Fuzzy Logic and Data Mining in the Talmud and Beyond – Lesson 1 – Rabbi Michael Abraham

[Speaker A] How’s the family?

[Speaker B] I’ll say this — coping.

[Speaker A] It wasn’t a huge surprise, because over the last year his medical condition had become very, very bad, because his brother-in-law passed away less than a year ago. And that really… in any case he hadn’t been healthy in recent years. So relatively speaking it was only a matter of time, and there was some kind of preparation for it.

[Speaker B] It’s never easy in any case. Fine, Rabbi, we can begin.

[Rabbi Michael Abraham] Okay, so let’s begin. As the title says, I want to talk about what I call soft logic, and also get to information reading. It’s not really my field, but a certain aspect of information reading will come up here. That part, though, is supposed to continue next week as usual for us. So this time I mainly want to devote to some sort of philosophical introduction, almost in a popular form, but still a philosophical introduction, because I think it’s no less important than the formalism I’ll present next time, because it’s important to understand what it actually means. And I think this also has all kinds of implications, as I’ll try to show.

So maybe I’ll start with a standard division in the world of logic into three forms of inference. There are analogy, induction, and deduction. The difference between them is the question of where you start and where you end up. That is, if we move from particular to general, that’s induction; if we move from one particular to another particular or from one general rule to another general rule, that’s analogy; and if we move from general to particular — to a particular that is included within the general, of course — that’s deduction.

Right? If I say, all human beings are mortal, Socrates is a human being, therefore Socrates is mortal — that’s deduction. If I say Socrates is a human being… no, sorry: Socrates is mortal, therefore all human beings are mortal — that’s induction. If I say Socrates is mortal, therefore Moishele is also mortal — that’s analogy. Okay? So that’s the standard division of forms of inference in logic.

I want for a moment to focus on deduction, because that’s what is usually associated with the field of logic, even though later on I actually want to deal with the other two forms of inference. But first let’s look at deduction for a moment in order to learn something from it.

There are — yes — two jokes I use to illustrate the point. One of them is about our father Abraham and the hat. In yeshivot they like to joke: how do we know every Jew has to wear a hat? Because it says, “And Abraham went.” Now obviously a Jew like him wouldn’t have gone without a hat, right? So if Abraham went with a hat, then all of us, his faithful descendants, must also go with a hat. Which is what we wanted to prove.

Now you ask yourself: okay, it’s amusing, but what exactly is wrong with this argument? On the face of it everything seems fine. What’s the problem? Why does it make you smile? So to save the process, I’ll say: it’s begging the question, right? Begging the question is considered a fallacy in logic when you’re trying to prove something, and the very thing you want to prove appears as one of the premises of the argument. So in effect you’re assuming what you want to prove, and then the whole thing is pointless.

What happens here? It says, “And Abraham went.” Okay, that’s written. “A Jew like him surely wouldn’t have gone without a hat.” What does that mean? Implicitly it means that every Jew has to go with a hat, right? Which is exactly the conclusion I was trying to reach. In other words, I smuggled the conclusion I wanted to arrive at into one of the premises — a hidden premise in this case — and therefore this is in fact begging the question.

Now it is commonly thought that begging the question is a fallacy. But I don’t agree. Begging the question is not a fallacy. Every valid logical argument begs the question. That is, when for example I say: all human beings are mortal, Socrates is a human being, therefore Socrates is mortal — then in effect, when I assume the two premises, all human beings are mortal and Socrates is a human being, implicitly of course… let’s break it down. What does “all human beings are mortal” mean? It means Yankele is mortal, Muhammad is mortal, David is mortal, and Socrates is mortal, and so on. Only instead of spelling out all those billions of premises, I say it as a general sentence. So you understand that the conclusion that Socrates is mortal was already… hidden within the premises. And that is actually the meaning of the fact that this argument is valid.

A valid argument — why does its conclusion follow necessarily from the premises? It follows necessarily from the premises because in a certain sense it’s there in them, in one form or another. In the case of Socrates, it’s there — say — you need both premises to see that it’s there, so maybe it’s less blatant begging the question, but essentially it still is begging the question.

More than that: why do we think a logical argument is valid in the first place? Why does it compel me to accept its conclusion if I accept its premises? Why does it compel me? Think of someone — let’s say the Little Prince arrives on earth. You say to him: nice to meet you, all human beings are mortal, just so you know. Okay, interesting. Then you say to him: and Socrates is a human being. Also interesting. Then you say: so you understand that Socrates is therefore mortal. “Impossible,” he says. “What do you mean? Why do you think that? He’s not dead yet, he’s still among us.” So I say to him: because the conclusion comes out of the first two premises. And he opens his eyes wide and says: wait, what do you mean? Why do you think that? I agree to the two premises and I don’t agree to the conclusion.

What can I try — how can I try to convince him that if he accepts the premises he also has to accept the conclusion? Only by showing him that if you unpack what’s inside the premises, you’ll find the conclusion there. In other words, in the end, when I talk about a valid logical argument, such that if you accept the premises you must accept the conclusion — why must I? Not because there’s some law that forces me, but because I already accepted it. I accepted it when I accepted the premises.

So in a certain sense, a valid logical argument always begs the question. That’s the meaning of its validity. Its validity comes from the fact that it begs the question. Begging the question in a somewhat broader sense, let’s say — I’m not being absolutely precise here — but it seems to me that…

[Speaker B] So everything — so everything is axioms, and all the conclusions are just a way of expressing them more clearly?

[Rabbi Michael Abraham] Right — not expressing them, but rather the conclusions simply extract more and more information that is already contained within the axioms. Okay, that’s basically what the conclusions of a valid logical argument are — a deductive argument, let’s say.

So that’s really the meaning of begging the question, or of a valid logical argument seen from another angle. In philosophy they call it the emptiness of the analytic. Again, I’m moving here between concepts that aren’t perhaps entirely identical, but I’m doing it on a relatively simplistic level.

So — yes — one more joke for this point. Two people are flying in a hot air balloon. They don’t know where they are. They see someone plowing a field below. One of them asks the fellow down there: tell me, where are we? He says: above my field. So the guy in the balloon says to his friend: that man down there is definitely a mathematician. Why? Because what he said is perfectly precise and completely certain — that’s one — and second, it doesn’t help us at all.

Now beyond the joke, you have to notice that these two aspects of mathematics are not independent. They’re two sides of the same coin. What does it mean that it doesn’t help us at all? It doesn’t help us because it’s precise — or it’s completely certain because it doesn’t help us at all. “Doesn’t help us at all” means it doesn’t add information beyond what we already knew. That’s what it means. But precisely because of that, the argument is completely certain. Because every argument that does help us in some sense — that is, adds information — is necessarily not certain.

Think about — so far I’ve spoken about deduction. Think about analogy and induction. In analogy and induction, I say: if Socrates is mortal, then all human beings are mortal. You understand that the move from premise to conclusion involves a very significant leap. In other words, there’s a very significant addition of information beyond what was in the premise. Okay? That basically means there’s a speculative dimension here. That is, maybe I’m mistaken in making that generalization. In deduction, by contrast, there’s no speculative dimension at all. I’m not adding anything in the conclusion beyond what I had in the premises, and therefore it’s certain.

So anything that adds information is not certain. This is basically a logical uncertainty principle, yes? In physics, the uncertainty principle says that the product of the uncertainties in position and velocity is bounded from below. Meaning: if you have high certainty in position, you have high uncertainty in velocity, and vice versa. Here it’s a similar game. If you want full certainty, zero information. If you want to add lots of information, your certainty will be very low. There is always an interplay: you have to decide how much information you’re willing to add, and you’ll have to pay for it in the currency of certainty. The more speculative you are, the more information you add, the less certainty you have — and vice versa.

Therefore deduction, which is completely certain, doesn’t help us at all — it doesn’t add information. Analogy and induction are not certain, and precisely because they add information… therefore they’re not certain. Since they add information, you can play around with the question: which is stronger, induction or analogy? It’s a slightly tricky question, because at first glance, if you look at the level of speculation, induction is more speculative. Because induction starts from one or more specific premises and reaches a conclusion about a general class. So it makes a rather broad speculation. Analogy takes one example and infers a conclusion about another example — more modest. In that sense it is less speculative. So induction would seem to be more speculative and less reliable than analogy.

But if you think about it philosophically — again, there’s room for sharpening this — when I make an analogy, say: this frog is green, that one is also a frog, therefore that one is also green. Okay, I made an analogy. What is that analogy based on? It is actually based on the assumption that the greenness of the frog I’m seeing is connected to the fact that it is a frog, right? Therefore I say: if there’s another frog, probably it too is green. What does that really mean? That implicitly, when I made the analogy, I actually made a hidden induction. Because I effectively said that the green color holds for every frog, not just for this particular frog. So in fact, at the basis of the analogy I’m making, I have already made a hidden induction.

And then it’s hard to say that analogy is safer than induction if it itself rests on hidden induction. Now this isn’t entirely precise, because many times we make an analogy without passing explicitly through the induction in the background. Something looks similar to me between these two frogs, so I say: okay, if this one is green, then probably that one is green too — without explicitly conceptualizing to myself that I’m actually tying the green color to the very fact that it’s a frog, in which case I’ve made an induction because it would hold for all frogs. But behind it, people tend to think — at least this is the common view — that behind analogy there sits, even if not consciously, some kind of induction. And because of that, it’s hard to create a clear hierarchy between analogy and induction.

Deduction is necessary — the conclusion’s following from the premises. Not the conclusion itself is necessary; its derivation from the premises is what is necessary. But between analogy and induction the picture is a bit more complex. It seems to me that in a simple way — yes?

[Speaker D] There’s some kind of game going on here, and something in the formalization still isn’t clear to me. Because how are we saying this? If we’re speaking about a world that is completely logical, induction isn’t speculative. There are conditions, there is an inductive rule, and if we accept that, then there’s no doubt here.

[Rabbi Michael Abraham] What do you mean? You’ve turned it into deduction. The moment you add the logical rule — say I say: this frog is green, therefore all frogs are green. If you add the premise that what is true of one frog is true of all frogs, then that’s not induction, that’s deduction.

[Speaker D] No, that’s not what I… I’m talking about it as a method. The inductive method comes and says: I assume — I basically need to assume premises, show that they exist in the world, assume and basically show the existence of some inductive rule of this kind, and then by means of those two I can infer, okay, in a way that follows pretty directly. I can define the natural numbers that way too. I can basically give an…

[Rabbi Michael Abraham] An inductive definition is not an inductive claim. That’s something else. You’re getting a little tangled up with Wittgenstein, but an inductive definition is not a claim, it’s a definition. You want to define the natural numbers — I’m not talking here about definitions, I’m talking about claims or arguments. An inductive argument is an argument that derives a conclusion from premises.

[Speaker D] What does “derives” mean? I derive. The inferential process in which I assume that what holds with probability — the part that’s hard for me to understand here is whether we’re talking about a world in which we have a known deterministic logic that we simply apply, and then you’re saying maybe there are elements of tautology because you put into the premise what you’re trying to illustrate — completely, but basically deterministic — or whether we’re talking about an inferential process that contains an element of probabilistic learning, and then you’re saying you’re basically looking at some sample, inferring some rule from it, and then applying it to populations, applying it to an entire population. You’ve done some probabilistic move here which, at higher probability, may err, because it’s speaking about a much larger space, so statistically it will eventually make mistakes. Both and both… yes. I understood you, okay, fine.

[Rabbi Michael Abraham] Probability, by the way, isn’t always the right language here, because in order to speak in terms of probability you need a sample space and so on, and evaluating the quality of probability in induction is usually very complicated. I think in general you can’t really do it. But fine — let’s say it’s not certainty, whether you call it probability or plausibility is something one can argue about. In any case, that’s the broad picture of these three forms of inference.

And I think a convenient way to look at it is to say this: logic or mathematics basically deal mainly with deduction, and therefore they do not essentially add information. Of course they extract more and more information from the axioms, but they don’t add information beyond what is in the axioms. Again, I’m speaking very roughly.

Science deals with adding information. Yes, science accumulates information, and therefore in its essence science rests mainly on analogies and inductions. Mathematics and logic don’t really deal with inductions — I’ll come back to that a little later — but they don’t really deal with analogies and inductions; they deal mainly with deductions.

Therefore, if I want to look at the process of accumulating information, I can never be satisfied with deduction alone. If I settle for deduction alone, I won’t be able to accumulate information. All I can do is uncover more and more information that already exists inside the premises. If I want to accumulate information, I have to pay in the currency of certainty — that is, I have to work with analogies and inductions.

Now if you think about induction, about analogy, the way I described it before — let’s say I move from one frog to another frog, and I do that through induction — I’m basically saying this: this frog is green, that’s also a frog, therefore it too is green. Now let me break down how this accumulation of information happens. I’ve added information that this frog too is green. In the premise I only knew about this frog, so there is added information here. How is it added? First I make an induction: from this green frog I infer that all frogs are green. And from that induction I say: and in particular, this frog. In other words, I particularize that general class to this individual case. So in fact one can look at the process of accumulating information as a process of analogies, where every analogy breaks down into an induction followed by a deduction. That is, I make an induction to some rule, and then I particularize that rule to another case belonging to that rule by means of deduction, and that’s how I moved from one particular to another.

So really this lies in a kind of circle. There aren’t three separate forms of inference such that you can simply ask which is better, which is worse, and which you use and which you don’t. In a certain sense they play in a circuit — well, not a circle, more like a triangle. You can always choose two nodes of the triangle and go by way of two sides, or directly by the third side, but overall…

[Speaker B] But why would you want to do that? Basically the only piece of information added, once you did what you called analogy through induction, is that you discovered it’s a frog. Once you discovered it’s a frog, that’s it.

[Rabbi Michael Abraham] Meaning: the process of information accumulation that you have in analogy happens in the inductive step. Once you’ve done the inductive step and you come back down from the general rule to another particular case, you’re not adding any information there. On the contrary, you’re even reducing a bit — you’re speaking only about one individual from within the whole class. Okay, right. The process of accumulating information is really built only on the inductive dimension; deduction doesn’t change the amount of information in your hands.

[Speaker D] I also find it very hard to accept this statement that you didn’t learn anything, because take the constraint satisfaction problem. A constraint satisfaction problem requires me, in order to say whether there is a solution or not — a thing that supposedly is already known from the formulation of the problem — to do a very significant amount of work in order to explore the space. I’m saying this: in the end, in order to know the answer, either I go in this inductive direction, where maybe by other techniques I can reveal more, but I still have to do work there to discover the information, or I go to the deductive world where supposedly it follows from the premises so I don’t have to go outside, and maybe you tell me it’s deterministic — but even there I still have to explore a large space, and therefore it’s not that the information is known. It isn’t accessible without the computational operation.

[Rabbi Michael Abraham] Yes. I’ll tell you: you’re looking at it as a computer scientist; I’m looking at it as a philosopher, or a logician. And I’m saying that no information is added in a very abstract sense, not in a practical sense. Think about the axioms of geometry. In principle, if you know the axioms of geometry, and the derivation rules, the definitions, whatever it may be, then you know all the theorems. The information about the theorem is there in some form. That doesn’t mean you have a way to extract it; it doesn’t mean that way is simple. That’s another matter. But you know the theorems in the philosophical sense.

You as a computer scientist say: okay, but I want to know the theorems in practice, and there it’s not clear that I know them until I do the work — if I can do it at all. It’s like the difference between mathematics that deals with existence theorems. Suppose you have an existence theorem for a certain type of equation, okay? It doesn’t tell you what the solution is, it only tells you that a solution exists. Now does that mean you know the solution? In your sense, no. But in the sense I’m talking about here, in this abstract sense, I say yes: in principle, if you have enough initial conditions and the differential equation, then you know the solution. The information is there. Now how to extract it — that’s another story, of course. That really is the viewpoint of computer science people. I’m not entering that here; I’m speaking on the abstract logical level.

[Speaker D] But I do think that even on the abstract level, since we can’t ignore the fact that our entity has only partial information, and from that information, in order to generate prediction, it has to do work — therefore I think that even in this abstract model it is right to give relatively clear attention to that dimension.

[Rabbi Michael Abraham] I’m willing to give it whatever attention you want, but I’m making principled claims here; it’s not just a question of “attention.” I’m not claiming that learning a theorem in geometry is worthless, or that you learn nothing after I teach it in a class. Of course you learn. I’m saying that in the principled, essential, abstract sense, no information is added beyond what was already in the axioms. That’s a very abstract statement. I’m not claiming any of this is unnecessary or requires no work. That is exactly the computational question: how do I extract that information?

[Speaker D] “No information is added” — I think you can say deterministically that if you perform the computation, you can obtain it, but you didn’t know it at time zero. You had to do the computational process.

[Rabbi Michael Abraham] Fine, that’s a terminological dispute. You know it — I call that knowing it in an abstract sense, okay? It’s just a question of wording.

[Speaker D] This definition matters, because I think it’s the foundation.

[Speaker E] By the way, can I add something? I think your debate is connected to entropy and to what’s called Kolmogorov complexity. When you train a machine learning model, you’re basically trying to minimize the entropy of the dataset, and in the end you get a model that is a compressed representation of the data — but you’re not adding information. The information isn’t being added, because the entropy was already effectively zero since you trained it on the dataset. But in the Kolmogorov sense, when you find such a representation of data in the most minimal description length, then in the pure sense you’re not adding information, but you are adding a kind of information that is useful to us, efficient for us; we understand the data better.

[Rabbi Michael Abraham] Exactly — that’s the computer scientist’s perspective. The computer scientist says: of course, I have work to do and I want this information concretely; I want to know it, not just know that I have it. Or, in analogy to what I said before, an existence theorem isn’t enough for me — I want to know what the solution is, not just that there is one. The mathematician is often interested in whether there is a solution, not in what the solution is. It’s just a question of areas of interest or terminology. No one should feel insulted here by any supposed disparagement of the people who actually extract the information.

Okay, so until now this was an introduction to the three forms of inference. I’m now moving to science — a bit of philosophy of science. In the philosophy of science, when we encounter a set of facts, we want to extract a theory from them. Okay? Now there’s a scheme of Carl Hempel — in philosophy of science he calls it the deductive-nomological scheme — which basically wants to say: how does the move from facts to theory happen? We look for a theory from which the facts can be derived deductively.

Now understand: this search itself is of course not deductive. That is, the move from facts to theory is some kind of induction — in a moment I’ll sharpen that more — but it is not deduction. Once I have the theory, how do I know the theory is correct? I simply check whether the facts can be derived from it deductively.

Now the scientific step in this whole business is, of course, only the first step. The first step is the step that adds information: I discover a new theory. The second step is really parallel to the deductive step. That is, if I have the theory and I need to derive the facts from it deductively — okay, that’s a logical step, not a scientific one. The scientific step that adds information is the first step, the quasi-inductive one — in a moment I’ll call it abductive — namely, the step that moves me from the facts to the theory.

Now clearly, first of all, this is not one-to-one. It’s not one-to-one because the same set of facts can have infinitely many theories that explain them deductively and nomologically. Right? There’s no problem generating infinitely many theories — there are theorems about this in mathematics if you want, but you don’t need theorems, it’s obvious. Every discrete set of facts can have infinitely many theories that explain those facts in a deductive-nomological way. Which means that Hempel’s scheme maybe explains what I’m looking for, but it doesn’t really help me define it fully or carry it out.

What I really need to do in order to get from particulars to theory is define a step that was later described by Charles Sanders Peirce as abduction. Abduction is like induction, but induction takes you from particulars to a general law of which the particulars are a special case. Abduction takes you from a set of particulars to a theory — not to a general law of which the particulars are a special case, but to a theory with theoretical entities, with all kinds of things not necessarily conceptually tied to the particulars, such that from that theory you can derive the particulars in a deductive way.

Okay? Therefore this form of inference Peirce speaks about is really an inference that in a certain sense resembles induction. It adds information, it takes me to some general description that can fit infinitely many facts — but that description is not just a description of the facts as such. If I were simply to take the facts themselves and describe them in a more general way — say I took a set of discrete points and gave a function that passes through them all, a fit, if you like — that would be induction. But if I give a theory with theoretical entities and tools and rules of derivation and whatever else you want, and within that theory I can explain — meaning derive — the facts from the theory by means of derivation rules that are part of the theory, then I have not merely made an induction. I haven’t just moved from particulars to a general law; I’ve moved from particulars to a theory. And a theory contains far more than a general law.

And of course there are many possible theories, just as there are many possible general laws, and therefore what Peirce says is that abduction is the pursuit of the best explanation, the optimal explanation. Okay? Not merely the pursuit of an explanation in the deductive-nomological sense, because that’s too general — there are infinitely many such explanations. I want the explanation that gives me the best explanation.

Now what counts as “best”? After all, among all the explanations I’m looking for the best one. So I have lots of explanations among which I seek the best. Those many explanations are reached by a kind of deductive-nomological move. But when I want to do abduction, I want to choose which one of them I prefer. I want to pick one of them. So how do I choose one? I need criteria for what counts as a better explanation. A better explanation might be more economical, simpler, more plausible — I don’t know, there can be all kinds of such rules. Very often…

[Speaker B] Like Occam’s razor.

[Rabbi Michael Abraham] Right. Very often it’s connected to Occam’s razor, to principles of simplicity of one kind or another. Occam’s razor originally speaks about the number of entities, but nowadays when people invoke Occam’s razor here they mean simplicity in a broader sense — not only how many entities are needed, but how many principles are needed, I don’t know, what is the dimension of the space in which you’re working. If you can describe everything in three dimensions instead of four, you’ll prefer three, right? Because in four you have redundancies, meaning it’s less simple. So that too is in a certain sense Occam’s razor — the drive toward the simplest explanation, let’s call it for now. Abduction.

Now here a difficult philosophical question arises. Suppose through abduction I arrive at the conclusion that this is the simplest theory, and from this point on I adopt it. Now the question is: is this rule itself merely methodological? Meaning: is there no real preference for the simpler theory over the others, since in the end they all explain all the facts? So what if something seems simpler to me? It just seems simpler to me because that’s how I’m built. So basically it’s only a methodological rule. If I have many theories, I choose the simplest one because why complicate things for no reason? But not because the simpler one is actually better.

Or is this a philosophical or epistemic rule, if you like — a rule saying that if my theory is simpler, then that is some indication that it is also truer? Again, not that it is certainly true, and not that I know how much truer, but that it gives me some indicator of truth. Meaning, this is not just an arbitrary methodological decision; there is something here that also directs me more toward truth — factual truth.

[Speaker D] So wait — aren’t you now circling back? Doesn’t simplicity now refer to computation? This seems a bit contradictory, because before you said we’re trying to learn new things about the world, and from my point of view things I learn by applying some computation don’t interest me; computation itself doesn’t interest me. So why, when we compare theories of the world — this model and that model — should I care that one is super complicated with eighteen dimensions and the other has three? The same thing follows from both of them exactly. Computation doesn’t interest us.

[Rabbi Michael Abraham] And that is exactly my question. What follows from what you’re saying is that the reason I choose the simpler theory is only methodological; it doesn’t say anything about the truth of one theory as compared to another. It’s a methodological question: why complicate things if I have a simple theory that does the job? That’s all. Okay?

[Speaker D] On the other hand, this consideration — listen, this consideration — when you came and said you’re presenting a model in which I felt uncomfortable, but okay, it’s philosophical — you said you’re presenting a model in which you completely ignore the work or energy that has to be invested. From your point of view, if it is known, it is known, no matter the route. Now in my world it’s not like that. I put into the abstract model this issue of investing energy, and then in my model, when I look at induction and abduction, I come and say: I have a good reason to prefer the simpler model, if simplicity can be translated, say, into saving energy.

[Rabbi Michael Abraham] But even you agree, Nimrod, that you have a good reason to prefer it because it simply requires fewer computational resources — but you’re not claiming that it gives better answers in the sense that the result is better. That’s an additional claim.

[Speaker D] No, I agree with you, but I’m saying that when I come out of a model different from the one you’re presenting, then choosing a simple model makes sense. If you say computation doesn’t interest you at all, then from your perspective you can certainly say it doesn’t interest you.

[Rabbi Michael Abraham] No, I didn’t say it doesn’t interest me. I said that that is precisely the methodological consideration: it makes sense only in the sense of why complicate things if you can do it simply. So in that sense it makes sense. But the question is whether it also means it is more correct — whether the outcome of this model rather than that model is more correct, whether this model describes reality more accurately, or whether it just gives me the results more easily and therefore it’s worth adopting. That’s a philosophical question one can argue about.

I’ll give just a couple of examples. There is a dispute among philosophers of science — again, nutshell version — between Thomas Kuhn and Karl Popper, and perhaps people don’t always notice that both of them are on the same side of the equation as I’m presenting it here. That is, Karl Popper too basically speaks about generalization as some kind of guess, and all I can do is try to refute it — either I succeeded or I didn’t — but the generalization itself is a kind of guess. And Thomas Kuhn, on the other hand, sees it as some kind of sociological decision, the sociology of the scientific community. Okay?

So in that sense, it seems to me that if you take what they say at face value — both of them also underwent some changes in their views, but I’m presenting it in a very simplistic way right now — then both are on the methodological side. They are basically saying that a generalization has methodological value. That is, the simplest generalization we adopt not because it is truer, but because it is more convenient in one sense or another. Okay? For Popper it doesn’t matter anyway, because for him the theory isn’t viewed as something true, but as something not yet refuted. And for Thomas Kuhn too, he sees it as a kind of sociological decision of the scientific community, and we choose according to one convenience or another, whatever you want to call it, one theory over another.

[Speaker B] Could you go back, please, to the explanation of the difference between plain induction, so to speak, and theory?

[Rabbi Michael Abraham] Yes. Maybe I’ll give a concrete example. When Einstein worked on black-body radiation, what was known before him were certain wavelengths and the intensities at which radiation was emitted. Okay? Now Einstein proposed — actually even before him they had proposed — some graph or function that describes the result for every wavelength. That is basically a generalization of the known results for specific wavelengths: I can give you an explicit function that describes the distribution of radiation, how much radiation comes out at each wavelength. That is called induction. Because you’ve taken the individual cases and given them a general description by means of one function. Instead of giving me a table — this value has this output, that wavelength has that output, that wavelength has that output — I gave you one function that does all the work. That’s induction.

But then Einstein comes along and says: wait, behind this I understand something. This function shows me that apparently light works with discrete photons, and not as something continuous. And then he basically opened quantum theory, which he later struggled with all his life. But he was the one who opened it, following black-body radiation. And that is already an abductive step. Because when you go from the individual cases to the function, all you did was generalize; you gave a general description of the set of facts. When you ask what theory stands behind this function — the first is a phenomenological theory, so that is the result of induction. The second is an essential theory, and that is already the result of abduction. Because now I generate all kinds of entities such as photons, electromagnetic fields, and so on, and from the theory with those entities and with derivation rules and formulas and principles and all of that, I need to show that the function…

[Speaker B] So I just want to say something. Seemingly, from what you’re saying, these are two different dimensions — even though they appear similar, they’re two different dimensions. One speaks about the underlying essence, and the other is the simplest way to explain the phenomenon. The thing is that you judge — at least to some extent, from what you’re saying — that very theory, what counts as theory, by tools that, if you applied them on the same scale, would make induction come out as the perfect result, because basically that is the simplest solution with the fewest entities in principle. But according to what you’re saying there is also an advantage in essence, in abduction, in your ability to explain essence, which is not there.

[Rabbi Michael Abraham] To explain phenomena — or to explain phenomena that aren’t only related to that graph. Afterward, once we reached quantum theory, now it already has implications far beyond black-body radiation. Now we’re talking about a whole set of many, many phenomena. That is the advantage of a theory.

But you’re right that the move from the phenomenological theory — yes, from the result of induction — to the underlying theory is to a large extent speculative. And the fact that you choose this theory rather than another is indeed a difficult philosophical question: why do you prefer the simpler one? So there are those who will say: right, it says nothing about reality, it’s just convenience — why work hard if you can work easily? And that’s Kuhn and Popper and many people in philosophy of science; many think it really is just a methodological rule.

I think that among scientists — and again, as a physicist I know a bit of my surroundings — you’d find percentages close to one hundred percent of people for whom it is obvious that a simple theory is also more correct. Philosophers play around with all sorts of possibilities, but I think — again, one can argue — that in practice scientists are pretty convinced that when they discover a theory, they discover some truth about the world. They’re not merely finding a convenient framework for dealing with facts, as the other thesis claims. Okay? So that’s just…

[Speaker D] You can still argue, and also look — I think this also connects to overfitting in learning. That is, at some point you move from memorization to learning. And if you have a very, very complex model, then it seems you haven’t really learned something about the phenomenon. I think there’s actually a connection between…

[Rabbi Michael Abraham] Again, you’re defining learning by how many facts I can derive from it. And again, that’s a definition of learning only in terms of results, not in terms of the truth of the theory itself.

[Speaker D] No, no — the opposite. I’m actually claiming that if in order to encode my theory I need to bring in a great many rules, then I think I probably have an incorrect theory. If I have to add another rule and another rule and another rule and another rule in order to make things work, then I’m losing something in the generalization. At some point I’m not actually generalizing; I’m just recording the cases I’ve seen. Exactly — just documenting reality. No, I don’t really have a model of the world, I just made patch after patch after patch. You can always take everything you saw and write it down, and you haven’t learned anything.

[Rabbi Michael Abraham] Yes. Now, if the number of rules is roughly the same as the number of facts, then that’s not a theory — it’s just a description of the set of facts in a different language. Exactly. Exactly. That’s true. But what lies behind your argument is indeed the conception that says simplicity is an indication of truth, not merely a methodological tool for convenience. Which is what I said: I think that is what almost all scientists believe, at least the ones I know, including myself. Even though on the philosophical level you can of course argue — it’s hard to prove it one way or the other.

By the way, I even have a statistical proof of this. I propose a statistical proof that this is not merely a methodological rule but a substantive one.

[Speaker D] I think intuitively I agree with you very much that it’s true, and one can probably prove it statistically. I think this connection — maybe not a natural one — people usually think about information compression when they zip a file on a computer. But really there is, in my view, a deep and under-discussed connection between representation and compression of information and learning — that it’s actually the inverse of the same operation. And that ties exactly into this issue of theory.

[Rabbi Michael Abraham] Because if you pass a line through a set of points, then you’ve compressed the information of the set of points into two parameters — the a and b of the straight line, I mean. Or least squares, whatever. That’s obvious. Compression certainly counts as learning in that sense. And again, one can argue whether that is learning only in the formal sense — I can represent the information with fewer parameters — or whether it is learning in the sense that I really think the straight line better describes the world. That’s a philosophical dispute.

[Speaker E] There’s also significance here to how you define the world.

[Speaker B] You need to grasp the essence, not the cases.

[Rabbi Michael Abraham] The question is whether there is such a thing as essence. That’s part of the dispute.

[Speaker E] By the way, by the way, the whole issue of unmodeled learning — in the large language model field, this whole discussion of world models, whether we should train models that are generative or models that are compressed, meaning they understand the compressed representation of the world better — that discussion is taking place. Maybe not in the pure form we’re conducting it, but it definitely exists.

[Speaker D] Right, right, I agree with you. But it’s not in the mainstream; it’s not taught in universities. It’s the kind of thing you know only while following the… in short, in my view it’s not prominent enough.

[Speaker E] Let’s say also the idea that the world is not what we see but just some representation we construct in the mind — I learned that a lot in university too. But that’s what we do with the knowledge graph.

[Speaker B] That’s what we do with the knowledge graph — trying to represent the world as much as possible in terms of essences and not cases. And that’s no easy thing, in short.

[Rabbi Michael Abraham] Let’s move on a bit, because I want to get through this. So look — I’ll share with you a Talmudic passage. It’s a well-known line from Rabbi Chaim of Brisk. The Talmud says as follows — in Chagigah 3a:

תנו רבנן: איזהו שוטה? היוצא יחידי בלילה, והלן בבית הקברות, והמקרע את כסותו. איתמר, רב הונא אמר: עד שיהיו כולם בבת אחת. רבי יוחנן אמר: אפילו באחת מהן.

The Sages taught: Who is considered mentally incompetent — meaning insane, not of sound mind? One who goes out alone at night, spends the night in a cemetery, and tears his clothing. It was stated: Rav Huna said, only if all of them are present at once — you need all the characteristics in order to declare someone mentally incompetent. Rabbi Yochanan said: even one of them is enough.

The Talmud asks: what are the circumstances? If he does them in a foolish way, meaning in a way that indicates there is no logic behind the action, then even one is enough. If he does not do them in a foolish way, then even all of them are not enough.

The Talmud says: actually, we are dealing with a case where he does them in a foolish way — and still: if he sleeps in a cemetery, perhaps he does it so that a spirit of impurity will rest upon him. In other words, maybe there is a rationale behind what he’s doing, so he’s not insane. One who goes out alone at night — perhaps he has been seized by a fever and is going out to cool off. And one who tears his clothing — perhaps he is preoccupied, absentminded, lost in thought. So we have local explanations for each one of the characteristics, such that someone who has one of them is not necessarily mentally incompetent.

Then the Talmud says: once he does all of them, they are like someone who repeated and repeated — he becomes established in it. What does that mean? It says that if he did all three things, then he is probably mentally incompetent.

Rabbi Chaim of Brisk asks: what do you mean? You’re telling me that if he has all three characteristics he is mentally incompetent — but what if he has two? Suppose there are only two. You say: look, the first characteristic may be because he was hot, so he went outside. Fine. But then there’s the second characteristic — he tears his clothes — maybe he was lost in thought? Right? So you can’t know he’s insane; each one may have its own explanation. What about the third characteristic? That too — maybe he wants a spirit to rest upon him. For all three characteristics, you can offer each one its own explanation or rationalization. Why do you think that if all three are present he is necessarily mentally incompetent?

And then he says: look, two characteristics, each with its own explanation — fine. But three characteristics, each with a different explanation, when you compare that to the possibility that there is one explanation that accounts for all three — clearly the second possibility is better.

[Speaker F] That’s entirely a matter of probability.

[Rabbi Michael Abraham] Occam’s razor — perhaps one can also make a probabilistic model of this, I don’t know.

[Speaker F] No, I mean it’s the multiplication of the probabilities of each of them, if you’re talking about it that way.

[Rabbi Michael Abraham] Okay, although you still need to set the threshold, of course — at what probability and above do you declare him mentally incompetent? Because it’s never one. But fine, that’s a separate discussion.

In any case, the claim is that we prefer one explanation that accounts for three phenomena — yes, that’s basically Occam’s razor — over the possibility that I have three explanations, each of which explains a different phenomenon.

Think about the law of gravity. I see that I’m holding this mouse, I let go, and it falls down. Fine — maybe that’s because it’s black plastic. Then I take that book, let go, and it also falls down. Fine — that’s because it’s made of paper. That proves nothing. So I say, fine, and what about the pen? I let go and it also… Fine, that’s because it’s made of plastic, and therefore it falls.

Now I have three possibilities: either give a specific explanation for each phenomenon on its own, or give one shared explanation, one explanation that will account for all three, namely that all of them have mass and therefore they fall toward the earth. In the scientific world we obviously prefer the second option. Right? Scientific generalization is always based in that sense on Occam’s razor. Because you can always have a local ad hoc explanation for each fact separately. And when you say: no, I prefer the line that stitches together the three facts, the general law that explains all the facts — then you are making a generalization, or an abduction, or whatever you want to call it, and using Occam’s razor. You are taking the simplest explanation.

Now let me ask you a non-philosophical question, from real life: what would you say — is he really insane or not? Because someone who says the definition is only methodological will say: honestly, if you ask me, I have no idea whether he is insane or not, but methodologically I prefer this explanation because it is more economical. I’d say: fine, but I’m not interested in methodology; I want to know whether he is insane. That’s what interests me.

Now if I answer that in the affirmative — and I think psychiatrists who make a diagnosis always do answer in the affirmative; there are a certain number of characteristics needed, but once they have enough of them, they answer yes and give the person a diagnosis — then they are basically assuming they found something real about the person.

Behaviorism, for example, is a view that says: I focus only on behaviors, and everything else is kind of… that is perhaps the closest thing to the view that Occam’s razor is merely a methodological principle. I don’t go into theories that stand behind the behavior, but if there is such-and-such a set of behaviors, that for me defines this syndrome or whatever. It depends on what kind of behaviorism, never mind — but behaviorism in the plain sense is roughly that.

But ordinarily, a regular psychologist or psychiatrist treats the diagnosis he gives a person as some sort of description of the person. He sees it as discovering something about reality, exactly as a scientific researcher sees the theory he discovered as something that says something about reality.

And therefore I say that these non-deductive tools — analogy, induction, abduction — are also tools, or mainly tools, that teach us something about reality. And now I’m basically reaching the end of the introduction. Because I’m saying: if that is really so, then according to the usual division, logic and mathematics deal with deduction, with deductive inferences. And science deals with analogies, inductions, abductions — softer tools, let’s call them. That’s the soft logic I’m talking about.

The question is whether I can also provide formal or substantive justification for these tools. Is it possible to formalize an inductive argument, an analogical one, and so on? There were already attempts of this sort by Francis Bacon back in the sixteenth century, when he tried to build an inductive logic. It’s mainly eliminative, really: you choose theories and eliminate them according to the facts, and you supposedly remain with the correct theory. So he tried somehow to formalize this inductive logic. I don’t think it’s really a formalization, but he did try somehow to propose a more formulated, defined, and systematic scheme for scientific generalization.

In mathematics these things are more obvious: how to formalize, how to work systematically — that is the whole essence of mathematics and logic. How do you do this in science, in law, in Jewish law? How can we use these tools in a way that gives us some confidence that we’ve used them properly? Because if I think it’s only a methodological tool, then I don’t need any special confidence. I just take whatever is simplest — why do complicated work? I take the simplest tool and use it. But if I really see this tool as a tool for uncovering truth about the world, then I would very much want — I don’t know if it’s possible, but if it is — some way to check formally the soft inferential processes. Not deduction — analogy and induction, and perhaps abduction as well.

And what I want to do — probably next time — is basically to formalize the non-deductive forms of inference systematically. I’ll try to show that this actually connects abduction with induction and analogy, and gives an overall framework for arguments as complex as you like, arguments that I can formalize in a very systematic way. It doesn’t turn them into deduction, by the way — that’s the trick here, and it’s interesting. It doesn’t turn them into deduction, but I can offer an orderly formalization.

And I’ll claim more than that, if I get to it — I’m not sure I will — namely, that this formalization is already in the Talmud. The Talmud already produced the building blocks of this formalization. You can already find them there. What we did — with two other people, we’re working as a team — is take those building blocks and try to build a general formalist framework. How do I formalize non-deductive arguments, when the building tools here are what in Jewish law are called a fortiori reasoning, paradigm construction, and their various combinations, along with objections to them and ways of rescuing them, and so on? It can be as complex as you want. But there is a formal, systematic way to formalize these forms of inference.

The important value of this method, beyond the fact that it gives me some peace of mind instead of using them only intuitively — here I have some measure of whether what I’m doing fits the formalization I’ve proposed, whether I’m working correctly — beyond that, I also hope to show that I can use these tools even where intuition has already run out. That is, you have no intuitive way to know whether this analogy makes sense or doesn’t make sense, or the induction, or something like that. You can work in a completely formal way, as people do in deductive logic, and reach a conclusion.

[Speaker B] I think that’s also what gives you, in a certain place, consistency, right? If you understand the essence of the thing, then when you get more examples and more things from which you derive laws, you always say: you can derive laws in all kinds of ways. I want some guiding line from which I’ll start deriving the laws, so that I can go on predicting things well.

[Rabbi Michael Abraham] Absolutely — exactly, that’s what I’m saying. Now the nice point here is — just as an anecdote — I once gave a lecture about this at Tel Aviv University, some seminar in computer science. Before that, my son, who was studying in a yeshiva called Merkaz HaRav, came to me and said: listen, there’s some Tosafot that we can’t understand — what kind of inference is it making there? Some kind of a fortiori reasoning with an objection and something else — what’s going on there?

And indeed, intuitively, it’s a little hard to understand what Tosafot did there. I said to him: leave it. I took out a sheet of paper, built the table, wrote out the formulas of the matter, and said: here, this is the result. You can do it in an entirely formal way even where you’ve lost your intuition. And that’s the advantage of formalization. Formalization helps you precisely where it’s hard to do it intuitively, and also where you might make mistakes, of course.

So I think what I’ve done until now is give some kind of justification or motivation for why such a thing matters, or what it can contribute. I claim that scientific inference also operates with this logic. I can try to formulate how scientific inference works.

[Speaker B] But then, in a sense, aren’t you creating for yourself some kind of cognitive limitation? Because you get so deeply into a certain direction that it’s hard to break free from it and look at and examine new facts in a clean way.

[Rabbi Michael Abraham] That’s always true. If you remind me, I’ll wait till next week.

[Speaker D] It sounds to me like a justification for statistics. Because every statistical method, by definition, comes and assumes something about the nature of the world, so one of those assumptions I can assume.

[Rabbi Michael Abraham] I don’t think you’ll be able to translate this into probability. I can, however, show a plausibility consideration behind it.

[Speaker D] I think again, plausibility and probability — the difference is whether I know how to assign the number. But in both there’s a shared element: you’re saying that under certain assumptions, I assume a certain process. Probability is a type of plausibility, yes.

[Rabbi Michael Abraham] Right. Fine, good, okay.

[Speaker B] Friends, I want to say thank you very much, Rabbi — excellent. Friends, take care of yourselves, stay calm, and everything will be okay. Professor Shaked, I’m glad to see you came, and I hope your time here in Israel passes quietly, but it’s good to see you with us regardless.

[Rabbi Michael Abraham] Thank you, thank you, it was a pleasure.

[Speaker B] And Mai, it’s also good to see you. And friends, it’ll be okay, don’t worry. Bye-bye.

[Rabbi Michael Abraham] Thank you very much.

[Speaker A] Goodbye.

[Speaker D] Thank you very much.

[Speaker B] Thank you, friends, thank you. שיר המעלות בשוב השם את שיבת ציון היינו כחולמים. אז ימלא שחוק פינו ולשוננו רינה. אז יאמרו בגויים הגדיל השם לעשות עם אלה. הגדיל השם לעשות עמנו היינו שמחים. שובה השם את שביתנו כאפיקים בנגב. הזורעים בדמעה ברינה יקצורו. הולך ילך ובכה נושא משך הזרע בא יבוא ברינה נושא אלומותיו. אשרי כל ירא השם ההולך בדרכיו. יגיע כפיך כי תאכל אשריך וטוב לך. אשתך כגפן פוריה בירכתי ביתך בניך כשתילי זיתים סביב לשולחנך. הנה כי כן יבורך גבר ירא השם. יברכך השם מציון וראה בטוב ירושלים כל ימי חייך. וראה בנים לבניך שלום על ישראל. (A Song of Ascents: When the Lord brought back the captives of Zion, we were like dreamers… Peace be upon Israel.)

We see in this psalm the wonderful combination of serving God and the work of one’s hands. “You shall eat the labor of your hands; happy are you, and it is well with you.” The Talmud says in tractate Berakhot 8a: greater is one who enjoys the labor of his own hands than one who merely fears Heaven, for regarding one who fears Heaven it says, “Happy is everyone who fears the Lord,” whereas regarding one who enjoys the labor of his hands it says, “You shall eat the labor of your hands; happy are you, and it is well with you” — “happy are you” in this world, “and it is well with you” in the world to come.

What does that mean? Heaven forbid — is work greater than Torah? Certainly not. Rather, someone who merits to combine both — who both fears Heaven and also enjoys the labor of his own hands — is on the highest level. He does not need gifts from flesh and blood, and he sanctifies God’s name in his business dealings.

We know about the famous partnership of Issachar and Zebulun. “Zebulun shall dwell by the seashore” — he goes out to work and supports Issachar, who sits in the tents of Torah. Moses blesses them: “Rejoice, Zebulun, in your going out, and Issachar, in your tents.” Zebulun comes before Issachar in the blessing because without his support Issachar cannot study. But the whole point of Zebulun’s going out is for the sake of Torah.

A person who goes out to work today is Zebulun. He needs to know that his work is a means, so that he can set fixed times for Torah, so that he can give charity, so that he can raise his children for Torah. Maimonides, in the Laws of Torah Study, chapter 3, strongly reinforces this issue of earning one’s living by one’s own labor. He mentions that great figures of Israel, like Hillel the Elder who chopped wood, and Rabbi Chanina and Rabbi Hoshaiah who were shoemakers, were not ashamed of their work. On the contrary: great is labor, for it honors the one who does it. A person should toil for his livelihood and not be a burden on the community. But the condition is that fear of Heaven always stand before him. “The labor of your hands” — only the hands should be laboring, but the head should remain free for words of Torah and holiness. If a person is wholly immersed in business and forgets Torah, then he has lost the way. The goal is “In all your ways know Him.” Even when you are at work, be a Torah person. Conduct yourself honestly, with good character. That is the greatest sanctification of God’s name. May we all merit God’s blessing in all the work of our hands, and may we always merit to cling to Torah and the commandments with expansiveness and joy. Amen and amen.

We find in this week’s Torah portion, Ki Tetze, the commandment of the parapet. The Torah says: כי תבנה בית חדש, ועשית מעקה לגגך, ולא תשים דמים בביתך, כי יפול הנופל ממנו (“When you build a new house, you shall make a parapet for your roof, so that you will not place blood in your house, if the fallen one falls from it”). Holy Rashi asks there: is it because this person built a new house that he is obligated in a parapet? Rather, one commandment leads to another. If he built a house, in the end he will make a parapet; in the end he will have a vineyard and charity and all the commandments.

And we need to understand the depth of these words. What is the connection between a new house and all the other commandments? The masters of ethics say that a person’s house is really his inner world. A person builds himself a personality; he builds himself a world. The Torah tells him: when you build a new house, when you begin a new path, the first thing you need to do is make a parapet. What is a parapet? A parapet is meant to prevent falling. The roof is the highest place in the house; there a person can feel pride, can feel that he is above everyone else. The Torah tells him: set a boundary to your pride. “You shall make a parapet for your roof.” Don’t allow yourself to fall from that height into bad places. “And you shall not place blood in your house” — don’t bring bad character traits into your home. “If the fallen one falls from it” — the Sages say: this person was fit to fall from the six days of Creation, but merit is brought about through the meritorious and liability through the liable. If a person does not make a parapet, he becomes the agent of liability. But if a person is careful and makes safeguards for Torah, and makes a parapet for his actions, he merits to be the agent of merit. And that is the foundation of all the commandments: one commandment leads to another. When one behaves carefully with one commandment, that gives strength to continue on to all the other commandments and to build a faithful home in Israel.

This matter of dignity, as we said, is not only something external. The Maharal explains in Netiv HaTzniut that dignity is related to returning inward. It returns to one’s inwardness. When a person walks in a respectable way, in clothing that represents his essence, he does not do it for pride. It’s not about showing others how important he is. On the contrary, it’s about reminding himself of his responsibility. When a person wears a frock coat, he becomes a representative of Torah. He cannot behave improperly when dressed like that. It obligates him. That is exactly the point of the priestly garments: “for honor and for glory.” The Torah says the garments must be honorable because they reflect the honor of the service, the honor of the Divine Presence. The honor is inward, but it has to be expressed outwardly through splendor. If there is no splendor, the honor remains hidden and does not affect the world. Real modesty is knowing how to combine the two: to keep the inwardness strong, but give it external expression that honors the person’s standing and role in this world. Therefore the conduct of a Torah scholar should be noble. That is part of sanctifying God’s name. The joy of the first-fruits is not only over the produce, but over the privilege of being part of this process of revealing His honor within the material world.

In this Torah portion we also see another very important matter, namely tithes. בערתי הקודש מן הבית (“I have removed the sacred portion from the house”). A person’s ability to testify about himself that he did everything according to God’s command — this is not only a matter of religious bureaucracy, it is a matter of connecting to the point of truth. When a person stands before God and says, “I did all that You commanded me,” he is really building within himself a place of trust: trust that everything he has is from God, and that he did not take anything for himself that did not belong to him. That spiritual cleanliness allows blessing to descend. השקיפה ממעון קודשך מן השמים וברך את עמך את ישראל (“Look down from Your holy dwelling, from Heaven, and bless Your people Israel”). Only after a person cleanses himself of every trace of theft, of every trace of selfishness, can he ask for the general blessing. This Torah portion, Ki Tavo, is a portion of building: building the land, building the Temple, and building the soul. May we truly merit to feel that joy — the joy of connection, the joy of gratitude, and of doing God’s will with a full heart.

Portion of Chayei Sarah. ויהיו חיי שרה מאה שנה ועשרים שנה ושבע שנים שני חיי שרה (“The life of Sarah was one hundred years and twenty years and seven years; these were the years of Sarah’s life”). Holy Rashi brings the famous midrash: at one hundred she was like twenty with regard to sin — just as at twenty she had not sinned, since she was not yet liable to punishment, so too at one hundred she was without sin; and at twenty she was like seven for beauty. And what it says at the end of the verse, “the years of Sarah’s life,” is to teach you that they were all equally good.

The Sefat Emet asks: how can one say of all Sarah’s years that they were equally good? Sarah our matriarch went through so many trials and difficulties in her life — years of sorrow, years of barrenness, years of wandering. How can one say they were all equally good? The explanation is that Sarah was refined through these trials. She accepted everything with love, and every single year of her life was used for the purpose for which she came into the world. Therefore, from the standpoint of the essence of life, all the years were equally good.

Later it says: ויבוא אברהם לספוד לשרה ולבכותה (“Abraham came to eulogize Sarah and to weep for her”). We find in the word “and to weep for her” that the letter kaf is written small. The בעל הטורים says that Abraham our father wept only a little, because Sarah was old and had already completed her days. And some say he wept only a little because he had to hurry to bury her and purchase the Cave of Machpelah.

The portion continues: ואברהם זקן בא בימים (“Abraham was old, advanced in days”). What does “advanced in days” mean? The holy Zohar says that he came with all his days. A person can be old in age but not come with his days, because the days were empty. Abraham our father filled every day and every hour with spiritual content — with commandments, with kindness, with bringing near those who were distant under the wings of the Divine Presence. Therefore when he reached old age, he came together with all his days. That is the great lesson for us: to use every moment and every hour. Sarah and Abraham taught us how to live a life of meaning, how to turn difficulties into steps of ascent, and how to reach the end of the road when all our days are with us and testify that we did the will of our Creator.

Blessed are You, Lord our God, King of the universe, who sanctified us with His commandments and commanded us concerning words of Torah.

The seventh day of Passover is the day on which we celebrate the great miracle of the splitting of the Sea. The verse says, אז ישיר משה ובני ישראל את השירה הזאת לה’ (“Then Moses and the children of Israel will sing this song to the Lord”). The Talmud in tractate Sanhedrin 91b brings this verse as a source for resurrection of the dead from the Torah. The Talmud asks: it does not say “sang,” but rather “will sing” — from here resurrection of the dead is derived from the Torah.

What is the connection between the Song at the Sea and resurrection of the dead? Why does the Torah hint to it specifically here? Rabbi Hutner explains in his book Pachad Yitzchak that the whole idea of song is the ability to see the connection between all events. In this world we see isolated events, one thing here and another there. But in song, everything joins into one great melody. At the Red Sea, when they saw the great miracle, they saw how everything they had undergone in Egypt — all the slavery and all the plagues — all led to that moment of “Israel saw the great hand.” In such a moment of clarity, when past and present connect, one can also see the future. Therefore the song was said in the future tense, “then Moses will sing,” because it contains within it all of history up to the resurrection of the dead.

The level of the Jewish people at the Sea was so high that the Sages say, “A maidservant at the sea saw what Ezekiel son of Buzi did not see.” She saw God’s kingship in the clearest way possible. That is the power of the seventh day of Passover: the ability to see God’s hand within our reality and sing Him a new song for redemption and for the deliverance of our souls. May we merit, with God’s help, to see with our own eyes when the Lord returns to Zion, and to sing this song speedily in our days, amen.

Peace to everyone, good morning. We are on the eve of the holy Sabbath, with the portions of Behar and Bechukotai joined together. Our portion opens with the well-known verse: וידבר ה’ אל משה בהר סיני לאמור: דבר אל בני ישראל ואמרת אליהם כי תבואו אל הארץ אשר אני נותן לכם ושבתה הארץ שבת לה’ (“The Lord spoke to Moses at Mount Sinai, saying: Speak to the children of Israel and say to them: when you come into the land that I give you, the land shall rest, a Sabbath to the Lord”). Rashi on the spot asks the famous question we all know: what does the Sabbatical year have to do with Mount Sinai? Weren’t all the commandments given at Sinai? Rather, just as the general rules and fine details of the Sabbatical year were said at Sinai, so too all the commandments, their general rules and details, were said at Sinai.

This midrash, which Sifra brings and Rashi quotes, comes to teach us a great principle. Why specifically the commandment of the Sabbatical year was chosen to be the paradigm for all the commandments? Why here did the Torah choose to emphasize that it was said at Mount Sinai? Obviously the whole Torah was given at Sinai. Rather, the Sabbatical year is the greatest test of a Jew’s faith and trust in the Holy One, blessed be He. A person works his land for six years, and in the seventh year he has to abandon everything, not sow and not reap, and rely only on God’s blessing. That shows complete submission to God’s will. And that is exactly the meaning of Mount Sinai. Mount Sinai represents accepting the yoke of the kingdom of Heaven, understanding that everything is from Him, may He be blessed. “For the whole land is Mine,” says the Holy One, blessed be He, later in the portion. We are not the homeowners; we are only agents.

In the portion of Bechukotai we read about the blessings and the curses. אם בחוקותי תלכו (“If you walk in My statutes”) — Rashi explains: that you should toil in Torah. Toil in Torah is the basis of everything. When a person toils in Torah, he connects to the root, he connects to Mount Sinai, and then he can also observe difficult commandments like the Sabbatical year with joy and trust. May we merit, with God’s help, to toil in Torah and to see with our own eyes the blessing resting on all the work of our hands. A peaceful and blessed Sabbath to all the Jewish people.

Why the language of walking? Torah is study, not walking. Why use the language of walking? You can explain it in several ways. First, when a person studies Torah, Torah is not static; it is dynamic. Torah changes the person. A person who enters to study Torah does not come out the same person. He moves forward, he walks. Torah is “you shall walk.” You go and advance, you go and change. Torah raises a person from level to level, from rung to rung. Therefore it says, “If you walk in My statutes.”

Another explanation: the Talmud says in tractate Niddah, “Whoever studies Jewish law every day is guaranteed a share in the world to come, as it is said: ‘His are the ways of the world.’ Do not read ‘ways’ but ‘laws.’” What is the connection between laws and ways? Jewish law is the way a person is supposed to walk. When a person studies Torah, he learns how to walk in life — on what path to go, on what road to go. Therefore it says, “If you walk in My statutes.” Study leads to action. Study instructs a person in the path they should walk.

Another explanation: Or HaChaim says, “If you walk in My statutes,” means that a person should not stop, but should always aspire to more. Walking is always forward. A person who studies Torah must know that there is no end to Torah. There is always more to learn, always further to progress. Therefore, walk — do not stand still; always be in motion, moving forward.

We are on the eve of the holy Sabbath of the portion of Shemini, the Sabbath that blesses the month of Iyar. The Talmud in tractate Yevamot 62b says: Rabbi Akiva had twelve thousand pairs of students from Gevat to Antipatris, and all of them died in one period, between Passover and Shavuot, because they did not treat one another with respect. And the world remained desolate until Rabbi Akiva came to our rabbis in the south and taught them — Rabbi Meir, Rabbi Yehuda, Rabbi Yosei, Rabbi Shimon, and Rabbi Elazar ben Shammua — and they were the ones who reestablished Torah at that time.

These days of counting the Omer, during which we mourn the death of Rabbi Akiva’s students, are days of repair. What does it mean that they did not treat one another with respect? They were great righteous men. Rather, each of them had his own path in serving God, and he could not contain the path of the other. He thought only his path was correct. The Talmud says: the world remained desolate. Without Torah that combines within it all the shades and colors, the world cannot exist. Rabbi Akiva went south and taught the five new students. With them, there was already a repair of mutual respect.

The month of Nisan is the month of miracles, above nature. The month of Iyar is a month of self-work: “I am the Lord your healer.” The work of the counting of the Omer is the refinement of character traits. Every week and every day we work on a different trait — lovingkindness, strength, beauty, endurance, splendor, foundation, kingship. The goal is to reach the festival of Shavuot, the time of the giving of our Torah, as proper vessels. It is impossible to receive Torah without unity. “Israel encamped there opposite the mountain” — as one person with one heart. When the Jewish people are united, they can receive the Torah. Therefore the central commandment Rabbi Akiva emphasized is “Love your neighbor as yourself” — this is a great principle in the Torah. The repair of these days is to increase love of the Jewish people, increase mutual respect, to see the virtue of one’s fellow and not his deficiency. May we merit, with God’s help, a good and blessed month, a month of healing, a month of spiritual ascent, and may we merit to receive the Torah with unity and joy.

Today we begin chapter seven of tractate Shevuot. The Mishnah says: all those who swear in the Torah swear and do not pay. That is, the oath is always for the defendant in order to exempt himself from payment. But there is a list of people who swear and collect. And these are they: the hired worker, the victim of robbery, the injured party, and one whose claim is against a shopkeeper.

Let’s explain the case of the hired worker. The worker says, “I did not receive my wages,” and the employer says, “I paid.” Usually the employer would have to swear and be exempt, but here the Sages enacted that the worker swears and collects. Why? Because the employer is preoccupied with his workers. He is busy; he does not remember exactly whom he paid and whom he did not. The worker, by contrast, remembers very well, because this is his bread. Therefore they gave him the power to swear and receive the money.

The same with the victim of robbery: if there are witnesses that a man entered his house and took objects, the robbed person swears and collects. The aim of the Sages was to help those people who are weak within this system. A person who works hard all day should not lose his wages merely because the employer forgot or got confused. Therefore the hired worker swears and collects his wages in the evening, as it is written: “On that day you shall give him his wages.”

So why does one need wine? The Sages are the ones who enacted that one should remember the Sabbath over a cup. But what is the status of that cup? Is the cup only an embellishment of the commandment, or is it an inseparable part of kiddush? There is a fundamental question here in understanding the definition of kiddush. Is kiddush a commandment that applies to the person, or is it a law in the day? On the one hand the Sabbath is already sanctified; on the other hand we are commanded to sanctify it. That is the meaning of “Remember the Sabbath day to sanctify it.”

And similarly we find in the Exodus from Egypt that the whole matter of matzah and bitter herbs is “upon” — meaning that the eating must be in such a way that it expresses the memory of the Exodus from Egypt. All the commandments of the Passover night revolve around the matter of “and you shall tell your child.” Speech is the main thing, and the acts — the eating of matzah and bitter herbs — accompany that speech. That is the depth of the simple meaning of “upon.”

We also see in the blessings over commandments the concept that the blessing must precede the act. The blessing has to be adjacent to the action. Speech and action join together into one complete commandment. And that explains the matter of kiddush over wine: praise and thanksgiving to God for the holiness of the Sabbath must be done in the most dignified way possible, and that is through a cup of blessing. The cup elevates the level of remembrance and turns it into something more tangible and festive.

The question is whether the wine is the object of the commandment or only a tool for the commandment. We find in the Talmud in tractate Nazir that there is a concept of sanctification taking effect on the wine. That means the wine itself receives a certain sanctity when we recite kiddush over it. It’s not just that we say words and the wine happens to be there; the wine becomes a cup of blessing. From here the later authorities learned that there are two aspects to kiddush. There is the remembrance in words itself, which is a Torah commandment, and there is kiddush over wine, which is a rabbinic enactment intended to give the commandment an aspect of importance and joy. The wine is not only an external addition; it changes the essence of the utterance. When a person recites kiddush over wine, he connects the holiness of the Sabbath with the world of action, with material joy. That is the meaning of “to sanctify it” — to distinguish the Sabbath from the other days also through physical means. Therefore it is very important to be careful that the cup be full and clean, because the cup is the practical expression of the honor we show the Sabbath day. In the end, this combination of speech and action, between the words of kiddush and the cup of wine, is what creates the wholeness of the commandment of kiddush as we received it from our rabbis.

The blessing “who gives sight to the blind.” The Talmud in tractate Berakhot says: when one opens his eyes, he should say, “who gives sight to the blind.” That is, the moment a person opens his eyes in the morning, he blesses the Holy One, blessed be He, for that wondrous gift of sight. But the depth of this blessing goes far beyond physical sight. The word “blind” in the holy tongue is related to skin. A person who sees only the skin, only the outer wrapping, is considered blind. He does not see the inside. “Who gives sight to the blind” means the ability to peel away the skin and see the innerness of things. A person who merits proper sight sees the Holy One, blessed be He, in every single detail of creation. He does not see only nature; he sees providence. He does not see only chance; he sees a guiding hand. It is written about the first man that he saw with the hidden light from one end of the world to the other. What does that mean, from one end of the world to the other? It means he saw the purpose, he saw the end, he saw what everything leads to. And that is what we ask every morning: “who gives sight to the blind.” Master of the universe, open our eyes so that we may merit to see Your truth, to see the good in every Jew, to see our mission in this world and not walk like blind people in darkness. Sight is the gateway to the soul, and when one sanctifies sight one merits the indwelling of the Divine Presence. May we truly merit to see a built world, a world full of divine light.

Good Sabbath eve to everyone. This week’s Torah portion is Vayishlach. Jacob our father returns to the Land of Israel and prepares for his encounter with Esau. He sends messengers. Rashi says: actual angels. He prepares in three ways: a gift, prayer, and war. At night he crosses the ford of Jabbok, and “Jacob was left alone.” He wrestles with the angel until dawn. The angel strikes his thigh, and from here comes the prohibition of the displaced sinew. “Therefore the children of Israel shall not eat the displaced sinew.” May we merit a peaceful Sabbath and good tidings.

And there is a deep connection between these two things. The wood gatherer — what did he want to prove? He wanted to prove that once the decree was made that they would not enter the land, then all the commandments were nullified. He said: all the commandments depend on the land. If we are not entering the land, then we are no longer obligated in the commandments. Therefore he went and desecrated the Sabbath publicly, to show that there was no longer any obligation. And God’s answer was the section of tassels. “And they shall make for themselves tassels on the corners of their garments throughout their generations.” Throughout their generations, in every place and at every time. This commandment accompanies a person always, and reminds him of all the commandments. “And you shall see it and remember all the commandments of the Lord.” That is the connection. The wood gatherer tried to sever, and the tassels came to reconnect. They tell us that even in the wilderness, and even in exile, and in every situation, the commandments are eternal and always bind us.

And Jacob our father is the one who contains all the Jewish people within himself. And the third Sabbath meal corresponds to Jacob our father, and it is the time of the “will of wills.” The “will of wills” is the highest time that exists on the holy Sabbath, when God’s will is revealed in the world in the strongest way possible. Therefore, the Talmud says that one who observes the three Sabbath meals is saved from three calamities: the birth pangs of the Messiah, the judgment of Gehenna, and the war of Gog and Magog. Why specifically these three? The Maharal of Prague says that these three calamities basically represent all the difficulties a person can have in this world. The birth pangs of the Messiah correspond to bodily hardships, physical troubles. The judgment of Gehenna corresponds to spiritual hardships, to the evil inclination. And the war of Gog and Magog corresponds to the collective troubles of the Jewish people, the wars and hardships the nation undergoes. This teaches us that even when a person goes through personal difficulties, he should not sink into himself, but continue to look outward and see where he can help others.

He said to them: what are you debating? Man has already been made. That means that the Holy One, blessed be He, established a fact on the ground. But the question remains: what about the argument of the angels? The argument of the angel of truth is indeed correct, for man is full of falsehood. So what was God’s answer? “And He cast truth to the ground.” The commentators say that the Holy One, blessed be He, said to truth: you are right — in Heaven there really is no place for such a being. But I cast you down to earth. On earth, truth is not something static, not something fixed and standing. On earth, “truth will sprout from the ground.” Just as one sows a seed in the ground and it has to decay in order to sprout, so too man’s truth. Man’s truth is built out of failures, out of the falsehoods he overcomes. It is a truth of growth, a truth of development. And that is the truth the Holy One, blessed be He, wants. He does not want angels; He wants human beings who create truth out of the earth. Therefore “man has already been made,” because the potential of truth that will sprout from the earth is greater than the absolute truth of the angels in Heaven. For heavenly truth is a truth of being, while earthly truth is a truth of renewal. And that is what is written in Hasidic thought: that the Holy One, blessed be He, specifically wanted this creation in which there is concealment and hiddenness, so that precisely out of that concealment the deeper truth would be revealed — a truth connected to His very essence, which is beyond the categories of truth and falsehood as we understand them.