[In the following essay, Malcolm considers whether Anselm's ontological arguments stand up to the scrutiny of logic as well as of faith.]

I believe that in Anselm's Proslogion and Responsio editoris there are two different pieces of reasoning which he did not distinguish from one another, and that a good deal of light may be shed on the philosophical problem of “the ontological argument” if we do distinguish them. In Chapter 2 of the Proslogion¹ Anselm says that we believe that God is something a greater than which cannot be conceived. (The Latin is aliquid quo nihil maius cogitari possit. Anselm sometimes uses the alternative expressions aliquid quo maius nihil cogitari potest, id quo maius cogitari nequit, aliquid quo maius cogitari non valet.) Even the fool of the Psalm who says in his heart there is no God, when he hears this very thing that Anselm says, namely, “something a greater than which cannot be conceived,” understands what he hears, and what he understands is in his understanding though he does not understand that it exists.

Apparently Anselm regards it as tautological to say that whatever is understood is in the understanding (quidquid intelligitur in intellectu est): he uses intelligitur and in intellectu est as interchangeable locutions. The same holds for another formula of his: whatever is thought is in thought (quidquid cogitatur in cogitatione est).²

Of course many things may exist in the understanding that do not exist in reality; for example, elves. Now, says Anselm, something a greater than which cannot be conceived exists in the understanding. But it cannot exist only in the understanding, for to exist in reality is greater. Therefore that thing a greater than which cannot be conceived cannot exist only in the understanding, for then a greater thing could be conceived: namely, one that exists both in the understanding and in reality.³

Here I have a question. It is not clear to me whether Anselm means that (a) existence in reality by itself is greater than existence in the understanding, or that (b) existence in reality and existence in the understanding together are greater than existence in the understanding alone. Certainly he accepts (b). But he might also accept (a), as Descartes apparently does in Meditation III when he suggests that the mode of being by which a thing is “objectively in the understanding” is imperfect.⁴ Of course Anselm might accept both (a) and (b). He might hold that in general something is greater if it has both of these “modes of existence” than if it has either one alone, but also that existence in reality is a more perfect mode of existence than existence in the understanding.

In any case, Anselm holds that something is greater if it exists both in the understanding and in reality than if it exists merely in the understanding. An equivalent way of putting this interesting proposition, in a more current terminology, is: something is greater if it is both conceived of and exists than if it is merely conceived of. Anselm's reasoning can be expressed as follows: id quo maius cogitari nequit cannot be merely conceived of and not exist, for then it would not be id quo maius cogitari nequit. The doctrine that something is greater if it exists in addition to being conceived of, than if it is only conceived of, could be called the doctrine that existence is a perfection. Descartes maintained, in so many words, that existence is a perfection,⁵ and presumably he was holding Anselm's doctrine, although he does not, in Meditation V or elsewhere, argue in the way that Anselm does in Proslogion 2.

When Anselm says, “And certainly, that than which nothing greater can be conceived cannot exist merely in the understanding. For suppose it exists merely in the understanding, then it can be conceived to exist in reality, which is greater,”⁶ he is claiming that if I conceived of a being of great excellence, that being would be greater (more excellent, more perfect) if it existed than if it did not exist. His supposition that “it exists merely in the understanding” is the supposition that it is conceived of but does not exist. Anselm repeated this claim in his reply to the criticism of the monk Gaunilo. Speaking of the being a greater than which cannot be conceived, he says:

I have said that if it exists merely in the understanding it can be conceived to exist in reality, which is greater. Therefore, if it exists merely in the understanding obviously the very being a greater than which cannot be conceived, is one a greater than which can be conceived. What, I ask, can follow better than that? For if it exists merely in the understanding, can it not be conceived to exist in reality? And if it can be so conceived does not he who conceives of this conceive of a thing greater than it, if it does exist merely in the understanding? Can anything follow better than this: that if a being a greater than which cannot be conceived exists merely in the understanding, it is something a greater than which can be conceived? What could be plainer?⁷

He is implying, in the first sentence, that if I conceive of something which does not exist then it is possible for it to exist, and it will be greater if it exists than if it does not exist.

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? My future child will be a better man if he is honest than if he is not; but who would inderstand the saying that he will be a better man if he exists than if he does not? Or who understands the saying that if God exists He is more perfect than if He does not exist? One might say, with some intelligibility, that it would be better (for oneself or for mankind) if God exists than if He does not—but that is a different matter.

A king might desire that his next chancellor should have knowledge, wit, and resolution; but it is ludicrous to add that the king's desire is to have a chancellor who exists. Suppose that two royal councilors, A and B, were asked to draw up separately descriptions of the most perfect chancellor they could conceive, and that the descriptions they produced were identical except that A included existence in his list of attributes of a perfect chancellor and B did not. (I do not mean that B put nonexistence in his list.) One and the same person could satisfy both descriptions. More to the point, any person who satisfied A's description would necessarily satisfy B's description and vice versa! This is to say that A and B did not produce descriptions that differed in any way but rather one and the same description of necessary and desirable qualities in a chancellor. A only made a show of putting down a desirable quality that B had failed to include.

I believe I am merely restating an observation that Kant made in attacking the notion that “existence” or “being” is a “real predicate.” He says:

By whatever and by however many predicates we may think a thing—even if we completely determine it—we do not make the least addition to the thing when we further declare that this thing is. Otherwise, it would not be exactly the same thing that exists, but something more than we had thought in the concept; and we could not, therefore, say that the exact object of my concept exists.⁸

Anselm's ontological proof of Proslogion 2 is fallacious because it rests on the false doctrine that existence is a perfection (and therefore that “existence” is a “real predicate”). It would be desirable to have a rigorous refutation of the doctrine but I have not been able to provide one. I am compelled to leave the matter at the more or less intuitive level of Kant's observation. In any case, I believe that the doctrine does not belong to Anselm's other formulation of the ontological argument. It is worth noting that Gassendi anticipated Kant's criticism when he said, against Descartes:

Existence is a perfection neither in God nor in anything else; it is rather that in the absence of which there is no perfection. … Hence neither is existence held to exist in a thing in the way that perfections do, nor if the thing lacks existence is it said to be imperfect (or deprived of a perfection), so much as to be nothing.⁹

II

I take up now the consideration of the second ontological proof, which Anselm presents in the very next chapter of the Proslogion. (There is no evidence that he thought of himself as offering two different proofs.) Speaking of the being a greater than which cannot be conceived, he says:

And it so truly exists that it cannot be conceived not to exist. For it is possible to conceive of a being which cannot be conceived not to exist; and this is greater than one which can be conceived not to exist. Hence, if that, than which nothing greater can be conceived, can be conceived not to exist, it is not that than which nothing greater can be conceived. But this is a contradiction. So truly, therefore, is there something than which nothing greater can be conceived, that it cannot even be conceived not to exist.

And this being thou art, O Lord, our God.¹⁰

Anselm is saying two things: first, that a being whose nonexistence is logically impossible is “greater” than a being whose nonexistence is logically possible (and therefore that a being a greater than which cannot be conceived must be one whose nonexistence is logically impossible); second, that God is a being than which a greater cannot be conceived.

In regard to the second of these assertions, there certainly is a use of the word “God,” and I think far the more common use, in accordance with which the statements “God is the greatest of all beings,” “God is the most perfect being,” “God is the supreme being,” are logically necessary truths, in the same sense that the statement “A square has four sides” is a logically necessary truth. If there is a man named “Jones” who is the tallest man in the world, the statement “Jones is the tallest man in the world” is merely true and is not a logically necessary truth. It is a virtue of Anselm's unusual phrase, “a being a greater than which cannot be conceived,”¹¹ to make it explicit that the sentence “God is the greatest of all beings” expresses a logically necessary truth and not a mere matter of fact such as the one we imagined about Jones.

With regard to Anselm's first assertion (namely, that a being whose nonexistence is logically impossible is greater than a being whose nonexistence is logically possible) perhaps the most puzzling thing about it is the use of the word “greater.” It appears to mean exactly the same as “superior,” “more excellent,” “more perfect.” This equivalence by itself is of no help to us, however, since the latter expressions would be equally puzzling here. What is required is some explanation of their use.

We do think of knowledge, say, as an excellence, a good thing. If A has more knowledge of algebra than B we express this in common language by saying that A has a better knowledge of algebra than B, or that A's knowledge of algebra is superior to B's, whereas we should not say that B has a better or superior ignorance of algebra than A. We do say “greater ignorance,” but here the word “greater” is used purely quantitatively.

Previously I rejected existence as a perfection. Anselm is maintaining in the remarks last quoted, not that existence is a perfection, but that the logical impossibility of nonexistence is a perfection. In other words, necessary existence is a perfection. His first ontological proof uses the principle that a thing is greater if it exists than if it does not exist. His second proof employs the different principle that a thing is greater if it necessarily exists than if it does not necessarily exist.

Some remarks about the notion of dependence may help to make this latter principle intelligible. Many things depend for their existence on other things and events. My house was built by a carpenter: its coming into existence was dependent on a certain creative activity. Its continued existence is dependent on many things: that a tree does not crush it, that it is not consumed by fire, and so on. If we reflect on the common meaning of the word “God” (no matter how vague and confused this is), we realize that it is incompatible with this meaning that God's existence should depend on anything. Whether we believe in Him or not we must admit that the “almighty and everlasting God” (as several ancient prayers begin), the “Maker of heaven and earth, and of all things visible and invisible” (as is said in the Nicene Creed), cannot be thought of as being brought into existence by anything or as depending for His continued existence on anything. To conceive of anything as dependent upon something else for its existence is to conceive of it as a lesser being than God.

If a housewife has a set of extremely fragile dishes, then as dishes they are inferior to those of another set like them in all respects except that they are not fragile. Those of the first set are dependent for their continued existence on gentle handling; those of the second set are not. There is a definite connection in common language between the notions of dependency and inferiority, and independence and superiority. To say that something which was dependent on nothing whatever was superior to (“greater than”) anything that was dependent in any way upon anything is quite in keeping with the everyday use of the terms “superior” and “greater.” Correlative with the notions of dependence and independence are the notions of limited and unlimited. An engine requires fuel and this is a limitation. It is the same thing to say that an engine's operation is dependent on as that it is limited by its fuel supply. An engine that could accomplish the same work in the same time and was in other respects satisfactory, but did not require fuel, would be a superior engine.

God is usually conceived of as an unlimited being. He is conceived of as a being who could not be limited, that is, as an absolutely unlimited being. This is no less than to conceive of Him as something a greater than which cannot be conceived. If God is conceived to be an absolutely unlimited being He must be conceived to be unlimited in regard to His existence as well as His operation. In this conception it will not make sense to say that He depends on anything for coming into or continuing in existence. Nor, as Spinoza observed, will it make sense to say that something could prevent Him from existing.¹² Lack of moisture can prevent trees from existing in a certain region of the earth. But it would be contrary to the concept of God as an unlimited being to suppose that anything other than God Himself could prevent Him from existing, and it would be self-contradictory to suppose that He Himself could do it.

Some may be inclined to object that although nothing could prevent God's existence, still it might just happen that He did not exist. And if He did exist that too would be by chance. I think, however, that from the supposition that it could happen that God did not exist it would follow that, if He existed, He would have mere duration and not eternity. It would make sense to ask, “How long has He existed?,” “Will He still exist next week?,” “He was in existence yesterday but how about today?,” and so on. It seems absurd to make God the subject of such questions. According to our ordinary conception of Him, He is an eternal being. And eternity does not mean endless duration, as Spinoza noted. To ascribe eternity to something is to exclude as senseless all sentences that imply that it has duration. If a thing has duration then it would be merely a contingent fact, if it was a fact, that its duration was endless. The moon could have endless duration but not eternity. If something has endless duration it will make sense (although it will be false) to say that it will cease to exist, and it will make sense (although it will be false) to say that something will cause it to cease to exist. A being with endless duration is not, therefore, an absolutely unlimited being. That God is conceived to be eternal follows from the fact that He is conceived to be an absolutely unlimited being.

I have been trying to expand the argument of Proslogion 3. In Responsio 1 Anselm adds the following acute point: if you can conceive of a certain thing and this thing does not exist then if it were to exist its nonexistence would be possible. It follows, I believe, that if the thing were to exist it would depend on other things both for coming into and continuing in existence, and also that it would have duration and not eternity. Therefore it would not be, either in reality or in conception, an unlimited being, aliquid quo nihil maius cogitari possit.

Anselm states his argument as follows:

If it [the thing a greater than which cannot be conceived] can be conceived at all it must exist. For no one who denies or doubts the existence of a being a greater than which is inconceivable, denies or doubts that if it did exist its non-existence, either in reality or in the understanding, would be impossible. For otherwise it would not be a being a greater than which cannot be conceived. But as to whatever can be conceived but does not exist: if it were to exist its non-existence either in reality or in the understanding would be possible. Therefore, if a being a greater than which cannot be conceived, can even be conceived, it must exist.¹³

What Anselm has proved is that the notion of contingent existence or of contingent nonexistence cannot have any application to God. His existence must either be logically necessary or logically impossible. The 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.¹⁴ 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.

Let me summarize the proof. If God, a being a greater than which cannot be conceived, does not exist then He cannot come into existence. For if He did He would either have been caused to come into existence or have happened to come into existence, and in either case He would be a limited being, which by our conception of Him He is not. Since He cannot come into existence, if He does not exist His existence is impossible. If He does exist He cannot have come into existence (for the reasons given), nor can He cease to exist, for nothing could cause Him to cease to exist nor could it just happen that He ceased to exist. So if God exists His existence is necessary. Thus God's existence is either impossible or necessary. It can be the former only if the concept of such a being is self-contradictory or in some way logically absurd. Assuming that this is not so, it follows that He necessarily exists.

It may be helpful to express ourselves in the following way: to say, not that omnipotence is a property of God, but rather that necessary omnipotence is; and to say, not that omniscience is a property of God, but rather that necessary omniscience is. We have criteria for determining that a man knows this and that and can do this and that, and for determining that one man has greater knowledge and abilities in a certain subject than another. We could think of various tests to give them. But there is nothing we should wish to describe, seriously and literally, as “testing” God's knowledge and powers. That God is omniscient and omnipotent has not been determined by the application of criteria: rather these are requirements of our conception of Him. They are internal properties of the concept, although they are also rightly said to be properties of God. Necessary existence is a property of God in the same sense that necessary omnipotence and necessary omniscience are His properties. And we are not to think that “God necessarily exists” means that it follows necessarily from something that God exists contingently. The a priori proposition “God necessarily exists” entails the proposition “God exists,” if and only if the latter also is understood as an a priori proposition: in which case the two propositions are equivalent. In this sense Anselm's proof is a proof of God's existence.

Descartes was somewhat hazy on the question of whether existence is a property of things that exist, but at the same time he saw clearly enough that necessary existence is a property of God. Both points are illustrated in his reply to Gassendi's remark, which I quoted above:

I do not see to what class of reality you wish to assign existence, nor do I see why it may not be said to be a property as well as omnipotence, taking the word property as equivalent to any attribute or anything which can be predicated of a thing, as in the present case it should be by all means regarded. Nay, necessary existence in the case of God is also a true property in the strictest sense of the word, because it belongs to Him and forms part of His essence alone.¹⁵

Elsewhere he speaks of “the necessity of existence” as being “that crown of perfections without which we cannot comprehend God.”¹⁶ He is emphatic on the point that necessary existence applies solely to “an absolutely perfect Being.”¹⁷

III

I wish to consider now a part of Kant's criticism of the ontological argument which I believe to be wrong. He says:

If, in an identical proposition, I reject the predicate while retaining the subject, contradiction results; and I therefore say that the former belongs necessarily to the latter. But if we reject subject and predicate alike, there is no contradiction; for nothing is then left that can be contradicted. To posit a triangle, and yet to reject its three angles, is self-contradictory; but there is no contradiction in rejecting the triangle together with its three angles. The same holds true of the concept of an absolutely necessary being. If its existence is rejected, we reject the thing itself with all its predicates; and no question of contradiction can then arise. There is nothing outside it that would then be contradicted, since the necessity of the thing is not supposed to be derived from anything external; nor is there anything internal that would be contradicted, since in rejecting the thing itself we have at the same time rejected all its internal properties. “God is omnipotent” is a necessary judgment. The omnipotence cannot be rejected if we posit a Deity, that is, an infinite being; for the two concepts are identical. But if we say, “There is no God,” neither the omnipotence nor any other of its predicates is given; they are one and all rejected together with the subject, and there is therefore not the least contradiction in such a judgment.¹⁸

To these remarks the reply is that when the concept of God is correctly understood one sees that one cannot “reject the subject.” “There is no God” is seen to be a necessarily false statement. Anselm's demonstration proves that the proposition “God exists” has the same a priori footing as the proposition “God is omnipotent.”

Many present-day philosophers, in agreement with Kant, declare that existence is not a property and think that this overthrows the ontological argument. Although it is an error to regard existence as a property of things that have contingent existence, it does not follow that it is an error to regard necessary existence as a property of God. A recent writer says, against Anselm, that a proof of God's existence “based on the necessities of thought” is “universally regarded as fallacious: it is not thought possible to build bridges between mere abstractions and concrete existence.”¹⁹ But this way of putting the matter obscures the distinction we need to make. Does “concrete existence” mean contingent existence? Then to build bridges between concrete existence and mere abstractions would be like inferring the existence of an island from the concept of a perfect island, which both Anselm and Descartes regarded as absurd. What Anselm did was to give a demonstration that the proposition “God necessarily exists” is entailed by the proposition “God is a being a greater than which cannot be conceived” (which is equivalent to “God is an absolutely unlimited being”). Kant declares that when “I think a being as the supreme reality, without any defect, the question still remains whether it exists or not.”²⁰ But once one has grasped Anselm's proof of the necessary existence of a being a greater than which cannot be conceived, no question remains as to whether it exists or not, just as Euclid's demonstration of the existence of an infinity of prime numbers leaves no question on that issue.

Kant says that “every reasonable person” must admit that “all existential propositions are synthetic.”²¹ Part of the perplexity one has about the ontological argument is in deciding whether or not the proposition “God necessarily exists” is or is not an “existential proposition.” But let us look around. Is the Euclidean theorem in number theory, “There exists an infinite number of prime numbers,” an “existential proposition”? do we not want to say that in some sense it asserts the existence of something? Cannot we say, with equal justification, that the proposition “God necessarily exists” asserts the existence of something, in some sense? What we need to understand, in each case, is the particular sense of the assertion. Neither proposition has the same sort of sense as do the propositions, “A low pressure area exists over the Great Lakes,” “There still exists some possibility that he will survive,” “The pain continues to exist in his abdomen.” One good way of seeing the difference in sense of these various propositions is to see the variously different ways in which they are proved or supported. It is wrong to think that all assertions of existence have the same kind of meaning. There are as many kinds of existential propositions as there are kinds of subjects of discourse.

Closely related to Kant's view that all existential propositions are “synthetic” is the contemporary dogma that all existential propositions are contingent. Professor Gilbert Ryle tells us that “Any assertion of the existence of something, like any assertion of the occurrence of something, can be denied without logical absurdity.”²² “All existential statements are contingent,” says Mr. I. M. Crombie.²³ Professor J. J. C. Smart remarks that “Existence is not a property” and then goes on to assert that “There can never be any logical contradiction in denying that God exists.”²⁴ He declares that “The concept of a logically necessary being is a self-contradictory concept, like the concept of a round square. … No existential proposition can be logically necessary,” he maintains, for “the truth of a logically necessary proposition depends only on our symbolism, or to put the same thing in another way, on the relationship of concepts” (p. 38). Professor K. E. M. Baier says, “It is no longer seriously in dispute that the notion of a logically necessary being is self-contradictory. Whatever can be conceived of as existing can equally be conceived of as not existing.”²⁵ This is a repetition of Hume's assertion, “Whatever we conceive as existent, we can also conceive as non-existent. There is no being, therefore, whose non-existence implies a contradiction.”²⁶

Professor J. N. Findlay ingeniously constructs an ontological disproof of God's existence, based on a “modern” view of the nature of “necessity in propositions”: the view, namely, that necessity in propositions “merely reflects our use of words, the arbitrary conventions of our language.”²⁷ Findlay undertakes to characterize what he calls “religious attitude,” and here there is a striking agreement between his observations and some of the things I have said in expounding Anselm's proof. Religious attitude, he says, presumes superiority in its object and superiority so great that the worshiper is in comparison as nothing. Religious attitude finds it “anomalous to worship anything limited in any thinkable manner. … And hence we are led on irresistibly to demand that our religious object should have an unsurpassable supremacy along all avenues, that it should tower infinitely above all other objects” (p. 51). We cannot help feeling that “the worthy object of our worship can never be a thing that merely happens to exist, nor one on which all other objects merely happen to depend. The true object of religious reverence must not be one, merely, to which no actual independent realities stand opposed: it must be one to which such opposition is totally inconceivable. … And not only must the existence of other things be unthinkable without him, but his own non-existence must be wholly unthinkable in any circumstances” (p. 52). And now, says Findlay, when we add up these various requirements, what they entail is “not only that there isn't a God, but that the Divine Existence is either senseless or impossible” (p. 54). For on the one hand, “if God is to satisfy religious claims and needs, He must be a being in every way inescapable, One whose existence and whose possession of certain excellences we cannot possibly conceive away.” On the other hand, “modern views make it self-evidently absurd (if they don't make it ungrammatical) to speak of such a Being and attribute existence to Him. It was indeed an ill day for Anselm when he hit upon his famous proof. For on that day he not only laid bare something that is of the essence of an adequate religious object, but also something that entails its necessary non-existence” (p. 55).

Now I am inclined to hold the “modern” view that logically necessary truth “merely reflects our use of words” (although I do not believe that the conventions of language are always arbitrary). But I confess that I am unable to see how that view is supposed to lead to the conclusion that “the Divine existence is either senseless or impossible.” Findlay does not explain how this result comes about. Surely he cannot mean that this view entails that nothing can have necessary properties: for this would imply that mathematics is “senseless or impossible,” which no one wants to hold. Trying to fill in the argument that is missing from his article, the most plausible conjecture I can make is the following: Findlay thinks that the view that logical necessity “reflects the use of words” implies, not that nothing has necessary properties, but that existence cannot be a necessary property of anything. That is to say, every proposition of the form “x exists,” including the proposition “God exists,” must be contingent.²⁸ At the same time, our concept of God requires that His existence be necessary, that is, that “God exists” be a necessary truth. Therefore, the modern view of necessity proves that what the concept of God requires cannot be fulfilled. It proves that God cannot exist.

The correct reply is that the view that logical necessity merely reflects the use of words cannot possibly have the implication that every existential proposition must be contingent. That view requires us to look at the use of words and not manufacture a priori theses about it. In the Ninetieth Psalm it is said: “Before the mountains were brought forth, or ever thou hadst formed the earth and the world, even from everlasting to everlasting, thou art God.” Here is expressed the idea of the necessary existence and eternity of God, an idea that is essential to the Jewish and Christian religions. In those complex systems of thought, those “languages-games,” God has the status of a necessary being. Who can doubt that? Here we must say with Wittgenstein, “This language-game is played!”²⁹ I believe we may rightly take the existence of those religious systems of thought in which God figures as a necessary being to be a disproof of the dogma, affirmed by Hume and others, that no existential proposition can be necessary.

Another way of criticizing the ontological argument is the following. “Granted that the concept of necessary existence follows from the concept of a being a greater than which cannot be conceived, this amounts to no more than granting the a priori truth of the conditional proposition, ‘If such a being exists then it necessarily exists.’ This proposition, however, does not entail the existence of anything, and one can deny its antecedent without contradiction.” Kant, for example, compares the proposition (or “judgment,” as he calls it) “A triangle has three angles” with the proposition “God is a necessary being.” He allows that the former is “absolutely necessary” and goes on to say:

The absolute necessity of the judgment is only a conditional necessity of the thing, or of the predicate in the judgment. The above proposition does not declare that three angles are absolutely necessary, but that, under the condition that there is a triangle (that is, that a triangle is given), three angles will necessarily be found in it.³⁰

He is saying, quite correctly, that the proposition about triangles is equivalent to the conditional proposition, “If a triangle exists, it has three angles.” He then makes the comment that there is no contradiction “in rejecting the triangle together with its three angles.” He proceeds to draw the alleged parallel: “The same holds true of the concept of an absolutely necessary being. If its existence is rejected, we reject the thing itself with all its predicates; and no question of contradiction can then arise.”³¹ The priest, Caterus, made the same objection to Descartes when he said:

Though it be conceded that an entity of the highest perfection implies its existence by its very name, yet it does not follow that that very existence is anything actual in the real world, but merely that the concept of existence is inseparably united with the concept of highest being. Hence you cannot infer that the existence of God is anything actual, unless you assume that that highest being actually exists; for then it will actually contain all its perfections, together with this perfection of real existence.³²

I think that Caterus, Kant, and numerous other philosophers have been mistaken in supposing that the proposition “God is a necessary being” (or “God necessarily exists”) is equivalent to the conditional proposition “If God exists then He necessarily exists.”³³ For how do they want the antecedent clause, “If God exists,” to be understood? Clearly they want it to imply that it is possible that God does not exist.³⁴ The whole point of Kant's analysis is to try to show that it is possible to “reject the subject.” Let us make this implication explicit in the conditional proposition, so that it reads: “If God exists (and it is possible that He does not) then He necessarily exists.” But now it is apparent, I think, that these philosophers have arrived at a self-contradictory position. I do not mean that this conditional proposition, taken alone, is self-contradictory. Their position is self-contradictory in the following way. On the one hand, they agree that the proposition “God necessarily exists” is an a priori truth; Kant implies that it is “absolutely necessary,” and Caterus says that God's existence is implied by His very name. On the other hand, they think that it is correct to analyze this proposition in such a way that it will entail the proposition “It is possible that God does not exist.” But so far from its being the case that the proposition “God necessarily exists” entails the proposition “It is possible that God does not exist,” it is rather the case that they are incompatible with one another! Can anything be clearer than that the conjunction “God necessarily exists but it is possible that He does not exist” is self-contradictory? Is it not just as plainly self-contradictory as the conjunction “A square necessarily has four sides but it is possible for a square not to have four sides”? In short, this familiar criticism of the ontological argument is self-contradictory, because it accepts both of two incompatible propositions.³⁵

One conclusion we may draw from our examination of this criticism is that (contrary to Kant) there is a lack of symmetry, in an important respect, between the propositions “A triangle has three angles” and “God has necessary existence,” although both are a priori. The former can be expressed in the conditional assertion “If a triangle exists (and it is possible that none does) it has three angles.” The latter cannot be expressed in the corresponding conditional assertion without contradiction.

IV

I turn to the question of whether the idea of a being a greater than which cannot be conceived is self-contradictory. Here Leibniz made a contribution to the discussion of the ontological argument. He remarked that the argument of Anselm and Descartes

is not a paralogism, but it is an imperfect demonstration, which assumes something that must still be proved in order to render it mathematically evident; that is, it is tacitly assumed that this idea of the all-great or all-perfect being is possible, and implies no contradiction. And it is already something that by this remark it is proved that, assuming that God is possible, he exists, which is the privilege of divinity alone.³⁶

Leibniz undertook to give a proof that God is possible. He defined a perfection as a simple, positive quality in the highest degree.³⁷ He argued that since perfections are simple qualities they must be compatible with one another. Therefore the concept of a being possessing all perfections is consistent.

I will not review his argument because I do not find his definition of a perfection intelligible. For one thing, it assumes that certain qualities or attributes are “positive” in their intrinsic nature, and others “negative” or “privative,” and I have not been able clearly to understand that. For another thing, it assumes that some qualities are intrinsically simple. I believe that Wittgenstein has shown in the Investigations that nothing is intrinsically simple, but that whatever has the status of a simple, an indefinable, in one system of concepts, may have the status of a complex thing, a definable thing, in another system of concepts.

I do not know how to demonstrate that the concept of God—that is, of a being a greater than which cannot be conceived—is not self-contradictory. But I do not think that it is legitimate to demand such a demonstration. I also do not know how to demonstrate that either the concept of a material thing or the concept of seeing a material thing is not self-contradictory, and philosophers have argued that both of them are. With respect to any particular reasoning that is offered for holding that the concept of seeing a material thing, for example, is self-contradictory, one may try to show the invalidity of the reasoning and thus free the concept from the charge of being self-contradictory on that ground. But I do not understand what it would mean to demonstrate in general, and not in respect to any particular reasoning, that the concept is not self-contradictory. So it is with the concept of God. I should think there is no more of a presumption that it is self-contradictory than is the concept of seeing a material thing. Both concepts have a place in the thinking and the lives of human beings.

But even if one allows that Anselm's phrase may be free of self-contradiction, one wants to know how it can have any meaning for anyone. Why is it that human beings have even formed the concept of an infinite being, a being a greater than which cannot be conceived? This is a legitimate and important question. I am sure there cannot be a deep understanding of that concept without an understanding of the phenomena of human life that give rise to it. To give an account of the latter is beyond my ability. I wish, however, to make one suggestion (which should not be understood as autobiographical).

There is the phenomenon of feeling guilt for something that one has done or thought or felt or for a disposition that one has. One wants to be free of this guilt. But sometimes the guilt is felt to be so great that one is sure that nothing one could do oneself, nor any forgiveness by another human being, would remove it. One feels a guilt that is beyond all measure, a guilt “a greater than which cannot be conceived.” Paradoxically, it would seem, one nevertheless has an intense desire to have this incomparable guilt removed. One requires a forgiveness that is beyond all measure, a forgiveness “a greater than which cannot be conceived.” Out of such a storm in the soul, I am suggesting, there arises the conception of a forgiving mercy that is limitless, beyond all measure. This is one important feature of the Jewish and Christian conception of God.

I wish to relate this thought to a remark made by Kierkegaard, who was speaking about belief in Christianity but whose remark may have a wider application. He says:

There is only one proof of the truth of Christianity and that, quite rightly, is from the emotions, when the dread of sin and a heavy conscience torture a man into crossing the narrow line between despair bordering upon madness—and Christendom.³⁸

One may think it absurd for a human being to feel a guilt of such magnitude, and even more absurd that, if he feels it, he should desire its removal. I have nothing to say about that. It may also be absurd for people to fall in love, but they do it. I wish only to say that there is that human phenomenon of an unbearably heavy conscience and that it is importantly connected with the genesis of the concept of God, that is, with the formation of the “grammar” of the word “God.” I am sure that this concept is related to human experience in other ways. If one had the acuteness and depth to perceive these connections one could grasp the sense of the concept. When we encounter this concept as a problem in philosophy, we do not consider the human phenomena that lie behind it. It is not surprising that many philosophers believe that the idea of a necessary being is an arbitrary and absurd construction.

What is the relation of Anselm's ontological argument to religious belief? This is a difficult question. I can imagine an atheist going through the argument, becoming convinced of its validity, acutely defending it against objections, yet remaining an atheist. The only effect it could have on the fool of the Psalm would be that he stopped saying in his heart “There is no God,” because he would now realize that this is something he cannot meaningfully say or think. It is hardly to be expected that a demonstrative argument should, in addition, produce in him a living faith. Surely there is a level at which one can view the argument as a piece of logic, following the deductive moves but not being touched religiously? I think so. But even at this level the argument may not be without religious value, for it may help to remove some philosophical scruples that stand in the way of faith. At a deeper level, I suspect that the argument can be thoroughly understood only by one who has a view of that human “form of life” that gives rise to the idea of an infinitely great being, who views it from the inside not just from the outside and who has, therefore, at least some inclination to partake in that religious form of life. This inclination, in Kierkegaard's words, is “from the emotions.” This inclination can hardly be an effect of Anselm's argument, but is rather presupposed in the fullest understanding of it. It would be unreasonable to require that the recognition of Anselm's demonstration as valid must produce a conversion.

Notes

1. I have consulted the Latin text of the Proslogion, of Gaunilonis Pro Insipiente, and of the Responsio editoris, in S. Anselmi, Opera Omnia, edited by F. C. Schmitt (Secovii, 1938), vol. I. With numerous modifications, I have used the English translation by S. N. Deane: St. Anselm (LaSalle, Illinois, 1948).

2. See Proslogion 1 and Responsio 2.

3. Anselm's actual words are: “Et certe id quo maius cogitari nequit, non potest esse in solo intellectu. Si enim vel in solo intellectu est, potest cogitari esse et in re, quod maius est. Si ergo id quo maius cogitari non potest, est in solo intellectu: id ipsum quo maius cogitari non potest, est quo maius cogitari potest. Sed certe hoc esse non potest.” Proslogion 2.

4. Haldane and Ross, The Philosophical Works of Descartes, 2 vols. (Cambridge, 1931), I, 163.

5. Op. cit., p. 182.

6. Proslogion 2; Deane, p. 8.

7. Responsio 2; Deane, pp. 157-158.

8. The Critique of Pure Reason, tr. by Norman Kemp Smith (London, 1929), p. 505.

9. Haldane and Ross, II, 186.

10. Proslogion 3; Deane, pp. 8-9.

11. Professor Robert Calhoun has pointed out to me that a similar locution had been used by Augustine. In De moribus Manichaeorum (Bk. II, ch. xi, sec. 24), he says that God is a being quo esse aut cogitari melius nihil possit (Patrologiae Patrum Latinorum, ed. by J. P. Migne, Paris, 1841-1845, vol. 32: Augustinus, vol. 1).

12. Ethics, pt. I, prop. 11.

13. Responsio 1; Deane, pp. 154-155.

14. Gaunilo attacked Anselm's argument on this very point. He would not concede that a being a greater than which cannot be conceived existed in his understanding (Gaunilonis Pro Insipiente, secs. 4 and 5; Deane, pp. 148-150). Anselm's reply is: “I call on your faith and conscience to attest that this is most false” (Responsio 1; Deane, p. 154). Gaunilo's faith and conscience will attest that it is false that “God is not a being a greater than which is inconceivable,” and false that “He is not understood (intelligitur) or conceived (cogitatur)” (ibid.). Descartes also remarks that one would go to “strange extremes” who denied that we understand the words “that thing which is the most perfect that we can conceive; for that is what all men call God” (Haldane and Ross, II, 129).

15. Haldane and Ross, II, 228.

16. Ibid., I, 445.

17. E.g., ibid., Principle 15, p. 225.

18. Op. cit., p. 502.

19. J. N. Findlay, “Can God's Existence Be Disproved?,” New Essays in Philosophical Theology,” ed. by A. N. Flew and A. MacIntyre (London, 1955), p. 47.

20. Op. cit., pp. 505-506.

21. Ibid., p. 504.

22. The Nature of Metaphysics, ed. by D. F. Pears (New York, 1957), p. 150.

23. New Essays in Philosophical Theology, p. 114.

24. Ibid., p. 34.

25. The Meaning of Life, Inaugural Lecture, Canberra University College (Canberra, 1957), p. 8.

26. Dialogues Concerning Natural Religion, pt. IX.

27. Findlay, op. cit., p. 154.

28. The other philosophers I have just cited may be led to this opinion by the same thinking. Smart, for example, says that “the truth of a logically necessary proposition depends only on our symbolism, or to put the same thing in another way, on the relationship of concepts” (supra). This is very similar to saying that it “reflects our use of words.”

29. Philosophical Investigations (New York, 1953), sec. 654.

30. Op. cit., pp. 501-502.

31. Ibid., p. 502.

32. Haldane and Ross, II, 7.

33. I have heard it said by more than one person in discussion that Kant's view was that it is really a misuse of language to speak of a “necessary being,” on the grounds that necessity is properly predicated only of propositions (judgments) not of things. This is not a correct account of Kant. (See his discussion of “The Postulates of Empirical Thought in General,” op. cit., pp. 239-256, esp. p. 239 and pp. 247-248.) But if he had held this, as perhaps the above philosophers think he should have, then presumably his view would not have been that the pseudo-proposition “God is a necessary being” is equivalent to the conditional “If God exists then He necessarily exists.” Rather his view would have been that the genuine proposition “‘God exists’ is necessarily true” is equivalent to the conditional “If God exists then He exists” (not “If God exists then He necessarily exists,” which would be an illegitimate formulation, on the view imaginatively attributed to Kant).

    “If God exists then He exists” is a foolish tautology which says nothing different from the tautology “If a new earth satellite exists then it exists.” If “If God exists then He exists” were a correct analysis of “‘God exists’ is necessarily true,” then “If a new earth satellite exists then it exists” would be a correct analysis of “‘A new earth satellite exists’ is necessarily true.” If the analysans is necessarily true then the analysandum must be necessarily true, provided the analysis is correct. If this proposed Kantian analysis of “‘God exists’ is necessarily true” were correct, we should be presented with the consequence that not only is it necessarily true that God exists, but also it is necessarily true that a new earth satellite exists: which is absurd.

34. When summarizing Anselm's proof (in part II, supra) I said: “If God exists He necessarily exists.” But there I was merely stating an entailment. “If God exists” did not have the implication that it is possible He does not exist. And of course I was not regarding the conditional as equivalent to “God necessarily exists.”

35. This fallacious criticism of Anselm is implied in the following remarks by Gilson: “To show that the affirmation of necessary existence is analytically implied in the idea of God, would be … to show that God is necessary if He exists, but would not prove that He does exist” (E. Gilson, The Spirit of Medieval Philosophy, New York, 1940, p. 62).

36. New Essays Concerning the Human Understanding, Bk. IV, ch. 10; ed. by A. G. Langley (LaSalle, Illinois, 1949), p. 504.

37. See Ibid., Appendix X, p. 714.

38. The Journals, tr. by A. Dru (Oxford, 1938), sec. 926.