Notebook 1 — The Ontological Argument

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This is an English translation (via GPT-5.4) of “מחברת 1 – הראיה האונטולוגית“. Read the original Hebrew version. Download original Word file.

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Page, with God’s help

The Ontological Argument – A Systematic Analysis

Michael Abraham

Chapter 2: Therefore, Lord our God, you who grant understanding to faith, grant me, insofar as you find me worthy of it, to understand that you exist as we believe, and that you are such as we believe. And indeed we believe that you are something greater than which cannot be conceived. Or perhaps no such nature exists, since "the fool has said in his heart, There is no God"? Yet surely that very fool, when he hears what I have said—namely, "something greater than which cannot be conceived"—understands what he hears; and what he understands is in his mind, even if he does not understand that this thing exists (in reality). For it is one thing for a thing to be in the mind, and another to understand that the thing exists. When a painter first thinks out in advance what he is going to create, that thing exists in his mind; but he does not yet think of it as something real, for he has not yet made it. But after he has painted it, that thing both exists in his mind and he also understands that it exists (in reality), since he has made it. The fool, then, must also be convinced that at least in the mind there is something greater than which cannot be conceived, because he understands this when he hears it, and whatever is understood is in the mind. But that which is greater than which cannot be conceived certainly cannot be in the mind alone. For in truth, if it were in the mind alone, it could be conceived as existing in reality as well, and that is greater. Therefore, if that being greater than which cannot be conceived exists only in the mind, then that being greater than which cannot be conceived is a being than which something greater can be conceived. But this surely cannot be. There exists, therefore, beyond doubt, something greater than which cannot be conceived, and it exists both in the mind and in reality.

Chapter 3: And this exists so truly that it cannot at all be conceived not to exist. For one can conceive a being that cannot be conceived not to exist; and such a being is greater than one that can be conceived not to exist. Therefore, if that being greater than which cannot be conceived can be conceived not to exist, then that very being greater than which cannot be conceived is not the being greater than which cannot be conceived; and this is a contradiction. There truly exists, therefore, something greater than which cannot be conceived; and to such a degree that it cannot even be conceived not to exist.

And you, Lord our God, are such a being. You exist so truly that you cannot at all be conceived not to exist, and rightly so. For if any intelligent mind could think of something better than you, the creature would rise above the Creator and would judge Him; and this is utterly absurd. Indeed, everything besides you can be conceived not to exist; you alone, therefore, uniquely among all things, possess being in absolute truth and to the greatest degree. For no other thing exists with the same degree of truth, and therefore each exists to a lesser degree. Why, then, did the fool say in his heart, There is no God, when it is so clear to every understanding and rational mind that you are the being of highest degree? Did he not say it only because he was foolish and base?

Chapter 4: But how can the fool say in his heart what he cannot conceive? Or how can he not conceive what he said in his heart, when "to say in the heart" and "to conceive" are one and the same? If he truly conceived it—or rather, precisely because he truly conceived it, since he said it in his heart—and yet did not say it in his heart, since he could not conceive it: this is because a thing may be said in the heart or conceived in more than one way. For it is one thing to conceive something when one conceives the word that signifies that thing, and another when one understands that thing itself. Thus, in the first way one can conceive that God does not exist; but in the second way this is impossible. For no one who understands what God is can also conceive that God does not exist—and this even if he says these words in his heart, whether he gives them no meaning at all, or gives them a meaning foreign to them. Indeed, God is that than which nothing greater can be conceived. And whoever properly understands this also understands that God is such that there is no possibility whatsoever of conceiving Him not to exist. Therefore, one who understands that this is what God is also cannot conceive that He does not exist.

I thank you, good Lord, I thank you; for what I first believed by your gift, I now understand by your illumination: even if I had not wished to believe that you exist, it would not have been in my power not to understand it.

(Anselm of Canterbury, Proslogion, Chapters 2–4)^[1]

Contents

Part One: Introduction and Background

Chapter 1: The ontological argument among the proofs for the existence of God

Chapter 2: On rationalism: the emptiness of the analytic and ontological arguments

Chapter 3: The structure of Anselm’s argument and our notebook

Part Two: Proslogion Chapter 2

Chapter 4: The meaning of the opening prayer

Chapter 5: Defining the concept of God

Chapter 6: The dilemma

Chapter 7: The body of the argument

Part Three: Proslogion Chapter 3

Chapter 8: Between ontic necessity and epistemic necessity

Chapter 9: The proof of the necessity of His existence

Chapter 10: A theological pause

Part Four: Proslogion Chapter 4

Chapter 11: The question: another look at the emptiness of the analytic

Chapter 12: The solution: two kinds of conceiving

Chapter 13: Simple faith and arguments with straw men

Part Five: Critiques and Discussion

Chapter 14: The Kantian critique: facts cannot be derived from pure logic

Chapter 15: Can one conceive as existing a being that does not exist: on skepticism

Chapter 16: Assumptions in the ontological argument: existence as a predicate

Chapter 17: Assumptions in the ontological argument: coherence of the concepts

Chapter 18: Gaunilo on the existing lost island

Chapter 19: Between thought and understanding, and conceiving

Part One

Introduction and Background

The ontological argument among the proofs for the existence of God

Introduction

The Christian scholar Anselm of Canterbury, a man of the eleventh century, was a highly influential philosopher and theologian in the Middle Ages. In one of his books, Proslogion (in Latin, Proslogium, a discourse on the existence of God), he presents the first formulation of what later came to be called the ontological argument. Throughout history this argument received extensive treatment and was even reformulated in a number of additional versions, some of them somewhat different. Thomas Aquinas first challenged it, and in doing so caused it to recede from philosophical discourse. Later it reawakened in Descartes, who gave it a new form in his Meditations; Spinoza used it, Leibniz proposed a corrected proof, and so on. It also received quite a few critiques. The earliest of them already appeared in Anselm’s own lifetime (such as the well-known critique of the monk Gaunilo), and later Aquinas as well. Kant purported to refute it once and for all, but Hegel strongly argued for its validity, and thereafter the philosophical world’s engagement with the ontological argument was divided between followers of Kant and followers of Hegel. The lively discussion of it continues to this day, as Malcolm and after him Plantinga proposed improved formulations, and even the famous logician Kurt Gödel offered his own (modal) version. Most philosophers and logicians hold that the argument is invalid, but some of the most important among them disagree. In any case, that proves that Kant probably did not entirely succeed in his attacks.

Among those who do not engage in philosophy, many tend to mock it and/or parts of it, and see it as a ridiculous and absurd argument. Precisely for that reason, I will say at the outset that in my view this text is one of the exemplary texts in the history of philosophy, and it is exceptional in its precision and systematic structure. As Bertrand Russell said of it (an important British mathematician and philosopher of the twentieth century, who was also a proud atheist), it is much easier to say that the ontological argument is wrong than to put one’s finger on the error itself. Reading the argument does indeed create the sense that something here is not logical, yet, as noted, it is difficult to identify where the defect lies. Perhaps for that reason many prefer to mock it and raise flimsy objections that upon closer inspection turn out to be baseless. This does not necessarily mean that the ontological argument is valid. My point here is only that it is worth careful and deep study before forming a view about it, and that is what I will try to do here.^[2]

Types of proofs for the existence of God^[3]

Kant, in his great book Critique of Pure Reason, divided the proofs for the existence of God into three kinds: the ontological proof, the cosmological proof, and the physico-theological proof. An ontological proof is a proof based on a purely logical argument, without assuming any factual premise. The next two kinds consist of proofs based on arguments whose foundations include some factual premises.

Beyond these three kinds of argument, there are other ways of arriving at belief. Some see it as a simple intuition that requires no proof—something like an axiom. Others arrive at God on the basis of the moral argument (also presented by Kant, in another of his books). Others arrive there through tradition, which transmits to us information about God’s revelation to our forefathers or to some previous generation. As we continue, we will see that each such argument assumes a different definition of the concept of God.

In the next paragraph we will sharpen the difference between the three kinds of argument in Kant’s classification.

On rationalism: the emptiness of the analytic and ontological arguments

Three kinds of logical argument

An ordinary logical argument assumes certain premises and infers from them a conclusion or conclusions. Such an argument can be challenged in one of two ways: either by showing that one of its premises is false or unnecessary, or by showing why the argument is invalid—that is, why the derivation of the conclusion from the premises was not done properly (the conclusion does not necessarily follow from the premises). A pure logical argument, by contrast, is an argument that derives its conclusion solely from definitions and assumptions.

The existence of such arguments is not surprising, because all of mathematics is essentially a collection of such arguments. One begins with certain definitions, together with a set of concepts that satisfy certain conditions (axioms, or assumptions), and by means of various logical tools derives conclusions from them (propositions, theorems). Since the basis of the arguments (the proofs) consists only of definitions and abstract requirements, the conclusions (the propositions) are also not factual in character. Mathematics makes no claim about the world. It deals with an abstract Platonic world created by the axioms and definitions. Thus, for example, the well-known result of Euclidean plane geometry—that the sum of the angles in a triangle is 180 degrees—says nothing about the world. Its only meaning is that if there is a system that satisfies the basic assumptions and defines the concepts (triangle, line, point, angle, and the like) accordingly, then it must conclude that the sum of the angles in a triangle is 180 degrees. The question whether this proposition holds in the world around us is a question in physics, not in mathematics. Indeed, after Einstein we already know that the answer is negative. Our world is not Euclidean (flat), that is, it does not satisfy the requirements of Euclidean geometry, and therefore the sum of its angles is not exactly 180 degrees. This does not, of course, refute the geometry. Its result is not subject to falsification, since it speaks about a Platonic world and not necessarily about our world. Applications—to our world or any other world—concern facts, and as such they do not belong to mathematics but to observational science. In contemporary mathematical language, one may say that Euclid proposed a mathematical theory, and the question whether it is applicable in our world is a physical question: whether our world is a "model" of Euclidean theory. A model is some context in which the assumptions of the theory are satisfied; and if they are satisfied, then one may infer that its conclusions are satisfied there as well. The question whether our world is a model of Euclidean theory—that is, whether it satisfies its assumptions—is a scientific-empirical question, not a mathematical one. Indeed, there are formulations of Euclidean geometry that include no drawings at all (even in the ordinary formulations drawings are used only for illustration), and the basic concepts (line, point, triangle, angle, and the like) are given abstract definitions in place of their usual visual meaning (we can now understand that that familiar meaning is merely one model of the theory). From those formulations one can see that what is involved is merely the manipulation of relations among concepts, definitions, and assumptions—and nothing more. Certainly not factual claims about the world.

In contrast to those two kinds of argument, the ordinary logical and the mathematical, our concern here is with an argument of a far more surprising character, almost like hocus-pocus, which we shall call a pure logical argument: such an argument derives a factual conclusion (unlike mathematics) from an argument whose basis contains no factual assumption whatsoever. We put nothing factual into it, yet out of it there comes, as if from nothing, a result that is a factual claim about the world. This is perhaps the chief source of the discomfort described above, and for many critics of the ontological argument it is itself the central critical argument against it.

Philosophical context: rationalism and empiricism^[4]

To understand this better, we must discuss this phenomenon within the rationalist-empiricist debate that runs through the history of philosophy from its beginning until today. Philosophical rationalism is willing to accept claims that say something factual about the world even if they arise from thought alone (without observation). Thought is regarded by rationalists as a tool for knowing the world. Therefore, for the rationalist there is no principled problem in what we above called a pure logical or philosophical argument, since in principle a logical argument based only on thought (without facts) can end in a factual conclusion. Empiricism, by contrast, denies the very possibility of such arguments. According to it, facts are learned only from observation. Therefore, if any logical argument yields a factual claim about the world, then necessarily at least some of its premises are factual-observational in character. Facts cannot emerge from pure thought alone. The empiricist holds that knowledge of the world requires observation; pure thought is not enough. The fact that we think in a certain way is the result of the structure of our thought, which is arbitrary and contingent. Therefore it may perhaps tell us something about ourselves, but in no way about the world outside us.

In this context, the ontological argument, like Descartes’ cogito argument, attempts to do the impossible: to derive a fact from a purely logical process of thought (without observation), and in essence to demonstrate the possibility of philosophical rationalism.^[5] Anselm, like Descartes after him, was a rationalist, and their arguments do not merely try to prove the existence of God but in fact to refute empiricism.^[6]

It is important to understand, as Kant explained היטב, that there is an inherent problem in an ontological proof, as in rationalism generally. It is not plausible that one can derive any conclusion about the world without observing it, merely from the fact that we think some thought. Why should our thought itself (without any observation) be able to bring us to any factual knowledge whatsoever? On its face this sounds untenable. This is Kant’s main claim against this proof, and in essence it is the core of the empiricist outlook. Admittedly, David Hume already showed that pure empiricism is a fiction. Laws of nature, which are factual generalizations (that is, general claims about the world), never emerge from direct observation.^[7]

We will discuss Kant’s critique in detail in the third part of the notebook, in Chapter 8.

The structure of Anselm’s argument and our notebook

The relation among the three chapters

Interpreters and critics of Anselm are divided over the relation among these three chapters. Some see the three chapters as repeating the same argument in different forms. Others see three different arguments here, each meant to prove the same conclusion (the existence of God). We will later see that both groups are mistaken. It is quite clear that the three chapters continue one another and form one long line of argument. The overall argument has a circular structure in a certain sense, since at the end Anselm returns and examines his point of departure. But as we shall see, it is not really circular. The first chapter (Chapter 2) proves the existence of God. The second (Chapter 3) proves that His existence is necessary, and in fact examines the meaning of the ontological character of the argument. And the third chapter deals with a question that follows from what was proved in Chapter 2: if the existence of God is indeed logically necessary, how could the fool say that there is no God—that is, how can there be denial of an argument whose conclusion is necessary.

The structure of the notebook

In this notebook I will try to offer a systematic analysis of the formulation of the argument from Chapter 2 of the Proslogion,^[8] and to indicate the role of each sentence in Anselm’s text. After that I will examine the remaining chapters and the role of each of them in the overall logical course. At the end I will discuss various critiques of Anselm’s argument, and I will try to reach a conclusion as to whether this argument is valid or not, and what its philosophical meaning is (whether a fact can indeed be proved on a purely logical basis) and its theological meaning (whether it has been proved here that God exists or not, and for whom the proof is valid and acceptable).

Part Two

Proslogion Chapter 2

The meaning of the opening prayer

The opening prayer and the difficulties it raises

Chapter 2 of the Proslogion opens with a sentence of prayer, which Anselm addresses to his God (whose existence he intends to prove immediately afterward):

Therefore, Lord our God, you who grant understanding to faith, grant me, insofar as you find me worthy of it, to understand that you exist as we believe, and that you are such as we believe.

This is one of the most disparaged passages in Anselm’s formulation of the argument. Many claim that what we have here is begging the question, since Anselm does not come to the discussion with clean hands. He already believes before he has found the proof, and perhaps even places his belief at the base of the discussion.

It is important to understand that this prayer is not part of the argumentative move, and therefore to see in it a case of begging the question is simply foolishness. A person can present a logical argument in favor of a certain conclusion even after he already believes the conclusion to be true. Thus, for example, hundreds of years after Fermat left us his opaque conjecture together with the declaration that he had a simple proof of it, while throughout that whole time many mathematicians who tried to find a counterexample failed, the mathematical world treated this claim as true even if unproved. Nearly two hundred years after this conjecture was formulated and regarded by many as true, the American mathematician Andrew Wiles came and proved it. Did he believe it beforehand? I do not know, but it is very likely that he did. Had he not believed it, he would not have invested years of his life in proving it. Intelligent people do not invest many years of their lives, and risk their entire career, in order to try to prove a claim for which they have no good indication that it is true. We may now ask ourselves whether Wiles came to the discussion with clean hands. Even if he believed the claim before the proof, the answer is yes. The fact that he believed Fermat’s claim to be true does not invalidate his proof. To invalidate the proof, one must point to a flaw in the proof procedure itself (in one of the two ways we described in the introduction). Of course, if one assumes Fermat’s conjecture itself within the logical procedure, that would indeed be a defect in the proof. The same applies to Anselm and his argument.

But beyond all this, even in the eyes of his sharpest critics, Anselm was certainly far from a fool. Why did he place this prayer at the beginning of the argument? Did he not understand that when he addresses an atheist and tries to persuade him of the existence of God, he cannot begin with a prayer? He surely could have foreseen that this prayer would be a stumbling block to the success of his argument.

Moreover, Anselm did not share with us the rest of his daily schedule before arriving at the ontological argument. He did not describe the fact that he ate breakfast or brushed his teeth, nor what he was wearing and other prosaic details. So why did he find it necessary to tell us about the prayer he offered before he found the proof? It is highly likely that this prayer has a role in the proof itself, and that is why it was placed there. We have seen that the prayer cannot be part of the argument, and indeed it is not. So what is its role? Why does Anselm place it at the beginning of his remarks?

Before answering that, we should note another point. It is reasonable to assume that this argument was not formulated within one span of time, such as a single morning, and therefore one cannot really read the text here as a factual sequence of events: prayer and then discovery of the proof. It is quite clear that the prayer was formulated as part of the literary composition that presents the proof, and is not merely a description of Anselm’s daily schedule. Moreover, it is highly likely that this prayer was uttered at the time these words were composed and written down, not at the time he found the proof itself. That is, Anselm composed this prayer as the opening of his work after he had already reached the conclusion that God exists (perhaps by means of this very argument). This means that the claim against him—that he believes before proving that God exists—is not necessary even on the factual plane. The prayer was apparently composed after he found the proof (and before he sat down to write it), and was placed here at the beginning for some reason. We must now examine its role: why is it located here?

Introduction to ontological proofs: the emptiness of the analytic

Here we will try to show that the prayer comes to place the argument in its proper context. It comes to explain to us the meaning of ontological proofs in general. Anselm keenly sensed the reactions likely to arise from reading his words—that is, the discomfort all of us will feel when we encounter an argument that derives a factual conclusion from a purely logical argument. To deal with this, he prefaces his argument with the prayer.

In philosophy one commonly speaks of "the emptiness of the analytic," that is, the informational emptiness of valid logical arguments.^[9] When we take two premises and infer from them a conclusion, the conclusion contains no information beyond what was already latent in the premises (this is the logical core of the Kantian critique of the ontological argument already mentioned above). Let us take, for example, the following argument: if all tables have four legs, and the object before me is a table, then this object has four legs. Why is this argument necessary? Why must anyone who accepts its premises also accept its conclusion? Because the information appearing in the conclusion was already hidden in the premises. The argument merely exposes and sharpens it; it brings it out into the open. When we assumed that all tables have four legs, and assumed that this object is one of them, we had already implicitly assumed that it has four legs. The validity of a logical argument stems from the fact that it is empty. It never adds information beyond what is in the premises. Therefore, anyone who accepts the premises (and only he) must also accept the conclusion, since it is contained in the premises and never contains information beyond what is latent in them.

In his prayer, Anselm is basically telling us that the ontological argument, precisely by virtue of being an a priori logical argument (not based on facts), addresses only believers. Therefore, when he sets out to seek such a proof, he opens with a prayer to that very God, since belief in Him is the point of departure of the argument (even if not part of it as such). If we return for a moment to the example of the tables above, someone who does not accept the conclusion that the object before him is a table with four legs will surely dispute the premise that all tables have four legs (for in his view there is at least one that does not). Thus this logical argument addresses only those who accept its premises, and as noted, the conclusion is included in those premises. A logical argument addresses only those who already accept its conclusion.

This sounds absurd. If every logical argument addresses those who accept its conclusion a priori, why formulate arguments at all? But this is a difficulty about logic in general, not something specific to the ontological argument. It is not clear why logical arguments are needed at all, or what use we make of them.

The transition from belief to understanding

To understand this, let us return to the example of geometry. We saw that Euclidean geometry, like every area of mathematics, begins with a set of definitions and basic assumptions and proves on their basis a set of theorems (propositions, or conclusions). As we have now seen, if this is a mathematical proof, that means the conclusion was hidden in some way within the premises. So why are geometry lessons needed, if the conclusions are already known to students before the study begins? An intelligent sixth-grade child knows and understands the axioms of geometry quite well (that only one straight line passes between two points, that two parallels do not meet, and so on), yet it is hard to believe that an intelligent sixth-grade child knows that the sum of the angles in a triangle is 180 degrees, or knows the Pythagorean theorem. Those theorems are present in some abstract way within the axioms that he understands, and yet he still does not know them. One may say that classroom study helps the student draw this information out from within. It is indeed there, but hidden and inaccessible. Study and proofs help the student extract more and more information that is already hidden in the premises he understands and knows. Anyone who has ever struggled over a geometry problem knows that even though he has learned and knows all the relevant theorems, he does not necessarily succeed in solving the exercise. The reason is not a lack of information, but imperfect skill in extracting from within himself the information latent in what is already accessibly known to him (the axioms, the rules of inference, and the theorems).

If so, when a proof is presented to us, its role is not to provide us with new information. A valid logical argument, or proof, can at most expose to us information that is hidden within us but inaccessible to us without the aid of proof and logic. When a proof is presented to us—that is, a valid logical argument—there are only three possibilities before us: (a) reject one of the premises; (b) point to a flaw in the logical procedure that derives the conclusion from the premises; (c) accept the conclusion and understand that we had been inconsistent (we accepted the premises and rejected the conclusion, and we discover that this is inconsistent).

The same holds with regard to belief. A proof of the existence of God cannot turn a genuine atheist into a believer. One who does not have this information within him will never accept the proof, for if he disputes the conclusion he probably will not accept some of the premises (as in the example of the tables above). If he agrees to all the premises and agrees that the argument is valid, then willy-nilly he must accept the conclusion and understand that until now he had been inconsistent. The purpose of an ontological proof is to help one who does in fact believe implicitly—that is, who assumes premises within which the belief that God exists is hidden—to extract this information from them (or to remove an inconsistency within himself). Exactly as we saw in the example of geometry. Logic cannot add to me information that is essentially absent from me, but it is not valueless. It can help me notice information that is within me but inaccessible to me. We have learned, then, that in his prayer Anselm explains that the path to a valid logical proof of the existence of God begins with belief. But not in a banal way—that is, not by taking the existence of God as a premise in the argument. That would make it banal and worthless. The goal of the proof is to take a person who believes implicitly, but has not yet given himself an account of why, and has not grounded his belief in rational arguments, to a state in which belief in God becomes understanding that there is a God.

This is the meaning of the shift in the language of the prayer (a shift that will also appear later in Anselm’s words), between understanding and faith. God is described there as the one "who grants understanding to faith," meaning that His role is to help us turn faith into understanding—into something intelligible and rational. Therefore Anselm asks Him to turn his faith into understanding: "Grant me, insofar as you find me worthy of it, to understand that you exist as we believe." The purpose of the prayer is to explain the meaning of the logical move: not to generate belief in the hearts of atheists, but to turn belief—which seems like something implicit and subjective within a person—into understanding, that is, into something intelligible, explicit, and accessible, objectively, to all.

To conclude, it is important to understand that up to now we have spoken about ordinary logical arguments, which are based on facts (like the cosmological and physico-theological arguments). But we have already seen that the ontological argument is a pure logical argument. That is, it derives a factual claim from nonfactual premises, that is, from logic and definitions alone. If so, here we are taking a step further. If in an ordinary logical argument disagreement with the conclusion means there is some disagreement about the premises, then here there are no factual premises, and therefore it seems there are no premises one could refuse to accept. The conclusion is that if this is indeed a valid argument, only one of two paths is open to us: either point to a logical flaw—that is, show that the conclusion does not follow from the premises—or accept the conclusion. Here there is no possibility of refusing the premises, because they are only definitions and not factual claims. This is the power of rationalism (which derives facts from purely logical arguments), and it is also what arouses resistance to it. We will return to this point below.

Defining the concept of "God"

Another duplication in the wording of the prayer: "exists" and "such"

We will open this chapter with a discussion of a duplication in the sentence that concludes the prayer. God is asked to help us understand "that He exists as we believe" and "that He is such as we believe." What is the difference between the two? We have explained the first. This is the transition from belief to our understanding of God. The second element that appears here is the link to the next sentence in the text: the definition. Here Anselm is telling us that the definition, too, comes out of faith. This is another role of faith in the course of the argument, and of course another explanation for the appearance of the prayer at its beginning. We have already seen that the prayer teaches us that the proof addresses only believers. The request that He show us that He is "such as we believe" means that faith is also the source of the definition of the concept "God" that is about to be discussed.

What does this mean? Why is faith the source of the definition? Is a definition not an arbitrary procedure?^[10] In mathematics it is customary to think of definitions as arbitrary. One may define concepts in any way one sees fit, so long as one maintains consistency and everyone understands what is being discussed. There is no point arguing over definitions, since they are a matter of mere convention. But that is not the whole picture. When one is speaking of defining a new concept—one not familiar to us from experience—this is indeed an arbitrary procedure. But most definitions are not like that. For example, when mathematics defines concepts such as convex and concave figures, a triangle, or a point, these are not arbitrary definitions created out of nothing but an attempt to place a familiar concept into an unambiguous framework that will serve us from then on. The reason we define something is so that we can analyze it more systematically. Understanding without definition does not always allow that—certainly not in mathematics, and certainly not when one wishes to prove things in a logically valid way.

Therefore, when we come to define a concept in order to prove its existence, we must ask ourselves: where did this concept come from? How is it familiar to us? Once we understand its source, we can try to capture its content through a sharp and unambiguous definition. Mathematical concepts such as triangle or convex figure originate in our experience. Without such experience, nobody would bother—and perhaps nobody could—define them just like that. Experience is also what hints to us at the logical and mathematical potential of these definitions (that interesting and nontrivial propositions can be proved about them). Arbitrary definitions are usually not productive; they remain inert and unused.

In this sense, a definition is a kind of observation, or cognition, and not pure thought. We contemplate (with the mind’s eye)^[11] some concept that is familiar and intelligible to us, and the result of that contemplation is the definition. Various arguments about it (such as a proof of its existence) are in many cases procedures of pure thought.

In light of this, the question of the source of the concept of God naturally arises. For the believer, it is his faith. That is the source of his acquaintance with the object described by the term "God." Later in the discussion we will touch on a point that is very important for Anselm’s logical move, namely that the atheist who claims that God does not exist must also rely on a sharp definition of this concept. There we will also address the question of how the atheist, who does not believe in God, sees this concept, and from where he derives it.

The definition

As soon as the prayer ends, Anselm moves to the next sentence:

And indeed we believe that you are something greater than which cannot be conceived.

At the foundation of every discussion stands a definition of the concepts that take part in it—the things being discussed. Without a definition, the discussion has no sharp meaning, and we may fall into contradictions, confusion, vagueness, and misunderstandings. Therefore, after Anselm concludes his prayer, he passes here, very naturally and as required by the prayer, to the definition. We have already seen that faith is the source of the definition of God, and contemplation of it yields the definition of the concept. Here he again draws on faith and extracts his definition from his faith.

What is the definition to which Anselm arrives by this contemplation? God is the greatest being that can be conceived, or alternatively, the being than which no greater can be conceived.

What is the nature of this definition? On its face it seems somewhat empty of content. It may appear that we are not saying anything about Him positively, but only negatively. But that is a mistake. In the previous paragraph I began with a positive formulation: the greatest being that can be conceived. The negative formulation is equivalent to it: if He is the greatest that can be conceived, then no greater can be conceived, and vice versa.

Does this definition provide the desired sharpness? It certainly does. It singles out the defined object and gives us tools to analyze it and deal with questions that arise about it. There is no need at all to describe what He looks like (if He has any appearance at all), or how much He weighs. What a definition is supposed to provide is the necessary and sufficient information to define the concept unambiguously, so that when we discern it (with the mind’s eye) we will know whether it is this thing or not. Many atheists claim that the believer in God does not really believe in a defined being, since He is always defined in rather amorphous and general ways. This claim is mistaken. A definition is not supposed to give all information about something, but only the information necessary and sufficient to individuate it, as noted. When I define a human being as a speaking animal, I have not given the full information about human beings. I have not said that he feels, that he has two legs, that he is social, that he begets children, and so on. But I have given information sufficient to distinguish him from other creatures—that is, information that gives me the tools to decide whether what stands before me is a human being or not. That is what a definition is supposed to do. Nothing more.

Different definitions of the same concept

In light of what was said above, it should be clear to all of us that there can be different definitions of the same concept. So long as the definition is sufficient to single it out, it is a legitimate definition. I can define a point as the set of intersection of two lines, or as a creature of dimension 0, and so on. Definitions that serve us for different purposes will sometimes differ. What matters is that they single out the same object.

Let us take the various proofs for the existence of God described in the introduction. Each of these arguments presupposes a definition of the concept of God, and naturally these are different definitions. The ontological argument deals with the perfect being and proves its existence. The cosmological argument proves the existence of the creator of reality (essential properties: the ability to create things ex nihilo). The physico-theological argument proves the existence of the planner and assembler of reality (essential properties: very high intelligence and impressive capacity for execution). The moral argument proves the existence of the source of values and the one who gave them authority (essential properties: authority to command, and the ability and authority to determine what is ethically proper and improper). Tradition proves the existence of a revealing God (essential properties: each religion offers different properties; in general, again, this is authority to command, but this time not only ethical commands).

Are all these one and the same being? Not necessarily. Each proof proves the existence of a being defined differently. On the other hand, are these necessarily different beings? Again the answer is no. It is entirely possible that each of these different definitions focuses on a different aspect of God, while all refer to the same object. According to Ockham’s razor (which tells us to choose the simplest explanation or theory), there is reason to claim that it is even more plausible that these are different definitions of the same object itself (why assume the existence of several objects if one will suffice?).

Another remark. None of the other proofs necessarily leads us to His perfection. The cosmological argument requires that He have the power to create all reality. The physico-theological argument assumes that He possesses very high intelligence. But those two arguments do not necessarily lead us to assume His perfection or omnipotence. The ability to create ex nihilo does not exist in us, but it still does not mean unlimited ability. Likewise, the ability to create complex things does not mean infinite wisdom, but at least high intelligence. And of course the moral argument or revelation does not lead us to an all-powerful or infinite being. Therefore, contrary to a common view, the philosophical God (the deistic one)—that is, the God whose existence philosophical arguments prove—is not necessarily the God of whom religions speak (the theistic one).

The ontological argument is an exception to this. The definition of God that underlies it is that of a perfect being. This perfection is infinite. For not only is there none greater than Him, but no greater can even be conceived. In fact, the definition of God with which we are dealing here is: the perfect being. In this sense, the ontological argument takes us closer to the concept of God with which religions are concerned. True, this is still a philosophical God, since His definition does not include commandments and revelations, but it is a philosophical God who is all-powerful and perfect, and in that sense there is here a greater fit with religious conceptions of Him.

The dilemma

The research question

Anselm’s next sentence is:

Or perhaps no such nature exists, since "the fool has said in his heart, There is no God"?

After Anselm has proposed a definition for the concept of God, here he places his research question on the table: does the concept defined in the previous sentence exist—that is, is it instantiated in reality (does such a nature exist)—or not?

On definitions and existence

There are concepts that have a sharp and good definition, but do not exist in reality itself. One can define a unicorn, or a fairy with three wings, even though those concepts have no instantiation in reality. Even a pure triangle does not really exist (because in reality the three lines will never be completely straight), nor does a point-mass, of which physicists speak so much, nor any character in a work of fiction. Here Anselm moves to the next stage of the discussion and poses the question at hand: does the concept defined previously, God, have an instantiation in reality or not?

Usually definitions are the result of thought, or at most of observation with the mind’s eye (as in the previous chapter). Claims of fact, by contrast, which speak about the existence or nonexistence of things, are the product of observation. The essence of an ontological proof is that it derives a factual claim from a definition. Therefore it is very important to clarify the difference and the relation between the two.

The hypotheses

When examining such a question, the most precise way to handle it is to place the thesis and the antithesis—that is, the opposing hypothesis—face to face. Anyone who has studied statistics knows that statistical research always begins by positing two hypotheses over against one another: H1 מול H0. The purpose of the inquiry is to reject one and validate the other, or vice versa.

The importance of this is that it now becomes clear to us what stands against what. The goal of the inquiry has been clarified. Too many philosophical discussions deal with questions in which the two hypotheses standing against each other are not really different from one another. The definitions are not sharp, and in fact sometimes what is involved is only wordplay and not a real question.

Who is the opposing hypothesis? The fool

The antithesis that Anselm sets before him in the discussion is the claim of that fool from the book of Psalms (in two places: 14:1 and 53:2)^[12] who claims that God does not exist. It has already been noted that the meaning of the term "fool" in the Latin translation of the Bible is not the same as in the Hebrew original. There it means an ignoramus or simpleton, whereas in the Hebrew original the connotation is that of a wicked person. There appears to be a difference here on the level of an implicit assumption: the Hebrew connotation is that belief is self-evident and certainly exists even in the atheist, and therefore denying it is a kind of wickedness. The fool is a wicked person who denies his belief in order to escape the religious obligation that follows from it. The Latin connotation, by contrast, reflects the assumption that at most this is ignorance, not wickedness.

Between an agnostic and a denier

For the continuation of the discussion, it is important here to be precise about the nature of this fool. Opponents of religious belief are divided into two main kinds: agnostics and atheists. The first kind are people who do not make a contrary claim; rather, they simply have no clear position on the matter. Perhaps there is a God and perhaps there is not. Most of them also claim that there is no way to know this (and mainly in that sense they disagree with believers). Atheists, by contrast, make a positive claim: there is no God! Anselm’s fool belongs to the second category, since he claims that there is no God.

This distinction will be very important later on. Atheists who claim there is no God are saying something about Him. Even when they claim that He does not exist, they are speaking about Him, and therefore they too must have a definition of the concept. Moreover, the definition must be the same definition as that of the believers, for otherwise there is no real dispute here.

There are indeed other kinds of opponents as well, who claim that the concept of God itself is unintelligible, contradictory, or not well defined. These may belong to either category. There are agnostics whose position is based on the fact that the concept is unclear to them, and therefore they have no position about it. And there are atheists who claim that the concept is contradictory and therefore cannot exist. Anselm places before himself only the positively atheistic type whose position is: the concept of God is clear to me, and I claim that it does not exist. The fool is a person who says, even if only in his heart, "There is no God," and therefore says something about Him. Such a person is supposed to share the believer’s definition of the concept, for otherwise there is no dispute between them.

Moreover, the atheistic fool also derives his definition from the same source as the believer. We saw above that the definition of God is grounded in faith. But where does this definition itself come from in the atheist, who lacks faith? Necessarily from the believer’s faith. The believer hewed the concept of God out of his faith, and of course the definition as well. The atheist who enters into discussion with him is necessarily speaking about the same concept and with the same definition. Therefore, for him too the source of the definition of the concept is faith. But not his own faith, since he does not believe, but the believer’s faith.

Later we will see that Anselm’s argument leverages this point and proves that the fool himself, precisely מתוך his denial of God’s existence, actually expresses a hidden belief. That is, the atheist is supposed to travel the road opposite Anselm’s. If Anselm moved from faith to definition, the atheist is supposed to move (by means of the ontological argument) from definition to faith. Therefore, in the final analysis, it is the believer’s faith that transforms the atheist’s conceptions.

It is important to note that here the insight we discussed in the first chapter (on the prayer) comes to expression: the argument addresses only the hidden believer, for otherwise no logical argument (which by its very nature assumes what is to be proved) could transform his belief. The logical argument only exposes before him the belief that was hidden in him, even though it had not been accessible to him beforehand. As we saw above, that—and only that—is what logical arguments can do.

Confronting fools

We can now also return to the connotation of the term "fool," which we discussed above. If indeed, as emerged, the fool is a hidden believer, then his denial necessarily expresses either wicked suppression of the truth or ignorance. If it is wicked denial, then apparently the whole move would be pointless. He already knew and believed; he is simply denying the belief because of his wickedness. Only if he is regarded as an ignoramus or simpleton is there point in teaching him understanding and showing him what he was unaware of.

But this is a mistake. Even if the fool is a wicked person who denies his belief in order to escape his religious obligation, it is still certainly important to confront his claims. Even a person motivated by ulterior motives needs philosophical justification for his deeds. A person clings to arguments of denial ("There is no God") in order to evade his obligations. But if we show him that his claim is absurd on its face, it will be harder for him to carry out these evasions. Therefore it is always right to address the claims a person raises, and to ignore his motives and any judgment about him.

The body of the argument

The beginning of the argument: the fool understands what he hears

After Anselm prays, defines the concept out of his faith, presents his interlocutor (the fool) and the counterclaim (atheism), he proceeds to the beginning of the investigation.

His argument to the fool opens as follows:

Yet surely that very fool, when he hears what I have said—namely, "something greater than which cannot be conceived"—understands what he hears;

Anselm argues, as we saw, that the fool who thinks there is no God probably understands what he is talking about. This definition is intelligible to him when he hears it. We should note that here he is using what we saw above. The argument is addressed to a person who understands the definition and denies it, not to those who claim they do not understand it at all. On what is this assumption based (that the fool understands the concept of God)?

Two justifications may be proposed: (1) If the fool says something about this concept (for he claims that God is only a concept not realized in reality), then he certainly understands it. Otherwise there would be no meaningful sentence here. Moreover, if he does not understand this definition, then what is his dispute with the believer about? (2) This definition is self-evidently understandable. It is composed of simple terms and concepts, and the claim that there is something unintelligible here is not sincere. It is not plausible.

There is a difference between these two reasons. The first reason addresses that fool who was presented in the previous chapter—the fool who positively disputes with the believer. But the second reason can equally address other opponents. How can they claim that the definition is contradictory or unintelligible if it is a simple sentence composed of intelligible concepts? Such an objection is disingenuous. You, the fool, may perhaps claim that you do not believe, but it is difficult to accept your claim that you do not understand the concept, or that it is contradictory or ill-defined. After all, we have defined it by means of intelligible concepts, and every reasonable person should understand such a definition. If so, it may be that this argument can persuade agnostics or opponents of the nonpositive type as well. It addresses anyone who understands the definition offered above.

From what follows, it seems he mainly intends the first argument, though it is not impossible that he is also asserting the second.

Existence in the mind and in reality

Anselm now continues and explains the difference between existence in the mind and existence in reality:

and what he understands is in his mind, even if he does not understand that this thing exists (in reality). For it is one thing for a thing to be in the mind, and another to understand that the thing exists.

Understanding is nothing but existence in the mind. The concept of God exists in the fool’s mind, even if, according to him, it does not exist (or is not realized) in reality.

In the closing sentence here, he compares existence in the mind with the understanding that some entity exists in reality.

We can also see here that with respect to an existing thing, there are three references and meanings of the concept of existence: (a) the entity exists in reality (this is a claim about the world: the concept is instantiated in the world itself); (b) I have in my mind an understanding of the entity’s definition (this is a claim about the concept, or about me: that it exists in my mind); (c) I have in my mind an understanding that the entity exists in reality (this is a claim about me and about my perception of the world itself).

Of course there are also existing entities of whose existence I am unaware. Perhaps there are even existing entities whose definition I do not understand. But existing entities of whose existence I am aware exist on two different planes: they exist in reality and they exist in my mind. It is important to understand that his main point is that the concept existing in my mind in such a case is different from the concept existing there in the previous case. Here what exists in my mind is the concept "X that exists," whereas previously what was in my mind was the concept "X" as such. The first concerns a grasp of a concept; the second, a grasp of an entity.

To summarize, Anselm distinguishes here among the following claims:

A nonexistent concept whose definition is intelligible to me in my mind. The concept X exists in my mind.
An existing concept whose existence is unknown to me and whose definition is not intelligible to me. The concept X exists in the world but not in my mind.
An existing concept whose existence is unknown to me but whose definition is intelligible to me. The concept X exists in my mind and also in the world, but I do not have in my mind the concept of X as existing—that is, the understanding that it exists in the world.
In principle there is also the possibility of an existing concept whose existence is known to me but whose definition is not intelligible to me (some claim this is God). We will ignore that possibility here, since it raises various difficulties unrelated to our discussion.
An existing and intelligible concept whose existence is known to me. The concept X exists in my mind and in the world, and beyond those two there also exists in my mind the perception that it exists. As noted, in fact this is another concept that is present in my mind. If previously the concept "X" existed in my mind, now the concept "existing X" exists in it.

Two kinds of existence in the mind

I again emphasize that the main point Anselm is making here is not the distinction between existence in reality and existence in the mind, but a distinction between two kinds of existence in the mind: grasping the concept X and its definition in the mind, or grasping it as an existing entity. For example, there is a difference between the understanding of a triangle in my mind and seeing a specific triangle in the reality before me. But the difference is not only between existence in reality and existence in the mind. The specific triangle standing before me also exists in my mind in a different way from the idea of triangle. Here what is in my mind is an existing triangle, as distinct from the grasp of the concept or idea of triangle. These are two different kinds of existence in the mind. But at the next stage Anselm goes on to argue that in fact these are two different concepts that exist in the grasping mind: triangle and existing triangle.

The conclusion is that the realization of some concept and its becoming an entity that exists in reality yields two different consequences: first, there now exists in reality an entity that is the instantiation of the abstract concept (the concept has passed from potentiality to actuality); and second, what now exists in consciousness is a different concept from what was there before the instantiation.

The painter example

We began with a distinction between existence in reality and existence in the mind. We moved to a distinction between two kinds of existence in the mind: an intellectual grasp of a concept versus a grasp of an existing entity. And we ended with a distinction between two kinds of concepts grasped in the mind: the abstract concept and the concrete concept (the entity). When the concrete entity is grasped in the mind, it itself becomes an abstract concept as well. The idea that exists in the mind that grasps it is a concept of an existing entity. This is an abstract object of a different kind (= the understanding and awareness that some entity exists in reality).

Many of his critics did not notice these transitions, although, as we shall see, they constitute the heart of the argument. Many of them think he is distinguishing here between existence in reality and existence in the mind, and then the continuation of the argument seems to them unacceptable (that is, invalid). Anselm apparently sensed the potential for misunderstanding in so fine a distinction, and therefore, in order to sharpen this distinction, which stands at the center of his argument, Anselm now brings an illustrative example:

When a painter first thinks out in advance what he is going to create, that thing exists in his mind; but he does not yet think of it as something real, for he has not yet made it. But after he has painted it, that thing both exists in his mind and he also understands that it exists (in reality), since he has made it.

Think of a painter planning some picture. At the end of the planning, the idea of the painting exists in his mind. But clearly what is now in his mind is not an existing painting but an idea. Yet after he paints it, not only has existence in reality been added (the realization of the idea), but also the concept that exists in the painter’s mind has been renewed. Now the painting exists in his mind as an existing thing and not merely as the idea of the painting (the plan). Anselm again returns and emphasizes that the comparison is between the existence of a concept and the existence in the mind of an existing thing, which is another abstract concept.

A Kantian remark: the distinction between phenomena and noumena

By way of aside, we may add that precisely one of Anselm’s great critics, Kant, many hundreds of years later, added an important layer to this distinction. According to Kant, one must distinguish between the thing as it is in itself and the thing as it is grasped in our cognition. Bertrand Russell, in his book The Problems of Philosophy, further sharpened this distinction by asking: what is the color yellow? Many would answer that it is an electromagnetic wave of a certain wavelength. But that is a mistake. The electromagnetic wave is a physical phenomenon, whereas the color yellow is only a cognitive phenomenon. If the information from our eye were routed to the auditory center, we would hear that electromagnetic wave vocally rather than see it. Color is a human translation of the physical phenomenon, but it exists only in our cognition and not in the world itself. So too with the well-known question: if a tree falls in the forest and no one is there to hear it, is there a sound there? Russell would answer no. Obviously there is no sound there. There is an acoustic wave there—that is, a pressure wave passing through the air and causing it to move. But so long as that acoustic pressure wave does not strike an eardrum, no sound is produced from it. Sound is a subjective phenomenon that exists only within us and not in the world itself. As noted, it is our translation of the physical phenomenon of an acoustic wave.

So it is with colors, sounds, and every other form we can think of. The various forms exist only in our cognition, not in the world itself. What exists in our brain is a translation of physical phenomena into our subjective language. The physical phenomena generate the cognitions that grasp and translate them, but there is no direct relation between the physical phenomena and our cognitions. One may say that the relation between physics and cognition is causal (physics causes the cognition) and not a relation of identity (cognition presents physics as it is in itself). Out there in the world there is no yellow color and no Beethoven symphony. There are physical phenomena which, when they strike our eyes or our ears, create a symphony or some appearance.

We can now sharpen further the distinction between the thing that exists somewhere out there and our cognition of it in the mind. The thing that exists in the world is not seen and not heard at all, and in our terms is in fact formless. By contrast, our cognition of it in our minds contains sights and sounds (and taste, smell, and touch). Therefore there is no room at all to confuse the thing as it is in the objective world with its cognition in our brain.

We can now move to Anselm’s distinction. As noted, he is not dealing with the distinction between an entity that exists in the world and a concept existing in consciousness. His distinction compares two cognitions: cognition of an entity as existing versus cognition of an imaginary concept. Neuroscience teaches us that the cognition of an existing entity, like that of an imaginary one, is carried out in exactly the same way. The same neurons in the brain work when I identify a person or some object standing before me, or when I remember them and raise their image in my imagination. It is evident that in both cases we are dealing with cognitions. And yet we are able to understand when we are inventing some image and when we are seeing a reality present before us. Neurologically, this means that alongside the cognition of the form in our consciousness there is another part of the brain responsible for distinguishing between imagination and cognition of a state or real object standing before me. In both cases, what appears in my consciousness is a presentation in my language of a given factual state. But when I imagine the thing, no act of translation is taking place. It is creation ex nihilo (which, of course, feeds on previous cognition of the thing that I am now identifying). By contrast, when I cognize an external object, I perform an act of translation—from reality into my subjective language. The neurons that distinguish between imagination and cognition are in fact the sensors that tell us whether an act of translation is taking place here or not.

The conclusion is that beyond the entity and its physical properties, there are two cognitive states that Anselm distinguishes between. In each of them a different concept or image stands in my consciousness: when I raise an entity or a state in my imagination, this is one image—the idea of the state or entity standing in my awareness. By contrast, when I cognize, a different cognitive object stands before me: the entity as existing (the visual-cognition neurons + the sensors indicating that an act of translation is taking place). Our ability to distinguish between imagination and reality is based on the fact that in each state a different cognitive object stands before our consciousness. This is the heart of Anselm’s introduction that we have seen עד now.

Experiential cognition versus cognition, or visual imagination

To complete the picture, let us make one further remark, to which we will return when discussing Anselm’s next two chapters. Until now we have dealt with the distinction between two visual perceptions, and in fact between two different cognitive ideas: cognition is the perception of a real entity present before us, and it places before us the idea of an existing entity (an image from cognition-neurons + a sense of translation). By contrast, imagining an entity or state produces in us a different idea. What stands before us is another cognitive object (an image without a sense of translation). But surely neither of these two states is identical with the state in which I think the entity or the concept. Thinking about a thing is abstract, and it is different from the state in which I experience or see its appearance in my imagination. Here we are dealing with a nonvisual grasp of an entity or concept. I think it rather than perceive it, and this is entirely different from the two kinds of visual perception discussed above. By the same token, the object standing before me in cognition is not really a visual object but an abstract idea—an array of ideas or features, not a picture.

A good illustration is the thought experiment known as "Mary’s room."^[13] Mary is a brilliant scientist who masters every intricacy of optics. She spends her whole life in a black-and-white room and has no experience of seeing colors. But of course she knows what occurs in every encounter involving colors, and what happens to every color in every situation, and the wavelength of a color, and so on. The question is whether she knows what the color red is. She can say everything about it, but one cannot say that she knows what the color red is. She understands everything connected to it, but she does not experience it.

So too with the example of the color yellow. The physical understanding of the color yellow is a nonexperiential cognition. It is an understanding of the ideas and properties of the color yellow, the equations governing its behavior, and the like. By contrast, there is an image of the color yellow (or of an object having the color yellow), which comes either from imagining it or from cognizing such an object in reality before me. Mary underwent the process of understanding, but not the process of immediate experience. We may note that there are also abstract concepts, such as democracy or kindness, for which there is no experiential cognition at all, only understanding.

The heart of the argument

Up to this point Anselm has been occupied with definitions and distinctions that seem innocent and agreed upon, almost boring, and it is not clear how any factual claim could be grounded on them. But now, suddenly, comes his intellectual knockout blow. It turns out that the key point in Anselm’s argument is a direct result of the innocent definitions we have been dealing with until now. This is the heart of the ontological argument.

Anselm expresses it as follows:

The fool, then, must also be convinced that at least in the mind there is something greater than which cannot be conceived.

He opens the heart of the argument from the end: straight with the conclusion. Only afterward does the reason come. The apparent reason for this is a desire to give the reader a sense of impact and surprise. What he is essentially saying is that nothing beyond the set of definitions and distinctions given thus far is needed in order to reach the bottom line: God exists. The fool who has gone with us up to this point will now have to admit, willy-nilly, that God exists.

What is the reason for this surprising conclusion? As noted, Anselm bases it on those very distinctions he has been emphasizing up to this point:

because he understands this when he hears it, and whatever is understood is in the mind.

The concept "something greater than which cannot be conceived" is intelligible to the fool and therefore is also in his mind (of course, at this stage it is still the presence of a nonexistent entity, without the translation-neurons).

The next step now comes:

But that which is greater than which cannot be conceived certainly cannot be in the mind alone.

This entity is in the fool’s mind, but it cannot be in the mind alone (and not in reality). Why? Anselm offers here a proof by reductio ad absurdum (a proof by contradiction), and this is the heart of his ontological argument:

For in truth, if it were in the mind alone, it could be conceived as existing in reality as well, and that is greater. Therefore, if that being greater than which cannot be conceived exists only in the mind, then that being greater than which cannot be conceived is a being than which something greater can be conceived. But this surely cannot be.

If the concept of God were only in the mind and not in reality, then something greater than it could be conceived: God who exists (understanding + translation-neurons)^[14]. It is important to note that the comparison here is between two representations^[15] in consciousness (the cognitive representation of X and the cognitive representation of existing X), and not between the entity X and the concept X, as we sharpened above. Anselm argues that there is nothing to prevent us from conceiving the representation of existing God as well, and that representation is greater than the representation of the abstract concept of God (without existence). But if so, then our consciousness contains another concept besides God that is greater than Him, and yet it can be conceived.

But this, of course, contradicts the definition of the concept God as the greatest being that can be conceived (or than which no greater can be conceived. Behold, we have conceived something else greater than it). Therefore the fool’s hypothesis that God does not exist leads us into contradiction. The concept God includes His existence within it, and therefore "God does not exist" is like a round triangle (or a stone that an omnipotent being cannot lift). This is a proof by contradiction that the fool’s view that God does not exist is not correct, and therefore he and we must adopt the opposing hypothesis: God exists (that is, He is instantiated in reality).

From here Anselm again arrives at the final conclusion:

There exists, therefore, beyond doubt, something greater than which cannot be conceived, and it exists both in the mind and in reality.

This is essentially the final determination. This sentence is the equivalent of the Q.E.D. that appears at the end of a mathematical proof.

Anselm smuggles into his words here an additional assumption that is in fact the heart of his argument: that the idea of a concept as existing (that is, with translation-neurons) is greater than the idea of that same concept without existence. This is a key point in his argument, and we will discuss it at length below in Chapter 10.

A remark that serves as an introduction to the second part

Anselm writes here that this determination is received "beyond doubt," that is, with certainty. This determination is based on a valid logical argument, and that in turn is based on agreed premises and self-evident distinctions, as we saw above. Therefore there is no way to challenge either the premises or the logical way the conclusion is derived from them, and therefore one must also adopt the conclusion. We will discuss this further in the next part, when we turn to Chapter 3 of the Proslogion.

Part Three

Proslogion Chapter 3

Between ontic necessity and epistemic necessity

Introduction

We already mentioned in the introduction that there are different interpretations of the role of the three chapters in the Proslogion and of the relations among them. Some viewed this chapter as another formulation of the same proof, and some saw it as a different proof of the same conclusion. But the very first sentence of this chapter, which defines its purpose, shows that it is a further stage of the proof:

And this exists so truly that it cannot at all be conceived not to exist.

If in the previous chapter we dealt with proving the existence of God, this chapter comes to show that not only does He exist, but His existence is necessary.

First, we must clarify the term "necessary." When I say that the table before me exists, that is a claim about the reality before me. When I say that the existence of the table is necessary, I am saying something beyond that. As for a table, one can conceive a situation in which this table does not exist. By contrast, when I speak of a being whose existence is necessary, this means that one cannot conceive a situation in which this being does not exist. This is not merely a claim about the state before me but about an entire range of hypothetical states.

A modal formulation^[16]

I already mentioned in the introduction that the logician Kurt Gödel proposed a modal formulation of the ontological argument. Here we will briefly consider the meaning of a modal formulation in general and in relation to the ontological argument in particular.

Because of various difficulties in the logical definition of the concept "necessarily true," modal logic was developed, which formulates the concept "necessarily true" (or "necessarily real") in terms of the concept "true." How is this done? The claim "X is necessarily true" is translated into the claim: "X is true in every possible world" (or in every world that can be imagined). Note that in the translated claim the problematic term "necessarily true" does not appear; only "true" appears—a concept, of course, much more familiar to us and one we know how to treat with ordinary logical tools.

For example, the claim that 2+2=4 is necessarily true, because one cannot conceive of a world—even an imaginary one—in which this does not hold. This is unlike the law of gravitation or any other law of nature, with respect to which there is no such necessity. One can think of an imaginary world in which objects with mass are not attracted to other masses, and there is no principled problem with that. Many distinguish between logic and mathematics, which are necessarily true (that is, true in every possible world we can imagine), and physics and the various sciences, which are true but not necessarily so (that is, true in our world, but not necessarily in every imaginary world we can conceive).

It should be noted that modal logic does not deal with the concept "necessarily exists" but only with the concept "necessarily true." What is the relation between these two? When we deal with the existence of things (ontology), we make claims about existence or nonexistence. One can translate the claim "X necessarily exists" in the following way: "The proposition ‘X exists’ is necessarily true." But it is not clear whether this is an exact translation. Here the necessity concerns us, not the thing itself. We know with certainty or necessarily that the proposition "X exists" is true. But can one derive from this the claim "X necessarily exists," that is, that it could not have failed to exist? In the modal translation one indeed assumes that there is no conceivable world in which the proposition "X exists" is not true, but this is still a claim about us. We cannot conceive that X does not exist; from our perspective that is true. But is it true in reality itself?

Ontic necessity and epistemic necessity

The meaning of this is that we are dealing here with two different senses of the term "necessary": (a) a claim about the thing (de re)—its existence is necessary; (b) a claim about propositions (de dicto)—the conclusion regarding its existence is necessary (we have an ontological proof of its existence).

The first meaning is ontic (it concerns the state of the being in the world itself). Necessity in this sense distinguishes between two kinds of beings and two kinds of existence. The first kind is beings whose existence is contingent (possible but not necessary). They depend on a cause external to them, some being or mechanism that created them. If it does not exist, or decides not to do so, they will not exist. The second kind is beings whose existence is necessary—that is, not dependent on or conditioned by any external circumstance outside themselves. Sometimes this is phrased by saying "they are themselves the cause of their existence," but that is not entirely accurate. There is no cause of their existence, because they have always been here and always will be here.

By contrast, the second meaning is epistemic (cognitive; it concerns us and our cognition of the being in the world itself): how certain we are of their existence. Necessity in this sense distinguishes between two kinds of propositions, or really between two different contents of our cognition of the existence of things: beings whose existence is certain to us—that is, beings for which we have an ontological proof that they exist—versus beings whose existence is not known to us with certainty. It is specifically an ontological proof and not observation, because a proof based on observations, or on any other route, never gives us complete certainty. When we see that X exists, this does not tell us whether its existence is necessary or not. Observation is not a tool for reaching necessity of existence.

Why is the distinction between these two senses of "necessity" important? At first glance they seem like two angles on the same phenomenon: a thing that is ontically necessary is also epistemically necessary, and vice versa. But that is not necessarily true. In principle, it is possible that some entity is a necessary existent in the ontic sense, but we have no (ontological) proof of that, and therefore it is not necessary in the second, epistemic sense. In such a case, perhaps we do not know that its existence is necessary, or we know it but not necessarily so. The converse, however, does seem correct: if we have an ontological proof of the existence of something—that is, if it is epistemically necessary—then it is clearly also ontically necessary. If the proof is ontological, this means that it is not based on facts and observations. Therefore, it must be based on the very definition of the object under discussion. Hence the existence of such a proof shows that the object’s existence follows from its definition, that is, that it is a necessary existent also in the ontic sense (not dependent on something external to it).

But here too there is a mistake. Although many identify the claim that the existence of some being is necessary (ontically) with the claim that its existence follows from its definition, this is not precise. Following from the definition is a logical property, not an ontic one. A thing’s definition is the set of essential properties that characterize it. But existence cannot follow from a property; at most, the conclusion "X exists" follows from a proposition whose content is some property of the object. Existence follows from something in reality, not from propositions. Therefore it is incorrect to say that if the existence of the being X is necessary, then it follows from its definition.

The definition of a thing really belongs more to the epistemic plane (because a definition is the set of our items of knowledge about the thing). It is not itself an existing being. If so, nothing can ontically follow from it. The derivation in question is a logical derivation. Therefore it is more correct to say that if the existence of X is ontically necessary, then its existence is derived from (or: is part of) its essence and not necessarily from its definition. But this claim is completely identical to the claim that its existence is necessary, that is, that a state in which it does not exist is impossible.

We can now see that the other direction of the identity mentioned above is also incorrect. Even if we have a logical proof of the existence of something, we must distinguish between two situations: if this is a purely logical argument, that is, an argument not based on any premises at all but only on conceptual analysis, then perhaps one may say that its existence follows from its definition. But if the argument rests on some premises (not factual ones, of course), then the truth of the proposition "X exists" depends on the truth of those premises. If so, the existence of an ontological proof does not mean that the existence of the thing proved is ontically necessary. It depends on the truth of the premises. Admittedly, if the proof is purely logical, then it would seem that the existence of such a proof indicates that the object whose existence has been proved does indeed exist with ontic necessity as well.^[17]

Kant notes this point in his book Critique of Pure Reason,^[18] in the second part of volume I, in the second section, book two, third division, at the beginning of the fourth chapter, which deals with the impossibility of ontological proofs in general:

Every proposition of geometry, for example that the triangle has three angles, is absolutely necessary; and thus people spoke of an object, lying wholly beyond the sphere of our understanding, as necessary, as though it were perfectly well understood what is meant when one attributes this concept to it.

All the examples given in this field, without exception, are derived only from propositions, and not from things and their existence. But the unconditional necessity of propositions is not the absolute necessity of things, for the absolute necessity of a proposition is only the conditioned necessity of the thing, or of the predicate in the proposition. The proposition above did not say that three angles are absolutely1 necessary; it said only: on condition that there is (that there is given) a triangle, there are also necessarily (in it) three angles.

From here Kant moves to his critique of the ontological proof. We will return to his arguments in Part Four.

Kant is basically arguing that even if the proposition that a triangle has three angles is necessarily true, nothing follows from it about reality, and certainly not about any necessity in reality. This is a conditioned necessity: if there is a triangle in reality, then it necessarily has three angles.

Steinitz’s arguments

In the third chapter of his book Tree of Knowledge, Steinitz deals with the distinction between existence and necessary existence. First, he argues that a necessary being either exists necessarily or is necessarily absent. After all, either it exists or it does not. If it exists, then by definition it follows that it exists necessarily (if it did not exist necessarily, then this object that exists would not really be a necessary being). And if it is absent, then if there were any possibility that it existed, its existence would be necessary, that is, there would be no possibility that it did not exist. If so, even if such an object is absent, it is absent necessarily. The conclusion is that it is impossible for the existence or absence of such a being to be contingent.

Steinitz goes on there to argue that if such a being exists, then there necessarily exists an ontological proof of its existence, even if it may not be known to us. And if such beings are absent, then their nonexistence is a necessary consequence of their concept, and again we have an ontological argument here (that is, an argument that derives a factual proposition, in this case a proposition whose content is nonexistence, from conceptual analysis). If so, we have here a proof against the philosophers who deny the existence of ontological proofs. And from this it follows that an ontological proof is certainly possible; and not only is it possible, but here is the proof that such a proof certainly exists. This is a dilemma argument that proves, by a "whichever way you turn it" reasoning, the existence of an ontological proof.

We shall now see that, in light of what we explained above, Steinitz is mistaken here all along the line. To refute his argument, it is enough to show that one of the two horns of the dilemma is false. But we will show here that he is mistaken in both directions, that is, both horns are wrong, and for the very same reason.

Above we saw that even if the existence of X is necessary, this does not mean that its existence follows from its definition (but rather perhaps that it is necessary from within itself), and therefore this does not mean that there is an ontological argument that proves its existence. A proof of its existence must be based on propositions taken from the definition of that being (that is, from its conceptual analysis), and this need not be possible even if its existence is ontically necessary.

Put differently, Steinitz is essentially arguing that the absence of such a being is necessary absence, that is, that its absence follows from its definition (or concept). In other words, that there is a logical contradiction in this concept. He argues that since we all understand the concept "necessary being," so long as it has not been shown to be contradictory, there is no reason to assume that it is. The burden of proof is on whoever claims that a concept we understand contains an internal contradiction. From this he concludes that such an object cannot be absent necessarily, and hence that it exists necessarily (because, as we saw, there is no third possibility).

And again, the same mistake appears here. The fact that such an object is absent necessarily does not mean that there is a contradiction in its concept (that is, that we have an ontological proof of its nonexistence). Necessary absence is an ontic property, not a logical one. It is not necessarily describable by means of a logical argument (because the absence is not the product of some property of the concept but of the nature of the world or of the very essence of the concept).

Back to Chapter 3 of Anselm

We saw that in the opening sentence of the chapter Anselm declares that in this chapter he intends to prove the claim that God’s existence is necessary. Which of the two meanings of necessity did Anselm intend, ontic or logical-epistemic? He writes that he cannot at all be thought as non-being, that is, when one thinks him, "he cannot at all be thought as non-being." It seems from this that we are dealing with an ontological proof (a proof on the basis of conceptual analysis) that he exists. This means that his existence is derived from his definition (and therefore it is impossible to think of him and at the same time think that he is not a being, because that is an oxymoron. This is a proof by way of negation for his existence). If so, Anselm wants to prove that he is necessary in the second sense, the epistemic one: his definition logically entails his existence. On the other hand, the way Anselm formulates the conclusion is ontic: that God is a being that exists necessarily. Below we will ask how, if at all, one can move from here to the ontic plane.

Why is a proof needed at all?

In Chapter 2 Anselm proved the existence of God by an ontological proof. From this it follows that his existence is derived from his definition, that is, that he is a necessary existent in the epistemic sense. According to Steinitz’s assumption, once there is an ontological proof of his existence, he is also necessary in the first sense. So why is a proof needed at all that his existence is necessary? In fact, this chapter is superfluous. Moreover, as we shall immediately see, Anselm himself does not prove this necessity by pointing to the ontological proof of God’s existence that was presented in the previous chapter. Here he repeats another logical argument (admittedly a very similar one) whose purpose is apparently to prove the claim of necessity. From this we can see that he was aware that the identification made by Steinitz between the two types of necessity is mistaken.

Moreover, it is possible that he himself understands that the proof presented in Chapter 2 is not purely logical. Beyond the conceptual analysis, it also contains hidden premises (see Part Four, in the discussion of the critiques), and therefore, as Kant determined, from it one can prove at most that his existence is necessary for us (in the second sense), but not that his existence is necessary also in the first, ontic sense. The conclusion of Chapter 2 is de-dicto and not de-re. In this chapter he tries to extend it also to the ontic plane (to prove by an ontological proof that he is a necessary existent). We will see this more sharply when we see the body of Anselm’s argument in the next chapter.

The proof of the necessity of his existence

The proof of the necessity of his existence

We have seen that the purpose of the present chapter is to prove that not only does God exist, but that his existence is also necessary. Anselm opens the body of his argument as follows:

For something can be thought that cannot be thought not to exist;

He argues that in principle we can think of some being whose existence is necessary (which cannot be thought not to exist). In this sentence Anselm is speaking at the level of principle: a person can think of the concept of a necessary entity, or of a being whose existence is necessary.

The next logical step is:

and such a being is greater than one that can be thought not to exist.

Anselm establishes here that a necessary entity is greater than a non-necessary entity. It is not clear whether he means a comparison in which the same entity stands on both sides of the equation, once thought as necessary and once not. From his wording it seems that he is speaking generally: every entity whose existence is necessary is greater than another entity whose existence is not necessary. But this is not plausible, and certainly not necessary, for the second entity may have other perfections that the first lacks, and then there may be an offset in favor of the second. Below we shall see that this difficulty is not relevant, and that the comparison is between two identical beings except for this aspect.

He now goes on to apply this to the being than which nothing greater can be thought (= God, as defined in the previous chapter), whose existence was proved in Chapter 2 of the Proslogion:

Therefore, if that than which nothing greater can be thought can be thought not to exist, then that very being than which nothing greater can be thought is not that than which nothing greater can be thought; and this is a contradiction.

If God himself can in principle be thought as non-being, then he is not the greatest thing we can think of, for we can think of that very same being as a necessary existent, and that would be a greater idea than God, and it can be thought. But by God’s very definition it is impossible that there be an idea greater than him that can be thought by us.

And therefore Anselm reaches the conclusion:

There truly exists, therefore, something than which nothing greater can be thought; and to such an extent that it cannot even be thought not to exist.

The conclusion is made up of two parts: a. the conclusion of the previous chapter—there is something greater than which cannot be conceived (that is, God exists). And the addition from this chapter—the being in question not only exists but exists necessarily (it cannot be thought not to exist).

Is this not simply a repetition of the previous chapter?

We must now ask ourselves whether Anselm is not repeating himself. After all, in the previous chapter he already proved that the thought that God does not exist is contradictory to the concept of God (= the most perfect being that can be thought by us). That is, we cannot think of him as nonexistent. Is this not equivalent to the claim proved here, that he cannot be thought not to exist?

Let us now use the introduction given in our previous chapter. In his Chapter 2 Anselm proved that it is logically necessary (for us) that God exists. This is de-dicto necessity. But his existence may be non-necessary on the ontological level, de-re. True, in the previous chapter he presented us with a logical proof that God exists, but it is still possible that we are dealing with a kind of existence like that of any ordinary being, that is, there is no ontic necessity to his existence. As we saw in the previous chapter, there can be beings for whose existence we have a necessary proof, but whose existence is contingent. It follows that in the present chapter Anselm’s aim is to show that the very type of God’s existence is also different: God is a being whose existence is ontically necessary.

Let us now return to the course of the proof. It begins with the fact that one can think of a being whose existence is necessary (ontically). Therefore, if God is a being whose existence is contingent (even if for us there is certainty that he exists), then he is not the most perfect being. But this contradicts his concept, and therefore it is clear that one of his perfections is that his existence is ontically necessary. This is precisely the addition of this chapter over its predecessor.

When one looks at the structure of Anselm’s argument in this chapter, one sees that it is an argument completely parallel to the one he presented in the previous chapter, except that here the issue is not God’s bare existence but his necessary existence. If we take the structure of the argument from the previous chapter, but wherever existence appears in the formulation of the previous chapter we now place necessary existence, we obtain the conclusion about necessary existence.

Note: is the argument in Chapter 2 purely logical?

This parallel between the chapters indirectly proves that Anselm’s argument is not purely logical. If it were a purely logical argument, then its structure would be formal, and therefore it should not change when different content is substituted into the variables. The fact that a different substitution requires another argument in a separate chapter means that Anselm too understood that his argument was not purely formal-logical.

The meaning of this is that several assumptions stand at the basis of the argument. True, not factual assumptions, for otherwise this would not be an ontological argument, but still assumptions that go beyond conceptual analysis. For example, his argument contains an assumption that establishes an order of perfections. In Chapter 2 it is the assumption that a realized concept is greater than an unrealized concept. The substitution gives us the assumption of Chapter 3: what exists necessarily is greater than what exists non-necessarily. This is of course a different assumption, and therefore in Chapter 3 we have a different argument. There is another assumption in Chapter 2, namely that concepts such as God, or the most perfect being, can be thought. In Chapter 3 this is translated into the assumption that a being whose existence is necessary can be thought. Again we have received a different assumption, and therefore the argument is different.

In Part Four we shall see that these assumptions were a primary target of attacks and objections to Anselm’s arguments.

Modal formulation

Above we presented the modal formulation of the concepts of necessity. We can now ask the question of the necessity of God’s existence in a different way: could we in principle imagine a world in which God does not exist? In our world he exists, and for us it may perhaps even be necessary to think that he exists (after all, we have an ontological proof, from Chapter 2 of the Proslogion). The question is whether his existence is necessary also in the modal sense. Can we imagine a world in which God does not exist?

Above we saw that each of Anselm’s arguments (in Chapter 2 and Chapter 3) contains at least two assumptions. Therefore, in principle the answer is yes. For example, in a world in which the assumption that existence is more perfect than nonexistence does not hold, we would not be able to infer the conclusion that God exists. Alternatively, we can imagine a fictional world in which God cannot be conceived, and therefore the previous proof is not valid.

To deal with this problematic aspect, Anselm performs a move similar to the one he made in the previous chapter. To solve it, he converts the question about necessity into a question about existence in our world, where it is easier for him to deal with it. Notice that this is a move similar to what modal logic does (it converts necessary existence in our world into ordinary existence in many worlds). In our world it is clear that a being whose existence is ontically necessary is more perfect than a being whose existence is contingent. Therefore God in our world must have ontically necessary existence, otherwise he would not be the most perfect being in our world. If so, we have reached the conclusion that in our world God must exist with ontic necessity. And from this we can of course return to the imaginary worlds and say that there too God must exist.

Admittedly, in those worlds God’s existence may be contingent (because we have not proved necessity in all worlds), that is, there he is not necessary in the ontic sense. To go on and show that even in those worlds he exists with ontic necessity, perhaps one would need to raise yet another argument similar to the one in the present chapter, one level back (to substitute in each such world "exists necessarily" במקום "exists"). But what interests Anselm is God in our world, since the other worlds are imaginary and were created only as a fiction that helps define ontic necessity in our world. Therefore he stops this chain of arguments here.

Theological interlude

Introduction

The second half of the chapter seems to have a different character, and therefore it is not clear what its place is in the logical sequence. Unlike the careful formulation up to now, here assumptions enter whose source is unclear, and there seems to be no logical argument here. In addition, this section is written in the second person, that is, it once again addresses God directly, unlike the philosophical sections that addressed the fool and were formulated as a philosophical argument.

It therefore seems that here Anselm abandons the philosophical discussion and returns to the theological plane. After the logical-philosophical move, the tradition and faith from which Anselm set out (see the beginning of Chapter 2, and our discussion there) again return to center stage. This section seems to be an intermezzo directed to the believing reader. At first glance, it would seem that anyone interested only in the philosophical move can skip this part. In the discussion below we will try to propose a philosophical meaning for this section as well.

The course of the theological passage

Anselm opens this passage and once again addresses God:

And you, Lord our God, are such a being. You are so truly that you cannot at all be thought not to exist, and rightly so.

Up to this point he has summarized the conclusion he reached in the previous chapter and in the first half of the present chapter. The words "and rightly so" do not merely indicate that the argument is valid. That has been implicit throughout the entire logical move conducted so far. It is therefore clear that here Anselm is trying to justify that conclusion. How can one justify a logical move? What is needed beyond logical validity? From what perspective is this justification being made?

Let us see:

For if any understanding mind could think of something better than you, the creature would rise above the Creator and would judge him; and this is utterly absurd.

Here the assumption enters that the most perfect being is also the Creator. This assumption has neither been proved nor even asserted until this point. There is an unclear logical leap here, and as stated it also does not fit the rigor that prevailed in the discussion up to now. This assumption seems to be drawn from the theological world, and it is not connected to everything that has been said so far. There is another assumption in this sentence as well, namely that the creature cannot judge its Creator. This assumption too is more theological than philosophical.

What is this "judgment" Anselm is speaking of? Is it simply the determination that something greater than him can be thought? If so, it is not correct to call this judgment, but only elevation above him. Moreover, is not the claim that God is the most perfect and that nothing greater can be conceived itself a judgment by us of our Creator? That too is some claim about him. The whole move made up to this point is a kind of philosophical judgment, so why, if the conclusion were the opposite, would it count as illegitimate judgment?

Again, it seems that he does not mean judgment in the sense of expressing some proposition about him. The judgment is the looking at him from a station higher than his, and that is absurd. If we can think of something greater or better than him, then we could also judge him (whether he is good or not). More than that, the very determination that something is better than him means judgment. This is a theological assumption that the judge must always be greater than the judged. The absurdity Anselm is speaking of is theological, not philosophical: it cannot be that the creature is greater than the Creator and presents comparisons (judgments) between him and things greater than him.

If so, the justification Anselm is trying to offer is a theological justification. At the beginning of Chapter 2 we saw that Anselm sets out on his philosophical path from within the theological sphere. Now he returns to the sphere from which he set out, and explains that the results he reached are justified on that plane (the theological one). Therefore he does not hesitate here to add assumptions accepted in his theological world, even though this compromises the philosophical purity of the move. This is an appeal to the believer, and an attempt to show him that the philosophical move has succeeded. It is justified theologically as well.

Anselm now continues:

And indeed, everything besides you can be thought not to exist; you alone, therefore, of all things, have being in absolute truth and in a greater degree than all. For nothing else is in the same degree of truth, and therefore it is to a lesser degree.

He explains how the philosophical consideration conducted thus far shows that God is the greatest. He is the absolute and greatest being, and in fact his very being is greater and more absolute than the being of any other being.

Anselm assumes here that a necessary being is a different kind of being, more absolute, than a non-necessary being. Does a necessary being (even ontically) really exist in a different sense from a non-necessary being? It is not entirely clear. This exists and that exists, and it is not clear that there is a difference between this existence and contingent existence any more than there is between the existence of a light wave and the existence of a massive object. The term existence in its purity relates to all of these in exactly the same way.

Perhaps his intention is to say that this being is absolute in the sense that its existence is not conditioned by something outside it. Since God is an ontically necessary being, his existence follows from his essence and depends on no external factor. Perhaps this is actually an argument hinting at why the most perfect being is also the Creator (something that was assumed in the previous sentence without justification). If his existence does not depend on any other being, and all the other beings have contingent existence, then when we trace the chain of the coming-into-being of all of them, at the beginning of that chain there must necessarily stand the being whose existence is unconditioned, namely God. In Kantian terminology, this is basically the cosmological proof of God’s existence. The cosmological proof proves God’s existence as Creator, whereas the ontological proof proves God’s existence as a perfect being. These are different definitions, and here Anselm is trying to tie them together. This is an initial connection between deism, which deals with the philosophical God (the perfect being), and theism, which deals with the religious God (Creator of the world).^[19]

And he concludes this passage with an indirect address to the fool (which on the literary level is formulated as the close of the passage addressing the believer):

Why, then, did the fool say in his heart, There is no God, when it is so clear to every understanding and rational mind that you are the being of the highest rank of all? Did he not say it because he is witless and foolish?

That is, the conclusion of his words to the believer concerns the phenomenon of foolishness. He identifies it with stupidity and wickedness, for philosophically it is completely clear that such claims have no standing. This is an interesting ending, and it also functions as a transition to the next chapter of the Proslogion (Chapter 4), which will discuss this point (how can fools exist at all?) from the philosophical perspective.

The philosophical God and the religious God

This is the place to pause briefly on an important point. Many attack theological engagement with proofs of God’s existence, for even if one reaches the conclusion that there is a God in the general and abstract philosophical sense (deism), this has nothing whatsoever to do with the religious God (theism). There are many people who believe in a higher power, in a perfect being, and perhaps even in a creator, and yet do not feel bound by the commandments he gives. Some because they do not accept the testimonies that he revealed himself and gave commandments, and others because in their opinion, even if he gave commandments, that still does not obligate us. Why should I be obliged to fulfill obligations just because someone defines them and imposes them on me?! If so, they argue, even God’s commands, even if he created me, do not necessarily bind me. This question requires reference to questions of gratitude, and really to the whole basic question of what can create an obligation to obey instructions.

Thus, in order to arrive at obligation to the religious commandments, we must adopt three claims in succession: 1. God exists. 2. He revealed himself and commanded. 3. There is an obligation to fulfill his commands. Each of these three claims has a different character. The claim about God’s existence is philosophical, and as such it can be clarified, or at least discussed, by philosophical tools. By contrast, the claim that God revealed himself and commanded us is historical in its essence (in the Jewish context: was there a revelation at Mount Sinai, and what happened there?), and therefore by its very nature it cannot and should not be discussed by philosophical tools. The next claim in the chain, that if he commanded then his commandments bind us, is a normative claim, and therefore the tools for clarifying it are normative-ethical tools. It follows that the Achilles’ heel of philosophical engagement with theology is claim 2, that is, the historical claim: God revealed himself and commanded. And yet, I will try to show here that the philosophical clarification of claim 1 is important even with respect to this claim.

Russell’s celestial teapot

To understand the matter, let us get acquainted with Bertrand Russell’s claim about the celestial teapot, which accompanies us throughout this discussion. Russell argued that the claim about God’s existence is similar to a claim about the existence of a small (and transparent) teapot orbiting the planet Jupiter. If someone were to come and claim that such a teapot exists, would we find ourselves in a state of doubt? After all, we have no other information, and therefore seemingly the teapot’s existence and nonexistence are equally possible. When I ask my interlocutor why I have not seen it, I receive a very reasonable answer: because it is small (and transparent) and far away. It cannot be seen. On the other hand, there is no reason to assume the existence of such a teapot. As far as I understand, even the speaker who informs me of it is not equipped with any tools for knowing that. Russell argues that in such a situation we should not be in doubt about the teapot. A rational person needs a good reason, or at least a reasonable basis, even in order to entertain doubt. Therefore bizarre claims with no visible basis should be treated dismissively and rejected, and it is wrong to remain regarding them in a state of doubt (equipoise), even in the absence of any information.

As stated, Russell compares this to the claim about God’s existence. When someone comes and claims that God exists, this is exactly like the claim about the teapot. When I (= the atheist) ask him why no one has seen him, or why I do not succeed in detecting his existence, the answer is: because he is abstract and cannot be seen (in the case of the teapot: small and transparent).

But on closer inspection the two cases are not similar. In the case of the teapot there really is no basis for doubt, and therefore the testimony/claim should be rejected. But in the case of God, if indeed we have a philosophical proof of the existence of a perfect being, and perhaps even of the claim that he created the world, and now someone comes and says I met him (he revealed himself) and he said such-and-such (he commanded), this is a claim that should be treated with greater seriousness. Here, if we have no other information, we really are in a state of doubt. What is the matter comparable to? A person who comes and says that he knows the president of UFO-land and that he is black. Such a claim should be rejected, since none of us has ever heard of such a place. But if evidence comes into my hands that such a place really exists, and now a person comes and tells me that the president is black, I can certainly accept his words, or at least not dismiss them out of hand.

This is the importance of the philosophical clarification of God’s existence for question 2, whether he revealed himself and commanded. If we have reached the deistic conclusion that such a being exists, there is no impediment to accepting testimony about revelation and command.

Of course, this does not mean that the tradition about revelation and command must now be accepted. At most, it means that it is not to be rejected. We must now examine the tradition and its reliability and plausibility by historical and other tools, and reach a decision. And yet, the philosophical clarification of deism is certainly relevant also to the rest of the route that leads from deism to theism.

Summary of Chapter 3 of the ‘Proslogion’

Let us now return to the course of our general discussion. In the previous part we saw that Chapter 2 proves the existence of God, and in this part we saw that Chapter 3 shows the necessity of his existence. Both of these moves were ontological, that is, they did not require a factual basis (factual premises).

Below we will discuss the question whether the "rationalist miracle," that is, a proof of a factual claim on the basis of an a priori ontological argument, is related to the nature of the object whose existence we proved. Is it accidental that the ontological proof dealt with a being that is a necessary existent? Can there be an ontological proof that proves the existence of a contingent being? True, we saw above that logical-epistemic necessity is not equivalent to ontic necessity, and neither of them follows from the other. And yet, there is a feeling that if an ontological proof is possible at all, it is no accident that it would deal with beings of this type, and not with ordinary beings.

We will return to this discussion in Part Five, when we address Gaunilo’s objection of the "existing lost island." There we will dwell on the distinction between necessary beings and contingent beings, and on its significance in the context of ontological proofs in general and Anselm’s argument in particular.

Part Four

Proslogion Chapter 4

Chapter 4: But how can the fool say in his heart what he cannot think; or how can he fail to think what he said in his heart, when "to say in the heart" and "to think" are one and the same? If he really thought it, and even more, precisely because he really thought it, since he said it in his heart; and if he did not say it in his heart, since he could not think it: this is because a thing is said in the heart or thought in more than one way. For it is one thing to think of a word that signifies a thing, and another to understand that thing itself, what the thing is. And so, in the first way one can think that God does not exist; but in the second way this is impossible. For no one who understands what God is can think that God is not, even if he says these words in his heart, whether without giving them any meaning at all, or by giving them a meaning foreign to them. Indeed, God is that than which nothing greater can be thought. And whoever properly understands this will also understand that God is such that there is no possibility at all of thinking him not to exist. Therefore, whoever has understood that this is what God is also cannot think that he is not.

I thank you, good Lord, I thank you, for what I formerly believed through your gift I now understand through your illumination: that even if I had not wished to believe that you exist, it would not have been in my power not to understand it.

The question: another look at the emptiness of the analytic

Introduction

We already mentioned in the introduction that the three chapters of the Proslogion function as three successive stages in Anselm’s philosophical move. As we saw in the previous part, here too the sentence that opens Chapter 4 expresses the aim of the chapter:

But how can the fool say in his heart what he cannot think; or how can he fail to think what he said in his heart, when "to say in the heart" and "to think" are one and the same?

The entire composition deals with the fool’s claim: "There is no God." But in the previous chapters we saw that this expression is actually an oxymoron, since the concept of God includes his existence. The expression "God does not exist" is meaningless, exactly like "round triangle," "married bachelor," "the round square dome of Berkeley College," or "a square whose diagonal is shorter than its side." The question this chapter addresses is how one can say in one’s heart, that is, think, that there is no God. After all, this is a meaningless expression, and therefore it cannot be said that it is entertained in the fool’s heart (or in his mind).

Contrary to what one might perhaps have understood, as though this were mockery at the fool’s expense, that is, Anselm’s victory celebration, the truth is that this is a continuation of the discussion. The question about the fool is very important to the substance of Anselm’s argument. If indeed the ontological proof is based on nothing more than conceptual analysis, that is, if it is a purely logical move, then there cannot be fools who say in their hearts "there is no God." The very existence of such a fool proves (by a reversed ontological proof) that Anselm is mistaken, for it means that this expression has meaning, that is, that existence is not necessarily derived from God’s essence (for if "there is no God" is thought by someone, then this is not a logical contradiction), that is, the ontological proof is not pure conceptual analysis.

This is the question with which this chapter deals, and therefore what we have here is in fact a closing of the circle and the conclusion of the discussion of the ontological proof.

The emptiness of the analytic

In Chapter 2 above we dealt a little with the emptiness of the analytic, and this is the place to expand on it somewhat more.^[20] A logical argument derives a conclusion from premises. For example: all human beings are mortal, Socrates is a human being, and therefore Socrates is mortal. What is the secret of the power of such an argument? Aristotle already noted that what gives such an argument its force is the structure and not the content. The structure of the argument is the following schema: every X is Y, a is X, and therefore a is Y. Whatever we fill into these variables (so long as we preserve consistency, that is, we place the same meaning everywhere in place of X, and so too with a and Y) will not change the fact that this is a valid argument, that is, an argument whose conclusion necessarily follows from its premises. Thus, for example, if we place frog instead of X, winged instead of Y, and Moses our teacher instead of a, we receive the following argument: every frog has wings, Moses our teacher is a frog, and therefore Moses our teacher has wings. This too is a valid argument, since its conclusion necessarily follows from its premises. This is so even though both the premises and the conclusion of this argument are of course false. Validity does not say much about truth. Admittedly, if the premises are true, then the conclusion is necessarily true as well, that is, whoever accepts the premises must also adopt the conclusion.

Why indeed must whoever accepts the premises also accept the conclusion? Because the conclusion adds no information beyond what is found in the premises. After all, to say that all human beings are mortal is really an abbreviation for the claim that Reuven is mortal, Moses is mortal, Socrates is mortal (since there is also a premise that he is human), Muhammad is mortal, and so on. If so, the conclusion that Socrates is mortal is implicit in our premises. Therefore whoever adopts the premises must also adopt the conclusion, for he has already accepted it as part of accepting the premises. The meaning of this is that every logical argument in fact begs the question.

The meaning of this is that if a person arrived at some conclusion from a logical argument presented to him, then he accepted the premises of the argument. But we saw that in a valid logical argument the conclusion is swallowed up in the premises, and therefore that person in fact already held this conclusion even before the discussion began and before the argument was presented to him.

Sharpening the question

Think of a debate between Reuven and Shimon, in which Reuven claims that Socrates is mortal, while Shimon, one of Socrates’ ardent admirers, disputes this. Reuven now presents Shimon with the above argument, and Shimon becomes convinced that he was indeed mistaken: Socrates really is mortal. If Shimon was convinced by the argument, it is clear that from the outset he agreed to its premises. But the conclusion that Socrates is mortal is swallowed up within the premises, and therefore even before the discussion he already agreed that Socrates is mortal. So what was the discussion about at all? How could Shimon say that Socrates is not mortal if from the outset he accepted the two premises that all human beings are mortal and that Socrates is a human being? If Shimon truly and sincerely thought that Socrates is not mortal, that itself is proof that either he did not accept the premises or the argument is not valid. For if he accepts the premises and the argument is valid, then to say "Socrates is not mortal" is an oxymoron.

This is exactly Anselm’s question about the fool. To Anselm it is completely clear that the ontological proof is a valid logical argument. If it is a purely logical argument, that is, nothing but conceptual analysis (without premises), then a fool who is convinced by it could not have thought otherwise from the outset, for otherwise he could not have been convinced. And even if this argument has premises, as we saw above (we presented at least two premises, though not factual ones), then the fool who was convinced by this argument presumably agreed to the premises (for according to Anselm they are self-evident). If so, the fool already knows from the outset that God exists, for that is contained in the premises. If so, how can he say "there is no God"? And if he can say this in his heart, then the argument is apparently not valid or he does not accept its premises (and then again the argument cannot convince him of the conclusion).

To Anselm it is completely clear that every fool must adopt his premises and be convinced by his argument, and therefore that option falls away. If so, the question now arises with even greater force: how is it possible that there is a fool who says "there is no God"?

Important note: what is the purpose of a logical, or ontological, discussion?

Before we continue, we must dwell on another point. From the description given above we can understand that in fact the question dealt with by Chapter 4 of the Proslogion is much broader than the one presented here in the opening sentence. He is really asking what the purpose of a logical or ontological discussion is. After all, if we succeed in convincing our interlocutor, that proves that he already agreed with us from the outset. And if he really does not agree with us, then we will never succeed in convincing him. So what is the point of talking?

Of necessity, the aim of logical discourse is not to bring something new to the knowledge of the interlocutor, but to expose before him beliefs or items of knowledge that are already hidden within him, or logical mistakes in his doctrine. The conclusion that Socrates is mortal may not be conscious to him, but it is in some way present within him. The purpose of the logical-ontological argument is to expose it before him. When he says "there is no God" or "Socrates is not mortal," he is in fact making a logical mistake. The logical argument shows this to him. A logical argument indeed cannot give us new information, but it can expose to us information that exists within us but is inaccessible to us. If we adopt the premises of the argument but reject its conclusion, then we have a logical inconsistency, and the argument exposes this before us.

Let us illustrate this by way of a parable. An average child in sixth grade knows and understands quite well all the axioms of Euclidean geometry. He understands that between two points only one straight line passes, that two parallels never meet, and so on. But if we ask him what the sum of the angles in a triangle is, he probably will not know how to answer. He may even guess that their sum is 234. How can he say this, if he adopts the premises, seeing that the conclusion follows from them by valid deductive logical tools? What, then, is the point of teaching geometry in high school, if anyone who accepts the axioms also accepts within them all the theorems? So why teach him the theorems of geometry? On the other hand, it is a fact that we all understand that there is indeed reason to study geometry even if we know and understand the axioms very well. Very few of us would succeed in proving all the theorems proved on the basis of those axioms. The teacher’s role is to expose before us the information already hidden within us (inside the axioms), but not in an accessible form. Alternatively, if we hold the (mistaken) position that the sum of the angles in a triangle is 234, the teacher exposes before us our logical mistake (for adopting the axioms together with the claim that the sum of the angles in a triangle is 234 is a logical contradiction into which we have fallen). This is exactly the purpose of logical discussion. One can convince someone by logical means of a certain conclusion only if it is contained in premises he agrees to, but the information is still not accessible to him. There is a contradiction or logical inconsistency in his doctrine, and the argument exposes this before him, just like the study of geometry.

Solution: two types of conceiving

Reformulating the difficulty

If so, the fool who says in his heart "there is no God" is in fact mistaken even according to his own view, since that proposition is not consistent with the premises that he himself accepts. A logical-ontological argument can only expose before him the fact that he has always been a believer, and can never turn him from an atheist into a believer. The ontological proof merely shows him this. But this sharpens the question even further: what does it mean to say in my heart something that is logically inconsistent with my own premises? In what sense can it be said that this thing is really thought by me? When the child says that the sum of the angles in a triangle is 234, is that really what he thinks? After all, I can prove logically that what he really thinks is that the sum is 180 (because this follows necessarily from the premises that he too accepts). It seems that there is a difference here between what he thinks (perhaps not consciously) and what is present in his head (or consciously thought there).

Saying in the heart versus conceiving

Anselm himself, in the opening sentence, hints at a possible solution to this difficulty: perhaps one can say in the heart even what cannot be conceived? True, when he presents the question he states simply that conceiving and saying in the heart are synonymous terms, but in the background of the discussion the possibility is already peeking through that there is a difference between them.

He now details this further:

If he really thought it, and even more, precisely because he really thought it, since he said it in his heart; and if he did not say it in his heart, since he could not think it: this is because a thing is said in the heart or thought in more than one way.

If the fool really did think it, and in fact let us assume for the sake of the discussion that he really did think it, since he said it in his heart, and conceiving and saying in the heart are one and the same. Alternatively, if he did not think it, that means he also did not say it in his heart. He is basically determining that both sides must be true. Therefore the only solution is that there are two different ways of saying something in the heart or conceiving it. He insists on not distinguishing between saying in the heart and conceiving, and yet it is still clear that both of these receive two different meanings.

He now explains this:

For it is one thing to think of a word that signifies a thing, and another to understand that thing itself, what the thing is. And so, in the first way one can think that God does not exist; but in the second way this is impossible. For no one who understands what God is can think that God is not, even if he says these words in his heart, whether without giving them any meaning at all, or by giving them a meaning foreign to them. Indeed, God is that than which nothing greater can be thought. And whoever properly understands this will also understand that God is such that there is no possibility at all of thinking him not to exist. Therefore, whoever has understood that this is what God is also cannot think that he is not.

He distinguishes here between conceiving the words that express an idea and thinking the idea itself. Perhaps דווקא the distinction he rejected above would be appropriate here: saying in his heart is thinking the words "there is no God," while conceiving is thinking the idea itself, that is, thinking of God as nonexistent or thinking the proposition (not the words) that God does not exist.

A small correction to the formulation

It seems to me that Anselm’s formulation here is not precise. The distinction he intends is not a distinction between thinking the words and thinking the thing itself, but between thinking the idea in an external way and understanding it itself. When I think "there is no God," it is not only words. It is clear that I am thinking some idea here. True, if Anselm is right, then it is an incoherent idea, but it is still clear that I am thinking something. Even when I think "round triangle" there is something in my mind beyond the words. Although here the logical contradiction is blatant, and therefore this thought is indeed found on a very shallow level. It seems that I hold in my head the meaning of triangle and of round, but it is not clear to what extent there is in my head something that joins them together. There is thought about each aspect separately, but the totality of the aspects does not create in my thought a conceptual unity. But in other contexts it is clear that there are several different levels of thought, between the verbal one (thinking the words) and the essential one (thinking the idea itself).

In these terms, what Anselm is arguing is that the fool not only thinks the words "God does not exist," but also thinks the idea that God does not exist. But he argues that the unified concept does not exist in his mind, since there is no such coherent concept. Let us note that such a state can exist even where coherent concepts are concerned, when a person understands different aspects of some concept or subject, and perhaps even all its aspects, but the concept as a unified and unitary idea is not present for him. The difference between these situations and the fool’s situation is that the fool’s thought deals with a concept that has no unitary content, and therefore here this is always the case.^[21]

A halakhic illustration

It is interesting to note that this distinction also arises in Talmudic and halakhic contexts, and is even sharpened there further. In the Gemara Berakhot 15a, tannaim (Rabbi Yosei and Rabbi Yehuda) dispute with regard to the Shema: whether it may be said in any language, and whether one must say it or whether it is enough to think it. Rabbi Yosei derives from the verse "Hear, O Israel" both the rule that one may recite the Shema in any language and the rule that one must make it audible to his own ear (one cannot recite the Shema in a complete whisper, or in the heart).

Such a situation raises a difficulty, for the accepted Talmudic assumption is that one cannot derive two different laws from the same verse. If it teaches A, then B cannot also be derived from it, and vice versa. The Rashba, in his novellae there, notes this point and explains the tannaitic dispute as follows:

And Rabbi Yosei would say to you: from it one automatically learns, "in any language that you hear." Rashi, of blessed memory, explained that one learns two things from it: when you also expound "hear" as "in any language that you hear," you also learn from it that one must make it audible to his own ear. But this is not satisfactory in my eyes, for from where do we know that one learns two things from it? And moreover, that is not what "automatically" means. It seems preferable to explain that this is what he is saying: once you derive from it "any language that you hear," you automatically learn from it that he must make it audible to his own ear, for if he did not need to make it audible to his own ear, why would the Merciful One need to permit any language that he hears? That is obvious, for if he does not need to make it audible to his own ear, then even mere contemplation of the heart would be permitted, as appears below [20b] concerning one who has had a seminal emission; and in contemplation of the heart, language is irrelevant. So we automatically learn that there is no preference between the holy tongue and all other languages. Rather, from the fact that the Merciful One needed to permit any language, we automatically infer that he must make it audible to his own ear. And it is possible that Rabbi Yehuda, who does not hold thus, is because he maintains that even though one need not make it audible to his own ear, one nevertheless must utter it with his lips and not by contemplation alone, and therefore the Merciful One had to permit any language that he hears. So it seems to me.

Some later authorities understood that the Rashba’s intention is that thought is not conducted in any language. Thought is nonverbal; it is not done in words, but rather brings up the ideas as such. Therefore, if we were supposed to think the Shema, then certainly there would be no point in speaking about the language in which this is done. Others proposed different interpretations of the Rashba’s words, and it seems to me that the most reasonable among them is that although the Rashba also agrees that one can think in a language (think words), when there is some law that is fulfilled in thought, halakha never obligates us to think in a specific language. A halakhic instruction directed toward thought relates to thinking the ideas and not to the manner of their representation, and in particular not to the language or the words. According to this proposal, one cannot infer from the Rashba’s words that thought is never carried out verbally at all. Factually too, this seems quite obviously incorrect.

The Gemara in Shabbat 40b states that it is forbidden to think about sacred matters in the bathroom. An incident is brought there in which someone spoke in the bathroom, and regarding this the Tosafists there write:

And if you should say that he said it in the vernacular—then although it is forbidden to contemplate, let us say that it is forbidden to contemplate only in the holy tongue, whereas he contemplated in the vernacular.

We see that in their view there is room for a distinction between languages even when a person is thinking. And indeed, the Rashash there comments that the Tosafot’s words stand in contradiction to the Rashba we saw above. He of course assumes that the Rashba maintains that thought is not conducted in any language or verbal form at all, but according to our proposal there is of course no necessity that the Tosafists disagree with him. The Rashba, like Tosafot, understands that one can think in words, and in the context of the prohibition of contemplation in the bathroom he too agrees that we are dealing with a prohibition against bringing words up in thought, and that this prohibition was stated only with regard to words in the holy tongue.^[22]

It is very likely that when these decisors speak about thinking in words, they do not mean bringing up the words themselves in thought. On the contrary, all the Rashba claims is that even when words are brought up, they are only a representation of the ideas. By means of the words we think the ideas. The prohibition of contemplation in the bathroom can also refer to the words themselves, or at least attach also to the representation and not only to the ideas.

The conclusion is that one can think on several different levels: 1. bringing up the words themselves in thought. 2. bringing up words together with understanding of the words, but still without creating a concept/unified idea that is a synthesis of all the aspects. 3. bringing up words together with understanding of the totality of the aspects and creating a unified concept/idea. The unified idea and concept exist only in the form of inchoate thought. Words are always a breaking down of the unity into aspects, and a representation of those aspects in words. Thus, when we think the collection of words "the first prime minister of the State of Israel," we can simply bring the words up in our head and no more. On the next level we can understand what a prime minister is, what first is, what a state is, or the State of Israel, and understand all of these separately. Finally, we can synthesize all these aspects and fuse them into a single unified concept. At this point there are still two possibilities: a. we are thinking of the man David Ben-Gurion. b. we are thinking of the unified concept that describes Ben-Gurion, "the first prime minister of the State of Israel." Not the words but the meaning they express/represent.

Anselm is basically arguing that the fool can hold in his head the idea or proposition "God does not exist" in the first two senses of conceiving. But he cannot conceive it in the third sense, in both of its versions: a. the object to which this concept refers (a God who does not exist) is a fiction. It does not exist in the world, that is, there is no state of the world of which this is the description. b. the idea "God does not exist" is contradictory, and therefore even in thought itself (beyond the question of representing an object or a state in the world) there is no unified concept that this is the representation of. Separate understanding of the set of aspects that make up this expression is possible: "God," "not," and "exists," and even the thought that they are joined together. What Anselm is claiming is that the result of this joining (this synthesis) does not exist, because it is empty.

Naive faith and arguments with straw men

Introduction

Before moving on to Anselm’s closing sentences, let us briefly discuss a question that is relevant to each of us: what is the meaning of the faith of a person who does not examine his faith on the philosophical level so as not to fail? Is it even correct to regard him as a believer?

The meaning of naive faith

There is a common approach in religious societies according to which it is not worthwhile (or even forbidden) to engage in critical examination of faith. One should not read books of philosophy at all, or at least books of heresy, which may raise questions that lead the reader (the unskilled one?) to incorrect conclusions. This approach is sometimes called "naive faith," and many in the religious world and in religious thought praise and extol it greatly.

Naive faith: first problem

There is of course an inherent problematic aspect in such an approach, for it assumes that a person should accept some ideological system simply because he was born into it. Thus this approach may require different people to arrive at opposite conclusions because they were born into environments that think the opposite. There will of course be those who say that one who was born into the wrong environment must examine the ideological system dictated to him, and that the prohibition in question applies only to those who hold the correct faith. But that of course raises the difficulty of how I can know that I indeed hold the correct system if I am forbidden to examine it critically against its alternatives. It is astonishing to me how intelligent people ignore so basic a difficulty and continue to advocate this absurd conception.

Naive faith: second problem

But beyond this obvious difficulty, the description we proposed above raises another question here. In what sense is this naive believer indeed a believer? Think of Reuven, who was born in a Jewish home and believes in the Jewish tradition. In the estimation of Rabbi So-and-so, if that Reuven were to open the critical and philosophical literature, he would arrive at the wrong conclusions, and therefore the rabbi forbids him to do so. Reuven of course obeys him, for he is a thoroughly God-fearing man, and is careful about the instructions of halakha in small matters as in great ones.

Is Reuven a believing Jew? If we analyze his present outlook, he is actually a heretic, except that he does not do what is required in order to expose this. If Shimon the atheist were to present him with this or that logical argument, Reuven would change his outlook and become an atheist. We have already seen that if Reuven is convinced by some logical argument, then it is clear that the conclusion of the argument was already within him unconsciously. If so, even before he heard the argument that would have led him to the conclusion that there is no God, he was in fact an unconscious atheist. If so, forbidding him to engage in these issues has accomplished nothing. The man is an atheist (concealed, even from himself) who observes the commandments.

In light of the picture we described above, one can say that he does indeed hold in his thought the idea "God exists," but only in the first two senses of conceiving. In the third sense—not. The essential content expressed in this sentence does not exist inside him, and therefore, at least on the essential level, he is an atheist.

The meaning of this is that a person who believes with naive faith can never know whether he is really a believer. He may be an unconscious atheist, since if logical arguments would really convince him to become an atheist, then even now he is one. Until he examines himself and his coherence, and exposes the assumptions implicit within him, he will not be able to know whether he is a believer or an atheist. This is the stage at which we can approach the final chord of Anselm’s ontological move: the closing prayer. But before that, a timeout with a needed clarification.

Clarification: naive faith as such is not invalid

It is important for me to clarify that I am not coming here to invalidate naive faith at all. A person who decides that he believes because this is his intuition is a believer in every respect. Each person has his own path to faith. Especially since, as we saw in Chapter 11, every argument in favor of faith must itself be based on foundational assumptions (axioms), and these too are accepted "naively" (that is, without proof). Therefore there is certainly nothing wrong with a person who declares that faith itself is his foundational assumption, and he accepts it because it is self-evident in his eyes.

My remarks here are directed only toward a person who is unwilling to examine his naive faith because he fears that the examination will change it (will convince him to abandon faith). About such a person, and only about him, I wrote that if he has such a fear and because of that is unwilling to examine, then even now he is not a believer. By contrast, if a person does not examine because he has no interest in examination, because he is convinced that he is right, then although I am not sure that I agree with his way and his confidence, he is certainly to be regarded as a complete believer.

To sum up, it is clear that there is no obligation to arrive at faith by means of arguments, for as stated they themselves are based on unproved foundational assumptions. Or, in another formulation, even the following trivial argument is a legitimate argument for faith: premise: there is a God. conclusion: there is a God. The conclusion follows from the premise, and therefore it is a valid argument. From the discussion in Chapter 11 it emerges clearly that such an argument is not essentially different from an argument that assumes several other premises and infers from them the existence of God. As we saw there, in every such argument the conclusion is implicit in the premises.

Let us now return to Anselm’s final chord.

Anselm’s closing prayer

As remembered, Anselm opened his move (at the beginning of Chapter 2) with a prayer, and now (at the end of Chapter 4) he also concludes it with a prayer of thanksgiving:

Here Anselm returns to the starting point. When we dealt with the opening prayer, we explained that this prayer that opens Chapter 2 indicates that Anselm’s move begins from faith. His aim is to move from faith to understanding, that is, to prove to himself (and to the fool) what he already knows. In this part we saw the meaning of the matter. The argument in fact exposed before the fool that he too had been a believer, though hidden and unconscious, from the very beginning. If so, what could be better than to return at the end of the process to a prayer that thanks God for helping us move from faith to understanding.

If we connect these things to the question of naive faith, Anselm in his logical move passed from a state of naive faith (when one can never know whether it is not unconscious atheism) to explicit and conscious faith. He now holds in his intellect the idea of faith, that is, the proposition "God exists," in the third sense as well.

To whom is Anselm’s ontological move addressed?

It is interesting to note that in these closing sentences Anselm speaks about himself and not about the fool. In this section it becomes clear that Anselm never intended to prove anything to the fool at all. Perhaps there is no such fool at all. Anselm uses the fool in order to prove to himself the existence of God. The fool is really a straw man that Anselm created in order to help himself move from faith to understanding. He set before himself an atheistic antithesis that is put into the mouth of a fool (for Anselm himself is a believer throughout, and therefore he himself cannot seriously state the claim of atheism), and his logical argument deals with it. But this fool is really a little figure within Anselm’s own soul. In the logical move he made here, Anselm showed himself that the heretical thoughts that pass through his mind are the product of misunderstanding or logical incoherence, and the logical argument exposes this before him. The fool is really Anselm himself, or a fictional phase that passes through him from time to time, but in fact this is a demon with no real existence.

We can summarize and say that Anselm and the fool within him each underwent in parallel a different process. If the (fictional) fool passed from a state of implicit and unconscious faith to explicit faith, then Anselm himself passed from a state of naive faith (which, as we saw above, it is doubtful whether it is even appropriate to regard it as faith) to a state of understanding, which is in fact full and genuine faith.

Psychological "projection": Tzemach Atlas

There is a psychological phenomenon that is in fact the mirror image of what we described here. We saw that Anselm essentially created an imaginary figure and projected onto it the heretical thoughts that pass through his mind. In this way he copes with his own thoughts. This is a kind of what is called in psychology "projection," which is defined in Wikipedia as follows:

In psychoanalysis, projection is a personal defense mechanism by which a person projects the negative sides of his personality onto the world outside him, and attributes them to other people, thereby allowing himself to ignore the sight of his own negative traits and drives. The psychologist Erik Erikson argued that although projection is usually distorted and full of hostility and fear, it contains a core of deep meaning; it is not by chance that the person projecting attributes it to the object onto which it is projected.

Projection serves us by distancing our negative sides from ourselves. In Anselm’s case, he took his negative thoughts (in his eyes) and built them into another figure, the fool. In tractate Kiddushin 70b we find, "Whoever disqualifies others does so by his own blemish," and from this it follows that one who calls others a slave is probably himself a slave. If Anselm defines the atheist fool and deals with him, then presumably these things are within him.

True, in psychology this mechanism serves to distance negative sides, but Anselm uses it positively: he deals with thoughts and claims that trouble him by constructing a straw man that expresses them. The distancing allows Anselm to deal with these claims more effectively. Once there is Anselm himself opposite the fool, the thesis and the antithesis are better defined, and one can try to decide the argument. Anselm performs an analysis on himself (not psychological but philosophical), and serves as his own therapist. For that purpose he creates another patient, who is a duplicate of himself, and treats him with logical and philosophical tools. As Anselm hints in his prayer here, the analysis in these three chapters is self-analysis.

There are additional psychological phenomena that come close to what we have seen here. The well-known Yiddish writer and poet Haim Grade composed two books with an autobiographical dimension, Tzemach Atlas and The Battle of the Inclination (which continues its predecessor). The background to this is the phenomenon of the Novardok yeshivas that spread at the beginning of the twentieth century throughout Lithuania and its surroundings. The Alter of Novardok, Rabbi Yosef Yozel, who saw that Jewish youth was losing its faith and being drawn after the Enlightenment, sent many of the young students in his yeshiva (Novardok) to establish yeshivas in villages for youth, and thus a situation was created in which young men of about twenty became heads of yeshiva dealing with very young youth (in their teens). Young and immature people, who had received a very extreme education, began to engage in the education and instruction of adolescent youth, with all the hesitations involved.

These two books deal with the figure of the head of a small Novardok yeshiva in the village of Volknik. This is a young man named Tzemach Atlas, who is described as gripped by lusts and heretical thoughts, and whose way of coping with them is to fight these phenomena fanatically among his tender students in the yeshiva. Opposed to him stands the figure of the author of the Vision of Abraham (it is known that Haim Grade used this as a literary name for the Hazon Ish. Grade himself had been a student in such a Novardok yeshiva, and lived in the Hazon Ish’s home for several years), who, despite his decisive and unequivocal views, had a pleasant and moderate character, without the fervor that characterized Tzemach Atlas and without wars against everything around him.

The comparison between these two figures expresses exactly the phenomenon we described above. A person who fights with fanatical extremism against phenomena of heresy or immodesty probably suffers greatly from them himself. The extremist usually tries to fight with the fool within him, and he does this by projecting him onto the people around him. These are the straw figures onto which he projects his problems. The Hazon Ish, by contrast, whose inner heart was whole in his faith, fought no one. He was moderate and measured, willing to listen to the hesitations of the young Haimke (whom Tzemach Atlas threw out of the yeshiva), and even to answer him patiently and attentively. Inner wholeness led to non-extreme behavior outwardly, unlike Tzemach Atlas, as stated.

Anselm too fought, in a certain sense, against his own straw man (the fool). But unlike Tzemach Atlas, Anselm did not persecute the fool; rather, he first created him as a straw man who held positions that Anselm himself wanted to examine, and afterward attacked him intellectually. As stated, the projection he carried out was not psychological but philosophical, and the treatment (analysis) he gave that figure was of the same kind. The purpose for which it was created was to achieve the distance needed in order to examine these ideas seriously. It seems that Anselm דווקא did not advocate naive faith, although he certainly placed faith at the foundation of his inquiry. Precisely from this starting point, which was essentially naive faith, he refused to remain in a state of naivety and insisted on examining it with his intellect, thereby passing from faith as a divine gift to understanding of faith in the intellect by divine illumination. His prayer here expresses the completion of this process.

The sin of the first Adam

The picture described here gives us an interesting look at an interpretation proposed by Rabbi Hayyim of Volozhin concerning the sin of the first Adam. In a gloss that appears in his book Nefesh Ha-Hayyim, in Gate 1, chapter 6, he writes:

And this is the matter of the Tree of Knowledge of Good and Evil: before the sin, although he certainly had complete free choice to incline himself toward whatever he wished, toward good or, Heaven forbid, the opposite, for this is the purpose of the whole of creation, and after all he sinned later, nevertheless the nature of his choice was not that the powers of evil were included within him. For he was an utterly upright man, composed only of the orders of the powers of holiness. All his matters were entirely upright, holy, and refined—pure good, without any admixture or inclination at all toward the opposite side. And the powers of evil stood to the side, as a separate domain and matter outside him. And he had free choice to enter into the powers of evil, Heaven forbid, just as a person has free choice to enter into fire. Therefore, when the Other Side wished to cause him to sin, the serpent had to come from outside to entice him. Not as it is now, when the inclination that entices a person is inside the person himself, and it seems to the person that he himself is the one who wants and is drawn to commit the sin, and not that another outside him is enticing him. And when he sinned, having been drawn after the enticement of the Other Side, then the evil powers were actually mixed into him. And so too in the worlds. And this is the Tree of Knowledge of Good and Evil: that the good and the evil became joined and mixed within him and within the worlds together, this within that ממש. For knowledge means connection, as is known. And the matter is explained for one who understands in Etz Hayyim, Gate of the Shell of Nogah, chapter 2, except that he abbreviated there on the matter. And study well in Gilgulim, chapter 1.

Before the sin, man was whole and upright, and built in such a way that he was good to the utmost. The forces of evil stood outside him, and the one who represents them is the serpent, which stands outside and entices man to sin. This is not like our condition, where the feeling is that the impulses entice us from within and not from outside. They are part of us and of our personality, and we feel that we ourselves want to do evil. This situation was created בעקבות the sin of the first Adam, when the enticing forces (the impulse, the serpent’s pollution) entered into us, and thus the feeling was created that the temptations come to us from within and not from without.

There is here a description of the struggle between good and evil that takes place within us and מול our impulses and thoughts, and this is done by projecting them onto a fictional figure that appears outside us and presents our evil thoughts before us. The way to deal with them is to distance them and understand that this is not what I really want, but something outside me that is trying to influence me. The projection here is a therapeutic method, and study of this passage from the beginning of Genesis is treatment of that fictional figure, and really treatment of ourselves through projection onto the figure of the serpent that supposedly stands outside. In this way it is easier for us to treat it and to cope with it.

Part Five:

Critiques and discussion

In this part we will deal with several central critiques of the ontological argument. Since this is a logical argument, we have already mentioned that it can be attacked on two planes: by challenging one of its premises, or by pointing to a flaw in the logical inference that leads from them to the conclusion.

The critiques we will address differ from one another in character. Some critiques attack the ontological character of the argument a priori. They point to the impossibility of ontological arguments in general, and of Anselm’s proof in particular. Other critiques challenge the validity of the argument. Yet other critiques accept its validity but claim that it does not really bring us into factual territory as it purports to do (this is really an objection to the conclusion. That objection maintains that it was not understood or presented correctly, and that in fact it is not a factual conclusion). Another type of critique exposes that Anselm’s argument is not purely logical (as we defined in Part One), because what we have here is not merely conceptual analysis. Such critiques show that assumptions (factual or not) underlie the argument, and therefore they can be attacked and the conclusion rejected.

Each chapter in this part will deal with a different critique. At the beginning of the chapter I will point out the logical character of the critique discussed in it.

The Kantian critique: one cannot derive facts from pure logic

Introduction

As I have already mentioned, over the years many very critiques of the ontological argument have appeared. The best known among them is the critique of Immanuel Kant from the eighteenth century. In this chapter we will discuss Kant’s critique, because it brings us back to the principled and broader background of the discussion: the essence and possibility of ontological proofs in general. As stated, this is an objection to the ontological inference, but it is an objection that does not attack the argument head-on. Rather, it points out a priori that an argument of this kind cannot be correct (not necessarily only with respect to God). This is also indicated by the title of the chapter in Critique of Pure Reason, called "On the utter impossibility of an ontological proof." He is essentially trying to show that there cannot be a logical argument that entails a factual existential proposition.

Kant’s critique: a general view

We mentioned in the first part Kant’s classification of the proofs for God’s existence, the first type being ontological proofs. Kant discusses God, whom he calls the "ideal of pure reason," in his book Critique of Pure Reason, in the second part of volume I, in the second section, book two, third division. In the fourth chapter, which has already been mentioned above, he deals with the utter impossibility of an ontological proof.

One can distinguish in his remarks two critical arguments, although he probably relates to them as two aspects of one critical argument. The first argument is based on a general claim that one cannot learn anything about reality from a purely logical argument and mere conceptual analysis. Kant’s second argument concerns the question whether existence can be regarded as one of the components of a concept’s perfection, as Anselm assumes. We will deal with the second argument below in Chapter 16. Here we will touch on the first argument.

The first argument: the emptiness of the analytic

Kant presents this argument mainly in the following passage:^[23]

I ask you: is the proposition, ‘one thing or another (which I agree may be possible, be it what it may) exists,’—I ask—an analytic proposition or a synthetic one? If it is analytic, then by the existence of the thing you add nothing at all to your thoughts of the thing; but then either the thought that is within you must be the thing itself, or you have presupposed existence as belonging to possibility, and then you infer existence, in seeming fashion, from inner possibility—which is nothing but a miserable tautology. The word ‘reality,’ whose sound in the concept of a thing is different from existence in the concept of a predicate, adds nothing at all. For if you call every positing (without determining what you posit) ‘reality,’ then you have already posited the thing with all its predicates in the concept of the subject, and set it down as existing, and in the predicate you merely repeat this. But if you admit, as every sensible person must admit, that every existential proposition is a synthetic proposition, how can you then claim that the predicate of existence cannot be canceled without contradiction? For this advantage is a property unique only to analytic propositions, and it is upon it that the nature of such propositions is based.

To understand the terminology he uses here, let us first say that Kant distinguishes between two kinds of propositions: analytic and synthetic. An analytic proposition asserts a claim grounded in analysis of the concept that appears as its subject, for example: the ball is round, or every bachelor is unmarried. A synthetic proposition, by contrast, asserts something that adds to the concept more information that is not contained in it by definition, such as: this ball is heavy, or: this man is married, or: this married man has two wives.

In this passage Kant discusses the statement "X exists," and asks whether it is a synthetic or an analytic proposition. If it is analytic, then the existence claim adds nothing to the definition of the concept. In other words, we have really assumed its existence in the very act of defining it, and therefore there is nothing in the conclusion beyond what we assumed. In effect, the ontological argument begs the question. And if it is a synthetic proposition ("as every sensible person must admit," in his words), then it is impossible for a logical argument to prove its existence necessarily. If such a logical proof exists, it follows that saying "X does not exist" is a logical contradiction, but that means that its existence is included in the definition of its concept, which does not fit the assumption that it is a synthetic proposition.

The connection to the question of the synthetic a priori

To complete the picture, let us add that Kant makes yet another distinction between two types of propositions: a priori (prior to observation) and a posteriori (based on observation). For example, the proposition 1+2=3 is a priori, since it can be known even without observation.^[24] By contrast, the proposition that the law of gravitation (like any other law of nature) is correct is a posteriori, since it is based on observations.^[25]

Until Kant, it was customary to think that this distinction entirely overlapped the distinction between the analytic and the synthetic. Every analytic proposition is a priori and vice versa, and every synthetic proposition is a posteriori and vice versa. The logic of this is very simple: if a proposition is based on an analysis of the concepts involved in it, why would we need observation in order to verify its truth?! And conversely, if some proposition can be known without observation, then it is reasonable to assume that this is a proposition based on a conceptual analysis of the subjects involved in it (for if not, how could we know it?!). Thus, until Kant, propositions were divided into only two categories: analytic-a priori and synthetic-a posteriori. For various reasons, Kant argued for the existence of a third category of propositions: synthetic-a priori. These are propositions that assert something about the thing itself (about the world) beyond what is contained in its concept, yet nevertheless are not based on observation. This is how laws of nature are possible: they are synthetic propositions (they make claims about the world, that is, they contain factual information) but a priori (they cannot be grounded on observation alone)^[26].

Is a synthetic-a priori proposition not exposed to exactly the same attack that Kant directs against the ontological argument? Seemingly, what we have here is a factual claim about the world that does not derive from observation, or in other words a reflection of a rationalist view. But if Kant is indeed a rationalist, it is not clear why he argues so forcefully against the ontological argument that it is impossible to add information about the world merely through logical conceptual analysis. After all, on his own view too, one can learn about the world by reason alone.

To understand this, we must distinguish between the problem of rationalism (which does not trouble Kant, as a rationalist) and the logical problem that later came to be called "the emptiness of the analytic." Kant is not arguing for empiricism, that is, for the claim that one can learn about the world only through observational tools.^[27] As stated, he was a rationalist and was certainly willing to accept claims about the world that were not obtained from observation (these are the synthetic-a priori propositions). The problem he saw in the ontological argument was that it is an argument that derives facts from nothing. The way to arrive at a synthetic-a priori proposition, according to Kant, is indeed a priori, but not purely logical. Even if, in his view, observation is not necessarily required in order to say something about the world, conceptual analysis and logical juggling cannot yield factual claims. So what, beyond observation, can yield factual claims a priori? Only what Kant called "transcendental arguments." We need not enter into their nature here, and so I will suffice by saying that they involve reflection on ourselves and on our cognition (the uncovering of the necessary conditions for the existence of cognition), and not pure logical arguments or conceptual analysis. Those, by their very nature, are empty and cannot add factual information about the world. An ontological argument, by its very nature, is conceptual analysis, and as such it can never yield new facts about the world.

It is therefore no wonder that in the concluding passage of the chapter, Kant sums up his remarks and writes:

That is to say, all the labor expended on the ontological (Cartesian) proof, which seeks to demonstrate the existence of a supreme being from concepts, is labor in vain. A man will no more enrich his understanding by mere ideas than a merchant will increase his assets if, in order to improve his financial standing, he adds a few zeros to his cash balance.

Kant is basically claiming that it is impossible to expand our knowledge of reality by means of ideas and conceptual analysis alone. A purely logical argument cannot end in a renewed factual claim, that is, in a fact that was not already assumed in the definition of the concepts involved in that analysis. And if we are dealing with a concept whose existence is included in its definition, then we have simply begged the question, and once again the ontological argument has no real philosophical significance, since from the outset we already assumed God’s existence in defining the concept.

At this point it is worth drawing attention to the fact that Anselm does not assume God’s existence. He assumes that the definition of God as a being with all perfections is coherent and intelligible (even to the Fool). Definitions are not assumptions. There is a difference between defining the concept under discussion, which is a necessary condition for philosophical inquiry, and assuming something about it. Anselm assumes a definition of the concept of God, but he does not assume anything about it (namely, that it exists). Even if we define X as something that exists by definition, this is still not an assumption claiming that it really exists. That is what Anselm proves, rather than assumes. See below in chapter 19, which deals with Gaunilo’s objection (by way of "the existing island"), where the background to the discussion is the distinction between defining something as existing and making an existence claim about it.

Negative a priori arguments: proof by contradiction

The ontological argument is a proof by contradiction, which is an accepted logical and mathematical way of proving things. We assume some proposition and show that it leads to a contradiction, thereby proving its opposite. The thesis concerning the emptiness of the analytic is really supposed to reject any proof by contradiction about reality. Yuval Steinitz, in the first part of his book The Tree of Knowledge, argues that such a position is absurd, since every empiricist accepts proofs by contradiction about the world.

Thus, for example, if I saw a triangular object, I can prove from that by contradiction that it is not round, since a triangle is not a circle. Quine proved in this way the non-existence of a square round dome on Berkeley College. But this is a logical procedure that yields a factual conclusion (that there is no such dome on the college). Non-existence too is a claim about the world, and if logic is empty, how can one derive from it a claim of non-existence? After all, this is a factual claim in every respect. We are learning something about the world from conceptual analysis alone.

It can indeed be said that a concept that contains a contradiction, such as a round triangle or a square round dome, is meaningless. The claim that such a concept is not instantiated is not an ontological claim but a logical one. If the concept X is meaningless, then every proposition containing the concept X is also meaningless, both the proposition "X exists" and the proposition "X does not exist."

But let us look at things from a different angle. After all, we did arrive here at some conclusion about reality: that no angles are to be found on Berkeley’s round dome. Here there is no contradictory term at all, and the proposition is entirely clear, reasonable, and true. So we arrived at a factual conclusion on the basis of conceptual-logical analysis, and we used no term that contains contradictions (such as a round triangle or a circle with angles).

But this presentation of the argument is also misleading. In part 1 we distinguished between a logical argument based on some factual premises and a pure logical argument (conceptual analysis). The fact that no angles are to be found on that round college dome is not the result of logic but of observation. The observation that informed us of the dome’s round shape itself also tells us that there are no angles there. When I saw the round shape, I also saw the fact that there were no angles in it. Thus the conclusion that there are no angles there is not the result of conceptual analysis but of a logical argument based on observation, and perhaps even a direct product of the observation itself. But this is, of course, a completely legitimate procedure from the empiricist point of view. The ontological argument, by contrast, assumes no factual premise, and certainly no observational one. It is a purely logical procedure (conceptual analysis) that yields a factual conclusion. But a purely logical argument is supposed to be empty, as Kant apparently quite rightly claimed.

If so, the claim about the non-existence of a round triangle is not a factual claim. A round triangle is a meaningless combination. By contrast, the claim that a circle has no angles is a perfectly legitimate observational claim. Therefore, neither of these two kinds of claims is connected to the emptiness of the analytic. So Kant’s claim that the analytic is empty sounds very reasonable and logical, and yet, as we shall now see, it is not enough to undermine Anselm’s argument.

The problem with Kant’s argument

Claims such as Kant’s cannot help against a logical move like Anselm’s ontological argument. After all, Anselm presented a logical argument whose conclusion is a factual claim (God exists). The conclusion of a logical argument follows necessarily from its premises. As we have already mentioned, in order to refute a logical argument we must do one of two things: either point to a false premise (or an inconsistent definition), or point to a flaw in the logical move itself, that is, in the derivation of the conclusion from the premises. Statements to the effect that the conclusion seems absurd or like hocus-pocus are irrelevant. If one does not point to a flaw in the logical procedure, or challenge one of the premises, one cannot reject it. In what we have seen thus far, Kant did neither of these things: he did not challenge any premise of Anselm’s, and he did not point to a flaw in the logical inference. If so, it seems that he must accept the conclusion of this argument despite his surprise that a fact can be derived from a logical argument.

Kant is basically assuming that the analytic is empty, but Anselm’s argument proves that he is mistaken. After all, Anselm offered a logical argument that extracts a factual conclusion from conceptual analysis alone, and by that very fact he refuted the view that the analytic is empty. So long as Kant does not point to a flaw in the argument or show that one of its premises is false, he cannot make do with the a priori assertion that the analytic is empty.

The claim that the ontological proof derives a fact from pure logic is indeed a correct description of it, but this should not be seen as a criticism or refutation of that proof. Anyone who sees this itself as a refutation is simply begging the question (he is assuming empiricism rather than proving it). To sharpen this, think of a person who is presented with Zeno’s paradox of Achilles and the tortoise. This is an argument that proves that swift Achilles never catches the tortoise in a race between them (if it begins with some lead in the tortoise’s favor). Many people who hear Zeno’s argument immediately respond that it is nonsense, since it is obvious to any sensible person that Achilles will catch the tortoise in a short time. Such a response can at most serve as motivation for seeking a refutation of the argument, but it is not itself such a refutation. So long as we have not pointed to a flaw in the argumentative procedure itself or rejected one of its premises, its conclusion is necessarily correct. This is probably what Bertrand Russell hinted at in the remark quoted above, that it is easier to feel that the ontological proof cannot be right than to put one’s finger on exactly where the flaw lies.

Summary

From what we have seen so far, it seems that the novelty of the ontological argument is even more far-reaching than we had thought. In part 1 we presented this argument as an expression of the rationalist position, which sees reason (and not only observation) as a legitimate tool for knowledge of the world. But now we have seen that Kant too shares this position, even though he opposes the ontological proof. His claim is that this proof is not merely rationalist, that is, that it infers a factual conclusion without observation. It contains a more serious flaw: it infers the factual conclusion on the basis of a logical argument and conceptual analysis (what we called in part 1 a pure logical argument). If indeed Anselm’s argument still stands, then it achieves something far more impressive than rescuing rationalism. It actually refutes the thesis of the emptiness of the analytic. Not only is observation unnecessary for learning something about the world; conceptual analysis and mere logical manipulations can yield factual conclusions.

Let us conclude with one remark. Kant’s second objection finds a flaw in Anselm’s argument, in fact in one of its premises. Contrary to what many assume, there is at least one premise at the basis of Anselm’s argument, that is, it is not a purely logical argument. If there is substance to the second objection, then Kant can return and make the a priori claim discussed here as well, namely that the analytic is indeed empty. The claim about the emptiness of the analytic by itself cannot be considered an objection to the ontological proof, but if one presents an objection to the logical procedure, then it really can be inferred that the analytic is indeed empty. As stated, we will discuss Kant’s second objection below in chapter 16.

Can one conceive as existing something that does not exist: on skepticism

Introduction

In this chapter we will deal with an expected criticism of the argument, one that returns again, but this time from a different angle, to the heart of its ontological character. As noted, the claim here is that the conclusion of the argument was not correctly understood, and that in fact it is not really a factual claim.

The critical argument

In the second part we saw that Anselm himself insists that there are two kinds of apprehension: apprehending some being in our mind and apprehending it as existing (the picture with the translation neurons). First, let us ask ourselves whether those translation neurons cannot be activated even when no real object stands before us. These are neurons like any other, and findings from neuroscience show that they too can indeed be artificially stimulated. Ultimately, every cognition we have is grounded in neurons, and so one can stimulate the relevant neurons and give a person the feeling that a real object stands before him, even when that is not the actual situation.

If so, what are we to say about the conclusion of the ontological argument, which indeed leads me to the apprehension that in my mind there is the conception of God as existing, and not merely the concept of God as such? Seemingly, the fact that this picture is in my mind says nothing at all about reality itself. We are still within the domain of our cognition, and not of the reality we wanted to reach. At most, an ontological argument allows one to infer something about me (and not about the world): that in my mind there is a picture of an existing being. If we wish to derive from this a claim about reality, then once again we are moving here from the mind to reality, or in fact making a rationalist move. The empiricist will say that even if the argument is valid, it still has no power to prove anything about reality itself.

Seemingly, Anselm’s own distinction turns back on him like a double-edged sword. We saw that he was careful to distinguish between a claim about the existence of the being in the world and a claim about its existence in the mind. He was also careful to add another distinction, while emphasizing that it is a different distinction, namely between its existence in the mind as a concept and its existence in the mind as a realized concept. This is a distinction between two types of objects or ideas that exist in the mind. But if there really is a distinction between these two, and if these distinctions concern existence in our cognition and not in the world itself, then the movement of the argument leads us at most to the conclusion that God exists as an existing being in our minds, but not necessarily to His existence in reality itself.

In fact, the empiricist critic will say, this is the solution to the rationalist puzzle posed by all those ontological hocus-pocus arguments that derive facts from pure logic (see Kant’s criticism in the previous chapter). Ontological arguments do not really move us from logic and definitions to factual claims, but at most to quasi-factual claims, which in fact deal with us and not with the world. In Kant’s terms, we have proved that in the realm of phenomena God necessarily exists, but we have not said anything about the noumenal realm.

This critical argument does not really attack any of Anselm’s premises or definitions, nor the logical movement of the argument. It is willing to accept the entire argument and even its conclusion, and yet it still does not see it as a move that ends in a fact. One may say that it attacks Anselm’s claim to the rationalist crown (that is, to the proof of a fact by purely logical means). This critical argument claims that Anselm does not prove the existence of God as an existing being, but merely compels the conclusion that we all believe in Him in our minds as an existing being. But, as stated, this is not a claim about the world but about us. We already remarked in the first part that when some logical argument convinces us of its conclusion, that conclusion was already hidden within us from the start (in fact, it was already contained in the premises of the argument, in its axioms). It turns out that here too we have not broken out of that circle. We started from premises that exist only in our heads (definitions and laws of logic), relied on them, and in the end remained there. The conclusion too concerns us and our heads (or our thinking).

Again and again we come back to the point that Kant is indeed right: there are no a priori arguments that teach us about reality itself. But unlike Kant, who was satisfied with pointing out that such a move is impossible, the criticism here also explains why this specific ontological argument (and indeed all others like it) does not prove a fact. It shows that its conclusion is not a fact about the world but about ourselves. In this sense, it is a stronger criticism than Kant’s, which was satisfied with the principled assertion that an ontological argument is impossible.

On skepticism

This criticism is probably correct in principle (on the logical plane). But now we must nevertheless examine its significance on the philosophical plane. What the critics are basically claiming here is that although we have reached the conclusion in our minds that God exists, this may be an illusion. In reality, He does not exist. Just as one can stimulate the neurons responsible for apprehending the concept as realized by electrical stimulation, Anselm did so by means of a logical argument.

But this claim can be raised against any logical argument. Even if we have reached some conclusion, who says that it is true in reality itself? We reached the conclusion that it is impossible for there to be a round triangle in reality. But this conclusion exists only in our mind. Who says that in reality itself there is no round triangle? More than that, this can be extended to non-contradictory claims, such as laws of nature. Even if we reached the scientific conclusion that the law of gravitation is correct, this is still only a conclusion that is correct in our minds. Does that necessarily mean that this law really exists in the world itself? Seemingly not. If so, this objection attacks empiricist conclusions as well, for the empiricist too accepts the results of direct observation, and even scientific generalizations.

We can now understand that this objection to the ontological argument is nothing but the standard skeptical claim. The skeptic says of every conclusion of every kind reached by any of us: even if this is what you think, who says that what you think is indeed true, that is, true in reality itself? We should recall here that Anselm, already at the beginning of the first chapter, explains that he is not directing his argument against skeptics, nor even against agnostics. He is arguing against positive unbelievers, the Fool who says in his heart that there is no God. Such a Fool is not a skeptic, for he too is making a claim about reality.

The ontological argument really will not prove anything to a genuine skeptic, but to such a skeptic nothing can be proved in any field. This is not a problem of the ontological argument but of thought in general and of all our conclusions about the world. Therefore, anyone who is not a skeptic cannot raise this claim against the ontological argument. Whoever is not a skeptic understands that if he reaches some conclusion in his mind, then it is probably true in the world itself as well. Otherwise he cannot say anything at all about the world, and not only believe in God. Therefore, if we have reached the conclusion that God exists (and not merely raised the concept of God in our minds), then if we are not skeptics, for us God indeed exists.

It is important here to return to Anselm’s distinction between the presence of a concept in the mind and the understanding that it also exists. The argument that says that even if there is a concept in my mind, this does not mean that it exists—this is a correct argument, and it has nothing to do with skepticism. One can indeed think about things even if they do not exist. But the argument that says that even if I reached the conclusion that the thing in my mind really exists, this too says nothing about the world—that is already skepticism.

The skeptic may ask: how do you know that what you think exists in reality? There is no good answer to that, but the fact is that this difficulty troubles a few esoteric philosophers, not any normal person. So if the price of not believing in God is skepticism, then Anselm has done his work. What he showed is that if you are not a principled skeptic and you are willing to accept anything at all about reality, then you are compelled to accept the existence of God as well. If his argument was directed at empiricists, then it seems that this objection will not save them.

Even the most devout and extreme empiricist, who rejects ontological arguments and logical inferences about reality, does not deny our very ability to know something about it. After all, the very fact that he defines himself as an empiricist means that he does accept the results of observations as valid. That is the alternative he offers to rationalism. But even observation at most convinces me that something exists, that is, it creates in my mind the sense that something exists, or is true, in reality. But this is only a mental conclusion. Does that mean that the thing exists or is true in reality itself? The empiricist says yes. But if so, empiricism is not skepticism, and the empiricist cannot raise this critical argument against the ontological proof.

Consider an example. If I saw three people enter an empty room, and afterward only two more people entered it, I infer that there are five people there. If I assume that there are six, I arrive at a contradiction. In the previous chapter we saw that such a conclusion is actually the product of observation and not of a pure logical argument (like the conclusion that a round dome has no angles). But now we must ask ourselves this question a bit differently: even if I became convinced in my mind that there are no angles there, that only means that in my mind I cannot think otherwise. But how do I know that this is indeed the state of affairs in the room itself? After all, that is already a claim about reality. Even an empiricist will admit that in reality there will be only five people in the room, although he reached that conclusion only in his mind.

Seemingly, it makes a great deal of sense to be an empiricist and oppose rationalism. How can one infer from a structure of my mind to reality itself?! Yet, as we have seen, if one takes this thesis consistently, it leads to total skepticism. The question of why we are not all skeptics is a good one, but it should be directed at each of us, not specifically at Anselm. If the accusation against him is that he is not a skeptic, or that he did not prove that what convinced us in our minds really exists in reality, then once again this accusation must be directed at all of us. The ontological argument is no worse than any other reasonable inference, whether logical-philosophical or scientific-observational. If I accept the law of gravitation because my mind has been convinced that it is true, then by the same token I should accept the existence of God if my mind has been convinced that this is true.

As Kant himself already explained, every conclusion we draw about the world does not concern the world as it is in itself (the noumenal realm), but the world as it appears to us (the phenomenal realm). Therefore, a proof that in the phenomenal realm there is a God is enough to make that claim. The claim that there is no God is also about the phenomenal realm, for even the Fool has no direct access to the world as it is in itself. The entire debate is conducted about the phenomenal realm and not about the noumenal one, and therefore it is enough for us to bring a proof that shows this in the realm of phenomena. That is as far as one can go. From here onward, the path depends on our basic philosophical position: are we skeptics or not?

Assumptions in the ontological argument: existence as a predicate

Introduction

In this chapter we will discuss Kant’s second objection, which, as we explained in chapter 14, from Kant’s point of view is part of the first objection that we discussed there. Up to this point we assumed that Anselm’s argument is of a purely logical character, that is, conceptual analysis and nothing more. But we have already seen in the previous parts, and we will also see in this chapter, that Anselm’s argument does rest on an assumption, and this opens a way to challenge the entire logical movement of his argument. Once we have identified some assumption in this argument, then even if the argument as such is valid (that is, free of logical flaw), we now have the possibility of challenging that assumption itself and thereby rejecting the conclusion. Moreover, in that way we may also be able to save the view of the emptiness of the analytic in general (see the discussion in chapter 14).

An additional assumption

At the heart of his argument, Anselm assumes almost in passing that a concept conceived as existing is greater than a concept conceived merely as a concept. This is in fact the essential step in his argument. It is important to understand that this is not a self-evident claim, and certainly not an analytic one. It is an assumption that says something more than mere conceptual analysis. The relation between the idea of a concept and the idea of it as existing does not follow from the very definition of those two ideas. To determine that, we would of course need a definition of what perfection is. But it does not seem that this relation follows from the very definition of perfection, and in any case it is clear that we have here a claim and not merely a definition. The moment a premise enters into the argument that is a claim and not merely a definition, it loses its purely logical character.

Already here we should note that even if we accept the fact that some assumption is indeed involved here, this assumption is not factual. It does not make a factual claim but determines a judgment about the relation between two concepts. Moreover, it does not even concern a judgment about reality, for as we have emphasized more than once, the comparison Anselm makes is between two concepts or ideas in our cognition (X versus existing X) and not between a concept and an object (which is the realization of the concept). We will return to this point at the end of the chapter.

Time out: the logical significance of assumptions

It is important to understand that the fact that an assumption underlies Anselm’s argument does not, in itself, refute the argument. It does lose something of its force and novelty, since the factual conclusion no longer follows from a purely logical procedure, that is, from conceptual analysis alone, but still, in order to reject it, we must reject the assumption that lies at the basis of the ontological argument.

Postmodern criticism holds that the mere existence of some assumption at the basis of an argument is enough to reject it. Since there is no way to justify assumptions precisely because they are assumptions, proponents of this position argue that adopting assumptions is an arbitrary procedure. The moment we expose that some argument rests on an assumption, that is already enough to present it as something subject to our arbitrary choice. According to this approach, the only thing that is admissible is the conclusion of a logical argument, while premises are arbitrary things that we can adopt or reject as we please. Therefore, the empiricist or atheist, in order to save his position from Anselm’s argument, can simply declare that he rejects this assumption, and that is enough for him.

If premises are arbitrary, then the conclusion of every logical argument is arbitrary as well. After all, it cannot be that a conclusion has a higher degree of certainty than the premises on which it is based. If so, such criticism is really a skeptical position, and we already mentioned in the previous chapter that Anselm is not dealing with skepticism but with the Fool who makes claims about reality.

And from another angle, we are not engaged here in a game whose purpose is victory or the rescue of positions. If we want to conduct a genuine inquiry into our position on the question of God’s existence, we must ask ourselves what our attitude is toward this assumption. If this assumption is acceptable to us, that is, if it sounds reasonable to us, then rejecting it ad hoc in order to save our atheistic or empiricist position would be an intellectually dishonest act. Therefore, the next step in the discussion is to examine our attitude toward this assumption, and to see whether it can be rejected and whether that is reasonable. If not, then while it is true that this is not a purely logical argument, we will nevertheless still have to accept its conclusion.

Kant’s criticism of this assumption

Let us now return to the assumption in Anselm’s argument. How, if at all, can it be attacked? In chapter 14 we quoted Kant’s statement that the proposition X exists is a proposition that combines rather than analyzes. He continues, in that same chapter, by arguing that positing the actuality of the thing is not yet another predicate of it:

It is obvious that being is not a real predicate, that is, a concept of something that can be added to the concept of a thing. It is merely the positing of a thing, or of certain determinations, in themselves. In its logical use, being is merely the copula of a judgment. The proposition ‘God is omnipotent’ contains two concepts, each of which has its own object: ‘God’ and ‘omnipotent’; the word ‘is’ adds no new predicate, but only posits the predicate in relation to the subject. Now if I take the subject (God) together with all its predicates (among which omnipotence is included) and I say: ‘God is,’ or ‘There is a God,’ I add no new predicate to the concept of God, but only posit the subject in itself with all its predicates, namely, the object in relation to the concept. Both must contain exactly the same content… And so the actual contains nothing more than the merely possible. One hundred actual shekels contain nothing more than one hundred possible shekels. For the latter signify the concept, while the former signify the concept and its positing in itself; and if the object contained more than the concept, then my concept would not express the whole object, and thus it would not be the adequate concept of it…

This passage seems quite similar to those quoted in chapter 14, but there is a different and perhaps subtler claim here. His claim is that existence (or realization in reality) is not a property of the concept. And from this it follows that the set of properties that bring the object X (= God) to its perfection cannot include its existence. Kant’s main claim is that if existence really did add something to the content of the concept (that is, if existence were another predicate of it), then there would be no full correspondence between the content of the concept and the object that realizes it. There would be something in the object beyond the concept, and then the object would not be the realization of the concept in reality. There must be full overlap in content between a concept and its object. Between the two there is nothing but existence (realization).

This claim can be formulated somewhat differently.^[28] Almost everything said about a being concerns its properties. Statements like "X is tall," or "X is kind," or "X is green," or "X is made of wood," and so on, all concern the thing’s properties or attributes. These are its predicates. Since the time of Aristotle, it has been customary to distinguish between the substance and its accidents (what happens to it and characterizes it, that is, properties or attributes). When I say of the table that it is made of wood, that it has four legs, that it is tall or low, comfortable or less comfortable, manufactured in a certain place by a certain person, and so on, I have said things about its properties. But who is the bearer of these properties? What gathers them together into a unified substance? After all, in reality something exists and it has all of these properties. All these properties characterize it. That something is the substance, and the properties are properties of the substance. Without assuming the existence of a substance, the set of properties of the thing is nothing but a collection of properties with no common denominator. It is not reasonable to regard the following collection of properties {the brightness of the midday light, the color of fig leaves in autumn, the pitch of the dove’s voice as it coos to its mate, and the number of clouds in the sky on a certain day} as a substance. Why not? Because there is no common something that bears all of them, that is, that owns them. That they are its properties. A collection of properties is not a substance. A collection of properties that characterize the same object can be considered the concept of that object (and the object is the referent of that concept).^[29]

What can be said about the substance that is not one of its properties? First of all, that it exists. The statement that this object exists is not a property. It does not describe it but says something about it. This is what Kant calls in this passage the "positing" of the concept in relation to its object (its realization). This is the meaning of the claim that existence is not a predicate or attribute of the concept. It is its positing in reality. Therefore it adds nothing to its content, because the content of the concept is the set of the referent’s properties and attributes. And even if the referent is unrealized, the collection of properties creates its concept. The question whether it exists, or is realized, is external to the description of the concept itself.

Now let us think about God’s perfection. Anselm is essentially claiming that this perfection necessarily includes His existence, since a realized (existing) concept is greater than an unrealized concept. But Kant argues against him that existence is not an attribute or predicate, and therefore it should not be included among the properties that create the perfection of any being. God’s perfection is the totality of His positive properties at a perfect level. But existence is not a property, and certainly not a positive property. It is a state, not a property.

If we return to the assumption that we identified in the ontological argument, namely that a realized concept is greater than an unrealized concept, Kant here challenges that assumption. Greatness or perfection have nothing to do with existence or non-existence. They express a relation between properties or descriptions, and not between realization and non-realization. Anselm assumes that existence is a predicate or attribute of God, and Kant argues that it is a positing and not one of the predicates.

Let us return for a moment to Kant’s objection discussed in chapter 8. Kant argued there that it is impossible for a purely logical argument to yield a factual result. We saw there that this claim is not an objection but a declaration. So long as we have not found a flaw in Anselm’s argument, the situation is that the ontological argument proves Kant wrong: there are logical arguments that yield facts. But if there is real substance in Kant’s second objection, presented here, then one can indeed argue what he argued there: the analytic is empty, and purely logical arguments that yield facts are impossible. And what about the ontological argument? Here we have presented a flaw in the inferential procedure or, in fact, an ungrounded (or at least non-necessary) assumption that lies at its basis. Now the emptiness of the analytic is a conclusion and not merely question-begging.

What can Anselm answer to this?

As we have noted, Anselm was not engaged in a comparison between a concept and a referent, or between a concept and a substance, but between two kinds of concepts: the idea of X in my mind (="X"), and the idea of "X exists" in my mind. In the previous chapter we noted that if one does not take skeptical claims and positions into account, the move from the statement "X exists in my mind" to the statement "X exists in the world" is reasonable and called for. And yet, when we posit a relation between these two concepts, it is not a relation between concept and referent (= substance), and so there is not necessarily here only positing and nothing more. At the stage in which I examine these two concepts side by side, there is certainly room to see the second as greater or more complete than the first. If I am not a skeptic, then there is a second stage, in which I move from the concept "X exists" to the claim that X (="X" realized in reality, an object and not a concept) exists, and there Kant is right that no gap in content can arise. But in the earlier transition, between the concept "X" and the concept "X exists," there definitely is a gap in content (the translation neurons).

Let us define this as a three-link chain, as follows: "X" "X exists" X (the quotation marks indicate a concept, as distinct from a substance). Anselm’s assumption compares the first two (the second is more complete/greater than the first), that is, two ideas in the mind, and not the first and the third, and certainly not the last two. Kant’s arguments, by contrast, concern the identity between the last two.

If so, Kant’s claim about the overlap between the concept and its referent is correct when one compares the concept "X exists" present in my mind with the substance X that exists in the world. The second is the realization of the first, and therefore there can be no difference in content between them. The transition from one to the other is nothing but positing, but the content of the two is identical. But the concept "X" present in my mind can indeed differ in its content from the concept "X exists" in my mind, and therefore also differ in its content from X itself (the substance that exists in the world).

Another answer: existence versus necessary existence

In the third part we saw that the conclusion of Anselm’s second ontological argument (the one in chapter 3) is that God exists necessarily, and not merely that He exists. This is already a more far-reaching conclusion, and it is certainly not simply contained in the premises of the argument.

Moreover, necessary existence is a better candidate for functioning as a predicate. Even if existence as such is not a predicate of the substance, necessary existence does seem to be a predicate. After all, the existence follows from the definition of the substance, and therefore it really is a predicate of it (one of its properties). If so, after arriving at the conclusion of the second argument, we can return to the first argument and say that even if Kant is right and the ordinary existence of some being is not a predicate, with respect to the perfect being existence is indeed a predicate. It is one of its properties, like square shape, kindness, year of manufacture, and so on.

The situation after Kant’s objection

Bottom line: this objection does indeed present a significant attack on Anselm’s argument. First, it points to the existence of an assumption in the argument. Second, it presents a consideration against that assumption. True, in the previous sections we saw that Anselm can perhaps reject this consideration in two ways, but the question certainly remains open. Kant can argue against the first answer we suggested that even between the first two stages in the chain there is no difference in content (this too is a process of positing that takes place in the mind). He can also say that even necessary existence is not a predicate, and thereby reject the second answer we proposed on Anselm’s behalf. Therefore, each of us must formulate his own position with regard to this assumption and to the defenses we have presented for it, and on that basis determine his attitude toward the conclusion of the argument (that God exists).

In order to understand where we stand now, we must return and remind ourselves of something that is clear in any case: the assumption that existence is a predicate is not a factual claim. It concerns a relation between concepts or ideas (which is more complete/greater than which). Moreover, various relations concern objects in the factual world: one person is taller than another, one place is north of another. But the relation with which we are concerned here does not deal with facts at all. This is not a comparison between objects in the world, and as we have seen, not even a comparison between an object and a concept. The relation of perfection dealt with by this assumption concerns the relation between two concepts (ideas). It does not concern reality but the mind, and only the mind.

If so, even if this Kantian objection is correct, Anselm’s argument still has considerable philosophical significance. One may, of course, argue with this assumption (as Kant did), but it is hard to deny the possibility that this assumption is correct. Even one who does not accept it understands that another person may well accept it. It does not seem meaningless or manifestly false, and certainly not contradictory. But if one adopts it, then the ontological argument yields a factual conclusion. What we have, then, is a logical argument composed of conceptual analysis and based on a non-factual assumption, which necessarily leads us to the factual conclusion that God exists. That achievement belongs to Anselm.

We have thus learned that the ontological argument is not, in fact, a purely logical argument, but neither is it a logical argument based on facts. It is a logical argument based on a non-factual assumption. What Anselm showed is that a logical argument that is not based on a factual assumption can yield a fact. The analytic may be empty, but the philosophical and the a priori certainly are not.^[30] Thus, metaphysics and ontology—and indeed rationalism in general—are still standing. That is, observation is not necessarily required in order to arrive at factual insights about the world.

The meaning of the term "greater than"

Behind this Kantian criticism stands a parallel point. Kant claims that existence is not a predicate, and therefore there is no possibility of speaking of existing X as greater than X itself. What lies behind his claim is a certain meaning of the term "greater than." The same objection could have been formulated differently: Anselm did not clarify what "greater than" means. Greater in what sense? What falls under this term? And from this it follows that one also cannot determine whether a concept realized in the world is greater than an unrealized concept. Kant assumed that greatness is expressed only in predicates, that is, in contributions to the content of the concept. But one can certainly adopt a different meaning of "greater than" that includes existence as well.

Does that help? Seemingly, question-begging arises again here. If we assume that the term "greater than" is affected also by the question of existence, then the ontological argument indeed succeeds in proving its conclusion. That is, the conclusion depends on adopting this meaning of the term "greater than." But none of this changes the situation described above. Assuming there is a person who adopts this interpretation of the concept "greater than," the Kantian objection should not trouble him. As far as I know, there are quite a few such people. For them, the ontological argument proceeds from non-factual assumptions and mere definitions, and arrives at a factual conclusion. As I wrote above, the ontological miracle really does occur.

And one final remark. The definition of the term "greater than" must enter the argument in one more place, namely the definition of the concept of God, for He is defined as the greatest that can be conceived. But if "greater than" includes within it the concept of existence, then there is a blatant begging of the question here. We assume in the definition that He exists; no wonder the conclusion is that God indeed exists. We already mentioned that a logical argument always begs the question in some sense, but the miracle in the ontological argument fades somewhat, since it now already appears to rest on a factual assumption (that God exists).

But this is not precise. There is no assumption here that God exists, but only a definition of Him as the greatest that can be conceived, when greatness is determined also by existence. It could be that God does not exist, and this definition would still stand. For example, He is indeed the greatest being that can be conceived, and this is true if no other object exists. Alternatively, if such objects did exist but could not be conceived as existing. Therefore, there is no begging of the question here in the blunt sense we described.

Assumptions in the ontological argument: the coherence of the concepts

Introduction

In this chapter we will discuss another assumption that exists in the ontological argument, one concerning the coherence of the concept "a being than which nothing greater can be conceived." These matters are intimately connected to the discussion that took place in the third part (and will continue in chapter 19), where Anselm distinguished between thinking about something and conceiving it. With regard to every coherent concept, one can think it and conceive it. An incoherent concept can perhaps be entertained in the mind, but it cannot be thought (or understood).

An additional assumption in the ontological argument^[31]

A close examination of Anselm’s argument shows that beyond the assumption about existence as a predicate, discussed in the previous chapter, there is yet another assumption at its basis: that one can conceive of a being than which nothing greater can be conceived. In this section we will repeat the analysis we carried out in the previous chapter with respect to the earlier assumption, but this time with respect to this one. We will see that the conclusions here too are quite similar.

An illustration from infinite sets

This assumption too, although it sounds quite reasonable, is not entirely simple. In modern mathematics, a distinction is drawn between open intervals and closed intervals on the number line. A closed interval is the set of points representing the numbers between 0 and 1, including these two endpoints themselves. In such an interval there is a greatest number among the numbers within it, 1, and a smallest, 0. But what about the open interval, that is, the same interval without the two endpoints (or even only without the point 1)? In this interval there is no point that represents the greatest number among the numbers within it.

From here we can infer that not every set has an element that is the greatest in it. In sets with a finite number of numbers, there is always one that is the greatest in the set, but in infinite sets this is asking for trouble. Take the entire number line. Is it open or closed? One cannot point to the point that represents the highest number on it. One can define mathematically an abstraction that signifies such a limit, and that is infinity.

God, in the standard religious conceptions, is called the Infinite. This name expresses His capacities, which are infinitely positive, or in Anselm’s terminology, His perfection. Can the set of all the things we can conceive be treated as a closed interval? That is, as one that necessarily has something that is the greatest? For the purpose of this discussion, we are ignoring for the moment the ambiguity in the term "great." Relations of greater and smaller among numbers are self-evident, but such relations among objects or concepts are, of course, more ambiguous.

We should note here that Kant already presents a criticism of the coherence of another concept in the ontological argument (Descartes’s), namely the concept of a "necessary being." And this is what he writes in the chapter we have already mentioned:

More than that: think of the fact that this concept, first ventured somewhat at random and later becoming thoroughly familiar, came to seem explicable, indeed by means of a great many examples, to the point that any further question as to whether it had content appeared unnecessary. Every proposition of geometry, for example that a triangle has three angles, is absolutely necessary; and thus people spoke of an object lying wholly beyond the sphere of our understanding as though it were perfectly clear what was meant when this concept was attributed to it.

Thus, the fact that something is perceived by us as meaningful and coherent is not sufficient basis for determining that it indeed is.

Is the concept really coherent? The question of the burden of proof

If we return to the assumption above, the fact that when we hear the expression "a being than which nothing greater can be conceived" we feel that we understand it does not really mean that we understand it. It does not necessarily mean that there is coherent cognitive content behind it. There are many cases of concepts that we feel we understand when we think about them, but that do not have a coherent and clear meaning. Among them are concepts that are seemingly simple and self-evident, such as the concept of a set, about which Russell proved by means of his set-theoretic paradox that it is not coherent. Another example is that barber in Seville who shaves all the people in Seville who do not shave themselves. This may sound to many of us like an innocent description of some barber, but closer examination reveals that it is a meaningless and contradictory expression. There are, of course, several more expressions of this kind. It may be that a concept like "a thing than which nothing greater can be conceived," even though it too seems innocent and understandable to us, and we seemingly conceive it easily, is in fact a meaningless expression.

It is difficult to dismiss this argument out of hand.^[32] On the other hand, it is not really well founded. If there is a sense that some concept is intelligible, one cannot simply say: perhaps it is not really intelligible, and perhaps it even contains a contradiction and is not coherent. To say that, one must point to the incoherence in it. So long as we have not pointed to the flawed point in the definition, the presumption is that the concept has a meaning, as we all think it does. If we do not proceed in this way, then every logical or mathematical proof would have to be rejected alike. After all, every logical or mathematical argument rests on basic concepts, such as point, line, greater than, and so on. We could always wonder whether one of these concepts is not coherent or contains a contradiction, and thereby reject the proof. When we operate in the logical sphere, we usually assume that our concepts are coherent until proven otherwise.

To this we should add Richard Swinburne’s claim,^[33] that one can prove that some proposition or concept is not coherent, but it is much harder (and perhaps impossible) to prove that it is coherent. To do that, we would have to examine all the infinitely many implications that arise from it, an obviously impossible task. Gödel made a similar claim regarding the inability to prove the consistency of a mathematical theory and of mathematics in general. Karl Popper presented a similar distinction with respect to scientific theory. He argued that a general theory can at most be falsified but never proved.^[34] It therefore seems more reasonable to place the burden of proof in a dispute about the coherence of a concept on the one who claims that the concept is not coherent.

Let us look at this from another angle. If we formulate an ontological argument about the open interval (0,1), and try to identify within it the greatest number in that set, then any number x that we may entertain as a candidate can be rejected by presenting a number greater than it (for example). But here we are not dealing with a proof that x is the greatest, but with a proposed hypothesis. It does not seem possible to prove by means of a similar ontological argument that there is a greatest number in such an interval. Therefore, the formulation of the ontological argument can stand as it is until a concrete flaw is discovered in the definition "a being than which nothing greater can be conceived." Anselm’s argument at least shows that whoever understands this definition must infer from it that God exists (that is, that the idea of God in his mind must be conceived as existing).

And yet, it is important to point out that this is probably an infinite set of ideas (those that we can conceive), and as we have already seen, infinite sets are suspect simply by being such, as containing a contradiction or at least an ambiguity. Therefore the suspicion here does not seem as groundless as the suspicion we described with respect to any other mathematical or logical concept.

A renewed meaning for Kant’s first objection

In chapter 14 we pointed out that Kant’s objection, which determines a priori that no ontological argument proving a fact from conceptual analysis is possible, is not enough to reject a valid logical argument. But if now a suspicion arises of ambiguity and incoherence in some concept required for the course of the proof, then the Kantian objection itself is sufficient basis for adopting that suspicion. If the price of assuming that this concept is coherent is that ontological arguments exist, and if that price does not seem philosophically reasonable to us, then a logical path now opens before us for rejecting it. We will suppose that the concept is not well defined, and therefore that Anselm’s argument is mistaken and its conclusion cannot be proved in this way. True, we have not shown where the incoherence in the concept lies, but the burden of proof now shifts to Anselm.

Is this a factual assumption?

In closing, we must examine the question whether the additional assumption we have uncovered here is factual. Seemingly it is, for it is a claim about us as beings in the world and about our ability to conceive things. When I say that Reuven has the ability to run a marathon, I have made a factual claim. When I say that someone loves someone, there too I have made a factual claim about that person’s feelings. Therefore, seemingly, when I claim that someone can conceive something, I am making a factual claim here as well. And yet, this is a fact about the way our thought works and not about the external world. Therefore, from the empiricist’s point of view, this is not a factual claim, since nothing that describes how my thought and cognition operate can serve as a basis for deriving a factual claim about the world outside me. If we see this as a factual claim, then the statement "I think that God exists" is also a factual claim. Can His existence in the external world be derived from it? The empiricist will certainly say no. Even if I offer a logical argument in favor of the existence of God, the empiricist rejects it as a procedure of thought that cannot yield facts about the world.

If so, although we have uncovered here another implicit assumption in Anselm’s argument, one that moves it even further away from the status of a purely logical argument, we still have here a logical argument based on non-factual assumptions, such that, at least for one who adopts them, a factual conclusion is proved at the end. Thus, even after exposing this assumption, Anselm’s fundamental philosophical achievement (proving a fact without observational assumptions) remains intact.

Gaunilo on the existing lost island

Introduction

The next criticism we will discuss is ancient. Already in Anselm’s lifetime, he received a response from the monk Gaunilo of Marmoutier, "on behalf of the Fool," containing several objections to different parts of his formulation of the proof. The best known of them is the objection from the island.

This is an objection of a similar character to Kant’s first objection, since it does not attack head-on the logical inference, nor any premise at its basis, but points to an absurdity that arises if we adopt such a pattern of argument. In this context, it is important to recall what we saw above in chapter 14 regarding Kant’s a priori objection. The fact that some pattern of argument seems to us a priori absurd is not sufficient to reject it. At most, it provides motivation to search for a flaw in the argument. But as long as we have not found such a flaw, the argument remains intact.

Gaunilo’s objection

A simplistic formulation of Gaunilo’s objection is the following. Let us define the concept of "the existing island." Now let us assume for the sake of discussion that it does not exist, and this will lead us to a contradiction. Thus, by proof through contradiction, we necessarily arrive at the conclusion that the island indeed exists. In this way, of course, we can prove the existence of the existing lion,^[35] the existing star, or thousands and billions of existing stars, the existing Flying Spaghetti Monster, the existing one-eyed, sharp-winged fairy, and so on. This is a generator that produces insane and bizarre entities at will, in an uncontrolled way and with no logical or physical limitation. We toss definitions into the air and they, by their very nature, turn into existing beings in our world—something that reduces the structure of Anselm’s argument to absurdity.

A more precise formulation of Gaunilo’s objection inserts his island into Anselm’s exact argumentative pattern. In the original, Gaunilo did not speak about the existing island, but rather defined the greatest conceivable lost island (GCLI), or more precisely: the greatest lost island that can be conceived. Now put this concept in place of God in Anselm’s argument, and the conclusion that will be obtained is that the GCLI obviously exists. Note that this is a lost island, that is, one whose existence is unknown to anyone. We have proved here the existence of an island that has not yet become known (and probably never will become known) to anyone. This is a nontrivial factual conclusion, for now we all know that there exists in the world at least one island whose existence is unknown to anyone.^[36]

A possible rejection

Gaunilo’s objection can perhaps be rejected as follows. The GCLI is not merely the physically greatest among lost islands, but the most perfect among them (otherwise existence certainly would not be a criterion of greatness for GCLIs). But unlike the case of God, with lost islands existence is not necessarily a criterion of perfection. The assumption that existence is one of the perfections was made regarding God because He is perfect in all perfections, but among the predicates that characterize lost islands it is not at all clear that existence is one of the predicates, and therefore it is also not one of the perfections by which greatness is measured relative to other lost islands.

Let us recall that in the previous chapter we saw that Anselm is in fact implicitly assuming a very specific meaning for the term "greater than," one that includes existence (existence is a criterion of greatness). We also saw there that this definition must also enter into the definition of the concept of God (for greatness appears there as well: the greatest that can be conceived). We raised the difficulty that, seemingly, this amounts to begging the question, since defining Him as existing yields the conclusion that He exists. We explained there that this is not question-begging, since it is possible that no other object exists, or at least that no other object can be conceived as existing, and then God is the greatest that can be conceived as existing. Admittedly, with regard to God, we ultimately proved that He exists, since He is measured in His perfection (His greatness) against all beings in the world, and if we are not skeptics then it is clear that some beings do exist in the world. But with regard to the island the situation is different. After all, the GCLI is measured only against other lost islands (it is the greatest among them), and it is possible that there are no lost islands in the world at all. In that case, even the greatest among them can be a non-existing island. So with respect to the GCLI this is a straightforward case of begging the question, whereas with respect to God this is not necessarily the case.

Anselm’s answer

Following Gaunilo’s criticisms, Anselm wrote his book Reply to Gaunilo. Against the argument from the island, Anselm claimed that Gaunilo had missed a very fundamental point in the ontological argument. There Anselm repeats his distinction from chapter 3 of the Proslogion (see our discussion of this in the third part) between two types of entities: a necessary entity and a contingent entity.^[37] The existence of a necessary entity is not dependent on any other entity, and it is necessitated by itself. A contingent entity exists contingently (because some other entity or some other mechanism created it). A necessary entity cannot fail to exist (because its existence depends on no circumstances whatsoever), whereas a contingent entity can (when the causes of its existence disappear).

In his reply, Anselm claims that God is a necessary being (see the third part). By contrast, the greatest conceivable lost island, even if it exists, does not exist necessarily but probably contingently. Its existence depends on circumstances (the sea around it, or the physical mechanism that created it). It seems that what he means to say is that God’s non-existence is a logical contradiction, and from that it follows by contradiction that God exists (the statement "God does not exist" is an oxymoron). But the non-existence of the GCLI is not a logical contradiction, but only contrary to a contingent fact known to us (that it exists, or that it is the greatest). A contradiction to the laws of nature or to a contingent fact known to us cannot constitute a logical argument. Even if it may perhaps be evidence for its existence, it is certainly not an ontological argument, since ontological arguments are of a purely logical character, or at least are free of factual assumptions.

And from another angle, if it has become clear to us that the existence of the GCLI is necessary and follows from its concept, then it has ceased to be an island. An island is a material entity, and we know how it is formed, and therefore we know that the existence of an island is not necessary. The moment we have found an island whose existence is necessary, it has ceased to be an island. But non-necessary (contingent) existence cannot be proved by an ontological argument. Therefore, at most the GCLI is God Himself, and Gaunilo has simply repeated the ontological proof here in slightly different terminology.

It is important to understand that one cannot prove the necessity of the island’s existence by means of the move in chapter 3, which Anselm used in order to prove the necessity of God’s existence. Therefore, the necessity under discussion here with respect to the GCLI is logical necessity (we have a proof of the island’s existence), but not ontic necessity (its existence is not necessitated by itself, and it is not independent of external entities or mechanisms).

Anselm himself raises there yet another argument. Let us try to make this island larger and larger. If it is not the greatest, then it will not be the greatest lost island that can be conceived, for one can conceive of a GCLI greater than it. If so, its area (indeed its volume) is infinite. But from a certain size onward, it ceases to be an island (and it also cannot exist in the world, because there are other objects in the world).

Seemingly, this is a technical argument. But I think there is a substantive argument behind it. Think: which is the greater being, God or the GCLI? Surely God, for He possesses all perfections and is the greatest of all beings that can arise in our minds, including the GCLI, whereas the GCLI is great only among the set of lost islands. If so, by definition it cannot be infinite (not necessarily in size, but in all its qualities). It can exist only if it itself is God, in which case we have again simply proved the existence of God.

Summary

In the third part we pointed out that the necessity of God’s existence is intimately connected to the ability to prove it by an ontological argument. The "miracle" of proving a fact on the basis of a logical argument without observational assumptions returns again and again to the point of the necessity of existence. Not for nothing did Anselm devote chapter 3 of his book to this point, for the whole proof stands on it.

Kant is right that the existence of things cannot be proved by ontological arguments, but his remarks are relevant only to ordinary beings that exist in an ordinary way. God is exceptional in that His existence is necessary. With respect to such objects, and only with respect to them, there is a possibility that an ontological proof of their existence may be found. We will return to this point in the next chapter as well.

Between thinking and understanding, and conceiving

Introduction

In chapter 15 we dealt with the possibility of our making a mistake, that is, thinking something nonexistent to be existent. In this chapter we will deal with a phenomenon that is seemingly similar but essentially different: our ability to think things that we ourselves know are not true. This objection was first presented already to Anselm himself by the monk Gaunilo (see another objection of his in the previous chapter),^[38] and it challenges the validity of Anselm’s second ontological argument (that of chapter 3), that is, it points to a logical gap in it.

Is it possible to think something false?

In chapter 12 of the third part, we presented the distinction between thinking and understanding, on the one hand, and conceiving at lower levels, on the other. We spoke about our ability to think a collection of words, then about a partial understanding of such a collection (understanding each aspect separately), and finally about the formation of an overall, unified concept or idea. That is what is called understanding the concept. One may say that this is thinking the thing, and not merely thinking about the thing. Partial thinking is thinking about the thing, but to think the thing means that the concept or idea itself exists in our mind in a unified and coherent manner.

Gaunilo claims that one can think the perfect being as non-existent, but one cannot understand it as non-existent. Even something that does not exist can be conceived as existing. A person who believes that there are no fairies in the world can still think of fairies that exist within our world. Another example that Gaunilo himself gives (centuries before Descartes’s cogito argument): I know with absolute certainty that I myself exist, but I can certainly think of myself as not existing. Moreover, I can do this simultaneously with the certain thought that I do exist.

So if I can think as non-existent even something that I know does exist, why can the Fool not think that God does not exist even though he knows (implicitly) that God does exist? And if I cannot think of myself as non-existent, what is so remarkable about the fact that the Fool cannot think of God as non-existent?

Let us clarify the second part of the claim more fully. Several centuries after Gaunilo and Anselm, the French philosopher René Descartes (who also proposed a version of an ontological proof for God’s existence) showed in his cogito argument that our existence is a certain conclusion (I think, therefore I exist). If so, there is an ontological argument for my existence just as there is for God’s existence. Therefore, if despite this one can still conceive the thought that I do not exist, then Gaunilo is right that by the same token one can also conceive that God does not exist. This is the second side of his objection to Anselm’s argument.

It is important to clarify the difference between this objection and what we saw in the previous chapter. In the previous chapter we raised the possibility that although the Fool indeed cannot think that God does not exist, this still does not mean that in the world itself God exists. As noted, that is a skeptical argument. Here we are dealing with a different phenomenon: the Fool, who knows that there is a God (because of Anselm’s conceptual analysis), can still conceive that God does not exist. It is simply not true that this cannot be thought.

One can think of oneself as not existing, even though it is clear to me (I know, or think) that I exist. This parallels the objection in chapter 15 above. But here this is no longer skepticism. Brown, toward the bottom of page 89 and onward.

What is Gaunilo objecting to?

This objection does not refute the ontological proof itself. Here too Gaunilo agrees that the Fool reaches the conclusion that God exists. His claim is that, from the Fool’s point of view, this conclusion is not necessary, that is, that the Fool who was persuaded by the argument in chapter 2 that God exists can still conceive that God might not exist. This refutes the second ontological argument, the one presented in chapter 3 (and in our third part), according to which God cannot be conceived as not existing, that is, that His existence is necessary.

Anselm’s answer

Anselm’s answer to Gaunilo is based on the distinctions that we already presented in the third part of the notebook, and indeed on the very distinction he used in order to answer the objection discussed in the previous chapter. First, he distinguishes between a being X whose existence is necessary and a being Y that exists contingently. If someone understands that Y exists, then there is one sense in which he indeed can think of it as not existing, but there is another sense in which that is impossible. He can say: "Although Y exists, I can conceive of a situation in which it will not exist." This is a claim about a hypothetical situation that can be conceived. By contrast, he cannot say: "Although Y exists, I think that it does not exist." Here he is already speaking about the present situation and thinking something about it. At this point there is already a logical contradiction.

All of this applies to the object Y, whose existence is contingent. But with respect to an object X that exists necessarily, he cannot say even the first statement. The hypothetical claim, "Although X necessarily exists, I can conceive that it does not exist," is a logical contradiction. If its existence is necessary, that means that one cannot conceive of a situation in which it does not exist (recall the modal meaning discussed in the third part).

Gaunilo is indeed right that it is clear to us that we exist. And if Descartes’s cogito argument is correct, then we even have an ontological proof of this. But we, as human beings, do not exist necessarily. Anselm’s second ontological argument (the one from Chapter 3) cannot be applied to the cogito; that is, one cannot prove that our existence is necessary (that it is inconceivable that we do not exist). In the terminology we presented in the third part, our existence is logically necessary but not ontically necessary. There is logical necessity in the conclusion that we exist, but there is no contradiction whatsoever in a state of affairs in which we do not exist in the world. True, that state could not have been considered by us had we not existed, but now that we do exist we can conceive of a hypothetical state in which we do not exist. That is true of us, since we are type-Y objects. But God is a type-X object, and therefore it is not true of Him that one can hypothetically conceive of a state of affairs in the world in which God does not exist.

I use here the translation by Prof. Yosef Sermoneta, which appeared in Iyyun 22 (1971), pp. 13–53. The translation also appears in the source anthology edited by A. Z. Brown, Selected Philosophical Texts – From Parmenides to Contemporary Thinkers: A Reader in Ontology, Magnes, 1977. ↑
See a brief discussion of this proof, and especially of its a priori character, in Chapter 7 of my book Truth and Instability. ↑
See Chapter 2 of my book God Plays Dice on this. ↑
Yuval Steinitz devoted an entire book to this subject, Long Live Metaphysics, Dvir, 1990. ↑
See Chapter 7 of my book Truth and Instability on this. ↑
Regarding Descartes’s cogito, in which he proves his own existence by means of a purely logical argument (which is a factual claim about the world), it is important to understand that his aim was not only to prove his existence, but to show the possibility of such a rationalist argument. In his day, a strong empiricist critique had already arisen, maintaining that one cannot learn about the world without observation, and Descartes advanced his argument against it. In the prologue to my book The Sciences of Freedom I showed why the cogito argument, ‘I think, therefore I exist,’ is not an argument based on a fact (‘I think’), but a purely logical argument. It derives the factual conclusion (‘I exist’) from a logical procedure without factual premises. Anselm’s argument, presented some five hundred years earlier, is of similar character and significance in this sense and in this context. ↑
Hume himself remained an empiricist, but his arguments in fact show the opposite. See a fuller discussion in my book Truth and Instability, Yedioth Books, 2016. ↑
A very detailed logical-philosophical analysis of the proof appears in Brown’s book, The Question of Being: Chapters in Ontological Analysis, Magnes, 1977. See also the first part of Yuval Steinitz’s book The Tree of Knowledge, Dvir, Tel Aviv, 1994. ↑
See a fuller discussion in the first part of my book Two Wagons and a Hot-Air Balloon, and also in my book Truth and Instability. ↑
The points made here are developed in more detail in Chapter 6 of my book Truth and Instability. ↑
On intuition as cognition by the ‘mind’s eye,’ see the entirety of Part V of my book Truth and Instability, especially Chapter 14. ↑
These two chapters are parallel and in fact almost identical to one another. ↑
See the relevant Wikipedia entry, and also Chapter 11 of my book The Sciences of Freedom. ↑
It should be noted that this is not a matter of visual rendition, for Anselm too does not claim that God stands before us as an object of observation. Still, there is a difference between an intellectual apprehension of something in the imagination and an intellectual apprehension of something that exists (including an understanding of its existence). ↑
Here, ‘images’ should be understood as ‘perceptions.’ The point is clearly about nonvisual cognitions. ↑
See the third book in the Talmudic Logic series, Deontic Logic in Light of the Talmud, Michael Abraham, Dov Gabbay, and Uri Schild, College Publications, London, 2010. ↑
The question whether our proof may be mistaken is not relevant here. There can always be error in our reasoning, and in our observations as well. But in order to cast doubt on them, one must present an argument that justifies doing so, unless one adopts a skeptical position. Thus, the proof that 2+2=4, or that the sum of the angles in a triangle on a Euclidean plane is 180, is taken as a sufficient basis for the conclusion that these propositions are necessarily true. See further below in Part IV, Chapter ???. ↑
I use here the Bergman and Rotenstreich edition, third edition, Bialik Institute, Jerusalem, 1983. ↑
Of course, belief in a Creator can also be included within deism, so long as that God commands nothing of us and does not create a binding religion. Even so, belief in a Creator already contains some information beyond perfection and completely abstract philosophical determinations, and very often it is one of the building blocks of religious faith. That is why I wrote that this is an initial connection that begins the movement from the deistic direction toward the theistic one. See more on this in the next section. ↑
See on this the first chapter of my book Two Wagons, and also my article in Tzohar, Abraham Our Patriarch and His Hat: In Praise of Begging the Question. ↑
The question whether contradictions are meaningless and unintelligible, or whether they do have meaning but simply lack instantiation, is disputed among philosophers. See Steinitz’s book, pp. 53–55, and also a bit on p. 64. In the halakhic illustration we will try to present a few distinctions that will clarify this issue further. ↑
See also Antonio Damasio’s book, Descartes’ Error: Emotion, Reason, and the Human Brain, Kinneret, 1998, translated by Dafna Banai. ↑
Critique of Pure Reason, pp. 305–306. ↑
Kant views such propositions as synthetic a priori, but I am not sure he is right about this. ↑
Kant shifts the entire factual discussion to the world as it is perceived by us (the phenomena) and not to the world as it is in itself (the noumena). In this way he explains our ability to accumulate information about the world without observations. We will not enter into this issue here. ↑
David Hume already pointed out that the common view according to which the laws of nature are learned from observation is mistaken. Observation gives us one particular event, and perhaps a few isolated events. A law of nature is the product of a generalization based on those observations, but that generalization has no observational justification. The same set of specific observations can be generalized in several different ways into several different general laws. ↑
To explain this, Kant distinguishes between the world as it is in itself (the noumena) and the world as it appears to us (the phenomena), which is what science deals with. The basic principles of the phenomena can also be learned without observation (rather, by means of transcendental arguments; see below in this paragraph). ↑
See a fuller discussion in the second part of my book Two Wagons. ↑
A wonderful illustration of this can be found in Borges’s story, ‘Tlön, Uqbar, Orbis Tertius,’ in his Fictions. ↑
Kant would join this as well, since we have already mentioned that he upheld the existence of synthetic a priori propositions, that is, propositions that make claims about the world and yet are still a priori (without observation, that is, not based on facts). ↑
Brown, in his book The Question of Being, p. 95, brings several such assumptions. As regards Chapter II of the Proslogion, there is only one assumption, the one given above. His assumption (2), that existence in reality is greater than existence in the understanding alone, also pertains to Chapter II, but it seems to me inaccurate. To the best of my understanding, Anselm nowhere assumes this. As I explained, Anselm compares two kinds of ideas that exist in the understanding, not a concept and an object. This comparison roughly parallels Brown’s assumption (4) there, though not exactly (it is related to the next chapter of the Proslogion, and therefore we will not enter into it here). ↑
Steinitz discusses this at length in the third chapter of his book The Tree of Knowledge (see especially from p. 69 onward). ↑
See a translated excerpt of his remarks in Steinitz there, p. 72. ↑
The theory that all ravens are black is empirically falsifiable: if we see even one raven that is not black. But it is not empirically provable, since even if all the ravens we observed were black, we could never know whether we had seen them all. ↑
A well-known objection to Descartes’s formulation of the ontological proof, attributed to Caterus, speaks of the existing lion. ↑
Incidentally, there are probably infinitely many such islands, for once we learn of the existence of one, it is removed from the stock of lost islands, and we must now look for another island that is the greatest among the group that remains, and so on ad infinitum. ↑
His response to the objection discussed in the next chapter is very similar. ↑
See Brown, at the end of p. 89 and onward. ↑

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