Non-Deductive Logic and the Limits of Scientific Thought – Rabbi Michael Abraham

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[Rabbi Michael Abraham] I’m not up to date anymore—what can I do. So at the next stage, adolescent rebellion emerges, and again, I’m talking about intellectual maturation; forget emotions for now. So on the intellectual plane, adolescent rebellion begins when the teenager asks his father, “Who says? Prove it.” Meaning, you say the sun will rise tomorrow too—how do you know? It rose until now, okay, but tomorrow? How will you prove it? Why should I accept your claim if you can’t prove it to me? At a certain stage, yes, the teenager’s basic assumption is that he’s not willing to accept anything that isn’t proven. At the third stage, or at the seam—this is the beginning of adolescence. At the seam between adolescence and adulthood, the point of maturation, the teenager reaches a rather gloomy conclusion: basically, he can’t prove anything. Meaning, I wanted to accept only proven things, but there are no proven things. Why? Because every proof is based on first assumptions, and if you don’t accept anything without proof, then you can never accept the first assumptions. And if you accept them on the basis of previous assumptions, then those won’t be accepted either. Right? Turtles all the way down. So in the end, the only thing you could accept would be what Kant called ontological arguments—that is, arguments with no premises, analytic arguments of that sort, which manage to produce a conclusion without assuming anything—and Kant ultimately claimed that this is impossible. I think he was right, even though his arguments aren’t always accepted by everyone.

[Speaker D] But on that, maybe you can expand further and say, for example, okay, there are different kinds of frameworks, each in its own field, and then maybe the next stage is that I choose some kind of framework from among all those claims.

[Rabbi Michael Abraham] “Framework”—you can call it whatever you want. But if you don’t accept anything without proof, then the framework itself is an arbitrary choice. You can choose whatever you want.

[Speaker D] I mean in the sense of frameworks—so if we have the first, second, and third stages, which I agree with, you could also say that after that you can conclude that this person comes to understand that there are frameworks, so it’s not absolute truth, but then maybe an even more mature stage within adulthood itself is that he chooses to believe something very specific within all those frameworks.

[Rabbi Michael Abraham] And what does “chooses” mean? Without proof? So let’s see. I’ll now describe the third stage. In other words, where we really are right now is in a crisis—the crisis at the end of adolescence, between adolescence and adulthood. What is that crisis made of? Two assumptions. One assumption is that only something proven is acceptable, only something certain is acceptable, okay? The second assumption: there is no such thing. There is nothing certain. Okay? So now you have three ways to mature from here. It’s simple combinatorics. One possibility is to say, okay, then nothing is acceptable, right? That’s the conclusion: nothing is acceptable, fine. Right? Except for that statement itself. But aside from that statement itself, there’s nothing you can accept. Okay? So you come out a skeptic. The skeptic is the person who remains with the two assumptions that accompanied him throughout adolescence and simply draws the conclusions. The second path of maturation is to give up one of the assumptions. The third path of maturation is to give up the second assumption. Those are the options. So if you keep both, you’re a skeptic. Because you’re basically saying: only what is proven is acceptable, nothing is proven, therefore nothing is acceptable. “Nothing is acceptable” means you can arbitrarily adopt frameworks, you can do whatever you want, but it’s arbitrary. Meaning, it’s not something I can rest my head on. The second possibility is to give up the assumption that nothing is certain. Indeed, only something certain is acceptable—but who said there is nothing certain? I said earlier there is nothing certain because every argument is based on assumptions, and assumptions as such have no proof. I’m assuming that proof is the only path to certainty. But, for example, a fundamentalist can come along and say: no, I have other ways of reaching certainty. God revealed Himself to me in a dream, or the Holy One, blessed be He, or my Rebbe told me such-and-such, and I have complete trust in it—it’s certain for me. And therefore I have a way of reaching the desired certainty even without logical proofs. That’s what I call fundamentalism. Fundamentalism at the philosophical level—you don’t have to murder anyone for this—but at the philosophical level, a fundamentalist is someone who places a certain claim in a way that is not subject to critical examination. In other words, it isn’t measured in logical terms. If some transcendent source of authority gives this to me, then I have certainty in it. Yes, many believers I know, for example, live with the feeling that faith for them is exactly that kind of thing. Meaning, you won’t be able to shake it in any way—not because they have an answer to the logical arguments, but because they don’t put it to a logical test. In other words, it doesn’t stand up to critical examination. So that is basically the second path of maturation. If you give up the assumption that nothing is certain, then you can say: okay, only what is certain is acceptable—but there are certain things. It’s not true that there are no certain things. What my Rebbe told me is certain.

[Speaker E] By the way, there are people who don’t necessarily avoid critical examination altogether—they just don’t put it to logical critical examination.

[Rabbi Michael Abraham] Okay, I’m willing to accept that correction.

[Speaker E] Their critical system is different.

[Rabbi Michael Abraham] Fine, although I’m not entirely sure you’ll manage to show me an actual critical system.

[Speaker E] The length of the beard of the one saying it. Okay, fine.

[Rabbi Michael Abraham] If that’s what you call a critical system, then accepted.

[Speaker E] Yes, you know, if a Jew from a certain yeshiva said it, then he said it, so to speak.

[Speaker A] More than that, Miki, you proposed non-deductive logic. Amnon told you what the definition is: it’s a system that enables us to reject theories in a way that will lead us to agreement. So if all the people in the yeshiva used the same system, then everything’s fine—logic in every sense.

[Rabbi Michael Abraham] And I already clarified to Amnon too that I don’t entirely agree with what Noshev understands from his words, because he talks about agreement and I talk about truth. So therefore, okay—but that’s in a moment. So the third path of maturation is to give up the second assumption. That is, to say: indeed, there are no certain things, but who said that only something certain is acceptable? In other words, I am willing to accept things that are not certain. Meaning, I give up the teenager’s second assumption. Okay? This maturation I call synthetic maturation; never mind the terminology, but I call it synthetic maturation, following Kant. So the claim is that you basically have three—well, you can also give up both assumptions, but that’s unnecessary on this map. So either I stay with both, or I give up one, or I give up the other. Those are the three possibilities. It seems to me it’s hard to see another possibility, although Amnon, this is your area of expertise—to find the possibility no one sees. So we have three possibilities: either skepticism, or fundamentalism, or syntheticity. Okay? Now, when I as a synthetic adult am approached by the teenager who asks me, “Who says? Prove it.” Meaning, I tell him—he asks me, “Will the sun rise tomorrow?” I say, “Yes, of course, it rose until now, why shouldn’t it rise tomorrow morning?” So he says, “Who says? Prove it.” Well now I’m already a synthetic adult, right? I don’t need proofs. I know that something reasonable is good enough for me. Okay? So I say: it’s reasonable that it will continue, and for me that’s enough. The teenager, of course, doesn’t accept that. Why doesn’t he accept it? Because he wants proofs. He doesn’t accept things without proofs. Okay? Now, almost nobody shaves on someone else’s beard. Meaning, he’ll have to go through the process himself and choose his own path of maturation. But I want you to notice for a moment how he sees me at the stage he’s in. When I tell him, “Look, tomorrow the sun will rise too, because it has risen until now,” what does he say? “Look, I was in that stage too when I was a child. I accepted things just because people said so and that was that—I was dogmatic too. He basically sees me as someone who has gone back to the dogmatic stage. Right? He’s essentially saying: fine, you accept things without proof, you’re dogmatic. I was there too, but I matured. In other words, when you grow up, you’ll be like me too.” Yes, that’s what the teenager says to his father. Meaning, yes, like the Mark Twain line everyone knows: when I was fourteen, my father knew nothing. Six years passed and listen to this—he matured in an extraordinary way, he’s starting to say sensible things. So the teenager’s view of the synthetic adult actually raises a real question. In other words, his claim is one that requires a response; it isn’t a stupid claim. Because what is he ultimately saying to me? You accept things even though they’re not certain. But why did the teenager decide to accept only things that have proof? Because really, otherwise why accept them? It seems arbitrary. Just because you’re built in such a way that something seems reasonable to you or not—so what? Why does that matter? If there’s proof, then fine, I’m willing to go with it. But if not, then is the synthetic adult just deceiving himself? Meaning, has he not really just gone backward while feeling, no, I’ve advanced to the third stage, I’m already a synthetic adult. No, no—you’ve simply gone back into the womb, right? You’ve gone back backward and you’re really just dogmatic. Meaning, you accept things because—well, who knows—because that’s what people say.

[Speaker A] But Miki, isn’t that only because people aren’t careful in how they express themselves? Meaning, if the teenager asks me whether the sun will rise tomorrow and I say yes, and then he tells me, “But you have no proof,” then I won’t tell him, “Well, but it rose every day.” I’ll tell him, “Okay, explain to me what you mean by whether it will rise tomorrow.” If you’re asking whether I have logical certainty that it will rise tomorrow, I’ll say I don’t know. And if you ask in what sense I meant yes, I meant that this is the highest level of certainty one could reasonably expect, and so on and so on. So there’s a recognizable difference between what the adult says and what the child says, and the skeptical teenager also hears a different argument. Because the child says, “The sun will rise, period,” and the adult says, “To the extent that one can say anything with certainty, it will rise.”

[Rabbi Michael Abraham] So let me continue a moment, and I’ll claim that no. Meaning, I want to argue—it’s obvious there is such a difference, I’m only asking whether that difference—

[Speaker A] —is a measurable difference that the teenager too would ostensibly recognize.

[Rabbi Michael Abraham] No, he can recognize the difference, but he won’t accept that it’s really a substantive difference. Why? Or at least he doesn’t have to accept it. Why? Because from his point of view, the fact that you think, at a high level of probability, the sun will rise tomorrow—you express yourself as cautiously as possible, okay? He says: on what basis? Meaning, why did you decide that you have some criteria governing probability? Proofs—I know what those are. But probability—who says that isn’t just a reframing of the child’s dogmatism? Meaning, you’re simply returning to the child’s dogmatism, only now you’re more sophisticated. You already know how to present it as, “It’s not certain that the sun will rise tomorrow; I’m saying that at the highest probability one can reach, I think the sun will rise.” That you think so—I know. But the question is: what connection does that have to reality?

[Speaker A] Okay, so if you take the teenager’s axioms as you described them, you can say: I can remain with the axiom that nothing not proven logically is known to me. And still I can ask myself, okay, given that I live in a world in which nothing can be known logically, do I create a hierarchy among the other kinds of— I don’t want to use the word “proofs.”

[Rabbi Michael Abraham] That is exactly the question. You formulated the question exactly right. And the question is—and here I say this is why I think it is so illuminating to present things in this chronological way, as childhood, adolescence, and adulthood—because you begin to think about what happens at the next stage compared to the previous stage, and you ask yourself whether he simply went backward and just knows how to phrase it in a way that covers it, wraps it up, or whether we really advanced. Now here, I think, it will depend—and here we move into the territory of syntheticity. We have left proofs and all that behind, and therefore in a certain sense there is some begging of the question here, but we already know that deduction also begs the question, so that’s fine. And what I basically want to say is that if I present a systematic way to justify my claims—justify, not prove; justify meaning I can show why it seems reasonable to me. Now, you can always cast doubt and say, “So what have you shown? It’s not proof, and I don’t see what you base it on; it’s just because that’s how you’re built.” So what? The world owes you nothing, as Mark Twain says; it was here before you. So yes—what if that’s how you think. But I think that at least for me as an adult—I don’t know what the child will get out of it—for me as an adult, I want to reassure myself that I truly did not go backward but advanced a stage forward. And I want to see that when I talk about probability, I have some control tools that tell me this is not just dogmatism because the all-knowing said so; rather, yes, I have some tools that help me understand why I think this is reasonable. Why I think this is—not true or certain—but acceptable. Okay? Acceptable in that sense. And I can establish some hierarchy of acceptability, even if I don’t accept proofs and certain knowledge and things like that. And therefore I think this nicely illuminates the need for inductive logic, or non-deductive logic. Because non-deductive logic is what can let me become convinced—maybe not convince others, but convince myself—that I’m not in the first stage, that I haven’t gone back to the first stage, but that I’m in a more advanced stage, the third stage. Okay? That is basically the claim. Now, regarding this three-stage development of maturation, I also made an analogy from an individual person to civilization—perhaps Western civilization in general. I think it too went through roughly, again in very broad brushstrokes, some such three stages. There is the dogmatic stage, when people dance around the fire and assume this will bring rain, or I don’t know what, or they put up a mezuzah and think that because of that they won’t die, or things of that sort. And afterward comes the rebellion of the Enlightenment—perhaps the encounter with Greece, we just finished Hanukkah—some demand to prove things, yes, logic, some kind of systematic, philosophical, ordered thinking. And I think that in the middle of the twentieth century the point of maturation arrives—with skepticism, the transition from positivism to postmodernity. I’m saying this very quickly, but there’s an interesting analogy here. And at that stage, say from the mid-twentieth century onward, it seems to me you can see these three paths of maturation struggling with one another. Meaning, there is skepticism—you can call it postmodernity, at least in its extreme expressions; I think that describes this maturation. Everyone with his own narrative, but you are trapped within some set of first assumptions that you don’t bother to justify and also don’t think are more justified than alternative sets. There is fundamentalist maturation; I think fundamentalism has raised its head in recent decades because of this. Meaning, it has a certain presence because of this crisis at the end of the Enlightenment period; positivism essentially brought about this crisis. And there is synthetic maturation, which in my view is a kind of solution in the political and social sense too—it’s not only a logical and philosophical analysis. Meaning, the question is whether you are willing to accept truths for which you have no proof, and are willing to fight for them against fundamentalists and against skeptics. Meaning, you offer another alternative. It’s not a game between fundamentalists and skeptics, and maybe pragmatists in the middle—those who adopt things even though they aren’t justified because you can’t live otherwise. No. I want to claim that there is some alternative that accepts certain claims even though it has no proof for them, and I am not a fundamentalist, but I’m also not a skeptic. Meaning, I do not doubt everything for which I have no proof; I have a position. And with that position, I’m not certain of it—on the contrary, anyone can try to challenge it, it needs to be examined, cross-checked, I don’t know—we’ll reach our conclusions.

[Speaker E] And maybe to make a paraphrase of the famous sentence—you say, I’m not sure of my opinion but it disappeared. I’m saying maybe one can paraphrase the well-known sentence: I’m not sure of my opinion, but I’m willing to die for my right to think it.

[Rabbi Michael Abraham] Yes. To think it. Yes. So that’s Rousseau the egoist, right. So the claim is that it is very important to formulate some mode of thought—I call it non-deductive logic, I don’t care about the terminology, don’t call it logic if you don’t want to—but some system of rules that critiques non-deductive decision-making. Because without that, then truly we have gone back to childhood. And science, which is usually associated with the camp of precise, certain thinking—science really belongs here. Meaning, you cannot accept science if you are not willing to accept unproven claims. And if you think unproven claims are unacceptable, then we get all the critiques—you know, the new criticism that attacks science too, yes, about male physics and all sorts of things of that kind. So that is the need. Now what does that actually mean? I think there are two distinctions that need to be made in order to sharpen the definition of what I call non-deductive logic. One thing is the distinction between emotion and intuition. And again, the terminology is mine; I don’t care whether the dictionary defines it this way, but I’ll use it because I want to distinguish between two concepts. Emotion is some subjective stirring that arises in me, and let’s say I say that I love a certain woman, and someone else doesn’t love her. We have no argument, right? Meaning, I love her, he doesn’t love her. Each according to how he’s built. I’m not making a claim about—

[Speaker E] If both of you do love her, then you do have an argument.

[Rabbi Michael Abraham] Yes, that may also be true. So the claim is that I’m not making a claim about the world; I’m reporting on my state. Meaning, if you report on your state and I report on mine, then we’re not talking about the same thing, so we have no argument. Okay? So that’s what I call emotion—very roughly, but that’s what I call emotion. Intuition is something very similar, and many times people use the term emotion when they really mean intuition, and that is very confusing. And it matters for our discussion. For example, think of someone working on a difficult mathematical equation, grinding away at it for half a year, doing calculations, checking, this way and that, and he arrives at the answer: eight. The answer is eight. Then his brilliant friend arrives, looks at the page, “So, what are you doing?” He shows him the equation, and the friend says, “Oh, that equation? Yes, the result—the answer is eight.” Says it on the spot. The first one asks, “How did you come up with that? How do you know?” And he says, “I just had a feeling.” Now you understand that the word “feeling” in this context is not emotion, right? Meaning, it’s not “emotion” in the same sense we were talking about before. What he means to say is: I had an intuition. I didn’t do the explicit calculation, but maybe I did some implicit calculation, and maybe not even that—I don’t know how it happens—but I reached the conclusion that the answer is eight. Meaning, because that’s how it seemed to me. Like you said earlier, there are people who see it—they see it and don’t need to do the calculation. Right? Meaning, he sees that the answer is eight. But he uses the phrase, “I had a feeling.” Why does he use the phrase, “I had a feeling”? Because our assumption is that anything not based on explicit reasoning is emotion. But that’s not true, or at least not necessarily true. Something not based on explicit reasoning can also be intuition. Right? Kahneman’s System 1 and Kahneman’s System 2. So sometimes it’s explicit, sometimes it’s implicit, sometimes it’s not even either one, but somehow you arrive. What is the indication? The indication is that when you claim the answer is eight, I can check and see whether it’s right or wrong. And if someone claims the answer is seven, he disagrees with you. It’s not like “I love her and you don’t love her.” We have a disagreement. Meaning, the claim that the answer is eight is a factual claim—as much as a solution to an equation in mathematics is a fact—but it is a factual claim. And that claim says it is correct, and anyone who says otherwise is mistaken. That is not the same thing as “I love her and he doesn’t love her.” In that sense, using the word “emotion” for this is very confusing. Not successful. Therefore I prefer to use the word intuition in this context. And intuition is some direct way of seeing this truth—but the claim in the end is that I saw something that is a claim about the world, something true. I’m not reporting a mental state. By the way, there’s a very interesting little book called The Abolition of Man by C. S. Lewis—the Narnia guy. He was a brilliant philosopher, by the way, one of the clearest I know, really an amazing man.

[Speaker E] He was very Catholic, by the way.

[Rabbi Michael Abraham] Right, very Christian. In certain periods he went through various changes. And at the beginning of the book there’s a truly illuminating passage. At the beginning he brings two school textbooks for literature in a high school, the Green Book and the Blue Book, he calls them by colors because he doesn’t want to say who they are—it would be slander; he’s attacking them. In any case, the claim they make is that they’re trying to teach the children of England literature. So they bring some phrase of Coleridge about two people who come to some waterfall, and one is overwhelmed—what a beautiful, inspiring waterfall—and the other is unmoved by it. The question is whether there is a disagreement between them. So these books, the green and the blue, say: there is no disagreement between them. One is describing his own mental state, and the other is describing his own mental state. There is no disagreement here. And Lewis argues: what do you mean? That’s a corruption of thought—as part of his war against postmodernity and narrativism. He says: what do you mean? Of course there is a disagreement. The disagreement is that when I say it overwhelms me, it is not a claim about me; it is a claim about the waterfall. I express it through the question of what it does to me, but I’m claiming that there is something in the waterfall that ought to overwhelm me, and if it doesn’t overwhelm you, then you missed something.

[Speaker E] Miki, that’s very interesting, because three classes ago—this is one of those things you all probably remember and I don’t—Shuki said something and we talked about whether it was overwhelming and surprising and amazing and all that, and you argued that it was banal and I said it was amazing. And since I’d already said a lot I didn’t want to add more, but I wanted to say that when two people argue, one thinking that something is overwhelming and the other not, most likely the one who says yes is right. Because it’s more likely that someone is blind to something overwhelming than that someone hallucinates that something is overwhelming. I mean, between two people who aren’t drunk and have roughly similar intelligence—

[Speaker G] And are in a—

[Speaker E] —reasonable condition, then it is more correct to tell the person who doesn’t get the wonder, “Make an effort, it’s a shame, maybe you’re missing something,” than to tell the other one, “Make an effort and stop being impressed, because really there’s no reason.”

[Rabbi Michael Abraham] No—

[Speaker E] Not that it never happens, but as a starting point.

[Rabbi Michael Abraham] But—

[Speaker F] Why are you going in the direction of right or not right? There’s no issue of right here. Each person is interested in and is impressed by something else, so I don’t understand why you’re saying—

[Rabbi Michael Abraham] —this one is right and that one isn’t.

[Speaker E] That’s exactly the claim of the literature textbooks. But Miki and I think one person is more right than the other.

[Rabbi Michael Abraham] Exactly—that is precisely the point. Really, the simple view says that obviously those books, those textbooks, are right. Meaning, I’m impressed and you’re not—what’s the difference between that and “I love her and he doesn’t love her”? I’m reporting my mental state and he is reporting his. But it’s like art criticism. Why am I interested that an art critic was impressed by some exhibition? Okay, so that happened to him—he’s built in a way that he’s impressed by that, while I’m impressed by seeing a bird in the sky. Why is that interesting? The claim, or at least the assumption here, is that when a textbook—or when he tells me he was impressed by the exhibition—he said something about the exhibition, not only about himself. In other words, he told me that it’s worth looking there, there is something valuable there, there is something there that will probably do something to you too—at least if you understand. And that is exactly the point Lewis wanted to make: that although at first glance it looks like emotion—the feeling of awe—in this case the emotion reflects some claim about the world, and therefore it really is a genuine disagreement. As opposed to “I love her and he doesn’t love her,” where there too maybe one could discuss it, but there I think more simply I’m willing to accept that it’s just an expression—I don’t know—a report of a subjective state.

[Speaker A] Okay Miki, I will note that you moved back and forth between two claims: one, that it is a statement about the objective world; and two, that it is something that can be checked. Those are not necessarily the same thing.

[Rabbi Michael Abraham] I didn’t say it can be checked.

[Speaker A] Didn’t you say the difference is like eight, where we can see whether it’s eight or not? Ah yes, but at the waterfall, precisely beyond the waterfall. That is, we have the question of whether this is a statement about my inner state or about an external state, but even regarding an external state one can have a discussion and say this is something we don’t think there is any way to decide.

[Rabbi Michael Abraham] For example, in mathematics, if it’s an NP-complete problem, then there’s no way to check it, but there is a correct answer. So yes, of course, I completely agree. So the point, in short, that I want to make is that one must distinguish between intuition and emotion. And when the teenager looks at the adult, he attributes it to emotion. Meaning, he says, what is emotion? Something subjective—not necessarily emotion in the emotional sense, but not a claim. What you’re saying is just—okay, you’re imagining things. And the adult who wants to convince himself that his synthetic position is different, that it’s not just dogmatism or arbitrariness or emotional or subjective or whatever—in effect says: no, I have some intuition that the sun will rise tomorrow. My intuition tells me it will rise tomorrow. Now if that’s the difference, then it’s a bit discouraging. It’s a bit discouraging because the feeling is that there’s no way to discuss it. Meaning, I have such an intuition, you don’t have such an intuition. So true, at the philosophical level I can claim that there is truth here and that this is a claim about the world—but precisely as Moshe just pointed out, if there’s no way to check it, then the conversation ends here. Meaning, there’s nothing more we can do with it. So I’m impressed by the waterfall and he’s not, and everything is fine, we can part as friends—even though philosophically one of us is right. Who knows which one. Meaning, there’s no way to check. Okay? What I want to claim as an additional point is: there is a way to check, or at least there is a way to discuss—not to prove. Remember, we are within a synthetic framework. There’s no way to prove, but there is a way to check, a way to try to become more convinced. And here I want, again in broad brushstrokes, to suggest that this may be the difference between logic and rhetoric. Rhetoric has a bad name in our circles; that was the subject of the book we once wanted to write, which I mentioned earlier. It has a bad name in our circles because it is perceived as synonymous with demagoguery. But rhetoric and demagoguery are not the same thing. Demagoguery is misleading rhetoric, perhaps even deliberately biased rhetoric. But rhetoric in itself, when it is not demagogic, is a system of tools that is very important—and by the way, it’s a great shame that it isn’t taught here—because it is a kind of system that allows one to discuss, you might say, first assumptions. Meaning, what logic perhaps does not allow, because logic is supposed to assume some first assumptions. The question is: how do I adopt the first assumptions themselves? So the way to adopt first assumptions, to argue about first assumptions, to persuade and be persuaded regarding first assumptions—I think, broadly speaking, one can call that rhetoric. Rhetoric is something I cannot prove to you, because then it would be logic, but I can try to show you that it is less reasonable. Meaning: try to look from my point of view and understand why I think this is reasonable and that is less reasonable. If I succeed in doing that—and that is perhaps a more literary than logical ability—I describe a situation to you, I bring you into my point of view or something like that, and again, this is not just emotion or intuition all the time, because otherwise it would merely be demagogic ability. Rather, I’m trying to get you to look at the issue from my point of view, and then it may be that I’ll succeed in persuading you, or vice versa, you’ll persuade me. But we do have a way to discuss first assumptions too, and that is by rhetorical tools. Rhetorical tools, for example, can show something that bothered me for years. For instance, we’re having a moral argument, okay? And then I bring you an example to illustrate the point. What example? I don’t know—people got stranded on a mountain in the Andes there; was it Manchester United? I don’t remember. And they had to eat someone in order to stay alive. There were other such cases. And now look—according to your view, it turns out they were allowed to eat someone, which shows you’re wrong. What do you mean, shows I’m wrong? Right, according to my view that’s what follows, and everything is fine. So where did this “shows I’m wrong” come from? We have some intuition that says, wait, that can’t be right, and therefore if your theory leads there, then apparently there is something problematic in it. There is something stronger in the example than in the theory, because regarding the example I have some intuition—

[Speaker F] I didn’t understand, Miki, I didn’t understand the example.

[Rabbi Michael Abraham] Let’s say we’re having a moral argument, okay? I claim that we need utilitarian ethics. I want to say that we should act in a way that brings the maximum benefit to the maximum number of people, okay? Now ten of us are stranded on a mountain, we have nothing to eat, we’ll all die of hunger. So there’s no choice—you have to kill one and eat him, and at least the other nine will stay alive. So according to utilitarian ethics, that is the conclusion. It’s all simplistic, just for illustration, okay? Now someone else can come and say: no, I have a different ethics, and one must not murder. So if you have to murder, then die—meaning, no. Incidentally, in a certain sense this is the dispute between Ben Petora and Rabbi Akiva: two people walking in the desert with one flask of water—it’s roughly that. And someone else says: no, it is forbidden to murder under any circumstances, okay? Sorry, I got ahead of myself. They’re arguing in general. One is utilitarian and the other is, I don’t know, deontological, okay? Now I tell him: look, I have the winning card, I pull the joker from my sleeve, I say: according to your view, if ten people crash on the mountain, it turns out they should kill one of them and eat him so the rest stay alive. Checkmate. Meaning, I won. Why did I win? Because I have, at least for me, some assumption that my moral intuition tells me such a thing can’t be right, and if that follows from your method, then apparently something is wrong with your method.

[Speaker E] No, but I think the more correct move, if one does it wisely, is to say: you claim that one should maximize benefit in this, and I also remember that you stated unequivocally that it is forbidden to murder in another discussion we had. Now let me show you that by deduction—this is an internal contradiction! If you find him a contradiction—

[Rabbi Michael Abraham] If it’s internal, that’s obvious. But then that’s logic, not rhetoric.

[Speaker E] Right, but that’s why I’m saying rhetoric is often—and here we’re talking now about—within non-logical tools, people do use deductive tools many times as part of the stages.

[Rabbi Michael Abraham] Like analogy, where we divided it into induction and afterward deduction—fine. But the whole move is an analogy. You can’t rely on the deduction and say that what I said is necessary. No, no, no. So that’s why I say that there is in any case a rhetorical dimension here. It is not pure logic. Obviously there are logical parts in rhetorical arguments too; you use logic all the time. But logic does not exhaust the matter. Meaning, you can’t formalize it into a purely logical argument.

[Speaker E] Right, right, but I’m saying the example you gave was a bit of a straw man, because usually it’s a little more sophisticated.

[Rabbi Michael Abraham] Okay, man, yes, fine, so it’s just a straw example. But I’m saying it also doesn’t have to be that way. It could be that I never heard the person say that murder is forbidden; he may really say, yes, true, if that is the result then that’s what I think.

[Speaker E] And then, as a good rhetorician, you didn’t make a good enough move.

[Rabbi Michael Abraham] True, true. I tried—I don’t know what would persuade him. But what I’m saying is that my hope is that even though I’ve never heard him talk about murder, I still have some hope that if he looks at this situation, he’ll be persuaded. That hope is rhetoric. Meaning, that hope says: I managed to get him to look at something from my point of view, and maybe I’ll succeed in persuading him that I’m right.

[Speaker E] One can formulate the strategy this way: take the other person’s position, derive from it—imagine some kind of star that shoots deductions in all directions—and hope that one of them will hit something he doesn’t agree with.

[Rabbi Michael Abraham] Right. So the first stage is deductive. But obviously that isn’t—it’s not that deduction is the whole story, because you never know whether you’ve derived all the conclusions, and you also don’t know whether you’ve landed on the conclusion that will actually produce the change among all the conclusions you drew. Therefore yes, again, there is a deductive aspect, but it is not all deduction. Meaning, there is something here besides deduction. That is the claim. And this is an illustration of what I mean when I talk about rhetoric. And therefore these two conclusions: first, intuition versus emotion; second, rhetoric versus logic—these are characteristics of the tools we need to use when we speak about a synthetic position. Meaning, how I form positions in a responsible way—not childish, not necessary, but also not emotion, not subjective, not some thing of that kind.

[Speaker H] Now and maybe I’ll do another—

[Rabbi Michael Abraham] Two things. I’ll try to do two more things. First, I want to point out how intuition appears within the scientific process, which is pretty clear overall, but I think there’s a good illustration of it in a phenomenon I saw in two different books that is really the same phenomenon. One book is called What Is History? by a British historian named Carr, and the second is Hempel’s book on philosophy of science, which the Open University also uses as one of the accompanying books. So, Carr talks about the question of how you do historical research. In the inductive logic of Francis Bacon from the sixteenth century, he tried to define a logical process underlying science. This is basically the first systematic attempt to locate, or create, non-deductive logic. And to this day, in one variation or another, people use the tools he formulated there, which are fairly intuitive overall. So Carr’s argument goes like this: suppose I want to explain why Napoleon lost the Battle of Waterloo. Okay? And suppose I have absolutely no knowledge of warfare, tactics, and how battles are won. Okay? So what do I need—what does Francis Bacon tell me? Gather the facts, generalize from them inductively to some conclusion, put it to the test, yes, things like that. So you start with the facts and then move to formulating a theory, and back and forth, testing it, and so on. But Carr says: which facts am I supposed to gather? There are infinitely many facts. What was the mother’s name of the lieutenant of the eleventh regiment? What was the height of the communications officer of Company C in whatever it was? What was the color of the sand hill they were standing behind? In other words, infinitely many facts. How do I know which facts to gather? Again, assume for the moment that I have no experience at all in military matters and warfare and tactics and things like that. I’m only now beginning to accumulate my strategic, military knowledge, okay? So there’s no way to gather the facts. How do you know which facts to gather anyway? So you say: you do some kind of filtering. You say: certain facts seem irrelevant to me, and these facts seem relevant. How do you know what’s relevant and what isn’t? In a certain sense, you already know what the result will be, or what it might be. Meaning, you know that the explanation won’t be the ABC’s of the mothers’ names of the lieutenants, even though you have no knowledge of military strategy. You do know that it might depend on morale, on equipment quality, on the number of soldiers. How do you know that? You have some kind of intuition. Of course, it’s something accumulated from many other things—you have some kind of intuition, and in a certain sense there is a kind of circle here. Because you need to know what the explanation will be in order to decide which facts are relevant, which facts to collect, because the relevance of the facts depends on the explanation. If the explanation is that morale was low, then some facts become very important—how many duels took place there the night before, how drunk they were, or something like that. But if the explanation is that you need—

[Speaker F] You need knowledge in order to have intuition.

[Rabbi Michael Abraham] So okay, so I’m saying—but no, let’s say just in this context, even before how I developed the intuition itself. In this context I’m basically saying there’s a circle here. The circle goes like this: you can’t collect the facts unless you know what the theory will be, but supposedly you arrive at the theory on the basis of the facts. So how does the process—right, the egg and the chicken—how does this process begin? So there’s no choice here but to say that at the first stage, when I collect the facts, I still don’t know the theory, but I have some intuition about what it could be and what it couldn’t be. Something pretty vague like that, which I gathered from various places, maybe a priori, maybe a posteriori, not important, but I gathered it somehow. And then I collect the facts. After I collect the facts, I try to build a theory, test it, go back, and so on. In other words, in short, you have no way to go from the facts to the theory the way Francis Bacon thought one does. You have to activate intuition already when you collect the facts. Meaning there is something a priori—well, I don’t know if it’s a priori, but earlier than this research. I don’t know whether it’s a priori, whether it’s the result of previous experience, but it precedes this research in order to know which facts to collect. And only after that can you formulate a theory and test it. It’s not certain it’ll succeed, but that’s how you make progress. If this weren’t so, we would still be today in an endless effort to formulate facts, theories—we wouldn’t get anywhere. Because there are infinitely many facts, there are infinitely many subsets of facts that you can try to test a theory on; you’d never get out of it. By the way, Hempel writes the same thing in another context, but it’s exactly the same phenomenon. He describes there an Austrian Jewish doctor—Hungarian—named Semmelweis, who was head of a department in a hospital in Vienna, and there was another maternity ward there—he was head of a maternity ward—and in his ward there was a high mortality rate from childbed fever, more than in the second ward. And they tried to understand what caused this. Now they hadn’t the faintest idea what caused it. So they started checking the direction the priest walked in, and the color of the lamps, or I don’t know what, the light there, and the direction of the windows and garlic—you’re shooting in the dark. Meaning you have no clue at all. Now when you don’t know what the explanation is, you have no way to know which facts to collect. Meaning, in order to know which facts to collect, you need to understand something about the explanation. But supposedly the explanation is the result of the facts. So once again you have exactly the same circle here; it’s exactly the same thing. And again the answer is that apparently they had some initial intuition, because in the end they did discover it. But they had some initial intuition even though they didn’t know the explanation, and it really was a shot in the dark, and the explanation was a completely new explanation involving microorganisms and all that, which they didn’t have at all—it would have sounded like witchcraft beforehand if you had said such a thing—but in the end, the fact that they discovered it, and they didn’t just wander around with infinitely many facts all the time without managing to advance—meaning here this is already a phenomenon, an empirical proof, meaning you see that intuition can also work. Meaning, the fact is that in the end they reached an explanation that also stood up to tests. Meaning that our intuition, which causes us to know which facts to collect and which not to, takes part at the beginning of the process. Without it we couldn’t collect the facts and get from them to a theory. And this basically means that scientific thinking—and this is quite clear—scientific thinking is not, certainly not deductive, but it’s not even observation plus deduction the way positivists might like to think. Meaning they think only direct observation plus deduction, that’s it, nothing beyond that. They’re the type of boys—the positivists are those boys who aren’t willing to accept anything that isn’t certain. And it can’t work that way. If it did, we wouldn’t arrive at anything in science, and that can’t be. There are a priori things that we use in the scientific framework, meaning things without which we couldn’t advance one step. So this, for example, is an indication—and since in science we also have some measures by which to see that we succeeded, with all the limitations of philosophy of science, yes, but we do have some measures—we put it to the test and check. And we see that it works, so we have some measures, and that gives some reinforcement to the synthetic thesis that says yes, intuition is also a tool. It’s not certain; science can make mistakes; scientific theories failed in the past and probably will continue to fail. But yes, it does give us some possibility of making progress. Now, here I could expand more, but I don’t want to right now because we don’t have time, I want to…

[Speaker A] But Miki, isn’t part of the problem again just the language a bit? Meaning, if one tries to use… after all, the fact that science can’t work on the basis of pure logic, we already know anyway from more basic things of… No, but that’s what I’m saying—after all, even if you see that the sun rises one more day and another day, no matter how many days, it still won’t help you, so in any case you can’t. So from the moment we understood that, meaning, maybe this is again just another kind of… basically what’s happening here is prior and posterior. I have a prior about the explanations, and then I made observations, and the observations caused my posteriors, each part of them—they added something.

[Rabbi Michael Abraham] But again, the question is whether that prior is an arbitrary prior, or whether that prior is what I earlier called intuition, which in my view is a tool for reaching truth—not with certainty, but it has some indication of reaching truth. That’s the question in the dispute here.

[Speaker A] No, but the statement that from any prior whatsoever, given that now you start using indications from reality, little by little your posterior will move closer to the truth—that’s a true claim. You can say that if you started from a prior that was really uniform over all the possibilities in the world it would take me almost an infinite amount of time, but still this… there’s no argument here. The scientific method works. Start from some prior and do… it’s exactly like… from any prior. I don’t agree that from any prior. It’ll just take an infinite amount of time. But it will happen. No, no, not infinite. A huge, huge amount—not infinite, yes. But it’s not really infinite, it’s a huge, huge amount but not infinite. No, infinite. Infinite because it would take infinite time, so it’s not really… No, infinite because… because… depends how you define uniform, yes? It’s a continuous space, blah blah blah, whatever. But it’s a bit like an optimization problem. It doesn’t matter where you started; start farther from the center, it’ll take you more steps, but in the end you’ll always get there.

[Rabbi Michael Abraham] I’ll make one more remark that I didn’t intend to get into because it touches on… yes, artificial intelligence or things of that sort. Basically there’s some feeling—at least for me, or for AI people too, I think—there’s some feeling that this is basically how it works. You start from any prior, right? And little by little, more examples and more examples, and in the end after some amount of time, maybe long, you reach the right result. I think there’s a mistake here. And correct me if I’m wrong because maybe I don’t understand artificial intelligence well enough, but in my view that’s a mistake. Because artificial intelligence itself has more human input in it. It’s not a technical process. For example, you tell it—let me give you an example. Wait. I’ll share… wait, what is it doing here?

[Speaker E] Wait, in the meantime while you’re looking, I haven’t heard Yossi’s voice at all today.

[Speaker H] Hear my voice—I wanted to comment. I remember a numerical analysis course I studied with you, Miki, of Schild, Hub Schild. Yes.

[Rabbi Michael Abraham] He always—

[Speaker H] told us that before you approach all the calculations and so on, it’s worthwhile to have a very good idea of roughly where the answer should fall. Because these calculations can run away very quickly.

[Rabbi Michael Abraham] So you—

[Speaker H] really need to know very well what neighborhood you ought to be in before you even start. And that was something he drilled into us again and again and again in his course. Ah. Good,

[Rabbi Michael Abraham] that fits exactly what I’m arguing. Exactly. Wait, what is it doing here? Okay, here my extraordinary abilities at pressing the above-mentioned buttons come into expression. Ah, here. Okay, I found the button. Here, look at this. Let’s say I’m measuring force versus acceleration. Okay? Newton’s second law, that force equals mass times acceleration. Meaning the mass is the slope of this graph. Okay? So now I made five measurements; look at the empty circles. One, two, three, four, five. Now I want to know: what is the general law? Right? The most trivial AI problem, basically, or least squares even before they invented AI. I want to know what the general law is. Now of course the general law could be a straight line, and everyone would bet on that because it sits on a straight line, but of course it could also be this. Right? It could also be this dotted line, and infinitely many other lines. Now the question is, why do I choose the straight line? Because it seems simple to me. Right? It seems to me the simple line. But in principle it could have been any line whatsoever. Right? In deciding that the straight line is simpler, that’s because to me it seems simpler. If you want, because it has fewer parameters, let’s say. Simplicity can be defined in many, many ways. And now I ask whether the AI, if you give it as many examples as you want, the assumption is that in the end it will arrive at the straight line. It will rule out all the other possibilities. But it seems to me—and here the AI people can correct me, yes, especially Moshe I think is here—I don’t think that’s necessarily true. Meaning it’s true if I tell it that you formulate the least-squares relative to the correct straight line. Meaning you put into it that the straight line is the simplest. If you put something else into it, it will arrive at some other generalization. It’ll do some very wavy sine-like thing that passes through all the points. Am I right?

[Speaker A] Yes and no. Okay. The classical theory said that you’re right. It said that if we want, basically—there’s really a phase transition that happens around 2016. It’s connected to what Shuki said about double descent. Basically, even before the new machine learning generation, we knew that if I want to move to what’s called an over-parameterized space, where I have more parameters than points and therefore I have infinitely many explanations, I have to add regularization. Regularization is that prior. I can actually model regularization as a prior and say I’m basically saying that models like these are more likely than those, and then I’m allowed to hold infinitely many models—infinite not only in number but also in richness—and the algorithm will find the model that in a certain sense minimizes, maximizes the posterior, which means it’ll say: somehow I’ll balance between looking for the model that explains the data best and on the other hand is least surprising. So for example, if the data fit a parabola, then it will prefer something that is a parabola over a linear model because the gap in explaining the points would be very large, but it will prefer the parabola over a third-, fourth-, and fifth-degree polynomial even if they explain the data a bit better, because it knows that degree two is more likely than degree three, and so on. That’s what we said for years. And then empirically we discover that this is not the case. It chooses a model that isn’t too complicated even though it has infinitely many possible explanations, including very complicated explanations, and therefore it succeeds in generalizing. Why? We have no idea—that’s the only honest answer. We have several families of explanations; the terms people commonly use for this are sometimes implicit bias or implicit generalization. That our type of optimization model, stochastic gradient descent, we assume for some reason prioritizes such solutions implicitly—not because we tell it that, but because the very form of this optimization prioritizes them.

[Rabbi Michael Abraham] It doesn’t matter—you tell it that through the form of—

[Speaker A] the optimization, you’re still telling it. Yes and no, because SGD is supposedly something objective, supposedly it’s not that we chose it, we didn’t say—meaning there’s nothing here like, if the world were such that the more complicated models were more correct, then we would invent a different optimization method.

[Rabbi Michael Abraham] We wouldn’t invent one because we’re human beings—that’s exactly the point. But our humanity enters through the optimization method; we didn’t know—

[Speaker A] that by means of this we were dictating to it. No, but this optimization method was supposedly chosen for—

[Rabbi Michael Abraham] objective reasons. Again, we didn’t know that when we put in an optimization method, we were actually dictating to it that the straight line is simpler than a parabola, but in fact we did do that, we just didn’t know it, we weren’t aware. So still, we put some bias into it by hand.

[Speaker A] That’s one way to say it, or the other way to say it is that there is something inherent in learning from data in general, independently of our mode of choice, that tries to maximize explanation under some minimization of information or something like that, and then there are various theories that claim there is something supposedly inherent—without our choice—every clean learning process from data will search for the simplest explanation according to some supposedly objective measure of simplicity.

[Rabbi Michael Abraham] What I’m smelling in your words, again, is of course similar to my prior, so that’s not much of a surprise. But I don’t—it’s hard for me to believe. Meaning, as long as I have an explanation that says this does somehow get put in by us, then whoever claims that it happens on its own bears the burden of proof.

[Speaker E] Meaning, I think it doesn’t happen on its own. It happens because… you know, it’s very interesting, because exactly—we don’t have time—but I think that these LLM models do exactly perform non-deductive inferences on the basis of some system that we still don’t understand what it is, but it does have some kind of systematicity that maximizes the probabilities of being right.

[Rabbi Michael Abraham] No, so that’s exactly the claim.

[Speaker E] That’s exactly what I’m claiming. Wait, yes, and then the reason it chooses the simple one is because… no one told it to choose simple, but from the collection of its interactions with human beings it extracted that human beings prefer simple.

[Rabbi Michael Abraham] And that’s what I said to Moshe earlier, that somehow even if we didn’t do it for that reason, it somehow came from us.

[Speaker A] Wait, but be careful not to mix up machine learning and LLMs. LLMs are… no, because the phenomenon I was just… Amnon, you’re talking about the fact that it read texts that human beings… that’s a property that characterizes LLMs. The phenomenon I was talking about also exists in an algorithm that looks at images in the world and learns to identify cats. So these are supposedly objective things. I’m talking about training,

[Rabbi Michael Abraham] but I’m saying either way…

[Speaker E] No, but images in the world too—even cats can convey a simple message. It’s like once in high school, I remember, we had some… I had a great teacher, David Gordon, in high school for mathematics, who later was head of the pedagogical administration in the Ministry of… he was a professor at Ben-Gurion University and came, out of Zionist reasons, to be a teacher for us in high school in Katamonim in Jerusalem. So once he gave us some exercise to prove some proof and all that, and I proved it. Then someone in the class… and this… and then he said some sentence, I don’t know, Thales’ theorem or something like that. So someone in the class said, wait, what does it mean that Amnon understands geometry like Thales? So he said no. Because after someone… then someone in the class really argued with me… went back and forth with him… he said to him, but then what does that have to do with it? Amnon never heard someone teach him this. He said yes, but in the structure of the world there is already that thing Thales proved.

[Rabbi Michael Abraham] And there’s a little saying like this in Bnei Akiva activities. You know that Hannah and her seven sons, that myth about the woman… after she sends her youngest son to die last, she says to him, go up above and tell Abraham our forefather that he offered one child and I offered seven—and in the end he didn’t even offer him, he remained alive, whereas I slaughtered all seven. So the standard answer is: then why do we always remember Abraham our forefather and not her? Because after Abraham our forefather did it, then she… he had already brought that idea down into the world. Meaning, it was already here. Now she does it because it’s already here. He was the first to invent the idea. There is something in… it’s like in machine learning. Something that exists in the world is easier even if you haven’t heard of it explicitly. You’re stuck. Okay, in any event I see I already have to stop here, so we’ll spare you the formalist issue. I’ll just say that on the principled level, what the next stage was that I really wanted only to demonstrate, was to take various arguments of the type of a fortiori reasoning, analogy, induction, and try to formalize them in an orderly way, and at whatever level of complexity you want. By the way, I did this with Uri Schild too, among other things. And one really can formalize this issue of non-deductive thinking. That non-deductive thinking—analogy and induction and a fortiori reasoning, which is basically some sort of analogy—and try to show that there are systematic logical control mechanisms over soft arguments, not deductions, but soft arguments, which may perhaps calm me a little that I really am synthetic and not just some child fooling himself. Okay, but that’s just a declaration. That’s it.

[Speaker G] Thank you very much. Thank you all.

[Rabbi Michael Abraham] It was excellent.

[Speaker G] More power, Rabbi. Thank you all. Thank you, Rabbi.

[Speaker E] Thanks, bye, good evening everyone.

[Speaker G] See you, good night, bye bye. Okay, we’ll continue.

[Rabbi Michael Abraham] What we just heard here is a very honest voice, and it’s a voice that asks about the very authenticity of religious life. The concept of being synthetic is usually perceived by us as something negative, as a fake. But let’s try to look at it differently. This world was created incomplete. The Holy One, blessed be He, left us room to complete it. And everything we build, everything that is culture, everything that is Jewish law, is in a certain sense synthetic. It doesn’t grow on trees. So when a person says, “I am synthetic,” he is basically saying: I am a product of my own hands, of society, of education. And the answer is that this is true, but that doesn’t make it any less real. Truth is not only what we were born with, but also what we chose to become. Rabbi Kook speaks about this in Orot HaKodesh, when he distinguishes between nature and the refinement of nature. The Torah is not natural; it is above nature, and therefore it demands from us work that is supposedly artificial until it becomes second nature. Let’s now open the first chapter of Mesillat Yesharim and see how the Ramchal defines a person’s duty in his world, which is first of all a clarification of truth as against falseness. We will see that precisely through effort and action, which sometimes seem external, a person acquires his true spiritual possessions. It’s not that he is fooling himself, but that he is building an additional level on top of his raw personality. Faith is not only a spontaneous feeling, but a psychological stance that we choose to adopt and cultivate day by day.