by Henry Piper (all rights reserved)
In principle at least, no single subject would seem more important to metaphysics than the existence of God. Metaphysics is the study of reality, of being, of what is and why what is is the way it is, and if God exists then that would, in the profoundest conceivable way, influence everything about the subject. If we take “God” to refer to an omnipotent, omniscient and omnibenevolent (all-powerful, all-knowing and all-good) being, then God’s existence would mean, presumably, that everything is from God and nothing that happens could be without God’s influence. Our skeptical inclinations might lead us to assert, however, precisely because of the transcendent nature of God, that God’s ultimate perfection implies that, even if God does exist, there couldn’t be any way to know it: since we humans are limited and imperfect, whereas God, if God exists, is unlimitedly perfect in every way and thus is everything we are not, then surely God would be totally beyond us and invisible to us. Thus, we might say, our relationship to God, if God exists, can be a matter of faith only and not of reason since our powers of reason would seem to be utterly insufficient to grasp the perfection of God.
Such skeptical inclinations are very reasonable, but even if true does that mean that we have nothing to gain from seeking to make rational sense of the possible existence of God, even to the point of seeking a proof for that existence? I am confident that such efforts are valuable: we stand to gain by the exercise of our powers of reason, even if our goal of “knowing God” is ultimately impossible, and, moreover, we may achieve all sorts of insights that, even if they do not include a conclusive rational proof or dis-proof of God’s existence, are impossible for us to foresee without our actual engagement in the effort. Many of the great accomplishments and discoveries of humankind, after all, have been achieved accidentally, or serendipitously―while an explorer was looking for something else.
The Nature of the Task: the Word “God” is “Dog Spelled Backwards”—it’s just a word!
Before we begin considering specific attempts to prove the existence of God, it is important to consider exactly what the nature of the task is―what it is that such a proof is trying to accomplish. Accordingly, it is vital to distinguish between proving that God exists, on the one hand, and saying anything about God, on the other, since to prove that God exists is not to say anything about God. In this regard we might recall Descartes’s famous argument, “I think, therefore I am.” In his Meditations, Descartes’s project is epistemological: he is concerned to determine whether he can know anything with perfect certainty—that is, anything that’s indubitable, beyond all doubt. In Meditation I he realizes that in his life so far he thought he had come to know many things; however, upon reflection he realized that he could give no account of why he should accept any of these things as true—how did he know that they were true? He thus determined to “withdraw his assent” from everything that he thought he knew—not to assert that all was false—for that would actually be more than he could know—but to doubt everything, since if there is any doubt about a thing then by definition it is not certain. He went on to realize that his senses are prone to deceive him, making near things appear larger than they are, for example; but what of simple things such as his sitting in his room by the fire—surely he could know that? But he realizes that he had dreamt of such things that of course turned out to be illusions, so he determines to “assume that I am dreaming, for argument’s sake,” so that he can avoid the error of thinking that what is before him is as it appears; he doesn’t in fact believe that he’s dreaming, but he cannot be absolutely certain that he’s not. Still, it would seem that some purely mental “truths” such as 2+3=5 would be true even if he were in a dream; however, what if my entire consciousness is controlled by an ”evil genius” intent on deceiving me—then even mathematical truths might turn out to be a lie.
In short, at the end of Meditation I Descartes is forced to conclude that all we can know is that we know nothing, but at least as long as we realize that the evil genius could be constantly fooling us we won’t think we know something that could in fact be false. But in Meditation II Descartes reflects that even if an evil genius is deceiving us, we must necessarily exist in order to be deceived! In other words, I have been thinking all along about whether I am awake or asleep, etc., and if I am thinking therefore I must exist: “cogito ergo sum”—“I think therefore I exist.” Descartes characterizes this insight—that he now knows something that must certainly be true—as an “Archimedean point”—a point of leverage—that might lead him to ever greater knowledge—a “crack in the door,” as I like to think of it. However—and this is the real point for our present consideration of the existence of God—Descartes immediately realizes that, though he has proven that something is true, namely that I exist—he still knows absolutely nothing about what that “I” that must exist actually is. So Descartes’s “I think, therefore I exist” is at once a tremendous accomplishment—since it represents a total transformation from knowing nothing to knowing something—nonetheless it is at the same time an utterly miniscule thing that he knows—a mere point, which, as we know from geometry, is an empty nothing taking up no space. Again, to know that something exists is to know nothing about what that something might be—a “something” that is very close to being nothing.
Thus, given our commitment to limiting ourselves to the question of God’s existence and to foreswear any claim that we might know anything of God’s nature—to know merely that God exists while yet knowing nothing about what God is—we must be mindful that our use of the three-letter term “God” is simply an empty placeholder—a sign for something but we know-not-what or, if there is no “God,” a sign for nothing. Many people are put-off by the very word “God,” but, for philosophical purposes, this term has no connection whatever and makes no assumptions about anything to do with any religion nor even with religion in general. Admittedly, it does stand for the possible existence of a theoretical kind of thing—something, if existent, that is a perfect being, omnipotent, omniscient and omnibenevolent—but, so far as it goes, this “something” (which, again, may be nothing) is simply an idea—simply the definition of what the word “God” is understood to mean—and the question becomes whether this idea stands for something actual or real, or rather whether this idea is merely a fanciful dream, pulled from thin air as it were, a “figment of our imagination.”
Thus, given the fact that we are considering the existence of something that we are admitting at the outset we can know nothing about and with which we can effectively have nothing to do, it may seem that the accomplishment of these philosophers, even assuming that there is a God and that their attempts to prove that God exists are successful, is a hollow, unsatisfying and fruitless one. What is the point? We already can be sure that there are lots of things that exist in the universe that we have never seen and know nothing about, so what benefit do we derive from knowing that there’s one more thing we can’t see and don’t know? Will we have learned anything? Another objection we might make is to question whether it really makes sense to say that we can know that something exists without knowing anything about the thing, because isn’t the existence of God something about God, and if so doesn’t that contradict our previous acknowledgement that we cannot know anything about God? All these objections imply that to know God’s existence is either to know nothing or that God’s existence cannot be known: in other words, if the proof of God’s existence, in and of itself, were meaningful, then it would be impossible, since any meaning it would have would in essence constitute some insight into God’s nature, which we’ve already acknowledged is impossible. I suggest, however, that though these objections might be valid and all of this might be a waste of time, it also might not be so; furthermore, even if our pursuit of the proofs themselves proves fruitless, the pursuit itself may, as suggested above, be good mental exercise and, more importantly, it may lead us to discoveries that might otherwise elude us. Further, given the gravity of the subject—God!—can we afford, in good conscience, to pretend it doesn’t matter? Just because we might suspect that no amount of reflection will ever succeed at determining the meaning of life, does that mean that we should, or even can, resign ourselves to the proposition that life has no meaning?
In any event, this will be an exercise in philosophical speculation about matters of metaphysics, matters that exceed the bounds of physical science, and we must be careful to assure that our thinking is rigorous in terms of reason, logic and proof. We shall see, I believe, that we can think rationally and fruitfully about the existence of God even if we cannot know God, just as we can determine that a gift exists inside a wrapped box even if we cannot know what the gift inside the box is. What we might gain, in the end, may be no more than some insight into the process of thinking rather than the content or subject matter of the thought; but that may turn out to be an immeasurably valuable gain.
To sum up, even if we learn nothing of God, we stand to learn a great deal about ourselves.
The “Indirect Proof,” a Vital Tool of Logical Thinking
To prove something we use logical thinking, and there are certain rules that apply to all such thinking, rules that are the same for all of us and which we all use, on a daily basis, to a greater or lesser degree, even if we are not aware of it. Typically, logic begins with one or more premises, which are statements we already know to be true, by personal observation or previous agreement, for example. From these things that we already know, the tools of logical thinking can be applied to determine what further knowledge, if any, can be derived from them.
As discussed in the Introduction, there are two kinds of logic, “inductive” and “deductive.” Inductive logic uses reasoning about things we cannot know with absolute, perfect certainty, often involving, for example, predictions about the future or educated guesses about physical occurrences that we cannot directly observe based on physical evidence we do have; an example of the standard form of this is that we predict that the sun will rise tomorrow based on our observation of its past pattern. Because inductive arguments concern matters that cannot be known with perfect certainty, the conclusions of inductive logic are essentially judgments of probability, so a “strong” inductive argument is one whose conclusion seems highly probable based on the premises or evidence we already know or agree on. Thus, we conclude that the sun will rise tomorrow based on the long experience of past sunrises and the absence of any good reasons, physical or logical, that the pattern of the past will not repeat itself tomorrow. I cannot be perfectly certain about anything that will happen tomorrow, of course, since anything can happen in the future—the future is not (yet); but the argument that the sun will rise tomorrow would seem to be a very strong, inductive argument.
By contrast, deductive logic achieves results that are perfectly certain, and is based on rules akin to those of mathematics, whose conclusions admit of no variation or uncertainty: “2+3=5,” for example, is, arguably, not merely very likely, rather it is absolutely and necessarily true―it cannot not be true, ever or anywhere. Similarly, if I know that A is larger than B, and I know that B is larger than C, then I know with perfect certainty that A must be larger than C (without knowing anything about A, B and C!). Deductive logic’s similarity to math is reflected by the fact that philosophers often use math-like symbols to express the logical patterns of deductive logic. Let’s consider an example of a deductive argument to see how they work. We know already, for example, that “if you jump in the Lake , then you will get Wet (L → W).” Note that this “if…then” statement is hypothetical: it does not say either that you will jump in the lake or that you will get wet, rather it expresses a logical relation between the lake and wet, which we know by definition to be true. And note also that it is a one-way proposition: it is not necessarily the case that if you get wet then you jumped in the lake, since there are other ways that you might have gotten wet—e.g. you didn’t jump but it rained. Now let’s assume that you do jump in the lake (L); clearly we can conclude, with absolute certainty, that you must have gotten wet. Pause a moment to reflect: we can confirm that this must necessarily be true because it can never stay dry if you jump in the lake.
That is an example of a standard deductive argument, which uses one or more premises, here two, to draw some necessary conclusion. To review, the form of this argument is:
Premise 1 L → W
Premise 2 L
Conclusion W
Now consider another possible second premise, namely “I got wet” (W). Adding this premise to our first, “If L then W,” (L → W), can we draw any certain conclusion—can we conclude anything certain about L, i.e. whether you jumped in the lake? If you consider it carefully, you will see that we cannot; that is, if you are wet you might have jumped in the lake, but, as noted above, you could have gotten wet some other way. Recall that we are using a deductive argument form here, which permits conclusions only when they are absolutely certain, so here, since the best we can conclude is that you might have jumped in the lake, we cannot draw a deductive conclusion from these premises. So “either you jumped in the lake or you didn’t”—"either L or not-L”—but that is a logically empty statement that contains no information at all since it is always true, and for anything: for any statement we can say conclusively, with absolute certainty, “either it is or it isn’t,” “either X is true or X is false,” but that doesn’t tell us anything. Such a statement, which cannot be false, or cannot not be true, is known as a tautology. Thus,
Premise 1 L → W
Premise 2 W
Conclusion L or not-L (i.e. no deductive conclusion is possible)
Now let’s try another second premise, namely that you do not jump in the lake (~L). Combined with the first premise, can we conclude anything certain about L? Again we cannot: the first premise, L → W, tells us that W follows necessarily if we know L, but it says nothing about what follows, if anything, from ~L. Indeed, if ~L is true, i.e. if you don’t jump in the lake, we know that you might be dry but it might have rained, so we don’t know for certain whether W or ~W. Thus,
Premise 1 L → W
Premise 2 ~L
Conclusion W or ~W (i.e. no deductive conclusion is possible)
There is one more second premise we haven’t considered yet. Using again the first premise from above, L → W, let’s now assume that we currently know that you are not wet. Our second premise now is “W is false,” or ~W. If we combine this premise with the first, L → W, can we draw any certain conclusion? If you are not wet then we can be sure that you could not have jumped in the lake since clearly had you jumped in the lake then you would certainly have gotten wet; but if we look simply at the form of the two premises, using only the formal symbols of logic, we cannot go directly from these two premises to that conclusion as we could in the first example. Then we had L → W and L, so there we could plug the L directly into the L → W to get the W, since by having the L we no longer have to wonder “if” and we simply know W. But here, when we have L → W and ~W, we can’t directly get rid of that “if” to get ~L.
Premise 1 L → W
Premise 2 ~W
Conclusion ~L ? (Can we conclude this?)
But there is still a way to use deductive logic to be able to conclude ~L in this case, and the term for this method is the “indirect proof.” We proceed by making an assumption that might in fact be false, and an assumption, moreover, that is exactly the opposite of what we want to prove. We have already guessed that, since ~W, it must also be the case that ~L, but, as we have seen, we can’t get to that conclusion directly. So let’s assume L and then see whether that can possibly be true. If it turns out that by assuming L we are forced to a logical contradiction—something that cannot possibly be true—then we can conclude that our assumption must itself be false. That is why this form of proof is often known by the Latin term, “reductio ad absurdum”―"reduce to an absurdity" or “demonstrate that it is impossible”―for that is precisely what we are doing here: by assuming something that must be false, we can be confident, if we follow that assumption out to see what it entails, that we will be forced into a contradiction—to conclude something impossible, or absurd—and that will permit us to be certain that our initial assumption must itself be false—that it couldn’t be true since it leads to an absurdity. In short, if the assumption of L turns out to lead to an impossible result, then the assumption itself must be impossible and its opposite (~L) must necessarily be true and thus deductively certain (which is precisely what we want to prove).
So what happens when we assume that L is true? Let’s look at what we already know, which is what is contained in our premises. We know L → W, so by assuming L we thereby must assume W; but we already know, from the second premise, ~W. So if we assume that L is true, then both W and ~W would have to be true, which is impossible, absurd, since either you’re wet or you’re not—W cannot be both true and false at the same time. So the assumption we made that led to this absurd result, namely L, must necessarily be false, therefore ~L is true, which is what we wanted to prove. Thus,
Premise 1 L → W
Premise 2 ~W
Assume L
Then W would have to be true
But we already know ~W (that W is false), so if L then W and ~W, which is absurd,
Therefore, our assumption, L, could not be true, so:
Conclusion ~L (must be true)
Consider that we use this kind of reasoning, without even thinking about it, all the time. Thus, for example, if on a workday I am considering whether to go to the movies or go to work, I would presumably be able to acknowledge the premise, “If I go to the Movies, then I will get Fired from my job,” or “M → F.” But I also know that “I can’t afford to get fired” (since I want to pay the rent), so my second premise is “~F.” It should be pretty clear, therefore, that I can’t go to the movies—that “~M” must be true if my two premises are true. But to conclude this, I have to go back to the first premise, and assume “M,” to determine that that would result in “F,” which is an impossible result, since I already have acknowledged ~F―that I can’t afford to get fired. So in this everyday example, I am considering the logical consequences of what I suspect to be the wrong choice―to go to the movies, M― to follow it to its logical result, a result that leads to a further result, namely getting fired, which I must avoid. Thus I can conclude, indirectly, that the assumption that I suspected was wrong is indeed logically wrong.
The Terms of Anselm’s Proof of the Existence of God
With the basic logical tool of the indirect proof at our disposal we are now ready to consider the terms of Anselm’s proof, which he sets forth in Proslogion Chapter 2. Before we proceed, let us be reminded that, in the nearly 1000 years since he proposed it, many have been persuaded by Anselm’s proof of the existence of God, though many have not, and it remains, yet today, a subject of intense discussion and debate. Thus we cannot expect to be able to decide conclusively whether or not to accept this proof as valid. As suggested above, we need not be able to decide this to gain, from the consideration of this proof, in intellectual exercise as well as personal insight, but such gains come only if we keep our minds open to its reasoning and engage ourselves in it. We shall see that Anselm proposes an indirect proof, so he will start by assuming that God does not exist, but if that assumption—that God does not exist—leads to a contradiction—if it leads to an impossible result—then we will know that the non-existence of God is impossible and therefore that God must exist.
Anselm begins his proof by setting forth a basic premise about the matter at hand, namely that God must be “that than which nothing greater can be thought,” or “that than which a greater cannot be thought.” Note that these two phrases are in fact two ways of saying exactly the same thing; Anselm uses the first one at the beginning of his proof and the second when he concludes it. They mean exactly the same thing because the distinction between them consists merely of changing the location of the negating terms. In other words, each phrase contains a negation, “nothing” and “cannot,” respectively; and in both phrases, the same idea is expressed, but with different word order, namely that it is not possible to think of an entity greater than God―a greater thing cannot be thought, or no-thing greater can be thought. From here on, I shall be sticking to the second expression, “that than which a greater cannot be thought,” since that’s the one Anselm uses in the proof itself.
Anselm’s formulation of this description of God is concise, so let’s elaborate on its terms to make sure we see what it expresses and what it doesn’t. When Anselm begins the phrase with “that,” he means “that thing” or “that entity” or simply “a thing” or “something.” When he says, “than which,” he means “compared to which” or “relative to.” And when he says “a greater,” he means “a greater thing” or “something greater:” specifically, “greatness” as here intended refers not to the sort of comparisons we typically make of things we see and know according to the hierarchy “great, greater and greatest,” but must be understood rather to mean “most real” or having the most being, for indeed God is that being alone whose existence Anselm will claim to be necessary rather than contingent or merely possible. So we can now expand the phrase to say, God must be “some entity compared to which a greater thing cannot be thought,” or, to reorder it for even greater clarity, God is something such that, compared to God, we can’t even think of anything greater. Pause to consider this: when we think of God, whether we believe in “God” or not, by definition the word “God” is just the word we use to refer to what is omnipotent and omniscient and omnibenevolent―all powerful, all knowing, all good―and the ground and source of all reality and being, of all that is. Now of course it may be that no such thing exists, and that this idea, as noted above, is just a product of human fancy; but the idea of God, if it were to exist, at least is clear—even an atheist understands the intended meaning of the term “God.” This is where the fool, as he appears in Psalms 14 and 53, comes in: “The fool has said in his heart, ‘there is no God.’” The fool is precisely one who does not believe that God exists in reality; but even “the fool” can see that God, if God did exist, would be “that than which a greater cannot be thought.” The fool’s point, of course, is simply that this phrase, “that than which a greater cannot be thought,” does not refer to anything that exists in reality; rather, it is no more than an idea in his mind, but an idea of nothing or “no-thing” that really is; it is a real idea, even if it happens that the fool is correct that it is only an idea that does not refer to any real thing.
Consider again that Anselm does not actually say “the greatest,” which might imply that God is somehow cognizable in everyday, worldly terms of comparison (as reflected in the terms “great, greater and greatest”). We use the superlative term “greatest” all the time, if perhaps too loosely; thus we speak of “the greatest home run hitter,” which we measure as the player who has hit the most home runs, or “the greatest sprinter” as the runner who runs the fastest sprint. But the home run hitter and the sprinter are only marginally different or “greater” than their adversaries, who do very nearly the same thing as the greatest, simply not quite as well. And since “records are made to be broken,” we can be sure that today’s “greatest” will be replaced by one still “greater” at some point. But God, presumably, is not like this; rather, the idea of God is an idea of a thing that is utterly beyond human “greatness” to the point that we cannot comprehend God at all and the existence of Whom is certainly not obvious, which is why we’re struggling with this proof. Indeed, Anselm himself says this explicitly in Chapter 15 of the Proslogion, where he says, “God is greater than can be thought”; in other words, we cannot think God at all. All we can say is that God is greater than anything we ourselves could ever think; and that is exactly what Anselm’s phrase, “that than which a greater cannot be thought,” expresses. In other words, Anselm is not making the mistake of comparing God to us or to anything we could know by implying that God is just “the greatest” among the things of this world; nor is Anselm making the mistake of comparing us to God by saying that we could actually comprehend God, since our understanding of the phrase “that than which a greater cannot be thought” says no more than that we cannot think of God, or rather that anything we do think of cannot be greater than God, and that, moreover, no thought can ever surpass, or even reach, God.
But Then, Can We Talk of God at All?
But if God is utterly transcendent—that is, totally beyond us and beyond our comprehension or understanding such that we cannot know God at all—is there really any point in pursuing a proof of God’s existence, or are we just playing with words when we presume to speak of God? We shall be returning to this issue when we consider the objections to Anselm’s proof made by his contemporary, the monk Gaunilo, later in this chapter; but for now consider Chapter 7 of the Proslogion, where Anselm addresses an apparent paradox concerning God’s immortality. In this discussion we find ourselves able to speak meaningfully about something that, like God, is totally beyond our own experience. Anselm observes that it may be objected that if God is immortal, then this implies that God is incapable of dying and thus lacks “the power” to die; but this seems clearly to contradict the standard assumption that God is omnipotent―all powerful. Since we mortals, we might say, have the power to kill ourselves whereas God does not, then God lacks a power and so must not be omnipotent. Anselm’s response to this is simply that this argument fails to acknowledge that mortality is a weakness and an indication of a lack of power and so not a positive power in itself. For God to be all-powerful, God must indeed lack all weakness, but it is just this “lack” that makes God omnipotent; so this “lack” only appears to us—from our limited and mortal point of view, as if we are “looking through a glass, darkly”—to be a lack but is not truly a lack at all. In other words, our language and use of words makes God’s power appear to us as if it involves a lack of power, but that is not due to an actual lack of God but rather to a failure of our words to grasp God’s nature; indeed, this argument objecting to God’s nature is, ironically, an effort to dispute God’s existence by appealing to the nature of the thing that one wants to disprove! In any event, as Anselm is the first to acknowledge, our words are inadequate to comprehend God for the same reason that our thoughts are inadequate: God is beyond all words just as God is beyond all thought.
Moreover, our language, as Anselm points out, frequently uses negative formulations to express positive ideas and positive formulations to express negative ones. Thus we say “this man is sitting,” which sounds like the man is doing something when in fact he is not doing anything; or we might say “the man is not resting,” which means that he is doing something. More fundamentally, we use the term “infinite,” meaning the “not-finite,” which seems to imply that the infinite is the negative version of, or less than, the finite; in fact, of course, it is the other way around, as the infinite is utterly and totally greater than the finite even though the word used to express it is negative in form. The same applies to “immortal,” the non-mortal, as if one who cannot live forever is greater than one who does live forever. In cases like this, it is probable that our language has assigned the negative formulations to “infinite” and “immortal” simply because they are completely alien to us; yet, we can still understand their meaning.
So, admittedly, we have no personal experience of things like immortality, indeed we cannot even comprehend it except as negation of what we do experience and comprehend; however, we can reasonably discuss it and understand something about it, so there is every reason to hope that we might similarly be able to talk and reason about God. Obviously, just because we have not experienced something does not mean it doesn’t happen, just because we haven’t thought something doesn’t mean it isn’t true and just because something is utterly beyond even our ability to experience or think does not mean it isn’t real; moreover, as our discussion of the apparent paradox of God’s immortality should make clear to us, even if we cannot comprehend God or directly think God or know what God is, still we can speak rationally and meaningfully about matters pertaining to God. Thus, as in the case of the wrapped present, we might be able, as Anselm claims, to prove that God exists, even if we cannot understand anything about what God is.
This brings us to consider the premises of Anselm’s proof for the existence of God.
The Premises of the Proof
“The fool has said in his heart, ‘There is no God.’” But even the fool must acknowledge, and we must accept as a first premise, as noted above, that God, if God exists, must be “that than which a greater cannot be thought.” So even the fool understands this concept; it’s just that the fool doesn’t think the concept refers to anything real. In short, it is the fool’s position that God exists only in the understanding and not also in reality. Anselm uses a painter and her painting to explain the distinction between a concept that exists in our understanding and the real entity that the concept is a concept of; thus, the painter can have the idea of a painting in her head without there being an actual painting in reality. The painter may paint the painting in accordance with the concept she has in her mind, or she may not; in either case, there is no difficulty in seeing that there is a difference between the idea of the painting and the painting itself, and moreover, there is no difficulty in seeing that an idea of something can exist in our understanding that does not exist in reality. Anselm then introduces another premise: whatever painting there may be that exists in my understanding, surely the “real,” finished painting is greater, since the mere idea of a painting is really no painting at all. This is easy to understand in the case of a thing like a painting, or of any thing, for that matter: the real thing is surely greater than the mere thought of the thing. So, the premises of Anselm’s argument, in brief, are:
- 1) God, if God exists, must be “that than which a greater cannot be thought”;
- 2) Even the fool understands the meaning of this phrase, “that than which a greater cannot be thought,” so it exists in the fool’s understanding;
- 3) Since this phrase exists in the understanding, it can be thought to exist in reality as well;
- 4) A thing that exists in reality is greater than a thing that exists only in the understanding.
Now, to use the indirect proof we must assume the opposite of what we want to prove; therefore, we shall assume that the fool is right and that the idea, “that than which a greater cannot be thought,” exists only in the understanding but not in reality. What are the consequences of this assumption―what logically follows from it? Clearly there is no contradiction in thinking that a painting that exists in my understanding does not exist in reality; however, does the same hold here—is it possible that “that than which a greater cannot be thought” can exist only in the understanding, or does that assumption lead to a contradiction? If it leads to a contradiction, then we must conclude that the fool’s assumption that “that than which a greater cannot be thought” exists only in the understanding and not in reality must be false, meaning that it must be true that it does exist in reality.
The Proof
Anselm opens his proof by setting out his conclusion, claiming that “surely that than which a greater cannot be thought cannot exist only in the understanding,” which will mean that is must exist in reality. “For,” he argues,
if it exists only in the understanding, it can be thought to exist in reality as well, which is greater. So if that than which a greater cannot be thought exists only in the understanding, then that than which a greater cannot be thought is that than which a greater can be thought. But that is clearly impossible. Therefore there is no doubt that something than which a greater cannot be thought exists both in the understanding and in reality.
That this is an indirect proof is indicated when Anselm opens the proof with the statement, “if it exists only in the understanding,” for the “if” introduces an assumption, and that assumption is that the fool is right—that God exists only in the understanding and not also in reality, which is the opposite of what Anselm is out to prove. So now we turn to the necessary logical consequences of that assumption to determine if they lead to a contradiction, in which case we will know that the assumption must be false. First, “if it exists only in the understanding” then, like the painting, it can be thought to exist in reality as well. Next, to exist in reality is greater than to exist merely in the understanding alone; thus something that exists in the understanding alone must be something than which a greater can be thought, since we can think of a greater thing than that, namely the thing that exists also in reality. But wait! The thing we are thinking of is “that than which a greater cannot be thought,” so if we are assuming that that thing exists only in the understanding and not in reality and so is “that than which a greater can be thought,” then we have just caught ourselves thinking that “that than which a greater cannot be thought” is the same thing as “that than which a greater can be thought,” which is clearly a direct contradiction and so “clearly impossible.” Since we are forced into this impossible conclusion by assuming that “that than which a greater cannot be thought” exists only in the understanding and not in reality, this can only mean that our assumption was false; therefore, we must conclude that “that than which a greater cannot be thought” does exist in reality, and since it is only God, by definition, that can be “that than which a greater cannot be thought,” therefore God must exist.
It might help to simplify the proof by substituting X for the phrase “that than which a greater cannot be thought,” so let X = “that than which a greater cannot be thought.” Accordingly, the fool asserts, “X exists in my understanding but X does not exist in reality.” If this is true, then we know that we can think of an X that also exists in reality, which would be greater, and that would mean that X = “that than which a greater can be thought.” When we now recall what X stands for, we realize that we have just asserted that “that than which a greater cannot be thought” = “that than which a greater can be thought.” This is precisely the contradictory conclusion we saw above, and because, as a contradiction, it cannot be true, therefore the assumption on which it is based cannot be true. That assumption was that God (i.e. “that than which a greater cannot be thought”) does not exist in reality, so evidently that assumption must have been false, thus God must exist in reality.
Note, again, that the assumption that X does not exist in reality only leads to a contradiction when X is “that than which a greater cannot be thought.” As we saw above, there is no contradiction in thinking that a painting that exists in my understanding does not exist also in reality; however, when we are thinking of “that than which a greater cannot be thought,” that idea is a unique, one-of-a-kind idea that can only refer to God; therefore, it is only God’s existence that Anselm has proven, which indicates that it is only God’s existence that is necessary. Again, if I am thinking of a painting I have not yet painted, there is no contradiction in claiming that it doesn’t exist in reality since I haven’t painted it yet and I might never paint it—it is not necessary that it get painted but only possible. Any painting, or anything else that can be thought to exist, can also not exist; it is only God that cannot not exist because God, unlike any painting or any other thing, is the one and only thing “than which a greater cannot be thought.”
A Restatement of the Proof
We begin with two premises, that is, two propositions that, arguably, must be true, whether you believe in God or not; thus, as Anselm says, even the fool accepts these. Then the proof proceeds, indirectly, by assuming that God does not exist—that is, that the fool is right and that while the idea of God exists in the mind of the fool, God does not also exist in reality. Then the proof goes on to consider what this assumption that God exists merely in the understanding but not in reality must entail—that is, what must follow, logically, if our initial assumption is correct. If it turns out that our assumption that God exists only in the understanding but not in reality leads to a contradiction, then we will know that our assumption must itself have been impossible; in this case, since our assumption will be that God does not exist in reality, this would mean that we would be forced to conclude that God does exist in reality.
So, here are the two premises, which even staunch atheists like the fool cannot fail to accept. First, if God exists, then God must be “that than which a greater cannot be thought.” Second, to exist in reality as well as in the mind or understanding is greater than to exist merely in the mind or understanding. Now let’s assume the exact opposite of what we’re trying to prove—that God is merely an idea in the mind and does not exist in reality. In this case, then God clearly must be “that than which a greater can be thought,” because if God exists merely in the mind, then we can think of something greater, namely a God that would exist in reality as well. However, this statement that “God is that than which a greater can be thought” directly contradicts our premise, which even the fool acknowledges to be true, that God can only be “that than which a greater cannot be thought.” Thus our assumption that God “exists only in the understanding” but not in reality forces us into the absurd or impossible contradiction that “that than which a greater cannot be thought is that than which a greater can be thought,” so the assumption that God does not exist in reality must be false and thus the opposite of that assumption, that God does exist in reality, must be true.
Anselm’s Second Version of the Proof in Proslogion Chapter 3
In Proslogion Chapter 3 Anselm articulates a different formulation of the proof. Here he asserts, “that than which a greater cannot be thought” cannot even be thought not to exist:
For it is possible to think that something exists that cannot be thought not to exist, and such a being is greater than one that can be thought not to exist. Therefore, if that than which a greater cannot be thought can be thought not to exist, then that than which a greater cannot be thought is not that than which a greater cannot be thought; and this is a contradiction. So that than which a greater cannot be thought exists so truly that it cannot be thought not to exist.
In short, if the thing we are thinking of is “that than which a greater cannot be thought” and if it can be thought not to exist, then it is not “that than which a greater cannot be thought.” To repeat, letting X = “that than which a greater cannot be thought,” if X can be thought not to exist, then it is not as great as the thing that cannot be thought not to exists and so X is not “that than which a greater cannot be thought.” But wait! X is “that than which a greater cannot be thought, so we have just concluded that X is not X.
- 1) A thing that cannot be thought not to exist is greater than a thing that can be thought not to exist;
- 2) If “that than which a greater cannot be thought” can be thought not to exist, then “that than which a greater cannot be thought” is not “that than which a greater cannot be thought” (because, per premise 1, a thing that can be thought not to exist is not as great as a thing that cannot be thought not to exist, so it is not “that than which a greater cannot be thought”) ...
- 3) …which is absurd, so “that than which a greater cannot be thought” cannot even be thought not to exist.
Restatement of the Second Proof
This second proof rests on the same foundation as the first—that, believe in God or no, we can agree that the term “God” must refer to “that than which a greater cannot be thought.” The proof then begins with the premise that “it is possible to think that something exists that cannot be thought not to exist,” and it goes on to mirror the premises of the first proof by asserting that “such a being is greater than one that can be thought not to exist.” In other words, a thing that exists necessarily is greater than one that merely possibly exists—as in the case of immortality, that which is always and forever is greater than something that comes to be and passes away and might never be at all. Like the first proof, it does not assume, just because we can understand the concept of “something that cannot be thought not to exist,” that such a thing actually exists in reality; it assumes only that we can think this idea―we can understand the distinction between necessity and possibility—as the fool has in the understanding the idea of “that than which a greater cannot be thought.”
Now we proceed to the proof itself, using the same indirect method as in the first by assuming that God—that is, “that than which a greater cannot be thought”—can be thought not to exist. But if this assumption is true—that is, if God can be thought not to exist—then God is not that than which a greater cannot be thought, since a being that cannot be thought not to exist would clearly be greater. This would force us to conclude that “that than which a greater cannot be thought is not that than which a greater cannot be thought,” as if to say “a tree is not a tree,” or “God is not God,” which is obviously absurd. Therefore, the assumption that God can be thought not to exist must be false, so its opposite must be true, namely that God cannot be thought not to exist.
Premise 1: God is “that than which a greater cannot be thought.”
Premise 2: Something that cannot be thought not to exist would be greater than something that can be thought not to exist.
Assume that God can be thought not to exist;
Then God is not “that than which a greater cannot be thought,”
Which means “that than which a greater cannot be thought is not that than which a greater cannot be thought,” which is absurd,
Thus the assumption that God can be thought not to exist must be false,
So it must be true that God cannot be thought not to exist.
The Objections of Gaunilo and Anselm’s Replies
In brief, for both of Anselm’s proofs, if you really focus on the meaning of “that than which a greater cannot be thought,” you cannot fail to conclude that this unique thing—this one-of-a-kind being to which this phrase refers—cannot not exist, and cannot even be thought not to exist (as long as you are really thinking it and not something else). However, following the writing of Anselm’s Proslogion, a fellow monk named Gaunilo composed a series of objections. Gaunilo was clearly no fool, and he did himself believe in God; however, he asserted that Anselm’s purported proof of God did not actually succeed and he detailed his objections, to which Anselm then replied. Though Gaunilo’s articulation of his objections makes it difficult to distinguish one from another, I see in his text five specific objections to which, in Anselm’s own texts, we can also discern the replies.
First, Gaunilo argues that I can “have in my understanding any number of false things that have no real existence at all in themselves.” By this observation he intends to contradict Anselm’s claim that, because I have God, or “that than which a greater cannot be thought,” in my understanding, this means that God must exist in reality as well; in other words, just because I am thinking something doesn’t mean that it exists. Anselm’s reply to this objection can be seen in Proslogion Chapter 4, where Anselm says,
In one sense of the word, to think a thing is to think the word that signifies that thing. But in another sense, it is to understand what exactly the thing is. God can be thought not to exist in the first sense, but not at all in the second sense. No one who understands what God is can understand that God does not exist, although he may say these words in his heart with no signification at all….
In other words, one can “think” a false thing only if one does not truly understand what that false thing must be. Thus one could “think” the words 2+3=6, but only as long as one did not think of what that “thought” truly signifies, that is, the actual meaning of what that “thought” truly stands for. In other words, “to think” that 2+3=6 is not truly to think at all, or not to think clearly or rationally or consciously: this sort of false thinking is simply an ill-founded belief. With respect to God, according to Anselm’s proof, if one really thinks about what God signifies, namely “that than which a greater cannot be thought,” and further if one thinks through what that implies, as Anselm does in his proof, then one cannot help but understand that “that than which a greater cannot be thought” must necessarily exist and cannot even be thought not to exist, for to think otherwise would lead to clear contradictions, as indicated by Anselm’s proofs. Note that the whole strength of Anselm’s proof is precisely that it does not apply to just anything (e.g. the painting), but only to that one thing—“that than which a greater cannot be thought.”
Gaunilo’s second objection to Anselm’s proof is that the painter’s painting is not a good analogy for God, since the idea of the painting in the painter’s understanding is a living part of the soul of the painter, a part of the painter’s intelligence, whereas the idea of God in the understanding represents something utterly distinct from the intelligence of the thinker. This is probably the weakest of Gaunilo’s objections, however, as it seems clearly to miss the point of the painter example, as Anselm himself points out. Anselm does not intend the painting as an analogy for God, for that would indeed be inadequate; rather, Anselm’s painting example serves the very limited function of establishing that the fool could be thinking of the idea of God (in his understanding) while at the same time failing to think of the existence of God—“thinking,” that is, of the word but not thinking through the full meaning and consequences of his own idea, the very idea of God that he himself acknowledges having.
Third, Gaunilo claims, in essence, that God is simply beyond our comprehension, thus we cannot reasonably claim to know enough about God to be able to establish the monumental fact of God’s existence. More specifically, Gaunilo argues that my knowledge of a thing can only be based on my comparison of it to other things like it. Thus, for example, I could form some knowledge of a stranger whom I have not previously known at all because I do have knowledge of other men, and so there is something to base my knowledge of the stranger on. God, however, is, by definition, entirely unlike any other thing and therefore cannot be compared to anything else I know and so cannot be known in Itself. To this Anselm replies that there are things that are themselves beyond the immediate grasp of my comprehension, which I can nevertheless know by comparison with things that are within my grasp. Thus, for example, I can clearly understand, while a thing that has a beginning and an end might be good, that a thing that has a beginning and no end is greater, and a thing that has no beginning and no end would be greater still; and I can understand these things despite the fact that my entire knowledge and experience are limited to things that do have a beginning and an end. Isn’t this, asks Anselm rhetorically, “an example of inferring that than which a greater cannot be thought on the basis of those things than which a greater can be thought”? So of course “that than which a greater cannot be thought,” that is God, is indeed beyond our comprehension, in Itself; nevertheless, we can grasp the relative greatness of God on the basis of things we can comprehend, and it is precisely on the relative greatness of God that the proof of God’s existence is based. This argument of Anselm’s recalls his discussion of immortality, which we discover we can know something about―namely, that it must be greater than mortality―even if we can not have any direct experience of immortality itself. In a similar vein, Anselm argues that “that than which a greater cannot be thought cannot be thought of as beginning to exist,” since clearly a thing that can begin is merely possible and not as great as a necessary being. By contrast, “whatever can be thought to exist, but does not in fact exist, can be thought of as beginning to exist”; that is, any possible being that does not now exist can at some time begin to exist. Thus, he can conclude, if that than which a greater cannot be thought “can be so much as thought to exist, it must necessarily exist,” for if we are truly thinking “that than which a greater cannot be thought,” then we can only be thinking of a thing that exists necessarily, that is, a thing that cannot not exist, a thing that can have no beginning or end.
Fourth, when I think of “God,” says Gaunilo, “I can think of God only on the basis of the word.” In other words, Gaunilo is arguing, in essence, that the word “God” is to human understanding merely a word, an empty abstraction, we might say, about which we can know nothing. This again is another version of the idea that God is so utterly beyond human comprehension as to render rational comprehension of God’s existence impossible: this amounts to the argument that we can “know” God only be faith and not be reason. This general line of argument is certainly reasonable, and Gaunilo may of course be correct; indeed, this is the line of argument that Thomas Aquinas will take when he refutes Anselm’s approach to proving God’s existence. However, to this line of argument Anselm poses the example of the sun (clearly echoing Plato and Augustine). Anselm points out that we cannot look at the sun, as to do so would blind us; indeed, though the sun is the source of our ability to see at all, ironically it is impossible for us to look at and see it in itself. However, argues Anselm, though the sun does evidently exceed, to the point of blinding us, our limited power of vision, nonetheless we can at least know that the sun exists, since without the sun we could see nothing else, and we see indirect proof of the sun’s existence in everything we do see. Thus, analogously, though God does evidently exceed our limited power of comprehension, nonetheless we can at least know that God exists even if we can comprehend nothing about God’s nature, just as we can know that the sun exists even if we cannot look at it. So God’s ways are unfathomable, but that there is some unfathomable way, suggests Anselm, can be known to us, in fact we cannot fail to know it if we think of it aright.
Finally, Gaunilo raises the now-famous objection of the “Lost Island.” If Anselm’s proof is valid, suggests Gaunilo, wouldn’t the same logic apply also to “the most perfect island” one could think of? Specifically, Gaunilo argues that we could have in our understanding an island more excellent than any other; thus, since this most excellent island would be more excellent if it were to exist in reality than not, then it must exist in reality, for if it were not to exist in reality then it would not be the most excellent. This argument is clearly a parody of Anselm’s argument, but it may at first seem to be a highly relevant and effective parody, for obviously it is absurd to think that the “most excellent” of anything must necessarily exist just because we can think of the most excellent of anything. What Gaunilo overlooks, however, as we have noted on several occasions above, is that neither the Lost Island, nor anything else in the universe, is remotely analogous to the utterly unique concept of God—“that than which a greater cannot be thought.” Gaunilo is obviously completely correct to observe that the argument he makes about the Lost Island is absurd; however, Anselm’s argument for the existence of God cannot be applied to “the most excellent” of just anything, or “the greatest of” just anything, because this idea of God, and our understanding of “that than which a greater cannot be thought,” can apply to one thing and one thing only. The very terms of the phrase, “that than which a greater cannot be thought,” already imply that there is only one thing to which this can apply, for if there are even two things that are somehow equal in being greater than everything else that could be thought, still neither of these would in fact be “that than which a greater cannot be thought” since the two of them together would be greater than either of them individually, and even the two of them together would arguably not be “that than which a greater cannot be thought” since a thing that possesses its complete unity and integrity within itself, and thus that is not composed of distinct and separable parts, would presumably be greater than the two-part thing.
This, then, brings to a fitting conclusion our consideration of Anselm’s proof, for this proof uncompromisingly comprehends the total and complete uniqueness that God must, if God exists, possess. Anselm’s God cannot be compared to anything else, God cannot be comprehended by human beings and God’s ways must remain an unfathomable mystery to us. But we might just as well say the same of the first origin of the universe, if the Big Bang theory is correct, since there cannot be any way that science can observe and thus know anything in the total absence of space-time, which must have been absent “prior to” the Big Bang, though it is hardly conceivable that anything can be “prior to” anything else in the total absence of time, or that anything could have begun moving in the total absence of space.
And yet, it is; and this is all that Anselm claims of God.
Conclusion
Let us not make the mistake of concluding that we have thus conclusively established that God exists, although Anselm seems convinced that we have. To be fair and reasonable, we might have proven it, and in any event God might exist, whether by the terms of this proof or otherwise; but we must also acknowledge that we might not have proven that God exists, indeed God might not exist.
We might well wonder again what the point of this has been: have we simply been playing with words? As I have suggested, I think there’s more to it than that. The words we’ve been using, notably Anselm’s characterization of God as “that than which a greater cannot be thought,” are meaningful, they make sense, even if they don’t refer to anything we can see or touch, or that exists at all. As we have seen, we often think of things that don’t exist or might not exist or even things that cannot exist: imaginary numbers, for example, such as the square root of a negative number, are not real in any ordinary sense, and are essentially or at least practically impossible, yet they can be thought and even have concrete, and vital, mathematical and scientific applications. Moreover, there may very well be some reality, at the heart of the universe, “than which a greater cannot be thought.” We know beyond reasonable doubt that the universe holds secrets greater than anything we can presently think, some of which seem clearly to be contrary to anything we have ever known in the past. Moreover, as previously suggested, if time and space were non-existent prior to the Big Bang, we may be forced to conclude that the answer to what preceded it is something beyond which we cannot think, and that is very close to Anselm’s own conception of God. Then again, maybe that is just another mystery greater than which we cannot think yet. Who knows? But simply what we have already been forced to think, in the consideration of Anselm’s proofs, has gotten us to think beyond anything we have been thinking up until now, hasn’t it? For this we can be grateful, and we can thus acknowledge that it has all been worth something, even if we are not quite sure what.
No comments:
Post a Comment