachusetts/Amherst
(^1) Bertrand Russell, “My Intellectual Development,” P. Schilpp, ed., The Philosophy of Bertrand Russell, 2 nd (^) ed.,
New York: Tudor, 1946, 10. (^2) New York: Simon and Schuster, 1945, 417. (^3) Ibid. (^4) More carefully, he thought, we couldn’t meaningfully and truly say of anything that it is not. For him ‘is not’
includes ‘doesn’t exist,’ but also ‘is not F,’ for example, ‘is not wise.’ Thus he thought, not only that we couldn’t get away with saying truly and meaningfully, “Socrates does not exist,” but equally, “Socrates is not wise,” on the grounds that the latter amounts to “Wise Socrates doesn’t exist.” (See Montgomery Furth, “Elements of Eleatic Ontology,” Journal of the History of Philosophy 6 (1968), 111-32.) (^5) ‘The fool says in his heart, “There is no God,” is the first verse of both Psalm 14 and Psalm 53. (^6) Cf. Dicker [1988], esp. 200-01. (^7) O. K. Bouwsma, in Bouwsma [1984], suggests that the psalmist’s fool might be someone who “stands grim at the
door [of the temple], looking in upon those old men in their little black caps,” but he does not go in. (Bouwsma [1984], 56) (^8) “Anselm’s Ontological Arguments,” Philosophical Review 69 (1960), 43. (^9) Ibid, , 44. This is a quote from Norman Kemp Smith’s translation of Kant’s The Critique of Pure Reason (London,
1929), 505. (^10) Kemp Smith, 504. (^11) Pro insipiente 6. (^12) Cf. Plantinga [1974b], 91ff. (^13) But see my “Aquinas on Saying that God Doesn’t Exist,” The Monist 47 (1963), 472-77. (^14) ST 1a.q2. (^15) Op. cit., 49. (^16) For a full discussion of Leibniz’s attempts to show that the existence of God is possible see Adams [1994], 135-
213 (^17) Cf. Gareth B. Matthews, “On Conceivability in Anselm and Malcolm,” Philosophical Review 70 (1961), 110-11. (^18) Alice Ambrose and Morris Lazerowitz, “Assuming the Logically Impossible,” Metaphilosophy 15 (1984), 93.
(^19) Adams [1971], 41-48. (^20) Hartshorne [1962], 50-51. (^21) Ibid. , 44-45. (^22) Ibid ., 48. (^23) Lewis [1970]. (^24) Ibid ., 20. (^25) Plantinga [1974a], 197-221. (^26) Ibid ., 216. (^27) Van Inwagen [1977], 380. (^28) Oppy [1995].
