Faith and Its Meaning – Lesson 6

Table of Contents

• [0:01] Introduction and presentation of the directions of the discussion
• [1:55] Presentation of the ontological proof – Anselm
• [3:43] Reading the Proslogion – Chapter 2
• [8:38] The structure of the three-stage argument
• [10:36] Begging the question in prayer
• [17:06] Logical arguments – uncovering existing information
• [24:01] The value of proofs – uncovering existing knowledge
• [25:57] The internal dialogue with the fool
• [28:06] The structure of the logical argument and its premises
• [29:22] The problem with the premises of the argument
• [31:55] Rationalism versus empiricism
• [33:35] Descartes and the cogito as ontology
• [42:05] Defining God according to faith
• [43:49] The definition of a triangle and mathematical definitions
• [49:01] Conventionalism and essentialism in concepts
• [54:17] Leibniz’s principle of the identity of indiscernibles
• [56:05] Existence as not a property

Summary

General Overview

The lecturer opens the discussion with ways of justifying faith / belief and now focuses on the ontological proof, a proof that is sometimes ridiculed, though it is worth analyzing in order to learn about the structure of logical arguments. He presents Anselm as a central formulator of the proof in the 11th century, describes its later versions in Descartes, Leibniz, and others, and proposes reading the chapters of the Proslogion as a single argument with three links: proving existence, proving necessary existence, and then clarifying how the “fool” can say that there is no God. Along the way, he defends Anselm’s opening in prayer and argues that this is not begging the question but rather an open declaration of a starting point, and he explains that a logical argument does not add information but uncovers a conclusion already implicit in the premises. Later he places the ontological proof within the tension between rationalism and empiricism and argues that the problematic novelty is the attempt to derive a factual claim about the world from definitions alone. Finally, he rejects the tendency to analyze the “heretic” psychologically and stresses that questions must be answered in a substantive and philosophical way even when one suspects motives.

The Course Framework and the Directions for Proving Faith

The lecturer notes that he has finished the introduction on the nature of faith / belief and on possible ways of arriving at it, and he removes Pascal’s Wager from the discussion. He says he intends to review four directions, especially tradition and direct intuition, alongside the three Kantian paths: ontological, cosmological, and physico-theological. At this stage he begins with the ontological proof and prepares the ground for adding a variation on logical arguments that he calls “revealing arguments” as opposed to “creative arguments.”

The Ontological Proof and Its Sources

The lecturer describes the ontological proof as one that people tend to dismiss, and he quotes Bertrand Russell, who mocked it, saying that it is easier to laugh at it than to point precisely to the flaw. He attributes the earliest formulation to Anselm, an Anglican scholar from the 11th century, and notes that the term “ontological proof” itself comes from Kant. He describes a chain of critiques and transformations through Aquinas, Descartes, Leibniz, Spinoza, and Hegel, and argues that the discussions continue to this day mainly in order to understand what is wrong with the argument, even though in his opinion it is ultimately unconvincing.

Reading the Proslogion and the Three-Stage Structure

The lecturer reads passages from Chapters 2–4 of the Proslogion and emphasizes that the text at first sounds like a prayer and then quickly turns into a proof directed against the “fool.” He presents a scholarly dispute over whether these are three repetitions or three different arguments, and instead suggests that it is one argument with three links, each resting on the previous one, with the third link returning to the opening point. He says that the first stage proves existence, the second proves that God’s existence is necessary rather than contingent, and the third asks how it is possible that the fool even entertains the thought “there is no God” if we are dealing with a necessary being.

The Translation and the Interpretive Framework

The lecturer notes that the Hebrew translation is by Sarmonta, who studied with him in the yeshiva high school and is a professor at the Hebrew University. He says that the translation appears in the anthology Torat Ha-Yesh and elsewhere, and that Avraham Zvi Brown edited the anthology and discusses the proof at length while presenting various interpretations. He uses these remarks to frame the multiplicity of readings and to support his claim that there is one three-stage structure here.

The Opening Prayer and the Claim Against “Begging the Question”

The lecturer presents a common criticism, namely that praying to God and then proving His existence assumes the conclusion in advance, and he rejects this as a conceptual confusion. He defines begging the question as inserting the conclusion itself as one of the premises of the argument, and argues that prior faith / belief or a prior position does not invalidate a proof. He illustrates this through Andrew Wiles and the proof of Fermat’s theorem, arguing that bias can be invoked as an explanation only after one has identified a flaw in the argument itself, not as a claim that automatically nullifies the argument.

Agenda, Theology, and Philosophy

The lecturer recalls something from a course by Asa Kasher about the distinction between a philosopher and a theologian: a philosopher assumes premises and derives conclusions, while a theologian assumes conclusions and derives premises. He says the distinction is correct in many respects and is connected to what he will later call “revealing arguments,” and he even argues that philosophers often work in a way similar to theologians. He says that what matters is the validity of the inference and the plausibility of the premises, not the question of agenda, and therefore the focus remains on examining the argument itself.

A Logical Argument as Revelation, Not as Adding Information

The lecturer formulates what he calls the “analytic emptiness” of logical arguments and says that a deductive argument does not add information but only reveals a conclusion already contained in the premises. He explains that the value lies in turning implicit knowledge into accessible knowledge, and compares this to a locked safe containing something that was always yours but that you could not use. He concludes that someone who is persuaded by a logical argument for the existence of God turns out to be someone who had always accepted premises that lead to that conclusion, and therefore “you can’t bring someone to repentance with logical arguments” in the logical sense, not the psychological one.

The Meaning of the Prayer Within Anselm’s Argument

The lecturer explains that placing the prayer at the beginning of the text is a deliberate move that pushes back against the illusion of the “tabula rasa,” arguing that no one arrives without premises. He suggests that the prayer announces that the believer already holds the faith / belief and seeks to turn it into “understanding,” in keeping with the phrase “who grants understanding to faith” and “to understand that You exist as we believe.” He argues that Anselm is also speaking to himself through the figure of the fool within him, and that the argument gives even Anselm himself a transition from unstructured intuition to intellectual understanding that presents faith as a conclusion of reason.

Ontology, an Argument Without Premises, and Kant

The lecturer presents the surprising part of the ontological proof as the attempt to build an argument without factual premises, only from definitions and their analysis. He attributes to Kant the central claim against Anselm: an analytic argument cannot yield a factual claim about the world, and therefore one cannot derive actual existence from a definition alone. He describes this as the difference between factual “input” and factual “output,” and says that the move looks like “hocus-pocus” if there is no factual premise at all from which the argument can uncover the conclusion.

Rationalism Versus Empiricism and Descartes’ Cogito

The lecturer places Anselm within the historical dispute over whether one can learn about the world without observation. He says that empiricists deny the possibility of factual knowledge without observation, whereas rationalists claim that thought too can teach us about the world. He presents Descartes’ “Cogito ergo sum” as an ontological argument that tries to establish a factual claim without premises, and argues that Descartes’ project was to save rationalism from the attacks of empiricism at the dawn of the modern era. He concludes that both Descartes and Anselm probably failed, because one cannot infer facts about the world from definitions alone.

The Definition of God: “As We Believe” and “Than Which Nothing Greater Can Be Conceived”

The lecturer interprets the prayer as containing a distinction between a claim of existence and a claim of essence: “that You exist” as opposed to “that You are such-and-such.” He says that defining the object comes before discussing its existence, and presents Anselm’s definition: “something than which nothing greater can be conceived.” He argues that presenting the definition from within faith gives the believer a certain privilege in setting the field of discussion, because without that there is no real disagreement, only people talking about different words.

Definitions, Conventionalism, Essentialism, and Real Disputes

The lecturer rejects the view that definitions are always arbitrary, as in mathematics, and presents disputes over “democracy” and “who is a Jew” as real disagreements about essential characteristics of the same concept. He distinguishes between conventionalism, which sees a concept as a collection of agreed-upon characteristics, and essentialism, which claims that a concept has an essence and that the characteristics describe it. He uses Borges’ story “Tlön, Uqbar, Orbis Tertius” to illustrate a world in which every collection of characteristics is an “object,” and presents that as strange and artificial because it lacks some unifying thing beyond the mere combination of characteristics.

Leibniz, the Identity of Indiscernibles, and Existence as Not a Property

The lecturer presents Leibniz’s principle of the identity of indiscernibles and the proof according to which if two objects share all properties, then they are the same object, and then argues that this proof assumes that an object is nothing but the collection of its properties. He says that existence is not a property, and that even “being non-identical to another” is not a property in the same sense, and therefore one cannot infer from numerical difference that there is a difference in properties. In this way he prepares the ground for a Kantian line of criticism of the ontological proof, according to which existence does not function as a predicate that enriches the definition.

The Fool’s Claim, Existence Versus Definition, and the Meaning of “Fool”

The lecturer presents the antithesis: it may be that no such “nature” exists even if the definition is understood and agreed upon, because a definition does not entail realization in reality, just as with the definition of a dragon or a unicorn. He notes that “fool” in biblical language does not necessarily mean a vile or depraved person in the modern sense; it can mean someone ignorant or mistaken. He adds that the link between heresy and moral deficiency is not necessary. He brings the Meiri’s view, which distinguishes between mistaken beliefs and reasonably moral human behavior, and stresses that there are idol-worshipping gentiles who behave with good morality.

Atheism, Agnosticism, and the Scope of the Argument

The lecturer distinguishes between the positive claim “there is no God” and the agnostic position that there is simply no evidence, and he argues that one cannot positively prove that there is no God, but only at most reject proofs for His existence. He mentions Dawkins’ scale of confidence and concludes that a rational atheist ought to be an agnostic. He says that Anselm’s argument, if valid, is directed both against someone who claims there is no God and against someone who merely doubts God’s existence.

Psychology Versus Philosophy in Questions of Faith

The lecturer rejects the approach that “the questions are the answers” as an evasion that replaces substantive discussion with motive analysis, and he argues that even if the opponent has moral or instinctive motives, his claims still need to be answered philosophically. He presents a symmetry: in leaving religion, the religious explain things psychologically and the secular explain them philosophically; in repentance, the secular explain things psychologically and the religious explain them philosophically. He says that both levels are always present. He argues that the discussion should be conducted around the question of whether the argument is correct or not, and that a serious answer can block rationalization even for someone who is looking for intellectual justification for a move he was already inclined to make.

[Rabbi Michael Abraham] Good. Now it looks okay. All right, sorry for the delays. Last time we basically more or less finished—actually, not more or less, I finished—the introduction. I spoke a bit about what faith / belief is, what kinds of paths can lead us to it, we cleared Pascal’s wager off the table, and now we can start working. And I said that I actually want to survey at least four directions. Tradition and direct intuition—that’s not something that needs a lot said about it, although I may comment on it at the end. But I do want to talk about the three Kantian ways: the ontological proof, the cosmological proof, and the physico-theological proof, and after that add some variation—I call these proofs a different kind of logical arguments, revealing arguments and not generating arguments, but we’ll talk about that when we get there. At the first stage I want to talk about the ontological proof. The ontological proof is a much-maligned proof. That is, a great many people dismiss it, and as Bertrand Russell once said—yes, the well-known and proud atheist—he said it’s much easier to scoff at this argument and roll your eyes at it than to put your finger on where exactly the problem is. And so I think it’s still worth going through this, even though in the end I too will comment that I don’t think it holds water. But it’s worth discussing, because I think that discussion will also teach us a few things that will help us later on. So this story really begins with an Anglican scholar named Anselm. In the 11th century, a very famous Christian philosopher and theologian, who first proposed this formulation of the ontological proof. The term “ontological proof” is Kant’s term, but the formulation of the proof, the initial formulation of the proof, was his. He took criticism for it from Aquinas and others; later it came back through Descartes and Leibniz and other versions, Spinoza, various later versions, Hegel. The discussions in the end continue, you could say, to our own day, in one direction or another, though I think the prevailing spirit is that these are discussions “to glorify and magnify Torah,” so to speak. Meaning, everyone understands that this argument won’t convince anyone, but still it’s amusing to examine what’s wrong with it, and whether one can put one’s finger on what exactly is wrong with it, and as I said before, in my opinion that too can teach us several things that are valuable with regard to other arguments. So I’ll start maybe just so you get the flavor—let’s quickly read a few selected passages. At first glance, it’s not even certain that everyone would notice there’s a philosophical argument here; it sounds like some ordinary religious text. “Proslogion” is the name of a book by Anselm, and I’m talking about three chapters from it, chapters 2, 3, and 4. So chapter 2 goes like this: “Grant me understanding, my God, giver of understanding to faith, grant me, as far as you find me worthy of it, to understand that you exist as we believe and that you are what we believe. And indeed we believe that you are something than which nothing greater can be conceived. Or perhaps no such nature exists, for ‘the fool has said in his heart, there is no God.’ But certainly that very fool, when he hears what I say—that is, something than which nothing greater can be conceived—understands what he hears, and what he understands exists in his mind, even if he does not understand that that thing exists in reality. For it is one thing for a thing to exist in the mind, and another to understand that the thing exists. Indeed, when a painter first thinks ahead what he is going to create, that thing exists in his mind, but he does not yet think of it as existing in reality, for he has not yet made it. But after he has already painted it, that thing also exists in his mind and he also understands that it exists in reality, for he has made it. Therefore even the fool must be convinced that at least in the mind there is something than which nothing greater can be conceived.” Certainly it cannot exist in the mind alone. For in truth, if it existed in the mind alone, it could be conceived as existing in reality, and that is greater. Therefore, if that being than which nothing greater can be conceived exists only in the mind, then that being than which nothing greater can be conceived is a being than which a greater can be conceived. That, of course, cannot be. Therefore, without doubt, there exists something than which nothing greater can be conceived, and it exists both in the mind and in reality. I read that quickly; I assume you didn’t follow all the details, but I wanted you to get a bit of an impression of the text. It’s actually pretty hard to notice—at first it looks like some kind of prayer he’s saying. Then he starts speaking with the Holy One, blessed be He, and at some stage he suddenly speaks to some fool standing opposite him and—boom—within a few sentences he suddenly moves to “which is what had to be proven.” It’s some kind of argument, a very surprising move. At first, a few very basic things, and within a line he suddenly shows you that in fact he’s proven that God exists. To you—the fool. That was chapter 2. Now look at chapter 3. Again, I won’t read it all now, but: “And this exists so truly that it cannot even be conceived not to exist. For one can conceive of 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 a being than which nothing greater can be conceived can be conceived not to exist, then that very being than which nothing greater can be conceived is not that than which nothing greater can be conceived, and that is a contradiction.” It’s the same argument, and therefore Anselm’s interpreters disagree among themselves. There is a lot of interpretation of this text. The Hebrew translation is by Sarmonta, whose son learned with me in yeshiva high school, a professor at the Hebrew University. And this translation also appears in an anthology called The Doctrine of Being, I think, and perhaps elsewhere too. In any case, it’s an anthology edited by Avraham Zvi Brown. Anyway, there the translation of this passage appears, and Avraham Zvi Brown discusses this argument at length, bringing various interpretations one way and another. There are those who say he’s simply repeating the argument three times. Yes, chapter 4 as well—look at chapter 4, this is the third chapter: “But how can the fool say in his heart what he cannot conceive, or how can he conceive what he said in his heart? Since to say in the heart and to conceive are one and the same. If he really did conceive, or more than that, precisely because he truly conceived it, for he said it in his heart and did not say it in his heart because he could not conceive it, this is because it is not said in one way alone.” In short, he goes back over the same pilpul-style distinctions: if he conceives it, if there is a greater, there is nothing greater, and so on. I’ll still spell it out; I just want you to see what we’re talking about. There are those who want to say that this is simply a threefold repetition of the same argument. That’s not likely to be what he intended. Maybe he didn’t succeed, but it doesn’t seem likely that someone writes three chapters in order to repeat the same thing three times. Another interpretation says that we have three different arguments here, and then one has to understand exactly what the difference is between them. I think both of these are wrong. It’s one argument composed of three links, and each link is built on the previous one. What’s confusing is that the third link returns to the beginning of the first. In the third link he is basically asking himself: wait, if I proved to the fool that he is mistaken, that even according to his own view God necessarily exists, then how could he have conceived from the outset that God does not exist? Since he doesn’t exist. After all, “the fool says in his heart, there is no God,” so he does conceive it. But I showed that he cannot conceive it as not existing. So can he or can he not? In other words, he is basically closing a circle when he goes back to the point from which he started at the beginning. So the structure, again broadly—that’s what matters to me right now—the structure is that we have here a three-stage argument. The first stage proves—I’ll already say here—the first stage proves God’s existence. The second stage claims that God’s existence is necessary existence and not contingent existence. You can prove the existence of something that exists not necessarily but contingently, but I’ll prove that it exists. I can prove to you that this Pentateuch exists—look, see, here, I proved it to you. Does that mean it exists necessarily? No, they might not have printed it, right? So saying I proved the existence of something is not the same as saying I proved that it exists necessarily. And third, after that he comes back and says: if it is necessary, then how can the fool conceive that there is no God? That’s a logical contradiction, because after all this is a necessary being. Okay? And that’s why this is the third stage. I think that’s how this text should be read. Now come, I want to start unpacking this, start breaking it into stages. I’ll begin with the prayer. The following is taken from a book I wrote, so that’s why I’m using it. What is the meaning of the prayer with which Anselm opens, one of the most maligned parts of these three chapters? People say, listen, this is a rigged game—you’re praying. Praying to God and then proving His existence? If you prayed to Him, that means you already presuppose that He exists. So wait with the prayer, prove that He exists, and then start praying to Him. No, he opens with a prayer, and then he proves the existence of the being to whom he is praying. So many people mock him over this, but these mockeries are of course nonsense, like all the mockeries of Anselm. In my opinion, by the way, this text is one of the most wondrous texts in the history of philosophy. A text precise in a way I hardly know another like it. There isn’t a word out of place. I’ll show you that. And all these mockeries are just people who don’t understand their own lives. What problem do they see in such a prayer? That he’s begging the question. You assume there is a God, then you pray to Him, then you prove His existence. Of course that’s nonsense. Think about Andrew Wiles, who proved Fermat’s hypothesis, Fermat’s theorem. He sat on that for many years, twelve years, thirteen years, something like that. He worked on it. Now do you really think—what would he have answered me if I had asked him before he sat down? Obviously he would have said, of course I’m convinced it’s true. By the way, almost everyone was convinced it was true. They just didn’t have a proof. For mathematicians, what’s obvious to you doesn’t get you to the grocery store. You need a proof. Okay, so if I had asked him, tell me, is Fermat’s theorem true? He’d say yes, certainly. But there’s no proof. So now he sits down and proves Fermat’s theorem, spends 12 years or whatever and proves it. But the fact that he thought it was true beforehand—does that invalidate his proof? Why? On the contrary: if I’m looking for a proof of something, that’s usually because I already have some prior assumption or belief that it really is true. Now I just want to find a proof for it. But does my having a position invalidate the proof? Understand what begging the question is. Begging the question is when the conclusion that I want to prove is placed as one of the premises of the argument. I use it itself. So if Anselm had assumed God’s existence and put that as a premise of the argument, that would be begging the question. But if Anselm says to me, look, I believe God exists, I even pray to Him, and afterward I’ll look to see whether there is also a proof. Maybe I’ll find one and maybe I won’t. Is there any problem here? Okay, so show him where he went wrong. That’s exactly the point. You can accuse him of being biased, but the accusation that he is biased is not an argument. Meaning, if you show there is a problem in the argument, point it out. He presented an argument; point and show me: here, there’s a problem in your argument. Afterward, as a conclusion, you can tell him, listen, apparently you were biased because you didn’t notice that there was a problem here. But to say that he is biased—that’s not an argument. So what if he is biased? If his argument is fine and you didn’t find a bug, then that’s the end of it. Why do you care that he had an agenda? A lot of the time, in our own public discourse too, things are built in exactly that way. People argue that someone is biased, and therefore don’t accept what he says. What difference does it make if he is biased? If he is telling you something you can’t know yourself and you have to rely on him—if he is biased, I don’t trust you, fine, that I understand. But if someone puts forward an argument, then why should I care whether he is biased? Look at the argument. If the argument holds water, excellent. If not, say you disagree. Afterward you can also say he was probably biased as a conclusion. But the claim that he is biased is not itself a claim. What kind of claim is that? At most it can be an explanation after you found a problem in the argument. If you found a problem in the argument, then the explanation is that he was probably biased. Fine, but that doesn’t make “he is biased” into an argument. Therefore this mockery of the prayers is nonsense. What, all these theologians who sought proofs for God’s existence—did they not believe in Him until the stage when they found the proof? I once heard a course by Asa Kasher at Tel Aviv University, called “A Systematic Introduction to Philosophy.” It was neither systematic nor an introduction nor philosophy, but among other things one thing did remain with me from it. He said: what is the difference between philosophy and theology? Between a philosopher and a theologian? A philosopher assumes premises and derives conclusions from them. A theologian assumes conclusions and derives from them the premises that will lead him to the conclusion he wants in the first place. Now that’s true in a great many senses; later on I’ll discuss this at length, because the fourth mode, the revealing arguments I mentioned earlier, is tied by the umbilical cord to this distinction. And I’ll show that philosophers too basically work like theologians. But regardless of that point—if in the end I found premises that lead me to the conclusion, and it really is convincing, then what? So I’m a theologian. Check my argument. So what if I’m a theologian? It’s like saying I’m biased. Check my argument. If my premises seem reasonable to you, and the conclusion follows from the premises, that’s the end of it. What’s the problem? Therefore the claim about begging the question is simply shallow. A lack of understanding. I’ll tell you more than that: why did Anselm really put the prayer there, at the beginning of the composition? Were I not afraid, I would say he even anticipated that people would laugh at him. He did not put it there by accident. He also didn’t write that he brushed his teeth that morning before trying to prove God’s existence. So why does he tell me he prayed to Him? He also got dressed; none of that appears in this chapter. Why did he choose specifically to place the part about prayer there? You understand that this is part of the text. It’s not just there to tell us what happened before he sat down at the table and found the proof. He probably didn’t sit down at the table and find a proof either. I believe it was a process that took time. So this prayer has a role here. But it’s not the role of serving as a premise, because then it would indeed be begging the question. So what is it? I think Anselm is trying to teach precisely this point. What do I mean? He says: let’s try for a moment to think—what are we really looking for when we look for a proof of God’s existence? So I want for a moment to talk about the meaning of logical arguments in general. I don’t remember if I spoke about this here—about deduction and induction—did I talk about it? Right? Okay. So I already said the thing about analytic emptiness. Meaning that logical arguments, or analytic arguments, do not add information, right? Did we talk about that? Okay. So what does that actually mean? That a logical argument, which derives a conclusion from premises—why does it really appear necessary to us? Why does it really appear necessary to us? Because the conclusion is somehow contained inside the premises. Right? Whoever accepts the premises—in the whole, yes, in the content—in particular has also accepted the conclusion. It’s there. Okay? And therefore a logical argument does not add information to me; it merely reveals information that was already present in the premises. Of course this can raise the question: then what value is there in such an argument? What value is there in such an argument? If all you are doing is extracting information that already exists in me, what did I gain? The answer is that many times this information exists in me in some hypothetical, implicit sense, but I myself am not aware that it is there. And someone needs to help me, by means of a logical argument, to show me that within the premises I assume there is also that conclusion that I didn’t notice. Therefore, for example, if I prove God’s existence to that fool or atheist standing opposite me, and if my argument is a logical argument that proved God’s existence to him, then it turns out that he was never an atheist all along. He was always a believer, he just wasn’t aware of it. But within the premises that he accepted, the conclusion that God exists was already contained; he just didn’t understand that it was contained there. So he was an unconscious believer, an implicit believer. And therefore if I succeeded in proving to someone by a logical argument that God exists—to an atheist, yes, that God exists—I have not actually brought him new information. I revealed to him information that was already present within him. Right? I spoke about the hot-air balloon and Abraham our father and the star and all that, right? So really the point is that what Anselm wants to say here is that when he approaches the search for a proof of God’s existence, he approaches it with an agenda, but he is proud of his agenda, he does not hide it. Why? Because there is no logical argument that doesn’t have an agenda behind it. Not only is that not a defect in a logical argument, every logical argument is like that. Because in fact a logical argument that proves some conclusion to you—clearly you already assumed that conclusion from the outset, because otherwise you wouldn’t have accepted the premises either. Yes, if I tell you: all human beings are mortal, Socrates is a human being, conclusion: Socrates is mortal. Suppose someone comes and says he doesn’t know that Socrates is mortal. I tell him: do you know that all human beings are mortal? Yes. Do you know that Socrates is a human being? Yes. Well then the conclusion is that Socrates is mortal. Ah, wow, I hadn’t noticed. What does that mean? It means that if he had really thought Socrates was not mortal, then he wouldn’t have accepted either the first premise or the second. He would have had to say either that not all human beings are mortal, because look, Socrates isn’t, or that perhaps all human beings are mortal but Socrates is not a human being. But he would have to reject one of the two premises, right? If he accepted both, then one of two things is true: either he was confused—meaning he doesn’t really accept one of them, he just didn’t notice—or he really didn’t understand that he also agrees that Socrates is mortal. He thought not, but he was mistaken. Meaning, he was simply living in a contradiction, okay? The same with a proof of God’s existence. A proof of God’s existence basically says: take these premises. Now there are three possibilities for the atheist standing in front of me. You can either question one of the premises, at least one of the premises, or question the inference, meaning say that the conclusion does not follow from the premises, or change your position and adopt the conclusion, right? Those are the three possibilities. There’s no—what does it mean to adopt the conclusion? It means to recognize that you were in fact mistaken before. You were actually a believer in God all along, only you were not aware of it; you thought you weren’t. Now it turns out that you are. You cannot bring people to repentance with logical arguments. That is not a psychological statement; it is a logical statement. You cannot bring someone to repentance with logical arguments, because if he truly does not believe, then no logical argument will bring him to believe. A logical argument can show you that you believe only if you already believed beforehand. If you did not already believe beforehand, then no logical argument will convince you, because you will probably not accept one of the premises that lead to belief, right? Because after all that conclusion is contained within those premises. So I think Anselm placed the prayer here in order to say to people: look, friends, I believe in God. That is my point of departure, that I believe in Him. And now come, I will present to you an argument that will show you that you too believe in Him. You should have joined me in prayer from the start, not only after the proof. You were living in error, and the proof will show you that you were living in error. And therefore it seems to me that the placement of the prayer at the start of the proof is something, I would say, provocative—something that basically says: do you really think you come as a blank slate? No one comes anywhere as a blank slate. After all, you always have premises. From the premises I derive the conclusion. But within the premises themselves there is already embedded, in some sense, either the conclusion or its opposite, in which case you would not accept the premise. But no one comes to anything as a blank slate. People live under some illusion that they are a tabula rasa, that they arrive clean, objective, without an agenda, without a stance, without anything. Okay? Yes, Ruth Gavison and Aharon Barak, for those old enough among us to remember. Fine. So the placement of the prayer, it seems to me, at the start of this proof-text, basically shows us that a proof is something that begs the question. And don’t be alarmed that I proved God’s existence to you, because that just means that you have believed in Him all along. You could have joined me in prayer at the beginning, and here I’ve put it on the table: I’m praying to Him even before I proved His existence. Because it’s obviously there in me, in the premises. Otherwise there could not be a logical argument that leads to that conclusion. Now, so what is really the significance of this? In an ordinary logical argument, say directed toward an atheist, I understand that it adds no new information to the atheist. It reveals to him information that was already present within him, okay? And that is something valuable. Meaning, to identify things that were inside you but you hadn’t noticed, hadn’t stood on them, hadn’t paid attention to them. I compared it then to things that I have inside a locked safe, but I have no way to open the safe. So those things were always mine, all along, but I couldn’t use them because they were inaccessible to me. So too, inside us there is some kind of intellectual safe in which there are various things that we in fact know, but we need someone to help us open the safe so that we can realize they are there. But once the safe has been opened, it turns out they were always there. So what, is that worthless? No, it’s not worthless. Yes? Like geometry. We talked about that too, right? What’s the value in learning geometry? You prove the theorems on the basis of the axioms. So if you proved them, that means the theorems were already contained within the axioms. So what value is there? The value is that none of us would have reached the theorems without the help of teachers. Right? That’s a fact. True, after the teachers help us we then understand that we could in principle always have known it, but it’s a locked safe—someone needs to help us open the safe. And therefore this has value. It does not add information to me; it reveals information that was already present in me. But the beautiful question is: what does this add for Anselm himself? After all, with whom is Anselm speaking? Anselm is speaking with the fool. Yes: “the fool says in his heart there is no God,” and he argues with him. He places before himself some kind of imaginary figure, no matter, but it could be that this figure is within him. He wants to persuade himself, so he places here the fool and argues with him. But if you pray from the outset, then what is this? Then the fool is not inside you, he is outside. What difference does it make? Why do you need this argument for yourself? Here Anselm has another sentence, I think that… look here, this is the wording of the prayer, Ashkenazic style. “Therefore You, my God, giver of understanding to faith.” Therefore—you see what’s blacked out there, so I’ll release that. “Therefore You, my God, giver of understanding to faith, grant me, as far as You find me worthy of it, to understand that You exist as we believe, and that You are what we believe.” So to whom is he trying to prove God’s existence? To himself, right? Meaning: grant me—as far as You find me worthy of it—to understand that You exist as we believe. So are you speaking with the fool or with yourself? He is speaking with the fool inside him. He is basically placing the figure of the fool in order to—what? He is placing within himself the figure of the fool in order for a dialogue to take place here. He wants to present this discussion as a dialogue between two positions. So there is the position of the fool and there is his own position. Later I’ll show this in more detail. But basically he is trying to show it to himself. But why are you trying to show it to yourself if you pray and already know in advance that God exists? Then the merchandise isn’t locked in a safe—you already know it’s there. So what value does the argument have? Why do you need this whole game of setting up some fool here? If there were a real dispute with a real fool, then you would be coming to convince him, and fine, you revealed something to him that he didn’t know, assuming you succeeded. Okay? But if there is no actual fool here—if you are positioning some figure of a fool within yourself in order to conduct the dialogue, a dialogue between the believer and the fool, but the whole thing takes place within him—then what value is there in that? So he says, look: “giver of understanding to faith.” There are situations in which I understand that I believe in God, but it seems to me like some kind of intuition. Direct intuition—we spoke about that as the final path to arrive at God’s existence, direct intuition. But can I show by means of a logical argument that this is connected to various premises that seem to me stronger, or clearer, or more objective? Okay? And if so, then clearly I myself will also gain from this. Before, I thought there is a God, and now I know there is a God. Because now it is understanding, not only faith. It’s something I understand intellectually, not just some abstract thing, or some intuition one way or another. And therefore it has value also in relation to the person himself, and not only in relation to the fool standing opposite him. I’ll tell you more than that: the nature of this proof, the nature of this proof, is basically of an ontological nature. What does that mean, an ontological nature? We spoke about this briefly in the previous lesson; now I’ll explain a bit more. A logical argument is usually built in the form of premises from which I derive a conclusion. Right? Whoever stands opposite me—if he does not accept the conclusion, then he must either show me some premise he does not accept, or show that the conclusion does not follow from the premises; there is a problem in the logic. Okay? If both the premises are acceptable and the validity of the argument is acceptable to him, then he must change his position. Right? That’s what a logical argument does. Now the question always arises: and where do you know the premises of the argument from? The argument grounds the conclusion on premises, and the premises themselves—where do you know them from? We spoke about that; I said it’s some kind of intuition, yes? I have some kind of—I understand that this is so. Some kind of direct understanding. Fine? We spoke about this as basically the faculty we call faith, intuition. Now, but if there is a way to bypass this need—because this is of course the shaky part of the structure. Right? I have premises, I derive from them a conclusion; as for the logic, that the conclusion follows from the premises, if I’m careful enough there won’t be any mistake there. The problematic part in such a structure is the premises. Who told you the premises are true? After all, you have no proof; you adopt them because that’s how it seems to you. So your interlocutor can always say: fine, and I disagree. That’s not how it seems to me. Okay? That’s the problematic part. What does Anselm do? He makes a very surprising move. He builds an argument without premises. No premises. An argument without premises. Can such a thing exist? It left us without premises, so to speak. Meaning: can there be such an argument, one with no premises? Anselm claims yes. Kant called such an argument an ontological argument. An ontological argument is an argument based on definitions and analysis of definitions, or basically an analytic proposition in the senses we discussed in previous sessions too. And Kant’s main claim against Anselm is precisely this: that his argument is an analytic argument, and an analytic argument cannot add information. It cannot be that you lay down certain definitions, and from the definitions you produce a claim about the world. Some kind of hocus-pocus. If you have premises, then there is some information within the premises, and the logical argument reveals information that was already within the premises. You put information in as input; at the end you got out the information you put in. That’s what logic does—it opens the safe for you. But if I have no safe and no key and no nothing, and suddenly—boom—I have money. Where did it come from? And I didn’t buy it from anywhere either. Where did it come from? How can it be that there is no input and yet there is output? I put in no factual item, no factual premise, nothing at all. I define concepts, and from the definition I can show you something that is a factual claim. Meaning, I show you something that exists in the world from the definition alone. How can such a thing be? It somewhat recalls Kant’s synthetic a priori. So that is really the focus of Anselm’s innovation and of the criticism he took: he is basically claiming that he can prove God’s existence—and we said this is a factual claim about the world, not feelings and not experiences and not anything of that kind—and he does this without assuming any premise. Hocus-pocus. Meaning, he defines a concept, and from the definition he performs some manipulation on the definition and—boom—up sprouts a factual claim about the world; you have learned something new about the world. Something here cannot be right. Now, that brings us back to the debate between rationalism and empiricism. What do I mean? This debate—I’ll define it this way, look. There is—and I think we spoke about this too, right?—the debate between empiricism and rationalism. Meaning, there is an ancient dispute in philosophy: can one learn things about the world without observation? The empiricists argue: only through observation. The rationalists say: no, by means of thought too I can learn something in the world—about the world, sorry. Now, this debate along the historical axis: rationalism ruled somewhat in the Middle Ages. At the beginning of the modern era empiricism began, and empiricism basically claims: with all due respect to Aristotle and the rationalist conceptions, you cannot know anything about the world unless you have observed it. Because all the other things are merely forms of your own thinking. And the world owes your forms of thought nothing. The fact that you think in a certain way does not mean that this is how the world behaves. Right? That is the empiricist claim. Now Descartes, in the 17th century—end of the 16th, beginning of the 17th, I think—Descartes, his cogito argument, “cogito ergo sum,” I think therefore I am, is also an ontological argument. It is an argument that tries to prove a factual claim about the world—that I exist—without premises. Without any premise. And therefore the significance of Descartes’ project—people don’t understand the context—Descartes’ project was not to prove that I exist, but to show that by intellectual tools alone, without premises and without observations, one can arrive at a factual claim. He basically wanted to save rationalism under the attacks that were already, at that time, very heavy from the empiricists—which also launched modern science, yes, the beginning of the modern era. And that was basically his claim. And he too failed. And Anselm probably failed too. We’ll see this later, but he probably failed because indeed, you can’t. You cannot learn things about the world merely from definitions, merely without assuming any premises. That isn’t plausible. Certainly not in a logical argument. You can raise conjectures, you can engage in one speculation or another, but you cannot say in a logical argument that analysis of concepts will yield for me a factual claim, a claim about the world. Such a thing cannot be. So if we place it in that context, what Anselm is trying to do—already in the 11th century, as we saw—is basically part of rationalist thought that says: by means of thought alone I can arrive at factual claims about the world. I do not need scientific tools for this; philosophy too is a tool for knowing the world. And in particular, he of course says much more than that. Because one could speak of philosophy in other senses: I do assume premises and from them derive a conclusion, only those premises are not the result of observation but the result of one a priori insight or another. The law of causality, or induction—we spoke about that. But Anselm wants to claim: no, I assume no premises, not even philosophical premises. No premises at all. Only definitions. I define a definition, and from that I can prove to you the existence of something. God, or my own self in Descartes, or whatever it may be. That is much more far-reaching than plain rationalism. Rationalism says: I have premises that I bring from home, not from observation, but I think they are correct; that is how I see the world, and from that I can draw conclusions about the world. And science assumes a great many such premises; there are people who live under the illusion that it does not, and that is an illusion. Science assumes many such premises. Okay? But that is still not an argument without premises; it is an argument with premises, only premises that do not come from observation but from some a priori reason, from intuition, from whatever. Anselm takes a more far-reaching step. Anselm wants to claim: I can build an argument with no premises at all, not even philosophical premises. No premise. I define a definition, and a definition is ultimately arbitrary, right? I define a definition, and once I have defined it, let’s do a logical analysis of that definition and I’ll show you that God exists without assuming any premise. That is rationalism on steroids. It is not merely to assume premises that are not the result of observation, which any rationalist will do, but not to assume premises at all and yet arrive at a result that is a factual claim about the world. That really is impossible hocus-pocus, and there are those who want to argue against Anselm on exactly this point. They see this as an objection and say: how can it be that you define a definition—and definitions are ultimately whatever you want them to be, right? Define whatever you want; as long as you remain consistent, everything is fine. With definitions there is nothing to argue about. Okay? How can it be that you merely define definitions, there is no input, and out comes output, a factual claim about the world? But of course that too is not really an argument. It’s very plausible, in my eyes too, but it’s not an argument against Anselm. Show me what is wrong in his argument. The fact that you say “it can’t be”—very nice that it can’t be, but look, he showed you. Do you know when people say “it is inconceivable” that someone would do such-and-such? When do they say that? After he already did it, right? Meaning, once he has done it, people say it is inconceivable that someone would do such a thing. So you say: it is inconceivable that someone would prove a factual claim on the basis of definitions. Well, Anselm did it. What do you mean “inconceivable”? It was conceived very well indeed. You can tell me: no, he didn’t do it. So show me where the flaw is, meaning show me what is flawed in his argument. I’m trying to show you that many of the claims—almost all the claims—raised against Anselm are not really refutations. They simply point out that some of our own foundations were shaken by Anselm’s argument. For example, in this context, what was shaken is this assumption that seems self-evident to us, to me too, that from definitions you cannot derive a factual claim. Well, he showed you that you can. Unless you show that he didn’t really show it—meaning, show me where his argument is flawed. Okay? So I am clearing off the stage many things that at first glance come up as though they were objections; they are not objections. All these claims are very nice claims: that’s what you thought, and Anselm shows you that you were mistaken. Yes, one can derive facts from definitions—unless you show me what in his argument is flawed. Okay? So let’s go into the argument itself. At the end of the prayer, before “Aleinu leshabe’ach,” I’m bringing you this point here: “Therefore now,” again yes, here, “therefore now, my God, giver of understanding to faith, grant me, as far as You find me worthy, so in the meantime we discussed the fact that he opens with prayer. He explains what the prayer means. ‘Giver of understanding to faith’—I want the faith to become for me something of understanding, not only of faith, but of intellect. ‘As far as You find me worthy, to understand that—’ What is the difference between these two? To me it sounds like a biblical study exercise. ‘That You exist as we believe, and that You are what we believe.’ Right. Meaning, to say that You exist is a claim of existence, that God exists. But who is God? What is God? Do you have a definition for the concept whose existence you are looking for? One of the most common claims of atheists against claims for God’s existence is that you never defined what God is; you yourself do not understand what God is, so what is the point of talking about it? Again, a silly claim, but it comes up a lot. Therefore Anselm says: I want to prove that You exist as we believe and that You are what we believe. What does that mean? The claim is basically this. After all, we said—we spoke about this—that every argument in favor of God’s existence has to assume some definition of the concept God, right? You need to assume the definition and then prove that an entity corresponding to that definition exists in reality. Okay? And we spoke about the fact that every argument in fact assumes a different definition of God, and we spoke about Ockham’s razor, that you can unify all those gods into one being, but on the conceptual level each argument proves the existence of a different entity. So Anselm is actually trying to point us to exactly this point, and he says: first of all I need to define for you who this God is whose existence I am going to prove. Otherwise I’m just talking about words—prove to me the existence of x-y-z. Well, I’ve said nothing. Tell me what you want to prove, then let’s see how one proves it and whether you succeeded. But first tell me whom you are trying to prove. So he says: I want to prove to you the God as we believe in Him. Meaning, don’t expect the definition to emerge from the argument. The definition will not emerge from the argument. The definition emerges from faith, and that is why it appears in the opening prayer. We believe that He is such-and-such. That is the faith. So now I have a definition. A definition that God is such-and-such. Now let’s see whether I have a proof that He exists. Meaning, I draw the definition out of faith, but that doesn’t make it a begging of the question either, because now I still have to examine whether the argument succeeds in proving the existence of such a being, whose definition indeed lies in faith, emerges from faith. Okay? So that is what he means by “that You exist as we believe and that You are what we believe.” I need to prove the existence of an object that is the very object in which believers believe. Otherwise I have not proved God’s existence but the existence of something else that I don’t know what it is at all. Okay? So what he basically wants to say is that the definition of God from which he sets out is actually drawn from faith. Now here there is a very important point. Because when we look at definitions, yes, in general. When we look at definitions, in mathematics they accustomed us to think that definitions are arbitrary. Define whatever you want, just remain consistent with your definition, right? You define a set of concepts or principles or whatever it may be, and you check by logical means what can be derived regarding that thing. You are not making any claim that it exists or does not exist, that it is really true or not true. I don’t ask whether a triangle is really a three-sided thing. The definition of triangle is a three-sided thing. It’s not a matter of true or false; that’s the definition. There’s no arguing with such a thing. You can tell me: I want the word “triangle” to describe, I don’t know, something nice and purple-pink. Fine, then we have a different dictionary, that’s not an argument. Okay? Therefore there is nothing to argue about with definitions; they are arbitrary. So it seems, at least that’s how mathematics is often perceived. But that is usually not true. Usually it is not true. Usually definitions can be right or wrong. Definitions are meant to capture some concept that we have some understanding of, and the definition tries to conceptualize it. And then one can discuss whether it captures it well or not. Let me give you an example. We have all kinds of disputes around judicial reform. Yes, what is democracy? Is democracy compatible with such-and-such a law, or with such-and-such a law, or with such-and-such a governmental structure or another? Fine, what is the meaning of such a debate? Fine then, call it democracy and he’ll call it democratanda. What, are you arguing over a word? Is the dispute over what will be written in the dictionary? When I say no, democracy must mean that there are only up to 15 ministers. And someone else says no, democracy can also exist with thirty ministers. That’s not democratic, I don’t know what. Okay. Or that the Supreme Court is chosen by other authorities and not by the vote of the public at large—that’s not democratic. And there are those who’ll tell you—or the opposite, they’ll tell you only that is democratic, never mind. Okay? So why are these arguments interesting? Fine, then I’m not a democrat, I’m “yekum purkan.” I believe in the form of government called yekum purkan. What is the point of arguing over the meaning of a word? Like the arguments over the question who is a Jew. Yes? So I say a Jew is someone who keeps commandments, and someone else says a Jew is someone who is a loyal citizen of the State of Israel, pays taxes, speaks Hebrew, and reads Amos Oz. Okay? So what’s the dispute? You call that Jew, I’ll call mine Israeli, and we’ll part as friends. What, the whole dispute is over the right to use a word? And what it represents? What I’m trying to define, no? Well, if you define something else, then it simply represents different things. So what’s the dispute? But there is a dispute. We shed one another’s blood over these arguments. Do you know why? Because with the concept democracy, we’re all speaking about the same concept. We have some notion of what democracy is. And now suddenly a disagreement is uncovered—a disagreement emerges. You say: wait, the public should choose the Supreme Court justices. And he says the Supreme Court justices should be chosen by the Knesset or the government or whoever. Okay? So what does that mean? That we’re simply talking about different concepts? No. We’re talking about the same concept, and we disagree over what its characteristics are. Or in other words, I’ll try to formulate it more abstractly and say this: there are conceptions according to which a concept is nothing but the set of characteristics that define it. That is what a concept is. And I claim that this is an incorrect conception. People will say this too is semantics. It’s an incorrect conception. Why? Because according to that, how can there be a change in the definition of a concept, for example? Once the definition is different, then it is no longer this concept, it is another concept. What does it mean to change the definition of a concept? Or how can there be a dispute over the definition of a concept? Like we spoke about before regarding the definition of democracy. What’s the dispute? You use concept X, I’ll use concept Y. What, just to attach the same word to two different domains? That’s simply a recipe for confusion. What good is that? Why is there a dispute? The dispute exists because we understand that there is something in the concept beyond its definitions. We have an intuitive grasp of that concept. We understand what democracy is. And now we want to understand how to conceptualize that abstract understanding. Meaning, which concrete characteristics can I give that will capture this abstract meaning of the concept democracy? And one says the Supreme Court should be chosen this way, and another says it should be chosen another way. And that is a real dispute. Not a semantic dispute. It is a real dispute. And therefore, in the context of God as well, when we argue over characteristics of God, one can of course say, as in Maimonides’ elephant parable, yes, someone who says that an elephant has two wings and this and that is simply not arguing with me; he’s simply not talking about an elephant. He is probably talking about a bird, not an elephant. Okay? So that’s not a dispute. Someone says an elephant has wings and someone says an elephant has no wings. That’s not a dispute; you’re simply talking about different concepts. So no, not necessarily. Sometimes there is a dispute over the characteristics of the same concept to which we are all referring. When there is a dispute over who is a Jew—whether someone loyal to Torah and commandments, or someone who reads Amos Oz, pays taxes, and serves in the army—that is a real dispute. Not a fake one. There is a real dispute here over what it really means to be a continuation of Abraham our father. What it really means to be a Jew in some very abstract sense. When we try to define this, to fit it into formal frameworks, to propose concrete characteristics of this abstract concept, disagreements can emerge. And that disagreement is a real one; it is not semantic. You know, there are these two conceptions that are called—at least I call them—conventionalism and essentialism. Yes, essentialism. What does that mean? There are those who understand that a concept is a convention. We agree that a certain collection of characteristics defines a concept. Okay? Others, essentialists, say no, a concept has an essence. The characteristics describe the essence of the concept. But the concept is something of which the characteristics are characteristics. Not that the collection of characteristics is the concept. Just as this table here—you could say what is this table? It is the collection of its characteristics: that it is brown and wooden and has two legs and so on, right? I claim not. The table is the object of which these are characteristics. The collection of characteristics is not the table. The table is an object. It has characteristics. The characteristics are its characteristics. Whose? The table’s. There is a wonderful story by Borges. Jorge Luis Borges, the Argentinian writer. An unmistakable genius. I mean, I don’t know if there is another writer of whom I can say clearly that he was a crazy genius. One of his stories is called “Tlön, Uqbar, Orbis Tertius.” He goes wild there too, dealing with Kabbalah and all kinds of strange things. In any case, in that story he describes some planet—he describes a planet called Tlön. And this planet is one on which solipsists lived, idealists, people who do not believe in the existence of an external world. They understand everything to be only experiences or cognitions that exist within us inwardly. There is no real world out there somewhere. That’s how they conceive it, and Berkeley was of course chief among them, since he really was an idealist philosopher. And Borges describes this planet as imaginatively as you could want. Among other things he says that on this planet they found a dictionary of that planet—an imaginary one, of course. They found a dictionary of that planet, and in that dictionary every collection of characteristics is a concept. Meaning, for example, the shriek of a bird in the distance and the color of the sunset on October fifth in Indonesia—that is a concept. You could call it yekum purkan, for example. Yes? Those are the two characteristics that make up the concept. Or being brown and dwelling by the seashore and also containing more than ten thousand inhabitants—that is a state, a certain kind of state to which one can attach a name. A state, I don’t know, “popolovite.” Yes, that’s what I want to call it. Now why does that seem strange to us? Because for us—or an entity, not a concept sorry—it creates an entity. But I claim: why is that strange? It is strange because for us a collection of characteristics organizes itself into being characteristics of a concept only because they really all characterize one concept. But to take any random collection of characteristics from the full dictionary of characteristics—take characteristics A, Q, Y, T, tav, bet and aleph 1542, fine? And these four characteristics are a concept; let’s call it, yes, Moshe. Fine? That’s how I define it. Now why does that seem artificial to us? Because there is no such concept. What do I mean? If the concept is the set of characteristics, then what does it mean to say there is no such concept? The collection of characteristics is the concept. What is the problem with there being such a concept? When you tell me there is no such concept, what you are really saying is: there is nothing whose characteristics these are. When I gather all the characteristics of a democratic state, for example, why do I take this collection of characteristics and call them a democratic state? Why don’t I take the previous collection of characteristics that I mentioned—a state that is brown, lies by the sea, and has up to ten thousand inhabitants—and let’s give that a name too, that is a popolovite state. Okay, I want to call it that. What’s the problem with that? Why does that seem strange to us? Because there is nothing uniting all those characteristics. They do not together form one whole. Just three random characteristics. What do you mean, irrelevant? In a democratic state, the collection of characteristics forms one whole. We understand that there is a connection between them. That the existence of all these characteristics constitutes, in some sense, say, a proper regime, okay? And that all these characteristics are required—again, one can argue—but on the conceptual level all these characteristics are required for democracy to exist or appear there. And democracy is not just a word that gathered under itself a collection of characteristics. Rather, only where these characteristics really come together and form some whole that has significance in its own right—or in other words where there is a real entity. There is a table. The collection of characteristics of this table really is a collection of characteristics of an object. Why? Because there is an object of which this is the collection of characteristics: the table. But a random collection of characteristics is not an object. Why not? Because there is no object whose characteristics these are. So what did I say by that? That in a concept, or in an entity, there is something else besides its collection of characteristics. The entity itself, of which these are the characteristics. They are its characteristics. Its—whose? The concept’s, or the entity’s, sorry. Okay? So the entity is not the collection of characteristics. Right? Leibniz argued what he called the identity of indiscernibles. What is the identity of indiscernibles? He says that if there are two entities with exactly the same set of properties, then it is one entity, not two. The identity of indiscernibles. Meaning, if they are indiscernible—if they have exactly the same properties—then identity; they are not two entities, they are one. Okay, that is his claim. Now he has a proof by contradiction. How does that proof work? It works like this. Let us assume there are entities A and B with the same set of properties and yet they are still two. Then A has the property of not being B, and B has the property of not being A. So they do not have the same set of properties. Therefore it is clear that if there are two entities with the same set of properties, it is one entity—they are not two. Where is his mistake? Not every property— No, but he shows you they’re not two. Because if they were two, then A would have the property that it is not B and B would have the property that it is not A. So they do not have the same set of properties. Either way, if they have the same set of properties, then it is the same object itself. If they are two, then they do not have the same set of properties. Right? A clean logical proof—and an incorrect one. Why incorrect? Because it begs the question. What do I mean? After all, what am I saying when I say that the object is the thing whose properties these are? It is not the collection of properties itself. The collection of properties characterizes the object, and not that the collection of properties is the object. The collection of properties characterizes the object. So what can I say about the object that is not a property? First of all, that it exists. That there is such a thing, right? Existence is not a property. And we’ll see in a moment that this will appear in Kant’s challenge to the ontological proof. But existence is not a property. To say of something that it exists is not to point to one of its properties. To say that it is red—yes; to say that it is wide, that it is wooden—all of those are descriptions. To say that it exists is not a description. To say that it exists is a claim about its very being, not about its properties. Okay? Now if that is so, then when I say that A is not B, that is not a property—to be not-B. It’s not that A differs from B in some respect, that it has a property different from B. It is red and he is yellow. No, I am not saying that it differs from B. I am saying it is not B. Meaning, B exists and A exists, and each has independent existence; both exist separately. But existence is not a property. Therefore to say that A is not B is not to say that A has a property B lacks, because being not-B is not a property. Fine. So if that is so, the proof falls. You can think that the object is nothing but the sum of its properties, but the proof you bring against me to prove that I am mistaken is not a proof. Because if I think there can be two objects with the same set of properties, what am I really assuming? Essentialism and not conventionalism. I assume that there is an object that is not the collection of properties, but the possessor of the properties. The properties are its properties, okay? And consequently, to say that it exists is not a property. Or that it is different from another—not different in properties, but not identical with another—that is not a property. And if I assume this, you cannot argue against me with Leibniz’s proof. He assumes his premises; according to my premises, there is no claim at all. What does that mean, basically? It means that when I try to characterize a certain object—and I claim the same applies to concepts as well, concepts too; there are concepts that exist in some sense in the Platonic world of ideas, and they have characteristics, various characteristics—defining a concept means identifying which characteristics are essential to that concept, which are the characteristics without which it is no longer itself. Okay? That is called defining a concept. But not that the definition constitutes the concept. The definition tries to characterize the concept correctly. And if we have a dispute, it is a real dispute; it is not that we are arguing over different concepts. The question is who is right—what really are the essential characteristics of this concept? It is a real dispute. Okay? Now if I say this, I need to understand: there is such a thing as a correct and an incorrect definition. It is not true that a definition is an arbitrary matter. There is a correct definition and an incorrect definition. Therefore, I could expand on this a lot, but for our purposes I’ll suffice with this. For our purposes, what I basically want to say is that you have to look for what the definition of God is, and that is not an arbitrary question. Why? Because