Faith and Its Meaning – Lesson 3

[Rabbi Michael Abraham] In the previous times—previous times? Once, I think. Actually twice. We got to the point that this is about faith being a claim, a factual claim. A philosophical position with a factual claim from which halakhic / of Jewish law obligation is derived, or can be derived. And the question that really arises in light of that initial discussion is: how do we get there? Meaning, if my faith in God is a factual claim, then I need to ask myself, okay, so how do you come to hold that factual claim? How do you know that fact? In light of what we saw, then let’s say meditation probably won’t help much here, and neither will emotional persuasion of one kind or another, or experiences, not even education, at least in a certain sense. Because in the end we need to justify to ourselves, not necessarily to others, our holding of a factual claim. Meaning, you can’t justify the claim—I don’t know—that quantum theory is true by saying that I was educated to believe it, right? That won’t help at all. Unless I think that this education reflects something true—but then I’ll have to justify that too. Why do I think the education reflects something true? Therefore, by the same token, someone could also claim that yes, a pagan can also say that he was educated into the way he behaves. Does that constitute justification? I don’t think so. Every one of us was born somewhere and educated somewhere. There is no guarantee that precisely because I was born in a certain place, that must be the right place. The fact that I was born in a certain place doesn’t depend on me; it wasn’t my decision—if it was anyone’s decision at all. So to justify holding a factual claim by saying that I was born or raised somewhere seems to me completely absurd. By the way, this is a very common argument. I think it’s obvious that it’s completely absurd, but it’s so widespread. You ask a person why do you believe, why do you observe commandments, and he says: because that’s how I was educated, after all that’s what we were raised on. Meaning, this is an atheist. He’s a complete atheist. The only thing is, he does what he was educated to do, just like the pagan does what he was educated to do. So I think all these justifications, even though you hear them quite a bit, in the end don’t seem to me to be serious justifications. So the question is: how nevertheless do we reach this factual conclusion? What are the ways in which we can even look for it? On the principled level, it seems to me that we have two—two principal toolboxes we can try to use, or examine the possibility of using. One toolbox is the scientific, observational, empirical toolbox, and the second toolbox is the logical, philosophical, a priori toolbox—yes, something that is not the product of observation but of some sort of logical philosophical argument. Those are the two toolboxes. I don’t think there’s anything else. I think I mentioned all those funny sayings about being beyond reason and all that stuff—it doesn’t matter, it’s just empty chatter. Meaning, I don’t know, “where philosophy ends, faith begins,” or all sorts of nonsense of that type that various atheists use to justify to themselves why they’re nevertheless not atheists but believers. For mortals like me at least—and I assume most of the people sitting here are the same—we have those two toolboxes, no more. Meaning, either the logical-philosophical toolbox or the observational-scientific toolbox. Science—how do you arrive at scientific knowledge? You observe, you generalize, you do—fine—scientific procedures. So I can either use scientific tools or philosophical tools. Yes, philosophy is not science. Why isn’t it science? Because it doesn’t meet the criteria of science. You don’t arrive at it through observation, or at least not directly, and it doesn’t stand up to observational testing. Meaning, a philosophical position that can be tested in a lab and refuted or confirmed is not philosophical; it’s a scientific position. Okay? Meaning, philosophy is apparently some other toolbox; it’s not the scientific observational one. And therefore, right now I’m putting the principled possibilities on the table, and we’ll see how far they go. He calls it by another name for some reason. How do you classify it? Tell me how you classify it, and then I’ll tell you how I do. Think—what does Maimonides say? You look at His created and beautiful works and so on, and you arrive at a conclusion. So what is that? Observation, no? Looking is usually observation, right? So apparently here too we have an observational scientific toolbox. But it’s still one of these two; it’s not a third thing. Okay, I’ll sharpen the difference between these two toolboxes, if there even is one, but for now I’m putting them on the table in an initial way to establish a framework. The framework within which we’re searching is this framework—meaning one of these two toolboxes. So let’s first try beginning with the observational toolbox. In the observational toolbox, in the scientific toolbox, it’s hard to reach the conclusion that there is or isn’t a God. Meaning, in the simple sense this question cannot be decided by scientific tools. Why? Because I can’t offer you a scientific experiment that would confirm or refute the claim that God exists. If someone has thought of such an experiment, I invite him to contact me. I’ve been looking for a long time. No, I’m not saying this sarcastically. I don’t think there is one, but if someone has an idea, by all means—I’d really be happy to hear it. I mean it’s not a joke. I don’t think there is one, but I don’t know, maybe there are smarter people who do know. What do you do with them? No no, I’m willing to look at the Hebrew Bible (Tanakh) too. What will you learn from the Hebrew Bible (Tanakh)? Did it perform a scientific experiment? I’m not sure, because it’s not a reproducible experiment. What? Yes, but it won’t recur; given the same circumstances, it won’t necessarily happen again. Meaning, that’s why it isn’t reproducible in the scientific sense, where in any laboratory you can build the setup, so to speak, and do the experiment and see. You also don’t need to get all the way to Elijah on Mount Carmel. Moses spoke with the Holy One, blessed be He; Abraham our father. That’s an experiment in front of his audience, meaning he says: come and see. I understand—meaning not the interaction itself with the people sitting there. Okay, correct, but for me that’s not it; I wasn’t there. So the claim in the end is that with scientific tools it’s hard to make progress regarding this conclusion, but I’ll qualify that a bit. I’ll qualify it a bit because what Maimonides, whom you mentioned earlier, for example, says—he, for instance, argues this. The fact that Maimonides says it is not itself proof of anything; he could be wrong. Meaning, I’m not using Maimonides as an authority here. I’m simply drawing on what he said because I think in this case he wasn’t wrong. Maimonides basically says that if you observe the world, see the wondrous acts of the Holy One, blessed be He, you understand that there’s something behind it. Okay? Let’s call it the physico-theological proof, perhaps later on in Kant’s terminology. And what is that? So I said before that it looks like something that belongs to the scientific observational toolbox, right? You look at the world, and from that you infer the conclusion. Now why is that not exact—or why do I not think it’s correct to characterize this as scientific? Because in the end you can’t submit this thesis to a falsification test, right? Popper’s criterion for a scientific theory is a theory that can be subjected to a falsification test. Meaning, propose an experiment: if the experiment comes out this way then the theory is refuted, and if it comes out differently then it’s confirmed, or I don’t know, or remains neutral. So I don’t think you can propose an experiment that does that scientific job. But on the other hand, there is indeed a scientific dimension here. There’s a scientific dimension in the sense that I infer conclusions from observation. True, I can’t subject the conclusion to a falsification test, okay? But on the other hand, I reached the conclusion by means of observations—facts that I observed—and the analysis, or what I think they mean. In that sense it does resemble a scientific approach. Okay? Meaning, that’s an important point, because it does belong to the observational toolbox, though not necessarily to the scientific toolbox. By the way, there are many observations we make that we wouldn’t classify as science, but they’re still observations. I don’t know—a shoemaker who accumulates some kind of experience about how to repair shoes most efficiently. Okay? I don’t think anyone would call that a scientific field, but it’s an accumulation of observational information—meaning, based on facts, experience, examining the world, it’s basically the accumulation of observational knowledge, right? Now more than that, he also doesn’t really have theses that can stand a falsification test—probably at least not precisely. Fine, but he still learned them by looking at the world. In that sense, this belongs to the observational toolbox, even if not to the scientific toolbox. Let me sharpen this a bit more. Let’s think about another ordinary scientific law—the law of gravitation. Okay? You know, my sister studied criminology many years ago, studied criminology here, and she told me that in almost every course there would come a moment when the lecturer would say: let’s take as an example the theory—and then think for a moment and say: say, the connection between frustration and aggression. And it was always the connection between frustration and aggression. They’d think for a few minutes as if choosing among the hundreds of theories they have, and in the end it was always frustration and aggression, there was nothing else. So here too I tend to use gravitation a lot, because it’s a simple and familiar theory, but in physics there are also a few other theories, and in biology and in the natural sciences too. What? No no, don’t drag me into that discussion now. Fine, anyway, there can be aggression without frustration, there can be frustration without aggression, there can be anything. In the social sciences too, a law in the social sciences has to be taken as such. Fine, anyway, the claim is that when we look at an ordinary law of nature—yes, that definitely belongs to the scientific world—the law of gravitation. How do we arrive at the law of gravitation? We observe the world. We see, say, I let go of this thing—whoop, it falls. Now I take this, it also falls. And this also falls. So apparently all objects with mass fall toward the earth, or attract one another if you want a more general formulation. Okay, that’s usually how a scientific law works. From that point on, the formulation I’ve reached stands the test of falsification. Right? Now I propose a hypothesis, which is a generalization of the facts I observed. That hypothesis says that any two bodies with mass attract one another. That can be submitted to a falsification test: I take two bodies and see whether they attract or don’t attract. Okay? The first part of this process—the arrival at the theory—is of course flesh of the flesh of the scientific process—sorry, of the scientific procedure. The product of this process, the hypothesis, is scientific because it can be subjected to a falsification test. But the way you arrive at the hypothesis is by generalization from observations. Okay? Right? Now that is exactly what we do in the theological context, let’s call it that, or at least according to Maimonides’ recommendation. Look at the world, see that it is complex; a complex thing does not come into being on its own; therefore apparently it has a creator. That is a scientific generalization in every respect; it is a scientific conclusion. True, the product cannot be subjected to a falsification test. Take a thing

[Speaker D] that is complex and seems to have no creator, for example.

[Rabbi Michael Abraham] Try doing it without an example—give me something concrete, a concrete experiment. I don’t think you’ll succeed. How will you find that it has no creator? I mean, once you see something complex, I assume that even if you don’t find the creator, I’ll tell you: there certainly was one, we just haven’t found him yet. It’s like when I once asked physics students in mechanics whether the law two plus three equals five is a scientific theory. Okay? According to Popper’s criterion, then, we need to check whether it can be subjected to a falsification test. Can it? What do you say? Here, I’ll propose a test for you. We’ll take a basket, put two walnuts into it. There were three walnuts, yes, like the well-known story. We’ll put two walnuts into it, then I’ll add another three walnuts, and I’ll count how many I have altogether. If it comes out minus pi, then the theory two plus three equals five has been refuted, right? If it comes out five, then it has been confirmed. Okay? So there you go—then the theory two plus three equals five is a scientific theory, no? Why not? That’s how we defined it. What do you mean?

[Speaker C] Two plus three equals five.

[Rabbi Michael Abraham] No, I didn’t define it—I’m making a claim, and now I can refute it. Take two, add three, see whether you get five. What? Why is that a definition? It’s a claim. Let’s do a thought experiment, okay? That’s what physicists always do when you can’t do an actual experiment—they do a thought experiment. What does that mean? Let’s assume we got minus pi. Okay? We counted the walnuts and got minus pi. Okay? What’s the conclusion? Of course not. The conclusion is that there was a mistake in the experiment. Yes—or that minus pi equals five exactly. Right. Nobody would conclude that two plus three does not equal five, admit it. Why not? Because it’s obvious to us that two plus three equals five. Clearly there was some mistake in the experiment; we’re not really subjecting that to a falsification test. It’s a façade, okay? No one is truly prepared to give up the theory that two plus three equals five. And why not? Because it really is the result of definitions and so on, what you said before—and those are already the explanations. But suppose—think even further. Let’s say it really did come out to minus pi and I found no mistake in the experiment, and you know what? The result is minus pi. I’m convinced. Have I refuted the arithmetic claim that two plus three equals five? The answer is no. I have refuted the scientific claim that adding walnuts into a basket is described by arithmetic addition. Right? Two plus three clearly equals five. Arithmetic is not what’s being tested here. At most I can say that the way to describe adding walnuts into a basket is not by arithmetic addition. Apparently it’s something else. Okay? That’s all. But I will never give up the fact that two plus three equals five. The arithmetic claim is not really standing a falsification test. No, it doesn’t matter—base ten, don’t complicate things for me now. So base six then, fine? Up to six and above. So the claim I’m trying to make is that mathematics is not really subject to a falsification test. If I refute it, all I’ve done is refute the assumption that this mathematics applies to the situation I examined in the experiment. And that assumption is an assumption in physics, not in mathematics. Because the assumption in physics says that this mathematics is appropriate for describing this situation. That is the claim I refuted—not the claim that two plus three equals five. Now what

[Speaker D] about the computer, the animation computer, right? It’s the marker, the animation computer.

[Rabbi Michael Abraham] No no no, that’s not the same claim.

[Speaker D] I’ll explain. Suppose we ran an experiment: I take a room, seal it so no one can enter, take materials of iron and whatever else, and after fifty years, having checked that nobody touched it, there was a watch there. A watch came into being there. Then I would say, okay, I have an experiment here showing that a complex thing can come into being.

[Rabbi Michael Abraham] No no, you’re already taking me to the analogy; I’m not there yet. Yes, we’ll get to that argument. It can be refuted.

[Speaker D] If a watch came into being there, then what we believed—that the way to prove that something complex requires a creator—let’s take something complex and no creator.

[Rabbi Michael Abraham] So then what? Then we’ve refuted it. Unless you just didn’t find the creator. What do you mean? That’s what I answered you before—didn’t you see what was new compared to the previous claim?

[Speaker D] That I knew no creator entered there.

[Rabbi Michael Abraham] How do you know? Here—you’ve refuted this piece of knowledge, not that one. You still have another assumption here, right? Maybe that’s what you refuted. What assumption? That nothing entered here. I checked, I checked. You checked? So what if you checked? You checked and still didn’t catch it. It was an invisible demon. Some heavenly jug slipped in there without anyone seeing it. The question is what you choose to give up. You have to give up something that you know. Fine, so leave it—that’s not it. So the point is that what I really want to say, and why I asked this of students in mechanics, is that in mechanics I told them: come, I’ll refute for you the claim that five plus five equals ten. In the lab, okay? Let’s take a body, apply to it a force of five newtons northward, plus a force of five newtons westward. What’s the total force acting on it? Five root two, the resultant magnitude, okay? Because that’s vector addition. Did I refute the claim that five plus five equals ten? No. What did I refute? I refuted the assumption—which is an assumption in physics, not in mathematics—that adding forces can be described by arithmetic addition. That’s not true; it has to be described by vector addition. Okay? The relevant mathematical framework here is not arithmetic but vectors, vector calculus. Okay? So you see that when I refute something by experiment, it is never the mathematics of the matter. In mathematics you can find a mistake in a proof, but you can’t refute something whose proof is sound. When you refute something in the lab, you are always refuting an assumption in physics, not an assumption in mathematics—some scientific assumption, okay?

Now I’ll say more than that. When I made the observations, I saw that this falls to the earth, and this falls to the earth, and this too. I reached the conclusion that all bodies with mass fall to the earth. That conclusion, which I reached on the basis of a collection of observations, is a generalization, right? I generalize from several observations and make a general claim about all bodies with mass. What is the justification for that? Hume’s problem of induction. What is the justification for that? Understand that this is not an observational procedure, right? It does not come out of observation. From observation I have the collection of facts, what I saw. Okay? The move from the collection of facts to the general law is not an empirical step. It’s a step we might call intellectual, right? It’s a step of thought, not of observation. Okay? Meaning that even in the scientific process, it is not correct to think—as the positivists thought—that in science we rely only on observation. Obviously not. Observation is the initial infrastructure. After you have observations, intellectual steps come in. Meaning, a scientific theory is not a record of a collection of observations.

Think of the example people bring—say Carl Hempel, a philosopher of science, also a well-known philosopher of science. He gives the example of refuting a scientific theory, yes, Popper’s principle. He says: all ravens are black. Yes, I think that’s his example—maybe it’s actually Popper himself, because with him there’s the paradox of the ravens, so maybe it’s Popper himself. All ravens are black. Okay? Now, I can’t prove that theory, right? There could always be some raven I haven’t seen. But I can refute it. If I find one raven that is pink, or not black, then I have refuted that theory. That’s the asymmetry between proof and refutation.

What happens if I enclose the whole universe in a net, like you suggested earlier, and I go over it centimeter by centimeter, over all the ravens, and I manage to check them all and document them, yes? I found that all the ravens really are black. Have I proved the theory? Why? Okay, but the theory about ravens now, let’s say, is fine, right? But then it’s not a theory. It’s just a collection of facts. I observed all the facts. A scientific theory, by definition, always has some speculative dimension. It always claims something beyond what I observed. It never merely records the set of facts that I observed. I can record the set of facts that I observed; that will simply be a collection of facts. The moment it becomes a theory, it always makes some claim beyond the collection of facts that I observed.

And therefore I argue that essentially, a theory is not a collection of facts. It’s a mistake to think that way—or a collection of observations. No. A theory is created from a collection of observations, but after those observations I take steps of generalization, steps of analysis, various intellectual steps, and I arrive at the scientific conclusion, the general scientific law. A scientific law is always general. Observations are always particular; they are always specific. The move from observations to law is not a move that involves observation; it is not an observational procedure, but a conceptual one. Okay?

So that means that even when I speak of the observational-scientific toolbox, the empirical-scientific toolbox, it’s a bit naive to think that we are talking there about observations alone. It’s not observations alone. Even in science people think that empiricism—yes, there are naive empiricists, or positivists, who think that the difference between science and philosophy is that science is built on observation and philosophy isn’t. That’s not true. Science is built on observations plus assumptions or philosophical principles that I bring from home. There are lots of those in the scientific process. And those I do not derive from observation—the principles themselves. Some of them I bring from home, and some of them are themselves generalizations from previous observations. Okay? Therefore, when I speak about the scientific-observational toolbox, it is not correct to identify it with observation pure and simple, only observation. There is generalization on the basis of observations.

Why am I saying this? Because now if I go back again to Maimonides’ formulation there in the Laws of the Foundations of the Torah, Maimonides says: “What is the path to loving Him and fearing Him?” and so on—“one contemplates His wondrous deeds.” By the way, that is about loving and fearing Him, not necessarily knowing Him. In the Laws of Idolatry he speaks about how one arrives at knowing Him. Yes—Abraham our forefather, who looked around and asked who turns the sphere, and so on. So that path that says: I observe the world—for example, I see that it is complex, or I don’t know, there can’t be nothing that created it or operates it, doesn’t matter, there are different formulations—that path is an observational-scientific path. It is not observation in the narrow sense. It’s not that I observe and see that the Holy One, blessed be He, is there. I don’t. The Holy One, blessed be He, is the theory that explains what I observe—what I am observing. All right? And in science too, that’s how it is. In science too, the theory is only an explanation for the facts that I observed. The scientific theory is not a fact that came out of observation. It is something based on observations. But after the observations I still make some intellectual moves—deductions, generalizations, things like that.

In that sense, this particular way of arriving at the existence of God is a scientific path—still with the reservation I mentioned earlier, that you cannot submit the result to a test of refutation. The result “all ravens are black” or the result of the law of gravity can be subjected to a test of refutation. I arrived at it in exactly the same way: I made a collection of observations and by generalization arrived at a general law. But that law is not the end of the road; now I put it to tests and check whether it is refuted or not, whether I can manage to refute it or not. Okay, that I cannot do with respect to the existence of God. But the path to arriving at the conclusion that He exists can still belong to the observational-scientific toolbox, okay? That’s on the one hand.

Let’s move to the second toolbox, the logical-philosophical toolbox, the a priori toolbox, yes—the toolbox that does not require observations but makes inferences. Here there are several a priori problems. Meaning, even before I present a particular argument—why can there not be, in principle, an a priori non-scientific path to arrive at the existence of God without observations? Why not?

I’ll formulate it this way. Mark Twain once said that the world owes you nothing; it was here before you. Fine. The fact that you think something does not say anything about what happens in the world. I can think something because that’s how my mind is built, or my brain, or my intellect—that’s how they’re built. That is not an indication of what really happens in the world, unless there is some claim that my cognitive structure fits the world in some way—and then of course I’ll ask: how do you know that? Okay, we’ll get back to observation, so we’re back in the observational toolbox.

And if I want to work without observations, in a purely philosophical way, that sounds impossible, because even if I reach the conclusion that there is a God from whatever considerations I have, why does the world or reality owe me anything? That’s what comes out of my cognitive or intellectual structure—so what? That’s how I was created, okay—what does that have to do with anything? Why should that say anything about the world? Okay?

That is why Aristotle thought that bodies fall to the earth at a speed proportional to their weight, their mass. Okay? Now, you don’t need a particle accelerator to check that this is wrong. Go up to some place ten meters high, say, drop a pebble and a large rock, and you’ll see that they reach the ground more or less together. With air resistance there’ll be some difference; I don’t think he would have been able to notice it. So he didn’t bother to do that experiment. Why? Because to him it was self-evident, obviously true: if it’s heavier, then it falls faster, no? It’s very logical. And that’s a nice example of this point, an example that empiricists really like in order to show that the world owes us nothing. Meaning, the fact that we are used to thinking in a certain way, or that something seems very logical to us, does not bind the world. The world behaves however it behaves, not necessarily according to the patterns that fit the way we are used to thinking.

Therefore, the path of philosophical inference is problematic when trying to infer a factual conclusion about the world. And again I remind you: my starting point is that faith in God is a factual claim. I am making a claim about the world: there is a God. And that is where this whole journey begins that I am trying to set in motion now: okay, so how do I get to that fact? Meaning, if it were not a fact but an experience, an emotion, or everything I ruled out in previous sessions—fine, how do I get to an emotion? I have an emotion—what does it mean, how do I get to it? But if I claim that faith is a factual claim, then I have to find ways of arriving at that fact, ways of justifying it.

We may arrive at something transcendent, I don’t know, whatever it may be—something beyond our reality, perhaps, that created the world. We’ll talk more about the different definitions. Maybe I’ll already say now: we are going to survey several ways of arriving at faith in God, to the existence of God. Every such path arrives at a different God, a different deity. Every such path really has to define the concept it is seeking and then prove its existence. And we’ll see that each path defines a different object. Therefore, when we speak of proofs for the existence of God, we have to define for ourselves who this God is, or what this object is whose existence we are trying to prove. And you’ll see that each path proves the existence of a different object, if one accepts it. Whether one accepts it or not is another story, but even if one accepts it, it proves the existence of a different object. And then we are left asking ourselves: okay, so maybe this leads to polytheism? To a multiplicity of gods. I don’t know—what kind of proof is that? What proof do you have that the statue is a god? I don’t understand. I don’t know. Say, if the proof is scientific then it can be refuted; if not, then not.

[Speaker D] That this statue created the world?

[Rabbi Michael Abraham] Okay. No, apparently not. No, as far as I’m concerned, this statue is a good answer to what I’m saying. At the moment I still haven’t said anything about the God I’m looking for. As far as I’m concerned, the statue is also a candidate. But that’s not… So the situation is this. Notice. The scientific toolbox, or the purely observational toolbox, certainly cannot do the job, right? You can’t observe the fact that God exists as a simple observational fact. So the observational toolbox does not do the job. But I did say, yes, that the scientific toolbox is not just observations, right? It does some work beyond the collection of observations—generalizations, conceptual analysis, whatever, theoretical construction, what is usually called abduction. Not induction as generalization to a general case, but abduction: building a theory that explains the facts I observed.

Okay, but that procedure is an intellectual one, not an observational one. And that takes me back to the philosophical side. Okay, and then I ask myself: fine, so if the observational toolbox alone can’t do it, I also have to use philosophical principles. Let’s see whether philosophical principles can do the job at all. We came to the conclusion that they cannot. Because the fact that I am used to thinking in a certain way says nothing about what happens in the world itself. Only observations can give me what happens in the world itself. Right? The fact that I think in a certain way—so what? So if that’s the case, then we basically fall between the chairs. The philosophical toolbox does not do the job, and therefore the observational toolbox also… the observational toolbox certainly does not do the job. The scientific toolbox is only a combination of observations plus philosophy. So if observations don’t do the job and philosophy doesn’t do the job, then apparently science also cannot do the job. So what can? That there is no way at all to arrive at… yes? That’s the broken trough. We have no way of arriving at this factual claim.

Okay. I’ll just say parenthetically that I could have asked exactly the same question about any scientific theory. Exactly the same thing. How can I arrive at a scientific theory? The fact that I make observations does not give me the theory, right? I still need to make generalizations or some intellectual processing. But the intellectual dimension, or philosophy, does not help me know the world either. So the same question could be asked about every scientific theory. This is Hume’s problem of induction, yes? How can we believe something that is the product of our own generalization? The fact that we generalize in a certain way—so what? Who says it’s true? Because that’s how we are built. We generalize like that because that’s how we’re used to thinking. Who says it’s true? What?

Okay, so you’re actually proposing an interesting solution to Hume’s problem of induction. You solve it by induction. Right? You’re basically saying: since induction has worked until now, why shouldn’t it keep working? That’s a bit problematic. I don’t know what probability means here. If you do not accept induction, then this argument won’t help you either. If you accept that induction is a reasonable thing, then you don’t need the justification; there is no problem. If you need the justification, that means you do not accept the process of induction as such, so how are you going to use induction in order to justify itself? It won’t help.

In short, this problem is really a problem that attacks our entire ability to know things about the world, aside from particular facts that we directly observed. But any general claim about the world—any claim that is not exposed to our sensory observational tools, yes, to our direct observation—is really a claim that can be attacked in the same way. If you want to go even further, then of course direct observations can be attacked this way too. Who says that what I see is really there? Maybe yes, maybe no. I assume that if I see something, then presumably it reflects something happening in the world itself. Okay, that’s how I’m used to thinking. But as we said, the world owes me nothing. So who says? If there is even such a world. If there isn’t, then it surely owes me nothing. So that claim won’t help us in the scientific context either.

So you have to understand that this skeptical picture that I presented here, which seemingly leaves us facing a broken trough when we come to prove the existence of God, really leaves us facing a much broader broken trough. Not only the question of God, but any claim that is not the product of direct observation—we can ask what the justification is for it, for our trust in it. Okay?

I’ll perhaps bring another claim, or another angle, to show this point. Look, a philosophical argument or a logical argument is a very problematic tool for learning things about the world. Why? Because a logical argument never adds information. Yes, you cannot accumulate information by logical means. That’s a theorem. Okay? Let me demonstrate it—not prove it, demonstrate it. Okay? This is not a theorem in mathematics; it is a theorem in physics. You can’t prove it, you can demonstrate it.

I’ll start, of course, with Abraham our forefather and the hat. Some of you may already have read this from me; I’ve used it quite a bit. Yes, the well-known yeshiva joke: what is the proof that every Jew has to walk around with a hat? Simple proof. It says, “And Abraham went,” right? There, there. A Jew like him surely didn’t go without a hat, yes, you understand. So if Abraham went with a hat, then we, his faithful descendants who walk in his ways, certainly also have to go with a hat. Which is what was to be proved. What do you say about this proof? In yeshivas this is accepted as a joke, but I’m not sure it’s a joke—tell me what you think. What do you say?

Right, it begs the question. There’s something problematic here because it assumes what it is trying to prove. What does that mean? When I formulated the argument that led me to the conclusion, I smuggled the conclusion into it as one of the premises. Let’s go over it again. It says, “And Abraham went.” Fine, that’s written; I know that. But a Jew like him surely didn’t go without a hat. Right? That was the next step. Why didn’t a Jew like him go without a hat? Because every Jew has to go with a hat. Because every Jew has to go with a hat. Right? A Jew like him surely didn’t go without a hat. Okay? In a minute you’ll tell me that he also enlisted in the army, God forbid. So what does that mean? He didn’t enlist; he took his 318 men, yes, and went on his own. The Haredi brigade.

So the claim is that you have actually inserted the conclusion into the argument as one of the pillars on which you built the argument, right? Without assuming the conclusion—that every Jew has to go with a hat—you would not have been able to follow the path that the argument leads you down. Okay? In other words, the proof that every Jew has to go with a hat contains within it the premise that every Jew has to go with a hat. That is called begging the question.

Okay. Now that’s the first step. The second step—which seems simple to me, but for some reason people are always terribly surprised when they hear it—is that there is nothing wrong with begging the question. Begging the question is not a fallacy, contrary to what you’ll see at the beginning of every logic book. It’s just confusion on the part of the authors. Begging the question is not a fallacy. Begging the question is a synonym for a valid logical argument. Every valid logical argument begs the question.

Let’s take a logical argument that has already become tiresome to those who studied philosophy or logic: all human beings are mortal, Socrates is a human being, therefore Socrates is mortal. Now you ask yourself: why must someone who accepts the two premises necessarily accept the conclusion? Right? That’s the meaning of a valid logical argument. Someone who accepts the two premises—“all human beings are mortal,” “Socrates is a human being”—those are the two premises. Conclusion: Socrates is mortal. There is no such thing as someone who accepts the two premises and does not accept the conclusion, right?

If some alien came from who knows where, came to earth, and they told him: peace be upon you, know that there is some kollel fellow here named Socrates. All human beings are mortal, and Socrates is one of them, therefore Socrates too is mortal—catch him quickly before he fulfills his mortality. Yes, try to meet him. And he says: okay, I understand that all human beings are mortal. I don’t know this planet, so I trust your word. I also understand that Socrates is one of these strange creatures you call human beings. But why do I have to accept that he is mortal? So asks him, yes, the Little Prince. If he asks me that, what am I supposed to answer him? He accepts the two premises, but okay—why should he accept the conclusion?

The first stage, of course, is hospitalization. Yes? There’s nothing to answer him; only hospitalization. But if I still ask myself what I would answer, like the students of Rabbi Yohanan—“and what do you say to us?” The point is that it’s not that according to some law, if you assume those two premises you must also accept the conclusion. The conclusion is simply contained within them. It’s a shorthand formulation for the following claim: Moshe is mortal, Yankele is mortal, Socrates is mortal, Ahmad is mortal, and Sinwar is mortal too—or was mortal. Okay? Everyone, right? The abbreviation of that whole collection is that we simply say, in short: all human beings are mortal.

Second premise: Socrates is one of those objects regarding whom we made the shorthand earlier. Okay? Meaning, when I say “all human beings are mortal,” I have assumed here many billions of premises about each individual human being being mortal; I just said it briefly. Okay? So you understand that someone who accepts the two premises—that Socrates is a human being and that all human beings are mortal—cannot fail to accept the conclusion that Socrates is mortal. Why not? Not because the law forbids it, but because he accepted it as part of the premises. Meaning, if you accepted the premises, then you have already accepted the conclusion. Okay?

So in other words, this argument is valid. Valid means: if you accept the premises, you must accept the conclusion. Why? Because there is nothing in the conclusion that was not already in the premises—or in other words, because it begs the question. And that is the meaning of a valid argument, understand. When you say that an argument is valid, you have said in other words that this argument begs the question; otherwise it would not be valid. What is a valid argument? It means that if you have the premises, you must accept. Why must I? I must because the conclusion is somehow swallowed up within the premises. Sometimes in a very sophisticated way, but it is there somehow, and therefore if you accepted the premises you cannot fail to accept the conclusion. That is the meaning of a valid argument. Or in other words, a valid argument always begs the question. That is what the phrase “valid argument” means. It is not a fallacy.

Sometimes there are stupid cases of begging the question, like with Abraham our forefather and the hat, and that’s why it’s funny. Why? Because to prove that if every Jew has to wear a hat, then the conclusion is that every Jew has to wear a hat—that implication, p implies p, is indeed valid. It’s just trivial; you didn’t add anything. Okay? So why is that interesting?

More than that: if you are trying to persuade me in a discussion between us—if you’re just presenting your own position, present whatever you like. But if you are trying to persuade me, and we have a disagreement over whether every Jew has to wear a hat or not, and you want to persuade me—then if we are arguing over whether every Jew has to wear a hat, you cannot build your argument against me on the premise that every Jew has to wear a hat, because that’s exactly the premise I am disputing. So it has no persuasive value. Not that it’s a fallacy—the argument is valid, the conclusion follows necessarily from the premises. Even with Abraham and the hat, by the way, the argument is completely valid. The argument p implies p is a valid argument; it’s a tautology. Okay? But it is worthless. It is worthless because you won’t persuade anyone with a valid argument. And actually that is always true.

If you assume that logic is not correct, I’d suggest not even saying this sentence—but certainly after that you can’t keep talking. Meaning, you’re just moving your lips; you haven’t said anything. Huh? Whether the conclusion is false or true? Of course. I’m talking only about entailment. Validity is only entailment. The conclusion can be true or false; that depends on the premises. The validity of an argument is only the derivation of the conclusion from the premises. Whether it is true or false is another discussion. I’ll get to that. I’ll get to that—it’s another very important point, and it will accompany us quite a bit.

Yes, once I heard this from Asa Kasher. I took some course with him at Tel Aviv University. I got seriously annoyed there, but never mind. One of the lines that I did adopt from there was this: what’s the difference between philosophy and theology? In philosophy you assume premises and derive a conclusion from them. In theology you assume a conclusion and derive premises from it—which is usually what really happens. Okay? Never mind—I later explained why that’s not really true, and I’ll explain it to you too, but that’ll come later.

In any case, for our purposes, what I really want to say is that a logical argument always begs the question. Yes? That’s the balloon joke. Two people lose their way in a hot-air balloon. For days they drift around with no idea where they are on the globe. They see some man plowing a field below the balloon. One of them shouts: tell us, where are we? So he looks up and says: above my field. So the guy up in the balloon says to his friend: the little fellow down there is a mathematician, for sure. Why? There are two main reasons. First, what he says is precise and absolutely certain. Second, it doesn’t help us at all.

Now beyond the laugh, there is something true here. Every joke has something true in it, otherwise it wouldn’t be funny. Mathematics is completely precise because it doesn’t help us at all. That’s the reason. What does it mean that it doesn’t help us at all? In the mathematical conclusion there is nothing that was not already swallowed up in the premises; otherwise there would be no proof, it would not be a valid argument. Mathematical proof is an argument. Okay? A valid argument means there is a proof for the conclusion on the basis of the premises. Right? Now, if I prove that conclusion on the basis of the premises, that means that the conclusion was already inside the premises. Or in other words, the argument didn’t help me at all, it didn’t add information. So why is it still useful to study mathematics, for those who think it is useful? Because sometimes it is hard for us to extract the conclusion from the premises and we need help.

Okay? When we study geometry—everyone studied that in high school, I hope, unless they’ve canceled that too already, I’m not keeping track—the conclusions, the theorems in geometry, were really swallowed up in the axioms. But I think very few students, and also very few adults, would manage to extract all the richness taught in a geometry course from the premises, even though it’s all there. But when the teacher shows me that this thing follows, they are not teaching me something new. They are merely helping me see how this conclusion is also contained within the premises. And that is also why it is so convincing—to those whom it convinces. Okay? Those whom it doesn’t convince simply didn’t understand.

So the point is that every proof, like every valid logical argument, cannot add information. They can only expose to me more and more information that I already possess. Why can that be useful? Only because sometimes it is difficult to extract that information from—yes, I have it locked in a safe. It is not always easy to crack that safe and reveal what is hidden inside it, but it is all in there. Meaning that in the end, what I need help with is cracking the safe in order to take out what is inside. That’s all. But in the very end, what I receive is what was mine from the outset, what was inside the safe from the outset. Okay? That is the meaning of a logical or philosophical argument.

And because of that, we basically have a problem with a proposed philosophical path for arriving at a factual claim. Because if there is a philosophical or logical path to arrive at this factual claim, that basically means that I hid this factual claim within the premises from which I started. Logic itself cannot add information; it simply reveals information embedded within the premises, information that was already embedded within my premises. Or in other words, a logical argument can at most reveal to you that you were always a believer. It can never take an atheist and persuade him to become a believer. That cannot be done with logical tools. You can take someone who, at the conscious level, thinks he is an atheist and show him that he is simply mistaken, that he does not understand himself correctly. He was really always a believer; he just didn’t know it, he wasn’t aware of it. Okay? That’s what a logical proof does.

So this basically means that I have no way to arrive at this factual claim. At most I have a way to expose the fact that I already hold it. That perhaps logic or philosophy can do. It cannot take someone who does not believe—who truly does not believe, not only implicitly but not at all, not even implicitly—and turn him into a believer. It is impossible to convert a heretic into a believer by logical means. That is impossible. It’s a theorem. No, you can’t do such a thing. At most you can reveal to him that he was always a believer, just not aware of it. That’s all.

So that means that the logical-philosophical route is not an option, the observational route is also not an option, and the scientific route is only a combination of the two. The whole is no greater than its parts—although there are counterexamples to that. What?

[Speaker D] Wait, two things. I connected them together—I said, notice that A is basically connected to B. Is that considered a logical argument, or is that considered something mathematical?

[Rabbi Michael Abraham] No, that’s a synthesis. A synthesis is— a logical argument is analytic. What you’re presenting here is a synthetic argument, with a synthesis of two things; it’s not an analysis. Let’s say that in Talmudic contexts—last year I spoke about this at length in one of the courses—I said that in passages in the Talmud there are two kinds of inference that look very similar, and they’re even presented in a very similar way. I called them a common denominator and conceptual construction. Very often there’s an argument—for example in the Talmud in Bava Kamma 6a, pit and fire—they derive there, through a common denominator, his stone, his knife, and his load that fell from the top of the roof and caused damage, and several other examples that appear there in the Talmud. Seemingly that’s a common denominator, and it’s presented there as a common denominator. It isn’t. At least according to some of the medieval authorities (Rishonim), it isn’t. It’s a conceptual construction. I’m actually making a synthesis between pit and fire, joining them together and producing from that a new primary category. A common denominator is an analytic process, not a synthetic one. A common denominator means: what is shared by pit and fire? There is some component that is common to both pit and fire, and that is actually what generates liability for the damages. And if that same component exists in the derivative case, then it too will be obligated to pay; we’ll also be obligated to pay for the derivative. That’s a common denominator. Just like the name says—a common denominator—that means the common side that exists in the two source cases, what they share. You see? That’s an analytic process. I analyze source A, analyze source B, and find what they share. In contrast, synthesis basically means I take one component from here, one component from there, join them, and produce something new. That’s a synthetic process, not an analytic one. Think, for example—the example is, maybe I’ll talk about this in the course on the categories of labor on the Sabbath. There’s something—I already noted it there, I think—there’s a very interesting phenomenon regarding Sabbath labors: unlike, say, primary categories of damage, in Sabbath labors there is no example of a derivative of two primary categories that is learned through a common denominator. Nowhere. Not in the medieval authorities (Rishonim), not in the Talmuds, not in rabbinic literature. What? No, obviously, that’s not a common denominator. Yes, obviously. The question is whether it’s a labor not needed for its own sake, fine, but that’s not a synthesis. In a moment I’ll bring one example that is a synthesis. Now, there is one example—only one example—I know of. And it’s from Rabbi Menashe of Ilya, a student of the Vilna Gaon. The Jerusalem Talmud writes—and this is brought as Jewish law in the Rema—that one who spits four cubits in the public domain is liable. Meaning it’s Torah-level; liable to stoning, a sin-offering, stoning if done intentionally, and so on. Now everyone discusses there: what does spitting mean? What’s the problem with spitting? So there are two versions there. One version says he is liable because of winnowing, and another version says he is liable because of throwing. What is winnowing? In winnowing I take the grain and the chaff, throw them into the wind, the wind blows away the chaff and the grain falls down. Right? So in effect I’m using the wind to carry out my action, so maybe spitting too uses the wind, so it’s like winnowing. That’s very strange. What does that have to do with winnowing? Winnowing is a labor of separating. Winnowing, selecting, and sifting—that’s all removing waste from food. Winnowing too is a process of separation. Spitting doesn’t separate anything. Fine, so the second option is throwing. What is throwing? Throwing means that if I throw something four cubits in the public domain, then one is liable likewise; it’s part of the labor of carrying, apparently a derivative of the labor of carrying. Okay, throwing four cubits in the public domain—so in spitting I’m basically spitting saliva four cubits in the public domain, so he is liable because of throwing. But that’s of course obvious, so there’s no need to say it; that’s clear. But Rabbi Menashe of Ilya says no, it’s a combination of winnowing and throwing. Or in other words, you could call it a common denominator. What does that mean? Winnowing teaches us that when I do the labor with the help of the wind, I’m not exempt, right? Meaning, even if the labor is done with the help of the wind, I’m liable. There’s a dispute between Rashi and the Rosh in Bava Kamma 60a, but it doesn’t matter why—whether that applies to all labors or only to winnowing—but it doesn’t matter; regarding winnowing at least that is agreed, okay? Spitting is a labor that tells me I’m moving something four cubits in the public domain. So it’s a derivative of carrying out. Okay? What happens if I throw, but my throw itself isn’t enough to move it four cubits in the public domain, and only thanks to the wind’s kindness does it go four cubits? Am I liable because of throwing? The answer is yes, says Rabbi Menashe of Ilya, because of winnowing. Winnowing teaches me that even if I make use of the wind, I still violate the labor of winnowing. Now notice: this looks like a common denominator. Winnowing and throwing together teach me about the case of spitting. But it isn’t a common denominator. There is nothing shared by winnowing and throwing, nothing. I didn’t use anything common to those two at all. What did I use? The opposite. I took a characteristic that exists in winnowing and not in throwing—namely the assistance of the wind. I took a characteristic of throwing that doesn’t exist in winnowing—namely moving something four cubits in the public domain, which is itself a labor. And now I join them, fuse them, and say: if I move something four cubits in the public domain with the help of the wind, I’m liable as well. You should understand that this is a synthetic process, not an analytic one. It’s not a necessary inference. You can accept both primary categories and still not accept the derivative. It’s not a logical deduction. Okay? That’s called conceptual construction. According to the Rosh, by the way, in Bava Kamma 6a as well, it’s the same structure. It’s fire and pit together; it’s not their common denominator, it’s the opposite. It’s taking a component of fire, a component of pit, gluing them together, and producing a derivative. There’s a dispute there among the Rosh and there are several views there. Fine, so that’s regarding what you asked about construction. Construction is a synthetic process. In short, for our purposes, what I want to say is that you might call this the philosophical principle of certainty. The philosophical principle of certainty basically says this: the level of certainty you have in an inference times the amount of information it adds is constant. Or in other words, the greater your certainty, the less information it adds. The less information you have, the greater your certainty, and vice versa. If it adds a lot of information, certainty decreases. If certainty is absolute, it adds no information at all. Okay? If it added all the information in the world, certainty would be zero. And there’s an interplay here, exactly like the uncertainty principle for those familiar with quantum theory. That is, there’s some kind of interplay here between two things, one at the expense of the other. Let me show you the illustration. In philosophy, in logic, they divide inferences into three kinds. There is deduction, induction, and analogy. Deduction is inference from the general to the particular. What I said earlier: all human beings are mortal, Socrates—who is one of the human beings—he too is a human being, right? Conclusion: Socrates is mortal. So I started from the general statement, all human beings are mortal, and the conclusion is one particular within that generality, that the general rule applies also to this one particular within the class. Okay? That’s inference from the general to the particular. That’s called deduction. Induction does the opposite process, right? From particulars to the general. Okay? Let’s say I saw this fall to the earth, I saw that fall to the earth; conclusion: all objects with mass fall to the earth. That’s induction. Not mathematical induction—I’m talking about scientific induction. Mathematical induction is deduction. Scientific induction means I take a few examples and create from them a general law. Analogy is from one particular to another. Say: this fell to the earth, this one also has mass, so probably this too will fall to the earth. This too is a marker, so this too falls to the earth. It’s moving from one particular to another. Or from one general class to another: all donkeys have four legs, so horses also have four legs. That’s moving from one generality to another, but it’s still analogy because we’re at the same level of integration. The general and the general are both separate, and I learn from one to the other. It’s like learning from one particular to another; just that here my particulars are groups, but never mind. Okay? So I basically have three ways of inference, and there are no others: either from the general to the particular, or from the particular to the general, or from particular to particular and general to general. Okay? Deduction, induction, and analogy. Deduction is necessary, right? If you accept the premises, you have to accept the conclusion. Induction and analogy are not, right? Now let’s think: which of these ways adds information? Deduction adds no information, right? If I knew the general rule, then that information about the particular is already included in what I knew. It didn’t add information. That’s why it’s certain: because it adds no information. Okay? Does analogy add information or not? It adds a little information, right? I say: if this fell to earth, then this too will fall to earth, right? Now my premise is that this falls to earth. The conclusion is that this will fall. The conclusion is not contained within the premise. In the conclusion there is information I did not have when I only knew the premises. So analogical inference adds information; therefore it isn’t necessary; therefore there may be an error here. Okay? Induction is the same: it too adds information, right? If this thing fell to earth and this one too, then all objects with mass fall to earth. I made an induction. Information was added, so the inference isn’t certain. Correct. The next question I wanted to ask: what do you say—which is stronger, analogy or induction? That sounds very decisive. What are the explanations? No, no, I didn’t test anything; on the contrary, in induction I’m not testing. I take examples, a few examples, and generalize them into a general law. Now I ask: what level of confidence can I place in the general law? How sure am I that it’s true? I used ten particulars—not many. A hundred, I used a hundred. A million. And I drew a conclusion about a billion objects. So okay, that’s better than analogy. Okay, and the other opinion? What I know here I project to all the— not to all, to another example. Not to all, no, on the contrary, to the same quantity. From one example to another example. That’s analogy. That what is true here, in this example, is also true in that example. Okay, so why is that better? You explained why it’s not good. I’m asking why it is good. It adds information beyond what I knew—that’s actually a reason to cast doubt on it. I’m asking why it’s stronger; you claim it’s stronger than induction. Look, the first intuition really says that analogy is stronger. Why? Because analogy adds only a little information, only about one particular. Induction adds a huge amount of information about an entire collection of particulars, right? What is more speculative adds more information; the level of certainty in it is lower, right? Because basically it can be refuted in many more ways. The risk of refutation is higher; it’s more speculative. So on the one hand it adds more information, but you pay for that in the currency of certainty. It’s less certain. By contrast, if I infer a conclusion about a single object—maybe I’m mistaken, maybe not—but I didn’t take many risks. Fifty-fifty, yes, as my wife says. Either it’s true or it’s not true, fifty-fifty, right? Induction, analogy—that’s what it is, as it were—analogy, induction into induction. Okay, you’re getting ahead of me; one moment. So apparently induction is shakier than analogy, less worthy of trust than analogy. But why isn’t that precise? Because if you think more about analogy, you’ll see that analogy is basically hidden induction. I say, for example, this fell to the earth—will this fall to the earth too? Why not? Why yes? Because it’s similar. In what way is it similar? Look at them—say because both are markers, okay? So actually I’m assuming that all markers fall to the earth, not just this one. This is a particular case, but behind it sits an induction. This is Mill’s challenge to deduction. Mill always argues that behind the major premise of deduction there is an induction. You say: all human beings are mortal, Socrates is a human being, conclusion: Socrates is mortal. That’s certain, right? Where do you know that all human beings are mortal from? You made an induction from the cases you knew, right? So this illusion that deduction is something certain is not correct, because the major premise of the deduction is itself drawn from induction. The strength of a chain is the strength of its weakest link, right? Now of course Mill is mistaken. He is mistaken because my confidence is not in the conclusion of the deduction but in the derivation. And the derivation really is necessary. The conclusion necessarily follows from the premises. My confidence in the conclusion itself is another question entirely; it depends on my confidence in the premises, and that will indeed depend on induction, but the derivation does not depend on that. In other words, what this means is the following: it’s not really three methods of inference. Everything we do in the universe is only analogies. We simply break analogy into two stages. In the first stage we do induction: take the example we know and produce from it a general law. Then we do deduction: from the general law we move to another example. Induction followed by deduction is basically just analysis of analogy into two stages, that’s all. We do only analogies. Deduction and induction are merely a way of breaking the analogical process into two stages, that’s all. Okay, and what this basically means—even though it’s just this kind of circle of analogy that I build by means of induction and deduction—but in terms of our fields of knowledge, or the toolboxes I spoke about earlier, different toolboxes handle different sides of this triangle. Deduction is handled by logic and maybe mathematics, philosophy, because mathematics is a branch of philosophy. So mathematics and philosophy and logic deal with deduction, okay? Science deals with induction and analogy. Why? Because induction and analogy add information. When in analogy you generalize—that’s what happens in scientific research. Okay? Deduction is a logical process; I don’t need observations for it and I don’t need anything else; it has nothing to do with science at all. It belongs to mathematics or logic, okay? Yes, the processes that add information belong essentially to science. Mathematical or logical processes don’t add information. Very often I’ll use them, but I’ll use them as a tool; they don’t add information. Yes, very often people think that physics is basically, yes, a branch of mathematics—you use mathematics to calculate various calculations. That’s a total misunderstanding. Mathematics is the language being used, but physics makes claims about the world; mathematics does not make claims about the world. Physics makes claims about the world, only it does so in mathematical language, okay? And mathematics is merely a tool that helps me refine my thought, that helps me move and make inferences from certain claims to other claims. But in the end, in science there are observations, and I can use mathematics and straight common sense—or crooked common sense—and philosophy in order to arrive at conclusions, the laws of nature, okay? The essence of science has nothing to do with mathematics at all; mathematics is merely a language. In principle there could be science with no mathematics at all. Now here there is another question, which we all already knew. Basically, we all knew this in advance. The moment I arrive at the conclusion that a triangle on a sheet of paper satisfies the Pythagorean theorem, that is a claim in physics, not in mathematics. Because that claim actually says that the sheet of paper is a flat Euclidean space. Okay, that’s a claim in physics, not in mathematics. But the claim that in a flat Euclidean space the Pythagorean theorem holds is a claim in mathematics. It can’t be tested in the world; it makes no claims about the world. In the world, the world may be a curved space, and then the Pythagorean theorem won’t hold for it, right? As they claim in relativity. So the claim, if I return to our issue, is basically that the two toolboxes won’t manage to do the job. We remain standing before a broken trough. What do we do? So how does one arrive at belief in God? Or in a more general question: how does one arrive at scientific laws? Ah, good. And one of the conclusions we really can draw from here is that if we want to add information, we need to give up certainty. Right? Absolute certainty exists only in processes that add no information—logic, deduction, and the like. Lower certainty enables us to accumulate information. But that still isn’t enough, because I need to understand what justifies these processes, even if it’s not 100 percent certainty but only 80 percent. I still ask myself: why? Why give 80 percent confidence to a process of this kind? So this broken trough actually brings me to the next step. Let me describe a person’s maturation process in three stages. Intellectual maturation, not emotional. Fine, psychology doesn’t interest me. So a person’s intellectual maturation can be divided into three stages: childhood, adolescence, and adulthood. What—how do I define childhood? Childhood is a dogmatic stage. Meaning, the child wants to know why. Who says the sun will rise tomorrow? So he asks his father: tell me, Dad, will the sun rise tomorrow? He says yes. Excellent, now I know: the sun will rise tomorrow. Why? Because Dad said so. That’s this sort of dogmatism. There are people who know things—Dad, the teacher, the Rabbi, the magician, it doesn’t matter who—they know, so fine, I accept it. That’s dogmatism. Then comes the adolescent rebellion. The adolescent rebellion comes when a child or teenager starts asking his father: who told you? Prove it. Why should I— you say, well, that’s what you said. Why should I accept it? Prove it. Right? I think this is a phenomenon we all know to one degree or another, one that people sometimes try to suppress, but if a person is healthy and they don’t manage to suppress it in him, then it seems to me he should go through such a stage. And “healthy,” as is known, means what I see in the mirror. So the claim is that at a certain stage there comes a point where the child no longer agrees to accept his father’s answers as all-knowing. He asks himself: who says? Prove it. He won’t accept things just like that. What stands behind this defiance? The assumption that he accepts only things that have a proof. Right? If there’s proof, I’ll accept it; I’m a rational person. But I won’t accept things without proof. Right? My father is an idiot, but I’ll be a rational, sensible person, a philosopher, a logician, a mathematician, however you like, and therefore as far as I’m concerned, if you prove it to me, I’ll accept it; if you don’t prove it, nothing. Okay? Then comes the crisis of adulthood. We have a few crises in our maturation. The crisis of adulthood is the stage at which the adolescent arrives, to his disappointment, at the conclusion that nothing can be proved. Yes, nothing can be proved. Why? Because every proof is built on assumptions. Now if you don’t accept anything for which you have no proof, then even something you do have a proof for you won’t be able to accept, because a proof is always built on assumptions. Right? I once asked students what is more certain, the theorems in geometry or the axioms. The theorems have proofs; the axioms do not. To prove theorems is to reduce them to the axioms, right? That is, to ground them in axioms—that’s what proof means. Now someone who doesn’t accept anything that has no proof for it accepts nothing. Right? He can’t accept anything, because every proof is built on foundational assumptions. Okay? And then basically we are in a real broken-trough situation, which by the way is the same broken trough I described earlier—we’ll soon see—and that trough is built in the following structure. There are two assumptions that the young man has basically accumulated over the years, until he reaches adulthood. First assumption: only what is proved is acceptable. Only what is certain is acceptable. That’s the adolescent rebellion. The second assumption, which he accumulates at the end of his adolescence, is that nothing can be proved. Nothing is certain. That is what creates the crisis, right? The combination of those two things creates the crisis. Why is it important to understand this? Because it means that there are three ways out of this crisis. The first way is to remain with the two conclusions I accumulated. One conclusion: only what is certain is acceptable. Nothing is certain. What follows? Nothing is acceptable, right? Skepticism. The natural adult product of this process is a skeptic, because he remains with the two assumptions he accumulated over the course of his biography. The second product of the process is a fundamentalist. So what is a fundamentalist? People think a fundamentalist is ISIS—those people who murder you if they don’t like how you look. That’s true, but that’s only one particular example of a fundamentalist. Mother Teresa is also a fundamentalist. A fundamentalist is someone who holds a position that he is not willing to subject to a critical test, to critical thought. Now, if his position is to murder everyone who doesn’t look like him, then it’s worth staying away from such a person. If his position is to help everyone without asking questions, like Mother Teresa, then it’s actually worth being around him. But both are fundamentalists on the philosophical level. Because fundamentalism means: there is something which for me is primordial, something basic that I am not willing to put to the test of critical thought. It is certainly true, period. Above reason, if you like, fine? Not willing to subject it to critical examination. So that’s the second form of maturity. Why is that the second form? Because in that form of maturity the person basically gives up on what? He still thinks that only what is certain is acceptable. He does not accept the second assumption that nothing is certain. Why? It’s true that logic can’t give me certainty, because there are always foundational assumptions, but I have some exalted sources above reason, and they are responsible for giving me certainty. The caliph, God, the Rabbi, the rebbe, the magician, Dad—whoever it may be, it doesn’t matter. All these things are sources that are free from the possibility of error; that is, they are certain for me. So there’s no problem. After all, I still maintain that only what is certain is acceptable. But I don’t have the problem because the second assumption doesn’t hold, namely that nothing is certain. No—there are certain things. Whatever the caliph said. Whatever the Hasidic rebbe said. So the first path, the skeptical one, is a path that remains with both conclusions: both that only what is certain is acceptable and that nothing is certain. And then of course the conclusion is that nothing is acceptable; every thing is as true as its opposite. The second maturation is fundamentalist maturation, which gives up the second assumption. That is, it says: only what is certain is acceptable, but there are certain things—whatever the caliph said. What is the third maturation? Simple combinatorics. What else could there be? Giving up the first assumption, not the second, right? What does that mean? To say: true, nothing is certain, because only logic—there’s nothing above reason, I’m not a fundamentalist. There is nothing above reason, and reason can’t give me certainty. Because a logical argument that gives me certainty does so only on condition that I adopt its premises with certainty. But something without proof has no certainty. But I do not accept the first assumption, that only what is certain is acceptable. Right? What you said. I am willing to accept things that are not certain. It’s 80 percent? Fine, that’s also good enough for me. What can I do? I have no certainty; there can be no certainty in anything. So something that isn’t certain—common sense, straight thinking—I’m willing to accept that too. I call this maturation synthetic maturation. Synthetic maturation is a term from Kant. Synthetic maturation is giving up the first assumption. Fundamentalist maturation is giving up the second assumption. Skeptical maturation is giving up neither of them. You know the saying attributed both to Rabbi Kook and to the Vizhnitz Rebbe, that I would rather fail through baseless love than through baseless hatred. I always think it’s preferable not to fail in either one. For some reason people always present you with two bad options and tell you, well, this one is less bad—but there is also a good option. Why do we always have to compare bad options? In any case, for our purposes: you can give up assumption A, give up assumption B, or stay with both. You can also give up both, but that doesn’t really add anything; it just leaves you a skeptic to the same extent. So these are the three paths of maturation. This analysis, by the way, is true not only of the maturation of an individual person; I think it’s also true, very schematically, of the processes our civilization undergoes in general, at least in the West. The West as distinct from the Far East, not as distinct from the Orient—I mean the Near East. The claim is basically that there too, at first, there was a kind of pagan, dogmatic period. Whoever wants to make rain fall has to dance around the fire three times and mumble some mantra, and that will bring rain. How do we know? Because the magician said so. That’s the equivalent of Dad. Or our tradition said so. Or “that’s how I was instructed,” yes? We opened the lesson today with that. “Because that’s how I was instructed.” Right? That’s for children; it’s good for children. So that’s the stage, the first period. The second period is the adolescent rebellion. You can identify it with, say, the beginning of Greek philosophy—though of course there were earlier stirrings too, but I’m giving a very schematic broad description. There they began to say: wait a second, proofs. Rational thought began. That is, so what if you have a tradition saying this and that? All the validation or all the threat that sages see in Greek culture or Greek thought, it seems to me, is rooted in this: traditional education is education for dogmatism. You accept it because that’s what tradition said. And when a young man comes and says, wait, who told you? Prove it. That threatens you. Especially if you have nothing to answer him. You can’t prove it to him, and then it really threatens you. Yes, usually when people declare you a heretic, it’s generally when they have no answers to your questions—but keep that as a rule in your hands; I know it from experience. So the claim is that the adolescent rebellion basically poses the same challenge posed by adolescent rebellion in the private individual. Then comes the stage of moving from adolescence to adulthood. I identify that with the beginning of the twentieth century, the early to mid-twentieth century. Yes, that’s quite a big jump. The adolescent stage of our civilization is, I don’t know, fifteen hundred years or two thousand years. What happens there is that people reach the conclusion that you can’t prove anything. Right? There was huge hope in science and this and that, legal science among the Germans, everything became science, everything was science, yes? Because science would redeem us from all our suffering—a substitute for religion, of course; gradually it became a religion itself. Then a crisis came. Some people tie this to World War II, but as I said, I’m not dealing with psychology, I’m dealing with logic. So I don’t care right now what sociologically, psychologically, historically caused it. In practice, a stage appeared here in which there is a kind of despair about the ability to reach certainty. Later this phenomenon was called postmodernism. Okay? Or skepticism in its current or newer version is called postmodernism. So postmodernity is basically an indication that we’ve moved to the third stage, the stage of adulthood, with postmodernity being skeptical adulthood. Because it remains with both assumptions: only what is certain is acceptable, but nothing is certain, because everyone has his own narrative, everyone has his own foundational assumptions, and foundational assumptions cannot be proved. And because of that I remain with skepticism. Rabbi Shagar’s circle of differences, if you like—I mentioned this in previous days—things of that sort. But as I said in the individual analysis, here too there are two additional options. One option is fundamentalism. A second one. We see that fundamentalism rises dramatically in the twentieth century, after people thought it had already declined completely, right? It takes off in the twentieth century. Why? Because that is exactly the second option for maturing: the reaction against skepticism is fundamentalism. Yes, people think Haredim become more and more extreme because the world around them is farther and farther from them. You could not be more mistaken. Haredim always fight only with themselves. They never fight something from outside. It’s simply that more and more ideas from outside penetrate into the Haredi world, and that makes the Haredi core more rigid, more fundamentalist, because it feels threatened from within, not from without. It’s always from within. I think every closed society is like that. In any case, the reaction to skepticism is basically fundamentalism in the broader world too. Why—what is stuck in the struggle between postmodernity and fundamentalism, or the marvelous symbiosis we see between them these days in universities around the world? Not only in universities, but especially in universities. A wonderful symbiosis between postmodernity and fundamentalism, right? It’s a remarkable phenomenon. Why? What do they have in common? What they have in common is that only what is certain is acceptable. Both of them accept that assumption. Their dispute is over whether to accept the second assumption. Right? Are there certain things? The fundamentalist says yes—whatever Allah said. Okay? The postmodernists say no, there is nothing, because only logic, philosophy, or science—nothing is certain. Okay? Therefore they cannot deal with one another. Because he says to him: look, I have certainty; I’m telling you, this is certain. So what can I say to him? If it’s certain, then you accept it. I too would accept it if I had certainty, but I don’t. Okay? You can’t confront him. You can only fight him, defend yourself, but there is no way to confront him. That is the helplessness of postmodernity in the face of fundamentalism. They share a common assumption. The only way to confront both of them—to confront them intellectually; to confront them on the ground, all you can do is shoot—but to confront them intellectually, the only way is to propose synthetic adulthood. What does that mean? To give up the assumption that only what is proved is acceptable, only what is certain is acceptable. I am willing to accept other things too. If you are a fundamentalist, very nice; you have your truth. But I also have things I believe in. And if you threaten them, then we will fight over that, because I think I’m right and you’re wrong. I’m not a postmodernist. Okay? True, I’m not 100 percent certain—80 percent. And for me 80 percent is also good enough. If you convince me, I’ll give it up, I’ll change my mind. But the fact that it’s 80 percent doesn’t mean I don’t hold it. Okay? Therefore this offers an alternative both to postmodernity and to fundamentalism—syntheticity. The only alternative; there isn’t another one, because that’s the combinatorics I did earlier. This is the only alternative. Therefore the other two will remain at war forever until one of them disappears. They have no way to talk except by joining forces to attack the synthetics. But the only path they have is to attack the synthetics together. This is what is called the conservatives in the world today, unfortunately—I don’t identify with them on many things—but the foundation that unites, for the conservatives, their critique of both these groups, the postmodernists and the fundamentalists, that foundation is syntheticity. And the willingness to accept something as true even though I’m not certain about it—but it is true, that’s what I think—and I think you, the fundamentalist, are wrong, and I think you, the postmodernist who says there is no truth, are also wrong. There is truth; the truth is mine—what I think, that is the truth. I’m not certain, 80 percent. Bring me arguments and I’ll reconsider; no problem. I’m not a fundamentalist; everything stands open to critical examination. Okay? But that is what gets attacked in this world. I think this conceptual and philosophical analysis sheds a tremendous amount of light on what is happening in this period today. Now one more thing—I already need to finish—so what I want to say, maybe in two more sentences. When the adolescent asks his father: tell me, who told you? Prove that the sun will rise tomorrow. Because it rose until today, so it will probably rise tomorrow too—by induction. So it will rise tomorrow. Okay? Then the child says: induction—I’m looking for proofs; I accept only proven things. I won’t be an idiot like you. I’m a rational person. Bring me proofs. What stands behind this? Why will I never succeed in convincing him or making him accept what I say? Because a person always shaves on his own beard. Right? A person doesn’t shave on other people’s beards. He won’t learn from my experience; he will learn only from his own experience. That’s how we are built, for better and for worse. What does that mean? What does he know from his own biography? He went through childhood and arrived at adolescent rebellion, right? That’s what he knows. Now when I tell him: look, the sun will rise tomorrow because obviously, that’s common sense—how does he diagnose me? I’m dogmatic, right? I’m still stuck in the womb; I’m stuck in my mother’s womb; I’m still in the stage of dogmatic childhood because I accept things without proof. And he says, okay, you’re a dogmatic idiot. I’ve already passed that stage; now I’m already in adolescent rebellion. He still can’t distinguish that there is another position here, a synthetic position. A position that says no, I’m not dogmatic. I’m willing to accept other things too, but I have a position. 80 percent is also enough for me, and that’s what I’m telling you: there’s an 80 percent chance the sun will rise tomorrow. And that’s what I go with. It may turn out that I’m wrong, and then I’ll update my beliefs. Okay? The adolescent is incapable of understanding that because he hasn’t yet experienced it in his own biography, he hasn’t yet gone through that stage. The hope is that when he grows up, he’ll mature. To mature means to become synthetic. The other two did not mature; they remained adolescents. But if he matures, he will understand the answers he received as an adolescent. Okay? But only after he matures. He can’t shave on my beard, only on his own. Okay, up to here this is the description of the schema. How does this connect to us? In many ways. First of all, I tried to sharpen the scientific and philosophical toolboxes. Deduction belongs to philosophy. Analogy and induction belong to science. And I tried to show that none of these ways can supposedly lead me to God. And now I’m translating this into a more concrete question. When I adopt a synthetic position, I’m basically saying this: true, I have no proofs for the existence of God, but I accept that He exists because my common sense tells me so. Or I have some argument based on foundational assumptions that seem reasonable to me. Not certain—nothing is certain. Eighty percent, ninety percent, sixty percent. I don’t know how much; each person with his own scale. Okay? So I accept those claims. This is the only point of departure, right? This is basically a translation of the broken trough I described earlier. You can’t do it through science, you can’t do it through logic because logic only gives certainty, but science isn’t certain, and after all only what is certain is acceptable. You understand that this is a translation of the same broken-trough problem? And what I’m proposing now as an alternative is to accept something that is not certain, to give up certainty, what you said earlier. Okay? Still, that isn’t enough. That’s a slogan. You have to tell me what it is based on. If you’re not certain, then that’s just how you are built; the world owes you nothing, it was here before you. The fact that you think in a certain way says nothing about what really happens in the world, about what is truly true in the world. That question I have not solved. This analysis only helped me identify the direction in which I can try to look for the answer, but it is not an answer. I still need to look for what justifies holding a synthetic position. And I want to claim that this is what is called faith. Faith is basically a cognitive faculty that underlies synthetic thinking. In every field—it has nothing at all specifically to do with God, not specifically with God—even in science, in any field whatsoever. That is basically what I want, and with this I conclude the process that is the introduction to the journey we’re about to begin. Okay? Up to here.