Conceptual Analysis – Lesson 10

Table of Contents

• Conceptual analysis: logical versus a priori, and earlier arguments
• Perfection and self-perfection: Rabbi Kook, penitents, and the value of the process
• The paradox of the concept of perfection and Rabbi Kook’s solution: “Give strength to God” and worship as a divine need
• The Book of Jonah and the a fortiori argument of the gourd: interest versus reason, and a theological reading
• The speaker’s addition: potential versus actualization through Zeno’s arrow paradox and velocity
• Completion: the perfection of the Holy One, blessed be He, without dependence on human actualization
• Ontological argument versus conceptual analysis with assumptions
• Thought experiment as a form of conceptual analysis
• Einstein, the constancy of the speed of light, and an analogy to conceptual analysis
• “No thought can grasp Him at all” and the validity of statements about the Holy One, blessed be He

Summary

General Overview

The speaker continues a series on conceptual analysis and shows how this kind of analysis can lead to surprising conclusions even outside Jewish law, while distinguishing between “destructive” logical analysis and “constructive” a priori analysis, and comparing them to arguments like the cogito and Anselm’s proof, the ontological argument. He presents the question of perfection and self-perfection in relation to the Holy One, blessed be He, through Rabbi Kook in Orot HaKodesh, connects it to penitents and to the principle that “worship is a divine need,” and develops his own addition through an analogy to the solution of Zeno’s arrow paradox by distinguishing between potential and actualization. Later, he defines a thought experiment as a form of conceptual analysis capable of exposing contradictions between assumptions, and demonstrates this through thought experiments about materialism, determinism, and Buridan’s donkey / Buridan’s man, clarifying that these moves are not an “ontological argument” because they rest on assumptions. In the end, he responds to a question about “no thought can grasp Him at all” and argues that the statement refers to sensory apprehension, not to the possibility of making statements and claims about the Holy One, blessed be He.

Conceptual analysis: logical versus a priori, and earlier arguments

The speaker recalls that in a previous lecture a distinction was made between analytic logical analysis, whose goal is to expose contradictions and is therefore mainly “destructive,” and a priori analysis, which can also build positive conclusions. He connects this to examples like the cogito and to Anselm’s proof for the existence of God, the ontological argument.

Perfection and self-perfection: Rabbi Kook, penitents, and the value of the process

The speaker presents Rabbi Kook’s claim in Orot HaKodesh, part two, that improvement itself is one of the perfections, and therefore a person’s perfection is determined not only by his condition but also by the direction in which he is moving. He understands the rabbinic saying, “In the place where penitents stand, even completely righteous people cannot stand,” as proof that the path and the change have intrinsic value, and not only instrumental value for reaching a spiritual goal. He rejects the effort thesis as an explanation for the superiority of a penitent and argues that the completely righteous person usually works harder, bringing examples from Rabbi Elazar ben Dordaya and from the Talmudic text in Ketubot about “Had they flogged Hananiah, Mishael, and Azariah, they would have bowed to the idol,” to emphasize that ongoing labor can be harder than a momentary act of transcendence. He concludes that the change thesis is the main point: self-perfection and positive change have value in themselves even if they do not reflect greater effort.

The paradox of the concept of perfection and Rabbi Kook’s solution: “Give strength to God” and worship as a divine need

The speaker formulates a difficulty: if self-perfection is a perfection, then it seems that the Holy One, blessed be He, lacks something, since He cannot improve. He presents the possibility of seeing this as an attack on the concept of perfection itself, similar to the paradox of “a stone that the Holy One, blessed be He, cannot lift,” as an embarrassment within the concept of “omnipotent,” and not necessarily as a direct attack on faith. He brings Rabbi Kook’s answer, according to which the Holy One, blessed be He, created deficient beings who can and are required to perfect themselves, and in this way the perfection of improvement appears through them, while quoting the verse “Give strength to God” and connecting it to “the secret that worship is a divine need.” He offers an understanding that compares this to a person’s ability to solve a problem by building a computer that performs a complicated calculation, and he raises the difficulty of dependence on free choice if human beings choose not to perfect themselves.

The Book of Jonah and the a fortiori argument of the gourd: interest versus reason, and a theological reading

The speaker analyzes the a fortiori argument at the end of the Book of Jonah between Jonah’s pity for the gourd and the Holy One’s pity for Nineveh, and asks how it is valid if Jonah seemingly pitied himself and not the gourd. He proposes a first answer according to which the existence of an interest does not prove that the action stems only from self-interest, and he reinforces this from the Aglei Tal in the introduction, where he distinguishes between the pleasure that accompanies study and study done for the sake of pleasure. He proposes a second answer according to which the Holy One, blessed be He, also “needs” Nineveh in the same way Jonah “needs” the gourd, and connects this to “there is no king without a people” and to the idea that worship is a divine need. He presents Rabbi Kook’s solution as “brilliant,” in that the Holy One, blessed be He, “needs” specifically what He cannot do because of His perfection—namely, to perfect Himself—and therefore human worship and self-perfection are the realization of that need.

The speaker’s addition: potential versus actualization through Zeno’s arrow paradox and velocity

The speaker returns to the solution he proposed for Zeno’s arrow paradox through the distinction between velocity and change of place, and argues that velocity is the potential for change of place and not the change of place itself. He emphasizes that change of place cannot occur at a point in time, because at a point in time a body cannot be in two places, and he presents this as a logical contradiction rather than a physical problem of “infinite speed.” He adds the example of a body striking a wall: at the moment of impact it still has “velocity” as potential, but the wall prevents the actualization as change of place, and the potential is expressed instead as heat or as an elastic rebound.

Completion: the perfection of the Holy One, blessed be He, without dependence on human actualization

The speaker applies the potential/actualization distinction to the question of self-perfection: the Holy One, blessed be He, has the potential to perfect Himself, but the “wall” of perfection prevents Him from actualizing this as improvement in practice, and therefore the potential is actualized through the creation of deficient beings who can perfect themselves. He argues that even if human beings do not improve, the Holy One, blessed be He, is still perfect, because the perfection lies in the very existence of the potential within Him, and not necessarily in its actualization in the world. He presents this whole move as the result of conceptual analysis that does not need empirical facts in order to produce conclusions.

Ontological argument versus conceptual analysis with assumptions

The speaker sharpens the point that the move regarding perfection and self-perfection is not an ontological argument, because it rests on assumptions such as the assumption that the Holy One, blessed be He, is perfect and the assumption that there is an idea of worship as a divine need. He compares this to geometry, where there are axioms and from them one derives logical conclusions, and argues that the power of conceptual analysis lies in the ability to extract surprising information from accepted assumptions.

Thought experiment as a form of conceptual analysis

The speaker defines a thought experiment as a theoretical scenario constructed in the imagination in order to test what ought to happen according to certain assumptions, and argues that its value lies in the fact that it can surprise us or expose a contradiction between assumptions. He gives an example from his book on the sciences of freedom about taking a person apart and reassembling him as a challenge to materialism, and argues that a materialist ought to agree to it, but many would not agree, and therefore they are not really materialists. He presents Buridan’s donkey to show that rationality does not require a “sufficient reason” for every choice, and develops “Buridan’s man” in order to argue that materialist determinism leads to the conclusion that a person in a symmetrical situation would die of hunger because of the problem of symmetry breaking. He distinguishes between a scientific experiment in a laboratory, which is decided by observational facts, and a thought experiment, which reveals internal contradictions between views and assumptions, and therefore requires giving up one of them.

Einstein, the constancy of the speed of light, and an analogy to conceptual analysis

The speaker notes that special relativity grew out of a thought experiment based on the assumption that the speed of light is constant and does not depend on the frame of reference. He emphasizes that here too there is an empirical assumption in the background, so this is not an ontological argument, but the conclusions are derived through conceptual analysis without additional observations.

“No thought can grasp Him at all” and the validity of statements about the Holy One, blessed be He

The speaker is asked how talking about perfection and self-perfection fits with “no thought can grasp Him at all,” and he answers that the statement refers to the absence of direct sensory apprehension of the Holy One, blessed be He, and not to any prohibition against thinking about Him or making claims about Him. He argues that statements like the Holy One, blessed be He, exists, created the world, brought us out of Egypt, and gave the Torah are claims accepted by believers and do not contradict “no thought can grasp Him at all.” He mentions Maimonides’ approach regarding negative attributes as depending on types of attributes, and concludes that the statement does not negate theological discourse, only direct apprehension.

Okay. We’re in the series on conceptual analysis, and now I want to go back again to a few topics—this time not halakhic topics—where it’s also possible to talk about… We spoke about this too, say, regarding a penitent; that was also an example that wasn’t halakhic. I want to bring a few more examples where conceptual analysis can lead us to different conclusions. Let me just remind you that last time—which was already quite a while ago—we spoke about… we spoke about the difference between logical-analytic analysis and a priori analysis, and the claim was that logical analysis is basically mainly destructive rather than constructive. Meaning, it shows that there’s a contradiction in an argument, and therefore there’s no reason to accept it. But a priori analysis can also build. We spoke a bit about the cogito, we spoke about Anselm’s argument, the proof for the existence of God, the ontological argument, and so on. Let’s talk about another topic that I’ve also already spoken about in the past, and that’s the topic of perfection and self-perfection. On this topic—I don’t remember at the moment—I think in one of the previous sessions, yes, one of the previous times, I spoke about Zeno’s arrow paradox, and I tried to show there the analysis of being located versus being in a place versus standing still in a place, and how that kind of conceptual analysis solves Zeno’s paradox. I want to take a similar topic. I actually wrote about it in that same article where I dealt with Zeno’s paradox, but in a different context. Rabbi Kook discusses the question of how… that is, if our assumption is that the Holy One, blessed be He, is a perfect being, meaning utterly perfect, then of course He cannot improve, because there’s nowhere for Him to improve to; He’s already at the maximum. Now Rabbi Kook argues—and this is in Orot HaKodesh, part two—that improvement itself is one of the perfections. Meaning, a person’s perfection is determined not only by the spiritual state he is in—the spiritual, moral, and so forth state that he is in—but also by the direction of his movement. Meaning, if he is in a state of improvement, that itself has value. In other words, the process of improvement is not merely instrumental; it’s not only a means for reaching a better or higher spiritual state, but progress itself has value in its own right, and not only as a device for reaching a better state. We can bring examples of this. I think maybe the clearest example is what the Sages say: “In the place where penitents stand, even the wholly righteous cannot stand.” And people infer from this that a penitent is preferable to a wholly righteous person. In one of the passages it appears as a dispute, but that’s usually what people derive—that a penitent is preferable to a wholly righteous person. Now how can we understand that statement, that a penitent is preferable to a righteous person? After all, suppose the penitent really did complete and perfect repentance, erased all his sins, and returned to a fully whole state. Then he became a wholly righteous person. How is a penitent preferable to a wholly righteous person? In what sense is he more… at a higher level than the wholly righteous person? Actually, you can suggest all sorts of answers. The initial intuitions say he put in more effort, but that’s not necessarily true. To get a reward for effort—first of all, even if that’s true, that means he deserves more reward, it doesn’t mean he is on a higher level. Right? Someone who gets to the same place as someone else, only he walked and the other one drove, “reward for steps,” as it’s called—so he deserves more reward because he exerted himself more, but at the end of the day they’re both in synagogue praying together. But he managed to make a change. What? He managed to make a change. So what? So you see… Because he made a move that the righteous person never had to make at all. Right, and therefore what? And still, in the end, that move brought him to become a wholly righteous person, so now he’s a wholly righteous person. Yes, but what extra value does that give him? On his résumé he has the fact that he made the journey. And what about the résumé? What about his spiritual level? In my opinion it should be higher than that of the wholly righteous person. Why? So I’m saying, if you’re talking about the reward he deserves, then of course he invested more effort; I can understand why he deserves more reward, like the one who walks to synagogue instead of driving—he has reward for steps. But the question is whether his spiritual level is really higher. If the whole goal of that walking was simply to get to synagogue, they both got to synagogue, they both prayed with devotion in a minyan together. So why is the penitent preferable to the wholly righteous person? Perforce, the progress itself is not only a means of reaching the goal—that is, the spiritual state that is the goal, the improved spiritual state—but rather progress has value in its own right, not only as a means of reaching the goal. I think that’s also what you meant, Shlomo, earlier. In other words, this thesis that says he is on a higher level stems precisely from that: when I measure a person’s spiritual state, I don’t measure only where he is. The path has significance. In physics they call this non-conservative forces. Meaning, you can’t define a potential function. It depends on the path by which you reached the same place; it’s not a function only of the place. So here too, basically the claim is that your state is not determined by looking only at the present—where you are right now—but we also look at the history, how you got to where you are now. I started to say in passing that some people would attribute this to effort, yes, as I said earlier. But then I said that effort, first of all, is more a consideration for reward than a consideration for spiritual state. You deserve more reward—that’s true. The question is whether you really are more righteous. Who says? But I’m saying I have a stronger argument against the effort thesis. I don’t think it’s true that a penitent necessarily needs more effort than a wholly righteous person. Not at all. On the contrary. Take Rabbi Elazar ben Dordaya, for instance—the Talmud in Avodah Zarah. Rabbi Elazar ben Dordaya, “who did not leave a single sin in the world that he had not committed,” and then in the end he understood what was happening, sat and cried and cried until his soul departed, and a heavenly voice came out and said: Rabbi Elazar ben Dordaya is destined for the life of the world to come. And when Rabbi heard this, he cried and said: “There are those who acquire their world in one moment.” What does that mean? The guy enjoyed life his whole history, paid for it with one hard hour at the end. Rabbi Elazar ben Dordaya is destined for the life of the world to come, everything is fine. And I—Rabbi says to himself—I’ve been working my whole life. I didn’t fail. But the fact that you didn’t fail is not an achievement that comes free. People think that, like athletes or whatever, all kinds of people with special achievements—special intellectual achievements or athletic achievements or artistic achievements or whatever—people think that someone with special achievements is probably a genius. Maybe he’s also a genius, but many times it comes with hard work. And the wholly righteous person is also not someone for whom it just rolls off the sleeve. He works hard. Only unlike Rabbi Elazar ben Dordaya, who worked only one hour at the end of his life after enjoying himself the whole time, the wholly righteous person works on it every single moment, his whole life. And he works so hard that he managed not to fail. Therefore I do not accept this thesis that the penitent works harder than the wholly righteous person. On the contrary, I think the wholly righteous person generally—there are no rules, but generally—it seems to me works harder. It’s like the Talmud in… I just remembered, the Talmud in Ketubot, I think 33. The Talmud says there: “Had Hananiah, Mishael, and Azariah been beaten, they would have worshipped the idol.” Meaning, Hananiah, Mishael, and Azariah were willing to be thrown into the fiery furnace in order not to worship idolatry. So the Talmud says, yes—to be thrown into a fiery furnace, that’s easy. But if they had been beaten constantly, without stopping, until they worshipped idolatry, they would have broken. And the Talmud wants to infer from there that lashes are a harsher punishment than death. Later it rejects that, never mind, there are interesting things there in the Talmud. But for our purposes—what does that mean? Lashes are obviously something that, in itself, is less threatening than death. But something that goes on and on and on, all the time, all the time, all the time, and you won’t get out of it until you worship idolatry—that no one can withstand. Meaning, there is a hard Sisyphean labor that goes on every moment throughout life, and it is much harder than some one-time exalted moment in which you make a great upheaval in life—which I’m not belittling at all. But to assume that the penitent is necessarily someone who worked harder than the wholly righteous person seems to me a baseless assumption. Therefore the thesis, it seems to me, is not the effort thesis but the change thesis. Now this is an interesting point, because it sharpens the point. When I say that change has value in itself, and not only arrival at the place but the change itself—I do not mean by this to hide the effort thesis behind it. Well, if you made a change, you probably exerted yourself, so really behind all this sits the effort thesis. No, no. I said earlier: I claim that the wholly righteous person exerts greater effort than the penitent, and still the penitent is greater. Why? Because the penitent made a change. And improvement—change in the positive direction, of course, meaning improvement, change in a positive direction—is something that has value in itself, not only as a means of being in a more improved state. Improvement is not just a means of reaching the improved state; it also has value in itself. Now, that’s Rabbi Kook’s claim. And then there is apparently a contradiction, a problem regarding the Holy One, blessed be He—or else He lacks improvement. That’s where I’m coming now, that’s where I’m coming now. That is basically Rabbi Kook’s question. Rabbi Kook asks: if improvement really has value in itself, then it means that one of the perfections cannot be found in the Holy One, blessed be He—the perfection of being one who improves. No, Rabbi, it’s not the same thing. The perfection of the Holy One, blessed be He, is a perfection that doesn’t need improvement; it doesn’t even begin with the issue of improvement. A righteous person, even when he is complete, still has to keep preserving himself all the time. With the Holy One, blessed be He, it doesn’t even begin. I didn’t understand. What do you mean, it doesn’t begin? Since He is perfect, He has nowhere to improve to. Perfection applies to someone who can have a deficiency, as the Rabbi says, yes? But someone who is complete… No—then you can’t really say the Holy One, blessed be He, is perfect at all, not just regarding improvement. But that’s not correct. The accepted assumption—again, what do you mean not correct—the accepted assumption is yes, the Holy One, blessed be He, is perfect. Anselm even defines Him that way: the being that has all perfections. Right. Now it’s not true that He has all perfections. This perfection of being one who improves—He doesn’t have it. Heaven forbid, Rabbi Kook says, if so then the Holy One, blessed be He, is not perfect. It’s not true that He is perfect. What he is basically arguing is that the concept of perfection contains an internal contradiction. This has nothing to do with the Holy One, blessed be He. It’s like the question: can the Holy One, blessed be He, create a stone that He cannot lift? That question is not about the Holy One, blessed be He; it’s about the concept of omnipotence. It doesn’t matter whether it’s the Holy One, blessed be He or not. Once you claim that X is omnipotent, you are immediately exposed to the question whether X can do Y such that He cannot do Z to it. Whatever you fill in for X, Y, and Z will create a paradox. Therefore this attack is an attack on the concept of omnipotence, not on faith in the Holy One, blessed be He. The claim is that the concept of omnipotence is undefined; it contains an internal contradiction. Same thing here. The claim here is not a claim about the Holy One, blessed be He, in principle; it is a claim about the concept of perfection. Meaning, the concept of perfection is not well-defined. It contains an internal contradiction. There is no such thing as “perfect,” because if something is perfect, that itself cuts off the branch on which its perfection rests. It cannot be perfect. Now of course the assumption that the Holy One, blessed be He, is perfect is attacked by this claim. It’s a claim that attacks the concept of perfection, but when we apply it to the Holy One, blessed be He, it becomes an attack on the belief in the perfection of the Holy One, blessed be He. So Rabbi Kook argues there in Orot HaKodesh that basically this is why the Holy One, blessed be He, created us. We are deficient creatures who can—and are also required to—perfect ourselves, meaning improve, become better, and this is essentially the completion of the Holy One’s inability to perfect Himself. He perfects Himself through us. He created deficient creatures, required them to perfect themselves, and in that way this perfection of improvement—we kind of discharge His obligation, so to speak; formulate it however you like—but basically we do it for Him. That’s Rabbi Kook’s claim there. So then He depends on us, so again He’s not complete. Right. What do you mean, depends on us? It’s not that if we didn’t perfect ourselves then He isn’t… So if there is no process of self-perfection, then He is lacking? But He created… but He can create us or not create us; He can require it of us or not require it of us. Suppose I build a computer that can perform some very, very complicated calculation. Does that mean I can do that calculation? That’s an ability of mine. How do I do the calculation? I build a computer that does the calculation and tell it to do the calculation. And once I can solve my problem, that means I don’t have a problem—I can solve it. I’m perfect in that sense. It doesn’t matter that in order to solve it I create some device or something or someone to do the work for me. As long as I can create it and require it to do the work for me, then that’s perfectly fine. Yes, but then we’re back to the previous course on free choice. If I have free choice not to do it, then the Holy One, blessed be He, is lacking, because I can say: I’m not doing it. If we all decide not to perfect ourselves, then indeed, apparently, He will remain lacking. Fine. Now in a moment I’ll add something that Rabbi Kook doesn’t write, but it seems to me it’s an important point that also solves this issue. In this way, this is what Rabbi Kook wants to argue. He wants to argue that basically the Holy One, blessed be He, created us as deficient creatures, required us to perfect ourselves, and our self-perfection is really the completion of that perfection which is lacking in Him—the aspect of improvement that cannot appear in Him, so it appears through us. That is basically Rabbi Kook’s claim, and he himself mentions there the verse: “Give strength to God.” Right—“Give strength to God.” The meaning is basically: give strength to the Holy One, blessed be He; you are the ones who give strength to the Holy One, blessed be He. This already appears in the Ari, of blessed memory, what is called in the language of the medieval authorities (Rishonim), “the secret that service is for a higher need.” It seems to me Rabbi Kook mentions that there too. “Service is for a higher need” means that we are basically doing work for Him. He needs us; there are things He cannot do, and because of that He created us so that we would do them. The medieval authorities (Rishonim) call this “the secret that service is for a higher need,” because it really is a statement that sounds difficult to the ordinary religious ear—that the Holy One, blessed be He, supposedly needs us. How can that be? Isn’t He omnipotent? So what does it mean that service is for a higher need? Meaning, in the final analysis our service is for Him; He needs us. So then He is actually not omnipotent. In this context, I think I once spoke about this, I don’t remember in what context. I remember I once wrote about it on the website. This a fortiori argument at the end of the book of Jonah. The verses there tell about the kikayon plant that the Holy One, blessed be He, grew there for Jonah so there would be shade for him in the wilderness where it was very, very hot. Then at night He sent some worm with an east wind, and the plant dried up and died. Then Jonah becomes very distressed, and the Holy One, blessed be He, says to him: “Is it good for you to be so angry about the plant?” He says: “I am angry enough to die”—“I am very angry, even unto death.” Then the Holy One, blessed be He, says to him: “You had pity on the plant, for which you did not labor and which you did not grow; and shall I not have pity on Nineveh, the great city, in which there are many people and much cattle,” and so on. And that’s more or less how the book ends. So this a fortiori argument that says: you pity the plant, so you should understand that I pity Nineveh—the plant is just a plant, you didn’t labor over it or anything, it was there one night and dried up, and that’s all. Here there is a great city with thousands of people and animals and everything, and you want them destroyed just like that? You should understand that if you pity the plant, then I certainly pity them. The background of this, basically, is probably that the whole axis around which the book of Jonah revolves is some argument between Jonah and the Holy One, blessed be He, about how one should relate to sinful people. The Holy One, blessed be He, sends Jonah to Nineveh so that he will bring them to repentance, that he will prophesy to them so they will repent. Jonah flees to Tarshish; he doesn’t want to perform that mission. And apparently the reason is that he is unwilling for the Holy One, blessed be He, to forgive sinners. If they sin, let them get what they deserve—strict justice. Or truth, if you like. Right—“They asked Wisdom, what is the punishment of a sinner?” This midrash—there are many such midrashim. And that is basically Jonah’s claim. Jonah’s claim is that sinners should not be forgiven; they should be destroyed. And then he flees from the Holy One, blessed be He, all the twists and turns happen until they get to the plant. And that’s really the crescendo of the book, because at the end of the book the punch line, the great lesson that emerges in the end, is: “You had pity on the plant, and shall I not have pity on Nineveh?” That is the decisive argument by which the Holy One, blessed be He, proves to Jonah that Jonah is mistaken in his attitude toward Nineveh. You even pitied a plant, and you argue with Me that I should not pity Nineveh? Now the question is how to understand this a fortiori argument. On its face it seems like a foolish a fortiori argument. What kind of a fortiori argument is it from Jonah pitying the plant to the Holy One, blessed be He, needing to pity Nineveh? The claim is that basically Jonah didn’t pity the plant at all; he pitied himself. Right, like the old comedy line: if a fisherman loves fish, then why does he catch them? A fisherman doesn’t love fish, he loves himself. So when Jonah supposedly pitied the plant, he didn’t pity the plant; the plant gave him shade. After the plant dried up, the sun beat down on his head, and then he asked for his soul to die. He didn’t ask to die out of sorrow over the plant; he asked to die because he was hot—he lacked the shade of the plant. So he didn’t pity the plant at all. So what kind of argument is this by the Holy One, blessed be He: “You pitied the plant, and shall I not pity Nineveh?” He didn’t pity the plant. So I once said to the guys in Yeruham—we would always go the day after Yom Kippur to pray at sunrise on Mount Avnon, above the Great Crater. So after the prayer we would talk a bit, and I told them I had two answers to this difficulty. Right, this is after Yom Kippur, so we had read the book of Jonah the day before. So I told them I had two answers to this difficulty. The first answer is an answer that may be nice for those days, though not for our topic; the second is important for our topic. The first answer says: who says Jonah didn’t pity the plant? I assumed Jonah didn’t pity the plant, that really he pitied himself. Who says? True, Jonah had an interest in there being a plant. Meaning, he suffers from the fact that the plant dried up. But that doesn’t mean he didn’t also pity it at the same time. The fact that someone has an interest in something does not necessarily mean that he acts only because of that interest. And that’s why I said this is a lesson that is important for these days too. In political interpretations or others, once we find that someone has a certain interest in an action—meaning he gains something from it—then we say that apparently when he does the action, he does it for the sake of the interest. And then all the commentators explain to us: he’s doing it to gain this, and he’s doing it… But there’s another option. It could be that he’s doing it because he thinks that’s the right thing to do. And not because he has no interest—he does have an interest. But who says that the interest is the reason he’s acting? Maybe he’s righteous? Maybe he’s doing it because he genuinely thinks so? It just so happens that he also has an interest—so what? It doesn’t necessarily follow that if you have an interest, then you also act because of it. Right? There is no logical leap here. So there is room for suspicion, you can examine it, you can suspect—but you can’t infer that conclusion unequivocally. Yes, many times, pay a little attention when we hear the news, commentary, or read criticism and things like that—many times people feel that it’s enough to point out that someone has an interest in the matter in order to finish the argument. “I rest my case.” I showed that you have an interest. The fact that you showed I have an interest still doesn’t mean that I’m acting in a non-substantive way. Check. It could be that this action really also stems from my views, my agenda, that I truly think this is the right way to act. The fact that I also profit from it—great—but it doesn’t mean I’m acting only because of the interest. Yes, I once mentioned, I think, the Eglei Tal. In the introduction, the Eglei Tal says there are those who mistakenly think that if someone studies and enjoys the learning, then it is learning not for its own sake. He says that’s a big mistake. Clearly, enjoyment of learning is part of the commandment. Not only does it not detract; it is part of the commandment. If you enjoy it, then you connect more to the material, understand it better, internalize it better. Obviously enjoyment only improves the quality of the learning. So enjoyment certainly does not detract from the commandment of Torah study. After all, in the morning, in the Torah blessings, we bless: “Please make the words of Your Torah sweet in our mouths.” We ask that it be sweet to us. So how can you say that if it is sweet to us, then it is poor learning or learning not for its own sake? We wouldn’t ask for such a thing in the morning. But… the Eglei Tal adds there—and this part is less well known—immediately afterward he says: “But I do admit” that if a person studies for the sake of the enjoyment, then that is learning not for its own sake. He says the fact that you enjoy it doesn’t disqualify the learning at all; on the contrary, enjoy it—it will only make the learning better. But if the enjoyment you have is the reason you are studying, if you study in order to produce the enjoyment, that really is learning not for its own sake. That is exactly what I said here: the fact that you have enjoyment does not necessarily mean that when you study, you are studying for the enjoyment. Two different things. The fact that you have an interest, the fact that you gain something, doesn’t mean your action was done for the sake of the interest. That’s a logical leap; there is no necessity to say such a thing. Right, so that’s one direction. And then what does Jonah’s a fortiori argument mean? It basically means that it’s true Jonah had an interest—sorry, true, Jonah had an interest—but that doesn’t mean he didn’t pity the plant. He did pity the plant. The Holy One, blessed be He, who examines the innermost heart, knows that in Jonah’s heart he genuinely also pitied the plant. He did not infer this as an external conclusion; He examines the heart, He knows what is in a person’s heart, and the Holy One, blessed be He, saw that Jonah really did pity the plant, and that is why He made this a fortiori argument to him. Maybe, maybe, maybe in Jonah’s case he didn’t pity the plant? If for the sake of not having to go to Nineveh you were willing for all of Nineveh to be destroyed, right—so if you didn’t pity all of Nineveh, then why are you suddenly pitying the plant? I didn’t understand—so what does the biblical a fortiori argument mean? Right, so you see that he didn’t pity the plant; he only pitied himself, like the Rabbi said at the beginning. Actually the Holy One, blessed be He, is not rebuking him for being immoral. The Holy One, blessed be He, tells him: you are mistaken in thinking that one should not pity Nineveh, and here is the proof—that you yourself pitied the plant. Is the Holy One’s claim against Jonah meant to teach him that he is a bad person? No, it’s meant to teach him that he is mistaken in his view of how sinners should be treated. But that’s not what the verse says. The verse says: you’re inconsistent; you’re mistaken. You say one should not pity sinners, yet you pitied the plant—so I should not pity an entire city? So one possibility is indeed to say that Jonah did pity the plant. The fact that he had an interest doesn’t mean he didn’t pity the plant; the Holy One, blessed be He, saw that he did pity the plant. That’s one possibility. The second possibility is of course the opposite, and this is what concerns us. The second possibility is that the Holy One, blessed be He, also doesn’t pity Nineveh; He needs it. Exactly as Jonah didn’t pity the plant but needed it, so too the Holy One, blessed be He, doesn’t pity Nineveh; He needs it. And He says to Jonah: you need the plant to give you shade. I have an entire city that I created here, with people and animals. You understand yourself that I need them; otherwise why did I make all this whole fuss? So just as you want the things you need to remain here, and you cry when they go away because of the interest, not because you pity—because of the interest—so too I want Nineveh to remain here not because I pity them, but because I need them. They work for Me. “There is no king without a people,” as they say. Yes, exactly—and that’s “service for a higher need,” “give strength to God.” The idea is that when we serve, it’s because the Holy One, blessed be He, needs us; there are things He cannot do, or rather there are things He cannot achieve except through us; without us it won’t happen. Now Rabbi Kook proposes an explanation for this that is brilliant. Because he basically says—he explains what everyone says: service is for a higher need, the Holy One, blessed be He, needs our commandments, needs this, needs that. Of course—why is it called the “secret” that service is for a higher need? Because it’s outrageous. It’s outrageous because what do you mean? Isn’t He omnipotent? He can do whatever He wants and achieve whatever He wants by Himself. So in what sense does He need us? Therefore people basically reject this, or keep it secret, or treat it as a statement that sounds theologically problematic. Rabbi Kook finds a brilliant solution to this. He basically says no—there is one specific thing that precisely because of the perfection of the Holy One, blessed be He, He needs us in order to do it, and that is to perfect Himself. To improve. That He cannot do by Himself because He is perfect. Not that this makes Him imperfect, but because He is perfect, He cannot perfect Himself. His way of perfecting Himself is to create us, and we will perfect ourselves, and that is “service for a higher need”; this is what we do for Him. Therefore the Holy One, blessed be He, needed Nineveh. By the way, as an aside, that may perhaps be the deeper reason why a penitent is preferable to a wholly righteous person. A penitent is preferable to a wholly righteous person—I said why—because change has value in itself; it’s not only a means of reaching the improved state, but has value in itself. Now we can understand why. Because the whole reason we were created here in the world was to be deficient and to perfect ourselves. That is the entire reason why the Holy One, blessed be He, created us. Therefore the Holy One, blessed be He, prefers the penitent to the wholly righteous person, because the penitent is doing exactly the work for which the Holy One, blessed be He, created him. And in that sense there is something very deep here. Meaning, theoretically, if I had to answer the question: look, would you rather sin and then repent, or would you rather be wholly righteous? I ought to answer: I’d rather sin. I would ideologically prefer to sin—not to surrender to the evil inclination. Because my role here is not to be wholly righteous. My role here is “A righteous person falls seven times and rises.” My role here is to make the improvement, because overall that is the work for which I came into the world. Therefore the concept of repentance is presented here in a very, very fundamental sense. The concept of repentance is the essence of our existence in the world. Repentance means to improve, right? To return from sin and become better. Everything we exist here for is not in order to perform commandments. We exist here in order to improve through performing commandments. Because the result of the commandment the Holy One, blessed be He, could have done by Himself. He does not need us for that. He needs us because He cannot improve through the performance of commandments. Therefore the concept of repentance is actually a concept perhaps even more fundamental than the commandments. The commandments are meant to provide a target—when you repent, something to aspire to. One should aspire to fulfill commandments, be righteous, and so on. Not that you repent in order to be righteous; rather, the concept of the righteous person was created in order to give meaning to the process of repentance. The whole thing works in reverse. And I think that is a brilliant idea of Rabbi Kook. Fine, there are additions here that I added—he only talks about the perfection of the Holy One, blessed be He—but I think this is really the essence, this is what stands behind the matter. Now let me just complete what I said earlier I would get to, to a certain point that I think Shlomo raised: what happens if we do not repent? Then the Holy One, blessed be He, basically remains lacking. Now here—I won’t go through it all again, but I’ll remind you of what we said about Zeno’s arrow paradox. I said there that a concept like velocity must be distinguished from change of place. Velocity does not mean change of place. Velocity is the potential to change place. If a body has velocity, we will see that actualized in the form of change of place: the body changes location, time passes, and it is in another place. That is an indication that it has velocity. But the concept of velocity itself is the potential that produces change of place; it is not the change of place itself. One of the indications of this is the arrow paradox; that’s how I proposed solving Zeno’s paradox. What I basically claimed there was that a body can have velocity at a point in time. A single mathematical point of time—a body can have velocity at a point in time. Obviously change of place cannot occur at a point in time. A body cannot change its place during a single point in time. To change place you need some little segment, if you like, but some interval of time with a certain positive duration. At a discrete point in time, a body cannot change place. By the way, just as a note for people with mathematical leanings—if you ask physicists, they’ll tell you: why can’t a body change place at a point in time? Because then it would be moving at infinite speed. Suppose it moved a meter in zero time, so what is the speed? The distance is a meter divided by the time, which is zero. One divided by zero is infinity. Infinite speed. That’s a mistake. Not true. Because that would mean that it’s physically impossible. I claim it is logically impossible, not physically impossible. Since a point in time is not a duration of zero length. A point in time has no duration. And in fact I wrote a column not long ago where I wondered whether a blind person—does he see a black image? Or does he not see at all? You understand that’s not the same thing. To see black—when you imagine what it means to see nothing, you are really imagining an image that is entirely black. But a truly blind person, someone who never saw—it seems to me, or at least that’s how I think, I don’t know how one measures this, how one checks it—he doesn’t see a black image; he simply doesn’t see. He doesn’t even have a black image; he has no image. It’s not the same thing. The same, I want to claim, is the difference between a point and a very short line. Differential, yes—whose length tends to zero. But that is exactly the concept of a derivative. Yes, a line whose length is zero is still a line—the dimension of that thing is one, right? It’s a line. But the length is zero or tends to zero. A point is not something of zero length; it has no length. That is not the same thing, because a point has dimension zero, not one. Something that has length must be one-dimensional. But the point differs from the short line not only in length, but in dimension. It is a different kind of entity. It has no length; it’s not that it has zero length—it has no length. There are mathematical theories that try to define length for a point too, zero length for a point too, but in the simple conception a point has no length, not that its length is zero. What does that mean? That when you say a body changes place over a point in time—not a very short interval of time but a single point of time—you are basically saying that at that same point in time it is in two places. That is simply a logical contradiction. It’s not because the speed is too great, infinite speed. It is a logical contradiction. If it is here, then it is not there, and vice versa. At the same point in time you cannot be in two places; you are only one being, not two beings. It’s a logical problem, not a physical one. Okay? So the claim basically is that velocity can be defined over a point in time. And when we… someone mentioned derivative earlier… when we differentiate the position function with respect to time—again, a parenthetical note for those who know a bit—when we differentiate the position function with respect to time, we get a velocity function. And the velocity function is defined for every point in time. Give me a point in time and I will tell you the velocity at that point. Meaning there is velocity at a point in time. In contrast, change of place, as I said earlier, cannot occur over a point in time. Which means velocity does not mean change of place. Velocity is a potential that a body has, such that if it has this potential, then if you wait a bit you will see that it changes place. Okay? But change of place obviously requires an interval, yes, it requires some stretch of time. Over a point in time you cannot change location. So basically what this says—let me maybe go one step further, I think I mentioned these things also when we spoke about the arrow paradox, but I need it here for our discussion so I’m repeating a bit. Suppose a body is moving at some speed and hits a wall. Okay? It either bounces back if it’s elastic, or if it’s plastic it sticks to the wall and produces heat or something like that. What is its velocity at the final instant when it is stuck to the wall? Zero. Right? What is its velocity an epsilon before? I don’t know, 100 kilometers per hour. Fine? I fired a bullet there. Now at the moment it hits the wall—and again I’m speaking like an ignoramus here, mathematicians and physicists will scold me, but I think this is still correct language—when you fire the bullet into the wall, at the moment it hits the wall I claim its velocity is still 100 kilometers per hour. Only now it cannot change place, because the wall does not allow this potential called velocity to be actualized in the form of change of place. Because it has nowhere to go forward; the wall stops it, so it cannot change place. What happens in such a situation? The potential for change of place is actualized in another way, in the form of heat. Or in the form of velocity in the opposite direction if it’s elastic. But there is no change of place of the sort we would have expected based on the velocity. That is my claim. What does that mean? It means there are situations where a body can have velocity but it will not be actualized in the form of change of place. There are external constraints that do not allow the body to actualize this potential. That does not mean it lacks the potential. It has the potential, it has velocity, only this potential is not realized—it is not brought from potential to actuality in the form of change of place—because the wall stops it. What I want to claim—and now I return to the Holy One, blessed be He, and perfection and self-perfection—I basically want to make the following claim: why do we assume that all perfections should exist in the Holy One, blessed be He? Because the Holy One, blessed be He, is basically the root of everything that exists and everything that happens in the world. No—there cannot exist in the world something whose root does not begin in the Holy One, blessed be He. That is the assumption behind this whole issue. Now if I make that assumption and ask myself: self-perfection is something the Holy One, blessed be He, cannot do, because He is already perfect; He has nowhere to perfect Himself. You understand that this is basically a kind of wall. Meaning, basically the Holy One, blessed be He, has the potential to perfect Himself—which parallels the concept of velocity that I defined earlier—but this potential cannot be brought from potential to actuality by way of improvement, because He has nowhere to improve to. There is a wall stopping Him, not allowing that velocity to be realized in actuality. So what does He do? The Holy One, blessed be He, creates other creatures—us—who are deficient and who can perfect themselves. Where do they draw their ability to perfect themselves from? From the potential that exists in Him. The Holy One, blessed be He, has velocity; only change of place cannot occur in Him. Change of place here is of course metaphorical—I mean change of spiritual level, if you like. He has the potential to improve spiritually, but He has nowhere to actualize it because He is already perfect. There is a wall stopping Him. So what does He do? It comes out in the form of heat. What do I mean? He creates human beings so that His potential for improvement will be brought from potential to actuality through them. Now you understand why the fact that we improve really does constitute some kind of completion for the Holy One, blessed be He. I’ll tell you more than that. Are we sort of part of Him? What? Are we sort of part of Him, of the Holy One, blessed be He? In this sense, yes. We actualize some potential that exists in Him and that in Him cannot be actualized. Now I’ll say more than that. Suppose we chose not to improve, we did not repent, we did not choose the good, we are not improving. The Holy One, blessed be He, is still perfect. Why? Because the potential for improvement exists in Him too. It’s just that we do not bring it from potential to actuality, but His perfection is basically the fact that He has the potential for self-improvement—and that He does have. The fact that we do not do our job is a great shame, but the potential exists in Him even when we do not actualize it. Therefore in that sense the Holy One, blessed be He, does not really depend on what we decide to do, whether we decide to improve or not. Now this whole rather grim affair basically shows us a result of conceptual analysis alone. Notice: Rabbi Kook did not assume any empirical fact, any Torah source; he simply carried out a conceptual analysis. And he asks himself: what is a perfect being? Is it possible for a perfect being to have a deficiency? Apparently that’s practically an oxymoron. Rabbi Kook says: certainly it is possible—not only possible, it must even be so. Because a perfect being has the deficiency that it does not perfect itself. That is the only deficiency a perfect being can have. Let’s continue. If that is so, then the only thing—in terms of “service for a higher need”—the only thing one can say our role is to do for the Holy One, blessed be He, what He Himself cannot do and expects us to do for Him, is only that thing which He Himself cannot do, namely to perfect Himself. Add to this the conceptual analysis of the concept of velocity and what we did in that lesson, and you essentially get the picture I described here. And you see that this whole picture ultimately emerges from conceptual analysis. You need no source for it, no innovations for it, nothing. Simple conceptual analysis yields it in a necessary and self-evident way. I think this is a beautiful example of an issue that really grows entirely from conceptual analysis. I just want to sharpen one more point. When I spoke about the cogito argument or the ontological proof, yes—the proof for the existence of God, Anselm’s proof—there I spoke about what is called an ontological proof. What does that mean? It means a proof that starts from a definition, and from within the definition it derives a factual claim about the world. From a definition. I simply define something. Here—and this is important—here we are not dealing with an ontological argument. What I just described regarding perfection and self-perfection is not an ontological argument. Notice: there are assumptions here. It’s not an ontological argument; I explained that the ontological argument is an argument without assumptions. It comes out of definitions; there are no assumptions. I assume nothing. That is the pretension. Again, after we analyzed it I tried to show that there are assumptions there too. But the pretension of Descartes and Anselm was to present an argument not based on assumptions but only on definitions. That is what Kant called an ontological argument. Now I want to explain: here we are not dealing with an ontological argument, this analysis of perfection and self-perfection that I did here. Why not? Because first of all I assume that the Holy One, blessed be He, is perfect. That’s not a definition; that’s an assumption. Now I ask myself: how can that be? He cannot perfect Himself—so what does He do? We do it for Him. Another thing: I assume “service for a higher need,” meaning that there is something we do that He does not manage to do. That too is an assumption. I drew those two assumptions from various places—from philosophy, from books of Jewish thought, from the Torah through letter-skipping, I don’t care however you want. But these are certain assumptions that I assumed before I set out. Therefore the analysis I did here is not an ontological analysis. It is not an analysis that relies only on definitions and no assumptions. There are assumptions here. But still, once those assumptions are in place—assumptions that are accepted, that the Holy One, blessed be He, is perfect, that is an accepted assumption, and “service for a higher need,” less so but it has sources too—these are two accepted assumptions. Now I ask myself: once those are the assumptions I have, what can I learn from them? From here on the conceptual analysis begins. Like in geometry: I have axioms, and now the logical analysis begins, deriving from those axioms various theorems, conclusions. So here too, one has to understand: this is not an ontological argument in the sense that there are assumptions in the background. But the conceptual analysis takes those assumptions and shows how much information can be extracted from them if you do the conceptual analysis correctly. Quite surprising conclusions can be extracted from this conceptual analysis. So in that sense, as I said earlier, this is indeed a good example of conceptual analysis—but it is not an ontological argument. And here I really want to continue to a few more examples that work similarly, like the analysis I did: conceptual analysis that is not an ontological argument. In this context I want to talk for a moment about the notion of a thought experiment, what’s called a Gedankenexperiment. Gedanken is German, of course, and I think Einstein coined the term. The theory of relativity began with some thought experiment he carried out. And what is a thought experiment? A thought experiment is basically some scenario that I construct in my mind—not in a laboratory—and I ask myself: according to the assumptions I am making right now, or according to the knowledge I currently have, what should come out in such an experiment if I were to perform it? I don’t perform the experiment. I don’t have the tools to perform it. I can’t perform the experiment. But I conduct some sort of thought experiment. Suppose these and these assumptions are true. I think of some theoretical scenario, I construct some experimental setup in my imagination—not in reality—and I ask myself what the result should be. Now on the face of it, this is a worthless mental act. What will you learn from it? All you’ll learn is what follows from the assumptions you already have. But it turns out that’s not so. There are thought experiments that teach us many interesting things. Why? Because a thought experiment sometimes confronts you with a result that surprises you, or that you are actually convinced is false, or perhaps it exposes a contradiction among the assumptions you are making. And suddenly that reveals to you—basically, a thought experiment is just another way of doing conceptual analysis. That’s all. How do you do this conceptual analysis? Let’s build a theoretical construction, an experiment; let us think to ourselves what should come out in this experiment in light of our assumptions, and let’s examine that result. Does it make sense? Sense? Does it fit the assumptions, or maybe there’s some problem here and I need to give up one of the assumptions? Look—you see that by sheer imagination, without doing the experiment in practice, I learned something about the world, because my assumptions are claims about the world. I learned that a certain assumption is not correct, which is pretty surprising when you think about it. Maybe I’ll bring an example not from relativity, because that requires more familiarity. I’ll bring an example from my book The Science of Freedom. There I presented various thought experiments that help a person formulate a position on whether he is a determinist or not. I spoke about these thought experiments at the end of the series on free choice. So among those thought experiments I brought various kinds. For example, suppose they offer to take you apart down to the level of your atoms or molecules and reassemble you, and they’ll give you a million dollars if you agree—would you agree? Now a materialist, apparently, should agree, because after all all he is is just a collection of molecules. So what’s the problem? I didn’t touch anything—I took it apart, put it back together, you came back alive, so you slept for a few minutes, what’s wrong? There were a few minutes when you weren’t among us, and then you came back. After I rebuilt your molecules, you returned to being yourself, and you got a million dollars. Isn’t it worth sleeping for five minutes to get a million dollars? So basically a materialist ought to answer this offer in the affirmative; he ought to agree. Now it seems to me that most materialists you ask will not agree. Maybe I’m wrong, but try it—I think they won’t agree. If they don’t agree, what does that mean? Look—we didn’t do it; it’s a thought experiment. So now I ask: if he doesn’t agree, what does it mean? It means that he is probably not a materialist, because materialism pretty much entails agreement to this offer. If he doesn’t agree, he isn’t really a materialist. He probably thinks that even if they return all my molecules exactly in the same arrangement, that still won’t be me. Conclusion: apparently there is something more in the “I” than just the collection of my molecules and the structure in which they are arranged. Which means that basically you are not a materialist. Okay? So this is a series of experiments suggested by Avshalom Elitzur in his book Time and Consciousness, so I brought it there. There’s another thought experiment I suggested there, and that is Buridan’s man. As I said, Buridan was a French scholar at the end of the Middle Ages, dean of the Sorbonne I think, and he discussed… he tried to define the concept of rationality. What is a rational decision? Now usually we understand a rational decision to be one based on sufficient reasons—when you do something, you have a sufficient reason that justifies that action, okay? That means you are rational. You don’t do things without there being a reason to do them. Okay? So he asks: what happens if there is a donkey—yes, Buridan’s ass—a donkey, a point-donkey as the physicists say, standing at equal distance from two identical feeding troughs. On both sides of him, in complete symmetry, there are two identical troughs. Now the donkey stands there and muses on philosophy for his own enjoyment. At some point he begins to feel hungry. What to do? Time to eat something. So he asks himself, all right, which of the two troughs should I choose? Which trough should I go to? I don’t know—I can go to the right one, I can go to the left one. By the way, the concepts of right and left in parliament were born in France, as is known. So yes, he doesn’t know whether to go right or left. He has no way to decide whether right or left. Now what does that mean? That if he decides to go right, that will be a decision for which there is no sufficient reason that justifies it. He won’t be able to justify to me why he chose to go right, so he is obviously a non-rational donkey. Buridan says this basically means—this was a thought experiment Buridan did in order to show that rational… that rationality does not necessarily mean the existence of a sufficient reason for every action you do, of a sufficient ground. That’s not true. In this case, a rational donkey under the standard definition of rationality would die of hunger. Because if there is no sufficient reason to go right, he doesn’t go right. But there is also no sufficient reason to go left, so he doesn’t go left either. Since he goes nowhere, in the end he will simply die of hunger. Perforce—and since a donkey is not a rational creature, then indeed that is what would happen to him. By the way, I think that’s true. I think a donkey in such a situation would die of hunger. Why doesn’t this happen in practice? Because in practice the situation is never truly completely symmetrical. There are always some differences. But if you imagine a situation that was absolutely, absolutely symmetrical to the finest hair, completely symmetrical, then the donkey standing there would die of hunger—that’s my opinion. Why? Because a donkey truly is, in my understanding, a completely mechanical creature. He doesn’t know how to cast lots. Or in other words, I would put it like this: if the donkey is a deterministic creature, that means his actions are the result of the laws of physics—through biology and chemistry on the side, but at bottom it’s physics. Okay, so in the end, when that donkey decides to go right, I ask myself physically, mechanically: how did that happen? I will try to find what force acted on him according to the laws of mechanics, and I won’t find one, because the initial condition was completely symmetrical. So there cannot be any mechanical explanation that shows me or explains the move to the right or the move to the left. Therefore, since a donkey truly is a fully mechanical creature in my understanding, in such a state a donkey would die of hunger. And again I say, in practice this doesn’t happen because in practice there is never complete symmetry, but if there were complete symmetry the donkey would die of hunger. Now I ask myself—that’s what Buridan said. Now I ask a different question, a cousin of his question. I want to examine not the concept of rationality but the concept of determinism. And I’ll do the same experiment. I now place a human being—not a donkey—between two troughs in a symmetrical situation: Buridan’s man, a different experiment, okay? I do it with a human being, not a donkey. He stands in a symmetrical state between the two troughs. Now if the materialist is right, that means the human being is a creature that is all physics—only physics and nothing but physics. Okay? Now if he really is a creature that is all physics, he will die of hunger. You know there is a theorem in mathematics that says the laws of physics are basically differential equations, and the solution of an equation has at least the symmetry of the equation itself, or more than that. When there is a solution to an equation that is symmetric between right and left, the solution may have circular symmetry, because a circle has right-left symmetry and several other symmetries too. But the solution cannot come out lacking the right-left symmetry. It has at least the symmetry of the problem. That is a theorem in mathematics. Now if the human being—if human actions are nothing but solutions to differential equations, then a symmetric human being standing between two troughs in a right-left symmetric situation will die of hunger. Because if he chooses to go right, you will not be able to find a physical mechanism that explains this. Since the physical mechanism is symmetric, the equation is symmetric, so the solution “go right” is a breaking of the symmetry—and so is “go left.” The only solution that can exist is to go straight ahead. But if you go straight ahead you will still die of hunger; you won’t reach the troughs. Or to stay in place—it doesn’t matter—that’s going forward at zero speed, staying in place. Right, the symmetric solution is on the axis, the axis of symmetry between the two troughs. Therefore this is a mathematical proof—you can’t argue with it. It is a mathematical proof that if a human being is a physical creature governed by the laws of physics, then if you put him in the experiment between the two troughs, he will die of hunger. Now it’s possible that this is indeed what would happen; that’s not a refutation of the materialist, right? It might be that this is what would happen. But now I ask the materialist: what do you really think would happen? What do you think would happen? We’re doing a thought experiment. Let’s place a person in such a symmetric situation. We’re not actually doing the experiment—the Helsinki committee would never approve it—and in any event it’s impossible to do it with perfect symmetry, but we’re doing it hypothetically, mentally, as a thought experiment. And now I ask my materialist friend: what do you think the results of the experiment would be? Now if he does the calculation, then materialism leads to the conclusion that this person will die of hunger. But if he uses his intuition and arrives at the conclusion: I don’t accept that, that can’t be true. It’s obvious to me that a person in such a situation would not die of hunger. Suppose a materialist says that. What does that mean? That basically he has discovered that, at least on the intuitive level, he is not a materialist. He lives under the illusion that he is a materialist, but the truth is that he is not. And what revealed this to him was this thought experiment. And a thought experiment is not the same as an actual experiment, a physical experiment, a scientific experiment done in a lab, which basically tests some kind of hypothesis. I have a hypothesis, say the law of gravity. Okay? So I build an experiment to test it. I put this bottle here and let go. If it falls, that confirms the law of gravity. If it stays in the air, that would refute the law of gravity—it would refute the law of gravity. Okay? What causes me to draw my conclusions is the observational fact that I watch what happened to the bottle. Did it remain suspended or did it fall? That fact is what taught me the conclusion—for example, the conclusion that the theory of gravity is incorrect. If the bottle remains hanging in the air, I throw out the theory of gravity; it is incorrect. But I arrived at that conclusion from observation of facts. Facts taught me that. Fine—that’s not conceptual analysis; that’s facts. But in a thought experiment, after all, we don’t actually do the experiment. We simply ask ourselves: if we were to do the experiment, what do we think the results would be? These are not facts; these are opinions. It’s what I think the fact would be. Either this Buridan-man dies or he doesn’t die—that’s my conjecture. So what’s the point of testing one of my conjectures by means of another of my conjectures? On the face of it, obviously they’ll always confirm one another; they’ll never be refuted. So what’s the point of doing thought experiments? The answer is that this is not true. A thought experiment does sometimes refute my assumptions, because I discover that one of my assumptions contradicts another one of my assumptions. For example, I have one assumption, namely materialism, and another assumption, namely that a person in the Buridan situation would not die. One has to do serious conceptual analysis to see that there is a contradiction between those two assumptions. If you think that this person would not die, that contradicts your materialist thought, your materialist assumption. You have to choose. Either the person dies, or you are not a materialist. Therefore, the fact that there are sometimes surprises is what justifies conducting thought experiments. Because otherwise, really—look—if I do this thought experiment and simply ask myself what would happen to a person in the Buridan situation, I know my theory is materialism. Now I ask what would happen to the Buridan person. I do the calculation and say: he will die. Then I didn’t learn anything—fine, that’s the result of a materialist view. When do I learn? I learn when I check what the result would be not by calculating what follows from my theory, but by other tools and from my other assumptions. In a laboratory experiment, it’s from observation of facts. But in a thought experiment, it’s from a different mode of thinking. And now I check whether this fits with the results of using my theory. If yes, then all is fine. If not, then I need to give up either the theory or the intuition that this person really would not die. Either decide that he would die, or decide that I am not a materialist. So I learned something, even though this experiment is only a thought experiment and everything is hypothetical—just about what I think. I learned that I have two thoughts inside me that do not fit together. I need to give up one of them. That is basically conceptual analysis. You understand that what I did here is conceptual analysis. Because what did I say? I said that basically if you analyze a materialist view, you discover that materialism means a person in a Buridan situation would die, because of the symmetry theorem and all kinds of things of that sort. That is conceptual analysis. And now I suddenly discover that this contradicts my intuition that a person in such a situation should not die. The conceptual analysis basically helped me arrive at… Therefore thought experiments are just another way of doing conceptual analysis. Okay? That’s basically the point. And indeed Einstein too—whoever knows the conceptual analysis that underlay special relativity—Einstein basically said this: let us assume that the speed of light is constant. Not dependent on the medium, not dependent on… well, on the medium yes, but not dependent on the frame of observation. Suppose I send out a beam of light from a moving car—what is the speed of light relative to the ground? Usually, if I threw a ball from a moving car, then the speed of the ball relative to the ground would of course be the sum of the velocities: the speed of the car plus the speed of the ball relative to the car. That’s the speed of the ball relative to the ground. But with light it isn’t so. With light, its speed is always the same. It doesn’t matter whether you switch on the flashlight from a moving car or when the car is standing still. The speed of light is always 300,000 kilometers per second—that is, the speed of light in the given medium. From that assumption Einstein derived special relativity by conceptual analysis alone. It’s genius. Okay? Genius in its simplicity. He did a simple conceptual analysis or thought experiment and arrived at that conclusion. And this opened up an entire field in physics, which is of course a scientific, factual, empirical field. And it all began from conceptual analysis. And of course there too the conceptual analysis does not float in midair. First there is the assumption of the constancy of the speed of light—that the speed of light does not depend on the frame of reference. That is of course an empirical claim. Therefore in the background there are assumptions that are factual assumptions. This is not an ontological argument. It is conceptual analysis. And that is not the same thing. An ontological argument, as I said, is an analysis not based at all on assumptions but only on definitions. Conceptual analysis does take assumptions, but it derives the conclusions only by logic, without observations and without anything else. It simply analyzes the concepts and out comes the conclusion. And we have seen quite a few examples of this throughout the series. Therefore in that sense a thought experiment is simply another way of doing conceptual analysis. Fine, I’ll stop here because the next section will take me a bit more time, so I’ll stop here and continue next time. Okay, does anyone want to ask or comment? Yes, if possible. Yes, yes. I wanted to ask about the discussion of perfection and self-perfection—how does it fit with the idea that “no thought can grasp Him at all”? What we discussed about perfection and self-perfection? No, I didn’t understand. I mean, in what we discussed with respect to the Holy One, blessed be He—perfect, not perfect, and so on—what we discussed, I’m asking where this stands in relation to the outlook that says the Holy One, blessed be He, “no thought can grasp Him at all.” Meaning what—people don’t hold that? Meaning what—Rabbi Kook doesn’t hold that? Not related. This is not grasping the Holy One, blessed be He. Claims about the Holy One, blessed be He, are not graspings of the Holy One, blessed be He. Grasping the Holy One, blessed be He, would mean seeing Him, hearing Him, or apprehending Him in some sensory sense. We don’t have that; “no thought can grasp Him at all.” But to say claims about Him—when I say that He created the world, does that contradict “no thought can grasp Him at all”? Or when I say that He exists—does that contradict it? So with respect to what do people say “no thought can grasp Him at all”? With respect to direct apprehension. You I can see; the Holy One, blessed be He, I cannot see. I have no direct apprehension of Him; I cannot grasp Him. But I can think about Him. I understood that the meaning was to define Him. What does it mean to define Him? To define what He is, what attributes He has, which ones He doesn’t have. So I said, for example, you can speak about the fact that He exists. Can one say that about Him? I’m asking you. I don’t know—maybe not. Maybe not? Then you’re an atheist. Fine, that’s no crime; the question is just whether that’s what you are. Someone who believes in the Holy One, blessed be He, thinks He exists, no? He also thinks He brought us out of Egypt, gave us the Torah, and wants us to keep the commandments. All these statements we say about the Holy One, blessed be He. I don’t know whether He has the shape of a triangle or the shape of a circle, if He has shapes at all. I have no way to apprehend Him directly through my senses, but certainly I can say things about Him. To me that is absolutely clear. Maimonides wants to argue that even the attributes of the Holy One, blessed be He, should be stated in negative terms rather than positive terms. But that depends on what kind of attributes—primary or secondary attributes—we can get into that another time. But yes, obviously one can say things about Him: that He is omnipotent, that He is perfect, that He always was, that He always will be, “He was, He is, and He will be”—is that not a statement about Him? It’s a statement about Him. That He is the Master of the world—is that not a statement about Him? It’s a statement about Him. We say millions of things about Him. Anyone else? Thank you very much, good night. Okay, goodbye then, Sabbath peace. There’s a lecture tomorrow, right? There’s a lecture tomorrow morning, yes.