Dispute and Truth – Lesson 15

Table of Contents

• Ukimtot, casuistry, and rules versus cases
• Dispute and truth
• Occam’s razor, simplicity, and truth in science
• Equivalent descriptions, teleology, and Copernicus
• Minimizing dispute and the principle of charity
• The presumption of three times, an established goring ox, and the presumption of three years
• “Give dew and rain,” ninety times, and the dispute between Maharam of Rothenburg and Rabbeinu Peretz
• Reversing the accepted understanding by means of Occam’s razor and “we do not multiply disputes”

Summary

General overview

The text presents a view of Jewish law and the Talmud as a casuistic system in which general principles, not always explicitly formulated, are expressed through specific cases, and the mechanism of ukimta rests on that assumption in contrast to the weaknesses of a systematic-positivist method that tries to capture a living, complex field by means of rigid rules. It then sharpens the point that dispute does not prove the absence of truth, criticizes the mistaken inference from a multiplicity of opinions to anti-realism, and develops the claim that Occam’s razor is not merely a rule of convenience but a tool for getting closer to the truth. From there it applies the principle of simplicity both in the philosophy of science and in interpreting halakhic disputes, including the use of “we do not multiply disputes” and the principle of charity, and arrives at a reversal of the conventional conclusion in analyzing the dispute between Maharam of Rothenburg and Rabbeinu Peretz through an understanding of the dispute between Rabbi Meir and Rabbi Yehuda regarding an established goring ox.

Ukimtot, casuistry, and rules versus cases

The text argues that halakhic discourse rests on general principles that are not always explicitly formulated, and that the Talmud, as a casuistic composition, expresses principles through specific cases; therefore ukimta is a natural mechanism within that structure. The text presents the aspiration to work in a positivist-systematic way as almost tempting because of its apparent precision, but maintains that a system of rules does not capture nuances and connotations in living systems such as language, law, and Jewish law. The text adds that updating rules for new circumstances is also not well resolved within a positivist framework, and therefore proceeding through cases is really the same argument and not a separate one.

Dispute and truth

The text states that the existence of dispute is not proof that there is no truth, because the fact that there are differing positions does not require that all of them be correct; there may be one truth and the others are mistaken. The text distinguishes between the fundamental question of whether there is halakhic truth and the technical question of who decides it and how one reaches it. The text points to the model of Beit Shammai and Beit Hillel as a focal point for thinking about approaching truth through majority and methodology, as opposed to sharpness and intellectual superiority.

Occam’s razor, simplicity, and truth in science

The text describes Occam’s razor as a tendency to choose the simpler theory when it explains all the facts, but rejects the understanding that this is merely a rule of convenience and argues that simplicity is an indication of truth. The text frames this through the philosophy of science by using Ze’ev Bechler’s distinction between actualism, in which a theory is a tool for organizing observations and not a claim about the world, and informativism, in which a theory carries information about the world and is regarded as the closest thing to the truth until it is refuted. The text argues that one can decide empirically against actualism, because if the simpler theory has no real advantage, then success in predicting future events would be “zero” against an infinity of possible fits, whereas in practice science progresses and many theories survive tests of refutation, so the rate of success is not zero.

Equivalent descriptions, teleology, and Copernicus

The text states that there are situations in which “more correct” has no meaning and only “more convenient” does, because these are mathematically equivalent descriptive languages. The text presents the equivalence between a causal description and a teleological description in physics through Lagrangian mechanics and Fermat’s principle in optics, and emphasizes that the rejection of teleology as an “anecdote” stems from the mistaken understanding as though the particle “is doing calculations,” when in fact this is simply a way of describing the laws of nature. The text argues that the example of Copernicus too is not a matter of “correct versus incorrect” but of choosing a coordinate origin that simplifies the equations, so there simplicity is convenience and not a criterion of truth, unlike questions in which there really is a true or false answer, such as “Is there or is there not God?”

Minimizing dispute and the principle of charity

The text presents an interpretive rule according to which one minimizes dispute as much as possible, formulating it as “we do not multiply disputes,” so that an explanation that places a dispute on one principle is preferable to an explanation that multiplies principles of dispute. The text presents the principle of charity as a requirement of seeking truth rather than winning an argument, and therefore one must formulate the other side’s position in the best possible way and not attack a weakened version of it. The text illustrates this through an argument about qualifying women for testimony, where a quick dismissal by means of the “naturalistic fallacy” misses the more serious argument, which adds an assumption about the reason for the historical disqualification, and it presents clarifying the assumptions as the heart of the discussion.

The presumption of three times, an established goring ox, and the presumption of three years

The text presents the “presumption of three times” as a halakhic induction that appears in menstrual cycles, circumcision, and marriages in which “her husbands died,” and brings the established goring ox as a central source. The text notes the connection in tractate Bava Batra between an established goring ox and the presumption of three years for land through Rabbi Yohanan’s statement in the name of “those who went up from Usha,” and the Talmudic discussion about the difference between three gorings that create established status and monetary liability that begins only with the fourth goring. The text sets this framework as background for understanding the relationship between repeated cases and the establishment of a halakhic status.

“Give dew and rain,” ninety times, and the dispute between Maharam of Rothenburg and Rabbeinu Peretz

The text cites the Tur in Orach Chayim 114 in the name of the Jerusalem Talmud, according to which for up to thirty days there is a presumption that a person says what he is accustomed to saying, and from then on there is a presumption that he says what he is supposed to say; therefore a doubt within thirty days requires repetition, while a doubt afterward does not. The text describes Maharam of Rothenburg’s custom on Shemini Atzeret to say from “You are mighty” until “who makes the wind blow and the rain fall” ninety times, corresponding to thirty days of three prayers, and then to rely on that in a case of doubt, as well as his proof from “If one who spaced out his gorings is liable, then all the more so one who brought his gorings close together.” The text brings Rabbeinu Peretz’s rejection: “I have not seen the elderly rabbis of France do this,” and the claim that “the case being discussed is not comparable to the proof,” because in the case of the established goring ox we are dealing with an ox that has been established as one that gores, whereas with rain “the matter depends on habituating his tongue,” along with the Rosh’s inclination toward Maharam’s reasoning.

Reversing the accepted understanding by means of Occam’s razor and “we do not multiply disputes”

The text argues that the conventional yeshiva explanation cannot be correct, and declares that the right conclusion is “exactly the opposite,” so that Rabbeinu Peretz holds that gorings are habituation, while Maharam of Rothenburg holds that gorings are an indication, contrary to the common attribution. The text raises a principled difficulty about citing Rabbi Meir’s reasoning when the Jewish law follows Rabbi Yehuda, and concludes that one who brings a proof from a position that is not accepted as Jewish law assumes that the point of dispute is not in the place from which the proof was taken. The text applies “we do not multiply disputes” in order to place the dispute between Rabbi Meir and Rabbi Yehuda on a single axis, rather than assuming that they disagree both on whether this is evidence or habituation and on whether drawing occurrences closer together is effective in habituation; on that basis it arranges the positions so that the criterion of minimizing dispute reverses the reading of Maharam and Rabbeinu Peretz, and likewise the implication for “Give dew and rain,” from the conventional understanding.

Okay, so we were basically dealing with the question of interpretive restrictions. Through that I tried to say something about the meaning of halakhic truth, or the halakhic statement, and the claim is that we’re talking about certain principles, not always explicitly formulated, general principles that are expressed in specific cases. And the way of the Talmud, which is really a casuistic composition, is to express those principles through cases, through specific cases. And that is really the underlying assumption of the entire mechanism of interpretive restriction. Last time I got a bit into the question of casuistry itself. Meaning: why work that way at all, and not in some systematic positivist, logical way—just give me the rules, and from them I’ll derive the particular conclusions? And I pointed to weaknesses or flaws in that kind of approach. Meaning, it doesn’t really succeed in capturing the essence of the matter, because a system of rules is not really something that can capture a complex and branched field, like language, or like Jewish law, or a legal system. It can’t capture the nuances, it can’t capture the connotations that accompany things, and therefore to force things into a rigid framework of rules—that’s something that on the face of it looks very attractive, because it seems precise, absolute, the legislator can tell me exactly what he wants, it doesn’t depend on analogies I make and so on—but in the broader test I think it’s actually a less successful method, a method that can’t work within a living world, not a mathematically precise but detached world, but a living world, like a legal system, like the halakhic system. But here you’re talking about the rule versus the ruling—say the laws are brought in. Yes, but that itself is the question: whether that’s good or not. And when you ask whether it’s good or not, you’re trying to avoid seeing the question as: if the rules don’t fit, then what are they… so change the rules. Even that process of change itself—you could say: okay, so let’s change the rules or apply them differently. But no, we want to mediate it through cases. It’s true that that gives a better grasp, and it also comes to expression in situations where we need adjustments and changes. But that itself is exactly what I’m claiming. Meaning, it’s not a different argument, it’s the same argument itself. Meaning, one could also have tried to handle the issue of updating and adapting to new circumstances in a seemingly positivist way; the claim is that you can’t. That’s exactly what I said before. Fine, so that’s regarding what we’ve seen until now.

I want to move to another topic or another discussion, and our subject, after all, is dispute and truth. Now I want to speak a bit about dispute. A few points that touch on the question of dispute. So we already spoke about the question of the relationship between dispute and halakhic truth. Is there one truth? We spoke about this, I think, last semester—whether there is one halakhic truth, or whether this is pluralism, that there are several views or positions, all of which can be considered true. So I’m not going to return to that issue here, but I do want to get a bit into the question of how I relate to dispute itself. Meaning: what does dispute mean? How do we treat disputes? What can be inferred from them regarding truth, beyond the general statement that the existence of dispute does not mean there is no truth—which I spoke about last semester. Very often people say, and philosophers say this too, “Obviously there is no absolute morality.” Why? “Because look—these people think this is moral and those people think that is moral.” That argument is nonsense on the logical level, because the fact that these think this way and those think that way does not mean both are right. When you say there is no single moral truth and you prove it from the existence of differing positions, you’re actually assuming, without noticing, implicitly assuming, that all positions are also correct. But maybe there is one truth, and there are disputes because people make mistakes. Some are right and some are wrong. I don’t know—that’s another question, who can decide? But that’s beside the point. The question of who can decide is a technical question, it isn’t important. I’m speaking about the principled question: is there halakhic truth or not? The existence of dispute does not prove that there isn’t. That’s my claim.

Now true, even if I assume there is halakhic truth, there is still the question of how I reach it—meaning who decides this. Excellent question, but that’s a different question. And a different discussion. And I also spoke about this last semester when I spoke a bit about the disputes between Beit Shammai and Beit Hillel and “these and these”—how do we approach truth? Through the majority, or through the superior methodology? That’s Beit Hillel—the majority. Beit Hillel is the majority and also the superior methodology, whereas in Beit Shammai it is sharpness, wisdom, greater intellectual superiority. What? I mean the mode of conduct, the method, how one proceeds. So that’s on the general level.

I want to get into more detail, and here I want to point to a point connected to the existence of dispute and the relation between dispute and truth, but from a somewhat different angle. There is a common mode of thought that says simpler things are truer than less simple things. The simpler a claim is, the truer it is. This is often called Occam’s razor. Occam’s razor. Occam with an O. Razor, razor. Yes. Occam’s razor. Razor means a knife. The principle of Occam’s razor. This was William of Ockham, a Christian scholar in the Middle Ages, and in proofs for the existence of God and so on he argued that a theory containing fewer entities is more correct. Okay? If I have one theory that contains two beings and explains the facts, and another theory that contains five beings and explains the facts, I’ll prefer the first. Why take a complicated theory if I have a simple theory that does all the work?

But one can discuss whether this principle is just a principle of convenience, a kind of methodology, efficiency, whatever you want to call it, or whether there is really a claim here about truth. Meaning, that if it’s simpler then it is probably also more correct. Now, I think people who give this serious thought usually conclude that it has nothing to do with truth. Both theories explain all the facts, so why take the complicated one if you have the simple one? Not because the simple one is more true, but because it also does the job—so why take a complicated theory? That is usually the assumption with respect to Occam’s razor. And then it means that Occam’s razor merely describes the form of behavior that is convenient for us, but it is not a tool for approaching truth. Okay? But in my opinion that’s wrong. Occam’s razor is a tool for approaching truth. The simpler something is, the more correct it is. And I’ll show this, say, through a discussion in the philosophy of science.

In the philosophy of science it is basically accepted that when we have several possibilities for explaining the data, we choose the simplest one. Everybody agrees on that. If I have a graph and I can draw a straight line that stitches together all the points, no one will think of drawing some crazy line like this. There’s a straight line, it’s simpler, I draw it. The dispute is of course over why I draw the straight line. Do I draw the straight line because it is more correct, or do I draw the straight line because it is simpler and also fits all the facts? So why do something complicated if I have something simple that does the job? Okay? That’s really the same dispute I spoke about before. And that dispute is present in the philosophy of science, very much so. And there, I think, one can try to show how it can be decided. Because on the face of it this dispute is a philosophical dispute. There’s no scientific way to decide it. How do you know that the simpler thing is also the more correct thing? You go with it because it’s convenient for you. Someone else says it’s more correct—on what basis? Can you show me? If you could show me that, then you could actually show that the straight line is right and not the curved one, and then this would no longer belong to Occam’s razor. Because that would mean there is an experiment that the straight line would explain and the curved line would not. But if so, then the straight line is the only theory under discussion here. Occam’s razor is always a choice where I have several options and I choose the simplest one. But if one of the options doesn’t explain all the facts, then fine, I don’t choose it because it’s wrong—that has nothing to do with Occam’s razor. Therefore whenever I speak about Occam’s razor, I am talking about two theories, both of which explain all the facts, both of which work. One is simpler than the other, so I prefer the simpler one. That’s Occam’s razor.

Maybe you should look for some prediction or something according to your resolution. If you need details—say, take a stock market graph. You say the general trend is like this. So? Then a straight line is enough for you. Maybe that’s what you go by. What do you mean “enough for me”? I’m asking relative to what I’m looking for—some kind of correct answer that I’m looking for. I have two… what is the trend of the stock market? Okay, it’s going up. Fine. Now if you’re looking for something more specific. I’m looking for precision. I’m looking for exactly what is happening in the market, not the trend. Relative to the precise question, there are still two options. Then you need all the points. And I get all the points. Now the question is how I stitch them together. And that’s what I’m talking about. Do I stitch them together with a straight line or with a line like this? Which of them is correct? It’s not a question of resolution. The question is which is correct. Not which gives me an answer at better resolution. Given a certain resolution, I have two possible answers, one of them simpler. Is it also more correct because of that? That’s the question. Obviously, as you raise the resolution, you need subtler tools to get the answer. But that’s not the plane of discussion I’m on. Okay? So that is the question, basically.

So I want to describe to you how I decide this question. The claim is essentially this. I’ll now call this by names following Ze’ev Bechler—he was a professor at Tel Aviv University, philosophy of science; he wrote a book, I think it was called Three Copernican Revolutions. And there he presents these two conceptions; he calls them actualism and informativism. What does that mean? A conception that says the theory is basically a statement about me, not about the world. What I know about the world is the collection of facts I have observed. Those are the facts I know—hard facts, assuming I’m not some skeptic who doesn’t even accept the observations. Okay? So: I observed things, those are my facts. I build a theory that explains them. The theory is merely my way of organizing the facts efficiently and effectively. But I am not claiming that this theory is really true in some sense, meaning that the world actually behaves according to this theory. But the theory explains the facts and I adopt it because it is convenient for me to work within a general theoretical framework rather than with a collection of individual facts. Okay? That is the actualist approach. Why is it called actualism? Because what is true, from that approach, is only what is actually present before my eyes: the observation, what I saw. The theory is not present before my eyes; it’s a structure I build on the basis of the facts. So it’s not actual. If it’s not actual, then for me it is not true. But never mind—I choose it for reasons of convenience, not for reasons of truth. That’s actualism.

Informativism says no. The theory contains information about the world. I claim that the theory too is a claim about the world, and not merely an efficient tool for organizing the facts for my own use. So for me scientific theory is a claim about the world, and not just an effective tool for organizing the facts so I can use them conveniently. Okay? Those are the two approaches.

Now both approaches describe the scientific process in the same way. You take measurements—in a very naive way, but for the moment that form is enough for me—you take measurements, you get some results, you make a generalization, as if proposing that this is probably the general law that explains those facts. Then you put it to a falsification test—the generalization itself—to a falsification test. I say: okay, let’s do an experiment and see whether this theory is correct or not. So we’ll test it on a new situation we haven’t yet seen and see what happens. If the theory fails, apparently it’s not correct. Popper, right? Apparently the theory is not correct. If the theory passed the test, then for now everything is fine; we move it on to the next test. And so on. Okay? That is how I proceed. The actualist agrees with this and the informativist also agrees with this. Both agree that this is how science operates. What’s the difference between them? The difference is in the question of how I regard the theory I currently have, the one that explains all the facts for me. The actualist says this says nothing about the world; it is merely the tool that is currently most convenient for me because it organizes the facts known to me. The informativist says no—for me this is the thing closest to truth that I have. Certain knowledge, certainty, there never is—but for me, this is the truth, until it turns out otherwise, and then it turns out not to be. Meaning, the difference between them is the question: when I conducted an experiment and the experiment falsified the theory and I threw the theory in the trash, did I learn something new about the world? The informativist says yes: I learned that the theory is wrong, and I need to look for another theory that will be right. The actualist says forget it—the theory never spoke about the world in the first place. I just now need to look for a new tool that will let me handle the new collection of facts, because otherwise I can’t deal with them. I didn’t learn anything about the world. That’s not the point. Theories do not talk about the world. Therefore when I replace a theory, it’s not that my conception of the world changes. I’m simply using another suitcase—instead of this one, which currently has too many things in it, I’m using another suitcase. And it has no significance; it’s a claim about me, not about the world.

But that is only a question of how you relate to the scientific process. In terms of how it actually proceeds, it proceeds the same way according to both conceptions. And so it is very common to think there is no real scientific difference between the two conceptions, and therefore no way to decide scientifically who is right. Two philosophical conceptions: these think this way, those think that way, there’s no way to decide. So here, I’ll show you that there is a way to decide. Not only is there a way to decide; that way is empirical. The dispute is not even philosophical—it is scientific. I can decide who is right, and the one who is right is the informativist. And I’ll show you this.

Look. For example… what? No, no, you’re talking about behaviorism, yes, characteristic of Americans, though not necessarily American. Behaviorism says: let’s stick to the facts. What do we see? All the psychoanalysis and all the theories around it are… well, there it really is a pile of nonsense, it’s not… Ah, here. I did this in one of the… maybe in… I didn’t do it here, right? This graph. Not here. My thoughts are suddenly falling on my head. Fine, let’s see.

I measure force against acceleration, Newton’s second law, okay? Force and acceleration. Force versus acceleration. We know here that Newton’s second law says force equals mass times acceleration. Meaning, if there is a body of mass m and I apply force F to it, then the acceleration that will develop will be F divided by m. Okay? That’s Newton’s second law. I want to measure—suppose I don’t yet know this law, I’m Newton. Okay? So now I want to test it. So I test, I measure this acceleration, and this, and this, and so on. And then I find different levels of force. Let’s say this sits here, and this sits here, and this sits here. Okay? These are the results I measured. Let’s say three; you can do ten too, it doesn’t matter. Now I ask: what is the general graph? What is the relation between F and a in light of this data? Well, naturally every physicist will tell you: a straight line, right? Connect these three points with a straight line and its slope is m, meaning F = ma. That’s it, I’ve found the relation.

Now I ask: why not this line? Which also stitches together all the points. Why not this line? Of course there are infinitely many lines. You can falsify it with more measurements. Do it with more measurements, there will still remain infinitely many lines. No, there will remain infinitely many lines. If you falsify each specific one… infinitely many lines will remain. Any finite number of measurements—for any line someone gives, you’ll be able to falsify it. So what? I take the straight line, I can falsify everything, I can falsify. No, you’ll be able to falsify… Why not? You don’t know; we’re doing experiments, we need to check. I’m saying: if I take one line and ask whether it’s right… okay. No, here I’ll take all the lines, not one line, all the lines. Why? Here, I take all the lines, and I say: everything that hasn’t been falsified is correct. Why does the straight line get special treatment? Now do another experiment—it will eliminate infinitely many lines. Do another experiment—it will eliminate another infinity of lines. You will always remain with infinity. For any finite number of experiments, one can fit through them—for any finite, discrete number of points—an infinite, uncountable number of curves. Meaning, you will never manage to get below an infinite number of possible lines, no matter how many experiments you do.

So what does that mean? It basically means that I have no real way of knowing that the straight line is the right one. Because if I do another experiment, and after that I draw the new relevant line, it changes nothing. I will never be able to rule out the possibility of another infinity of lines. Therefore there are now basically two possibilities. I still choose the straight line. It’s convenient. Why? Simplicity. The actualist says: because it’s the simplest, it’s convenient. Not because it’s correct. It is no more correct than all the other lines that fit the facts. Okay? But I choose it because it’s convenient. The informativist says: no, I choose it because it is correct. Not certain—and if it is falsified then apparently I was wrong—but my current assumption is that it is correct. Or in other words, the informativist claims this is not a shot in the dark, drawing a straight line. It may not be right, but it’s not a shot in the dark. I think it is right—let’s test it. The actualist says forget it—it is a shot in the dark; this line is no more correct than all the other lines so long as they explain all the known facts. Okay, that is the claim, that is the dispute.

Now let’s see that it can be decided. If the actualist were right, okay? And now I ask a question about the next experiment I’m going to do, not the previous one I already did. What is the probability that in the next experiment I’ll hit the target, that the theory won’t be falsified? Zero, right? There are infinitely many lines that fit every set of points. The chance that precisely the straight line is right—after all it has no preference at all, simplicity says nothing about correctness. Okay? That’s according to the actualist. So it means the chance, assuming I know nothing, is one divided by the number of lines, which is zero. Right? By contrast, what does the informativist say? What is the chance that the next experiment will succeed? Not one hundred percent, because certainty never exists, but I don’t know, sixty percent, forty percent—not zero. Okay? Because I think simplicity is in fact some indication of truth. So it’s not one hundred percent, but it is a tool. Meaning, this isn’t a shot in the dark. The straight line does not stand on the same level as all the other lines. Okay? That is the claim.

But that can be tested. Let’s look over the history of science, or modern science, where measurements were already being made. Okay? And let’s see how many of the predictions of the theories at any given stage came true and how many were falsified. Now I haven’t done the experiment, but one thing is clear: it is not zero percent. I don’t know whether it was twenty percent or sixty percent or eighty percent, but not zero—that’s clear. Why? How do I know? Because if it were zero, our science today would be the science of Adam. We would just be constantly replacing theories: build a theory, do an experiment, it’s falsified, build a new theory, do an experiment, it’s falsified. We would not be advancing anywhere. Then we would have no knowledge of the world. Our science would be the science of Adam. If we are advancing, that means there are theories that withstand the tests, that are not falsified, and those are the theories that survive in this intellectual evolutionary struggle. The theories that survive are the theories that pass the empirical tests. Okay? That means that among the experiments performed thus far in the history of science, a certain percentage of experiments succeeded. And that is an empirical proof that actualism is wrong. Because according to the actualist, in principle no experiment should ever have succeeded. If you want, taking into account the resolution of measurement, then almost no experiment should have succeeded. Fine? I’m not talking about an exact line, but a line within some thickness of error. What do you mean? There is no combination. There is actualism and there is informativism. Informativism does not say it is certain that the straight line is right, but it claims it is not a shot in the dark. In that sense it is a binary dispute. Either you are an actualist or you are not an actualist. There’s not much middle ground here.

So what is the claim? The claim is that when we look at this graph and say the straight line is the right line, we are really making the claim that the straight line is right, not merely convenient. And that claim is confirmed in the history of science. Or in other words, what appears simple to us is an indication that it is also correct. This is not a shot in the dark. That is really the meaning of the matter. It’s very strange: this is a philosophical dispute that looks completely irresolvable—these think this way, those think that way. Yet there is an empirical decision. One side is simply wrong. Even though this philosophical dispute continues in full force to this day. It’s simply a mistake. There is no possibility of being an actualist. It’s a mistake.

What bothers people? Why do people become actualists? Because there really is a serious question—how do you know the theory is correct? Why assume that… just because something seems simple to you, does that mean the world behaves that way? Why? Who decided that? What caused it? Why assume it? By the way, if you were built differently, then something else would seem simple to you. If you were built in such a way that space had circular axes rather than Cartesian axes, such that it was more convenient for you to think in terms of circular axes rather than these Cartesian axes, then what would seem simpler would actually be circles. That, by the way, is what gave rise to Ptolemaic cosmology—that everything was circles. Circles and epicycles and deferents. Because they thought the circle was the simplest. Today we think a straight line is the simplest because it has two parameters—yes, it’s ax + b. Meaning, that which has as few parameters as possible is the simplest thing. By the way, all AI, yes—machine learning—is essentially built this way. You assume it is a straight line and then you do least squares to find the parameters of the line, a and b. That’s all. And you assume there is some straight line here. The computer doesn’t assume that—you assume that, the computer’s programmer assumes that. You are basically assuming the form of the solution, and from there on the computer works. People think the computer replaces them. The computer doesn’t replace them. The computer is built on intuitions that come from us—from its programmer. It doesn’t replace the programmer. It is built on the programmer’s intuition, but it knows how to use it faster, more intensively, and with larger data. That’s all.

So in the end the claim is that Occam’s razor, which tells us to choose the simple solution, is an ontic razor. Meaning, it speaks about reality itself. It is simpler and therefore more correct. Not that it is simpler and therefore more usable, convenient, effective—choose whatever term you like. It is more correct. Meaning, what appears simple to us is probably some sort of indication that it is also more correct. The fact is, reality shows this. Why is it so? One can discuss that. For me it goes all the way up to the Holy One, blessed be He. But never mind—for the moment, that is the fact, and it is hard to deny it. We have within us certain capacities that are fitted to how the world behaves. Meaning, what appears simple to us is apparently connected in some way to how the world behaves, because we are part of the world. Some will attribute that to evolution, never mind. Okay? And what about the theory of…? All the laws of physics—what do you mean? All the laws of science, not just the laws of physics. How often does an accepted, widespread scientific law, one that has already passed tests, collapse? It almost never happens. At most it gets corrections, like Newtonian mechanics at high velocities receiving relativistic corrections, or at small scales quantum corrections—relativity and quantum theory. And it is still correct; it did not collapse. And relativity too, by the way, is basically just a generalization of Newtonian mechanics; the forms are exactly the same forms. The relations are still the same relations. It passes experimental tests, yes. Again: a theory cannot prove itself in the sense of being shown to be true. It can pass falsification tests and perhaps recover, receive confirmation. Meaning, it grows stronger insofar as it passes more falsification tests. There is no such thing as proving a theory, yes, that is clear.

So why am I giving this introduction? Because there is some connection between simplicity and truth, between correctness, and that is surprising. But these are the facts of life; that’s how it is. It’s good that… it’s convenient too, so fine. It’s surprising but good. It’s a good surprise, not a bad one.

Now this has many applications. In Ockham originally, he speaks about a situation where there are two theories and one contains fewer entities. Therefore he says the theory that God created the world is a more convenient theory because it is a theory built entirely on one single being. That’s the simplest possible. Meaning, every other theory basically requires a combination of all sorts of more complicated things. And therefore he claims that this is the more correct theory because it is the simplest. In that formulation I don’t agree so much, but in more updated formulations I do agree. There is some booklet by Rabbi Kellner—what is it called? Fanaticism and Generality something and something else, I don’t remember anymore. The claim there is that the more general a claim is—which also means simpler—the more correct it is.

In any case, another application: now I’m not speaking about a theory that contains fewer entities. Throughout history several axiom systems were proposed. For example, there is a system of Hunter that grounds ordinary natural logic on three axioms. But today we already know that there is an axiomatic system with one axiom that can unfold all of logic. So we prefer it because it is simpler. Even though in logic there isn’t much room to talk about “more correct” and “less correct”; it’s all just different forms of description, so this is not really a matter of correct and incorrect. One can bring another example, say in physics. It is common among physicists to think that when someone offers a teleological explanation, a purposive explanation, that’s an anecdote; it isn’t really the true explanation. You know, there is Lagrangian mechanics. Lagrangian mechanics describes everything we know from regular mechanics, Newton’s laws that I mentioned here and so on; one can describe it in terms of optimization of functionals. Meaning, I’m looking for a path that is optimal in some sense—I won’t go into the terms now. Meaning, the path that satisfies some optimum condition is the path chosen by the particle, or the light, or whatever. That’s one description. Another description: a force acts on it and it develops acceleration according to Newton’s second law, or it diffracts, bends, bypasses, and so on. So there are two forms of description in physics. Let’s take optics—it’s simpler.

In optics this is known as Fermat’s principle. Familiar? Fermat’s principle in optics: in geometric optics there is a ray of light moving along, okay? And it can be reflected, refracted, interfere, and so on. Say when there is a medium and it moves from air to water, it refracts—the angle changes. The relation between the angles is Snell’s law. Okay? The refractive indices of the water and the air determine the relation between the angles, never mind, and we know how to describe how that refraction will happen, how it will continue onward. That is the causal description: the light moves in a certain way, it hits a boundary between two media, and it undergoes refraction. Like a body acted on by a force and an acceleration is generated: that is a causal description. Okay? And there is another way to describe geometric optics: the light always chooses the shortest path. That contains all of geometric optics. One can prove that this is completely equivalent to the causal description of geometric optics. You understand? The classic illustration always given in this context—think about the boundary between the water and the shore. Here is the shore and this is the sea. Okay? Now the lifeguard sees a person drowning here in the water, and he is standing here. How should he run? Apparently the shortest path is like this. No—but that’s not right. Why? Because his speed in the water is lower than his speed on land. It is better for him to take a longer path on land and minimize the distance he has to cover in the water. Therefore he should really take a path something like this, and then break toward here. You get refraction. This will give you Snell’s law. If you do the calculation, the ratio between the speeds in the water and in the air is the ratio between the refractive indices. So this gives you Snell’s law. Okay? So refraction can be described either as hitting a boundary that causes refraction, or alternatively I calculate what path will be the most efficient path to bring me to the target, and that is the path I take.

Now this is true in mechanics too, perhaps even more familiarly. When you speak about a force acting on a body, okay? A body is on a mountain and begins to go downhill. Why does it go downhill? Two forms of description. One form: the force of gravity acts on it and pulls it downward, the projection of the gravitational force on the slope, okay, pulls it downward. A second description: it wants to minimize its potential energy. It strives to reach lower potential energy. Do you understand what “strives” means? “Strives” means this is a teleological description. It is performing some optimization, in this case a minimum—bringing the potential energy to a minimum. Okay? Now one is a causal description: a force acts on it and produces downward acceleration. The other is a teleological description: it chooses to go downward because its purpose is to minimize potential energy. Okay? And thus there is Lagrangian mechanics, which describes all mechanics in a teleological way. Meaning, I choose a path that will optimize something. Okay? It doesn’t matter what, some quantity.

Which of the two descriptions is more correct—the causal or the teleological? Now there is a mathematical proof that they are equivalent. Completely, mathematically. There is no difference. Whatever this predicts, that predicts too, and vice versa. It is just two languages for describing the same thing. If you like, it’s like describing a point in two-dimensional space in Cartesian or polar coordinates. Say x and y, or r and theta. It’s just two languages for describing the same thing; they are completely equivalent. Okay? So there is no meaning to the question of which is more correct. Fine? It’s just two languages.

But if you ask physicists casually, speaking off the cuff, they will tell you the causal description is the correct one and the teleological description is an anecdote. There is some interesting mathematical anecdote that one can describe it this way too, but in nature itself it is obvious that when a force acts, acceleration is produced. The particle doesn’t do calculations about what will optimize energy. That doesn’t suit particles as we conceive of them. Aristotle’s physics, by contrast, for example, was teleological, purposive. So he said: why do bodies fall downward? Not because there is a force pulling them, but because they strive to return to their source. They strive. After all, a stone is made of earth, so it wants to return to the earth from which it was taken. Therefore it falls downward. Right? That is a teleological description. Today we speak in terms of a causal description: a force acts on it and the force produces downward acceleration. Now who is right? There is no “right” here, by the way. What does “right” mean? There are two forms of description: you can describe it this way or that way. But we have some kind of feeling that says stones don’t carry out optimization calculations. Right? Meaning, one can act on stones, but stones do not exercise judgment and decide what path to take. But that is a mistake. It is a mistake because Aristotle did not claim that the stone exercises judgment. I don’t think he thought the stone had consciousness and judgment and intellect. What he meant was to describe the nature of the stone. The nature of the stone is, in quotes, to strive to return to its source. That is simply another form of description of the laws of nature. It does not really mean that the stone is a human being. Aristotle didn’t mean that either. Therefore it is incorrect to reject Aristotelian physics because of its teleology, because it proceeds teleologically rather than causally. That is a misunderstanding. Teleological does not mean the stone or the particle or the ray of light is really making a deliberation. Rather, it is just another way of describing the laws of nature.

But which of the two forms is correct? They are completely equivalent, so what does “correct” even mean? It’s like with Copernicus, which people always bring as an example of the primitiveness of religious thought that thinks the earth is at the center—both Christian and Jewish. And Copernicus taught us that this isn’t true. Look at the primitiveness of modern thought. Copernicus did not teach us that this isn’t true. There is no truth or falsity here. If you put the origin of the axes on Earth, then the sun revolves around the earth. If you put the origin of the axes on the sun, then the earth revolves around the sun. The whole question is simply where you choose to place the origin of the axes. Correct. What Copernicus discovered was only that if we place the origin of the axes on the sun, the equations come out simpler, because then everything is a circle—or actually an ellipse—around the sun. Then everything comes out around the sun, and that is much simpler than putting the origin of the axes on the earth, where everything revolves in a mess. That’s all. So this is merely a simpler language for describing the same thing. And who said it was more correct? This brings me back to Occam’s razor. Because earlier I said that what is simpler is also more correct. But not in cases like these. Because in these cases it is simply a simpler language for describing the same thing; you are not really making a different claim. So there is no question here of truth or falsity at all.

Where there is truth and falsity, the simpler description is the more correct one. But there are questions for which there is no such thing as truth or falsity, just two languages, and of course you choose the simpler language because it’s more convenient. Here too I am an actualist. I too would choose the simpler one because it is more convenient, not because it is more correct. Because here there is no truth or falsity. Just as when I solve a mathematical problem, if the problem has circular symmetry, I will do it in polar coordinates and not Cartesian coordinates. Not because it’s more correct, but simply because it is more convenient to work that way. That’s all. Okay?

But in places where there is truth and falsity—say the question whether God exists or not. Either He exists or He doesn’t; there is truth and falsity there. That question cannot be decided by observation; it isn’t a question science can decide. But there is truth or falsity there. So on that question, if the God theory is, say, simpler, then yes, it has an advantage, and is probably more correct. Okay? Because here there is truth or falsity. That is the meaning of Occam’s razor.

Now I want to speak about another application of Occam’s razor. Suppose I have a dispute between two people. In Jewish law or not in Jewish law, generally. There is a simple assumption that says I minimize the dispute as much as I can. If I can explain the dispute in a way that narrows it, that explanation is preferable to an explanation that makes it broader. In the language of the commentators they call this: we do not multiply disputes. We do not enlarge disputes unnecessarily. Meaning, if there is a dispute between two people, we assume it is as narrow as possible. There is no reason to add more points of disagreement if we don’t need to. To make the dispute extend beyond what I am forced to say. Suppose I found one principle over which they disagree. There is no reason to say that they also disagree over something else if I don’t have to. If I can explain the dispute as a dispute over one principle, why assume their dispute revolves around another principle as well? Okay? Even though there could be another explanation according to which their dispute revolves around two principles. Here I return to Occam’s razor and say: no, if I have an explanation—and this time it is an explanation of a dispute—that contains one principle, that is preferable to an explanation based on two principles. Right? This too is Occam’s razor. So here we have an application of Occam’s razor that says I look for a minimal, or simplest, explanation of the dispute. And the meaning of this is that if I found between them a dispute over one principle and that explains the entire dispute for me, and someone else proposes that the dispute revolves around two principles—meaning one accepts principle X and Y and the other accepts neither X nor Y—then I will prefer the first explanation. Like everything else, in disputes too I will prefer the simplest explanation.

And as you’ll see in a moment, this has implications—very interesting implications. But perhaps before I move to the implications, one more aspect. There is what is called the principle of charity. What does the principle of charity mean? When you argue with someone and he puts forward some position, now you can seize on it and show that his position is nonsense. But stop and think for a second: maybe he doesn’t mean the absurdity you think you’re hearing from him. Give him credit, practice interpretive charity with him. Interpret his position in the best possible way, and only then begin to argue with him. That is called the principle of charity.

Suppose someone says something that seems to us absolutely ridiculous. Stop and think: maybe he simply didn’t formulate himself precisely. Maybe he thinks something less foolish, something a bit more intelligent. So interpret him that way and now begin the discussion. It’s very easy to defeat someone in an argument by presenting his position as idiotic and throwing it out the window. But usually—or at least the optimistic assumption says—most people are not complete idiots. Different levels of foolishness, yes, but not all of them are complete idiots. Okay? Therefore, if you have the option of interpreting his position in a more intelligent way, do that, and only then begin the discussion. Even though it would be easier to win if you made him look ridiculous. What role does his personal interest play with regard to his second claim? I didn’t understand. Charity is also limited. Now if he has some personal stake in doing charity, then he’ll avoid doing charity. That’s psychology; I’m speaking philosophy, not psychology. I’m saying that on the philosophical level, when you deal with a position, give it the best formulation possible, and now start dealing with it. Don’t present it in the worst possible way, then attack it and throw it away. That’s very easy; you come out the macho winner, the biggest bully around, but it isn’t serious. You just dealt with a straw man.

By the way, people think—and I wrote about this too once—that the principle of charity is some sort of interpersonal niceness, a bit of mercy on the person, give him a break. No. If you want to clarify the truth in an argument, not defeat the other person, then you should present the opposing position in the best possible way, and now discuss whether you accept it or not. Because that is how truth is really clarified. Meaning, if you present it in a ridiculous way and therefore reject it, that’s no great wisdom, because there is a more intelligent presentation of it, and perhaps against that you have no arguments; perhaps there he really would overcome you. So if you aspire to truth and not to defeating the other person, then you really have to formulate it in the best possible way before you begin to discuss it. So it really assumes that not everyone is an idiot. Exactly. It’s productive. Right. Usually the accepted assumption is that this is based on the idea that not everyone is an idiot. I say forget it—even for the productivity of the argument, even if the person opposite you really is an idiot, you should defend his position for him yourself. He did not mean to defend it that way—defend it that way yourself, and now discuss whether it is true or not, because that gives a more genuine clarification. Okay? That happens very often.

Look, for example, I’ll give you an example. Suppose we have a debate over whether women should be accepted as witnesses. The Talmud disqualifies them: “Then the two men who have the dispute shall stand before the Lord.” Now someone will come and say: but women today are educated, intelligent, enlightened about what goes on in the world, so they should be accepted as witnesses. Now I can throw his argument in the trash in a second. A foolish argument. Why? Because his argument suffers from what is called the naturalistic fallacy. Meaning, the fact that women used to be less educated and today are more educated—that’s a fact. That’s clear. But the conclusion that therefore they should be accepted as witnesses is not a fact; it is a norm. You can’t derive a norm from facts. That is called the naturalistic fallacy. Your conclusion does not follow from your premises. Go home. You didn’t say anything; you’re talking nonsense. I could close the discussion right there. Right? I’m saying: this wall is white, therefore this wall is beautiful. Invalid argument. “The wall is white” is a fact, and “the wall is beautiful” is a judgment. A judgment is never derived from facts. What do you need for the judgment to work? You need to assume that what is white is beautiful. Add another premise. Not only that this wall is white, but also the extra premise that whatever is white is beautiful, and now indeed you can derive the conclusion that this wall is beautiful. What did adding that premise do? It transformed my set of premises into something that also contains a non-factual dimension. “What is white is beautiful” already mixes in judgment; it is no longer just facts. So now one can try to derive from it a conclusion that is a judgment and not merely a fact. But from premises that are only facts, you cannot derive a conclusion that is a judgment. Not an aesthetic judgment, not an ethical judgment, no judgment of any kind—not halakhic either.

Now in that context I say: you’re saying women once were not educated and today they are educated. Fine, two facts that I accept. How do you get from here to the conclusion that they should be accepted as witnesses? That conclusion is a halakhic norm, not a fact. You can’t derive a norm from facts. So if you want to defeat him, you’ve defeated him. But if you want to discuss seriously, then apply the principle of charity. What he means to say is that women once were not educated, today they are educated, and the reason they were disqualified as witnesses then was because they were not educated. That is an additional premise. Conclusion: today they should be accepted as witnesses. Now that is already a good argument. One can still argue with that additional premise—that they were disqualified because they were not educated. That needs discussion. But now it is no longer a foolish argument. Now we understand what the discussion is about. Now we need to investigate. But he himself didn’t think of that; I could have thrown him in the trash immediately and he would have gone home defeated. No. I need to defend him in the best possible way, present his position in the best possible way, and only then begin the discussion. That’s how one really clarifies what the truth is, not by winning arguments. Okay? So this too is connected to giving the optimal interpretation. In this case it’s just for the effectiveness of the discussion.

Okay, now I want to return to disputes. I want to give you an example of applying the principle of Occam’s razor to a dispute, to the interpretation of a dispute, and how it turns the whole picture upside down. Completely upside down. Meaning, all the later authorities here simply said the opposite. The opposite of what is correct. Because they didn’t notice this point. So look at the following.

Okay, can you see? Yes. In Jewish law there is a presumption based on three occurrences. Fine. Yes, if something happens three times, the assumption is that this is a general rule. This is basically halakhic induction. Something happened three times, the assumption is that it is a general rule. For example, menstrual cycles of women—by date or interval or whatever—or cases where sons died because of circumcision, or husbands of a woman died. If she married three times and each husband died a day after they married, then she is not allowed to marry again, because presumably the fourth husband will die too. That’s induction. If three died, then presumably the fourth will die too. Okay? Or if three children died because of circumcision, then the fourth child is not circumcised, because there is concern he will die, and so on. There are all sorts of cases.

One of the sources brought for this rule is the forewarned ox. A forewarned ox is basically an ox that has gored three times. If it gored once, it is an innocuous ox and pays half damages as a penalty. After three times, from the fourth time onward it pays full damages—not a penalty but compensation. And why? Because after—now, in tractate Bava Batra at the beginning of chapter three, the Talmud connects the forewarned ox to the presumption of three years. The presumption of three years with regard to land is when someone occupies land for three years, eats the produce, and the original owner, the prior possessor, does not protest. Then after three years of his sitting on the land, he no longer needs to preserve the deed. Meaning, if he claims that he bought it and had a deed and the deed was lost, he has a three-year presumption and does not need to bring proof. Be careful: this is not a presumption of acquisition. If he has no claim that he bought it and had a deed and so on, it won’t help him that he sat on the land for three years. But if he sat on the land for three years and says, “I had a deed and it was lost after three years,” and the fact is that you didn’t protest for three years, for three years I gathered crops and you didn’t protest—then apparently the land is not yours. That is evidence. After three times there is evidence against you and this land is mine.

Rabbi Yohanan said: I heard from those who came from Usha, who used to say: From where do we know the presumption of three years? From the forewarned ox. Just as with the forewarned ox, once it gored three gorings, it left the status of innocuous ox and stood in the status of forewarned ox, so too here, once he consumed produce for three years, it leaves the possession of the seller and stands in the possession of the buyer. The Talmud says: If so, just as with the forewarned ox one is not liable until the fourth goring, so too here perhaps it should not stand in his possession until the fourth year? A forewarned ox only becomes liable for the fourth goring, not the third. So here too, maybe require four years and not three? Fine, but that’s not right. Is that comparable? There, once it gored three gorings it became forewarned. As for the fourth one, if it didn’t gore, what would it pay for? The need for four gorings is not because it takes four gorings to become forewarned. After three gorings it becomes forewarned. The fourth goring is needed because without it there is nothing for which to pay as a forewarned ox. There has to be a goring in order for payment liability to arise. But it becomes forewarned after three times. Here, however, once he consumed produce for three years, it stands in his possession. After he consumes for three years, it stands in his possession.

So the Talmud brings this here—this is in the chapter on presumptive ownership. Let’s leave that aside for a moment. Now the Talmud says: let’s see what happens regarding the forewarned ox. What is the meaning of warning it? So let’s start from the Mishnah in Bava Kamma 23b: Which is an innocuous ox and which is a forewarned ox? A forewarned ox is one regarding which testimony was given on three days, and an innocuous ox returns to that status once it refrains for three days—these are the words of Rabbi Yehuda. If for three days it didn’t gore—someone was before it and it didn’t gore—it returns to the status of innocuous ox. Rabbi Meir says: A forewarned ox is one regarding which testimony was given three times, and an innocuous ox is one that children handle and it does not gore. Meaning, if testimony was given that it gored three times, it becomes forewarned even if this didn’t happen on three different days but all on the same day. It doesn’t require three distinct days. Where is the dispute? If an ox gored three times in one day and there is testimony on those three times in one day, according to Rabbi Yehuda it does not become forewarned, according to Rabbi Meir it does become forewarned even in one day.

The Talmud asks: What is Rabbi Yehuda’s reasoning? Abaye said: “Yesterday”—one, “the day before yesterday”—two, “the third day”—three, “and its owner has not guarded it”—this brings us to the fourth goring. And so on, and Rava says something else. So there is a textual source that it requires three days. And what is Rabbi Meir’s reasoning? As it was taught, Rabbi Meir said: If spacing out its gorings makes it liable, then all the more so bringing them close together. Right? The verse says three days are needed, but Rabbi Meir says: if when it gores over three days it becomes forewarned, then when it gores three times in the same day, all the more so it becomes forewarned. If spacing out its gorings makes it liable, then all the more so bringing them close together. What does Rabbi Yehuda say? Maybe it just had a bad day. Rabbi Yehuda says no—what kind of a kal va-homer is that? Maybe it had a bad day and so it gored three times in one day; that doesn’t mean its nature is a permanently goring nature. There is some dispute between them over the relation between spaced-out gorings and closely clustered gorings. According to Rabbi Meir there is a kal va-homer, and according to Rabbi Yehuda there is no kal va-homer.

The Tur brings a dispute in Orach Chayim 114 about saying “Give dew and rain for blessing.” The Jerusalem Talmud says: one who prays and does not know whether he mentioned it or not—within thirty days, the presumption is that he says what he is accustomed to say; from that point onward, he says what is required. For thirty days, if he is in doubt whether he mentioned it, he has to repeat, because presumably he did not mention it. And the same applies for thirty days after Passover: presumably he did mention it and so he must repeat. And Maharam of Rothenburg would customarily say on Shemini Atzeret, in the blessing “You are mighty,” ninety times, until “He causes the wind to blow and the rain to fall,” corresponding to thirty days in which one says it three times each day; and now if he was in doubt, he would not need to repeat.

What is he saying? He says this: in principle, in order for me to have the presumption that I said what is correct, thirty days have to pass. Fine? After thirty days, the presumption is that you’ve already said it ninety times, three times a day. Ignore the Sabbaths and everything, so it’s approximately that, but the assumption is ninety times. After ninety times that you’ve said it correctly, the presumption is that you’re already accustomed to saying it correctly, and if you’re in doubt then you can rely on the assumption that you said it correctly and not repeat. If you are within the thirty days, then you haven’t yet said it enough times, it’s not likely that you’ve gotten used to it, you’re still accustomed to your prior habit, and therefore if you have a doubt, out of doubt you must repeat. “He says what he is accustomed to say” and “he says what is required”—that is the basic law.

Now Maharam of Rothenburg comes and says: I have a trick. I’ll say “He causes the wind to blow and the rain to fall” ninety times on Shemini Atzeret, all on that same day. What? Like weight training, yes. “He causes the wind to blow and the rain to fall” ninety times, and then that is like thirty days, three times every day, and he gets used to saying “He causes the wind to blow and the rain to fall,” and from then on I have no problem— all my doubts are resolved. We had a Jew in the yeshiva who has since passed away, and he always insisted that when they danced on Simchat Torah they should sing: “He causes the wind to blow and the rain to fall, and give dew and rain, he causes the wind to blow and the rain to fall and give dew and rain for blessing.” They would sing this with great enthusiasm until they’d passed ninety times, and then everything was fine. Maharam of Rothenburg. Really, nonsense of a rare sort—rare in its intensity. In any case, that was the claim. And anyone who thinks this really gets me used to it, so that now in a doubtful case I’ll say “He causes the wind to blow and the rain to fall”—that really is… It was the opposite. In basic training, I’ll never forget this, I had to remember my personal ID number and one day I forgot it, so he told me: tonight you’ll write it a thousand times and it will be engraved in you. He was right, true. Punishment in the army is famous, yes. In any case, that’s a memory aid; that’s something else. Here I’m talking about habit, not memory. Not the same thing. Memory means putting it into your memory. Habit means putting it into your limbs, not your memory—that you get used to acting this way, not that you remember what was. Obviously repetition helps memory. Fine.

In any event, Maharam of Rothenburg says that if you say it ninety times in one day, that’s good enough. And his proof, says the Tur, is from the chapter “How the Foot Damages” in Bava Kamma, where it says regarding the forewarned ox: if spacing out its gorings makes it liable, then all the more so bringing them close together. So too here: since after thirty days if he is in doubt he need not repeat, then all the more so if he said it ninety times in one day. Yes, a kal va-homer, Rabbi Meir’s kal va-homer: if spacing out the gorings makes it liable, then all the more so bringing them close together.

And Rabbi Rabbeinu Peretz, of blessed memory, wrote: I did not see the elder rabbis of France doing this. Right, the Tosafists in France, Rabbeinu Peretz, one of the Tosafists. “I did not see” is not proof, but he probably means they did not accept it. The case under discussion is not similar to the proof. There, the reason is because the ox has become established as one that gores, and if it became established through the first three, then all the more so by three close together. But regarding rain, which was instituted in prayer, and the matter depends on habituation of speech, we do not say this. And my father, the Rosh, of blessed memory, leaned toward the view of Maharam and not Rabbeinu Peretz.

What does Rabbeinu Peretz say? He says: your proof from the gorings of an ox is no proof. Because in the ox, what’s the difference? What do you mean, “character”? What is the difference between the ox and human beings? Not just an automaton of instincts, same thing. But a human being can learn behavior. And an ox can’t learn behavior? You can’t train an ox? No, right, he means the opposite—it adapts. You want its actions to testify whether it is this or that. Ah. That is apparently the difference. What does Rabbeinu Peretz say? A forewarned ox becomes… after three gorings it does not become forewarned in the sense that the gorings habituate it and change its nature into a goring one. Rather, they are evidence that by its very nature it is a goring animal. It’s just that in order for the proof to be clear, this has to repeat three times, so that I can be certain. So long as it hasn’t happened… now once it happened three times, I know that this was already true from the beginning, so it’s not that it now became a gorer. But you need three times for it to gore in order for me to understand and be certain of this. That is the forewarned ox.

But with “He causes the wind,” it’s not that I naturally say “He causes the wind to blow and the rain to fall”; I need to train myself to say it. Who said that what is said regarding evidence about the character of an ox—that Rabbi Meir’s kal va-homer—also works regarding habits? And certainly regarding memories, what you said before, that’s a third thing. Okay? That’s what he says. Now whether it works or doesn’t work one can argue. But don’t bring me proof from there. It’s not proof. Meaning, even if Rabbi Meir says that three gorings over three days testify to the ox’s goring character, then okay, perhaps three gorings in one day testify even more strongly, suppose I accept that. That still doesn’t mean habit works the same way—that if spread over thirty days it works, then obviously if in one day it will also work. No—who says? There are very good reasons for the opposite. But even before the reasons, first of all it’s not the same thing. Don’t bring me proofs from there. Okay? That is basically Rabbeinu Peretz’s claim.

What would Maharam of Rothenburg say? Good question, no? And a kal va-homer. Why? But why? Rabbeinu Peretz asks a good question. Why are you bringing me proofs from gorings to here? Gorings are an indication of the nature of the ox and here we are talking about habituation. What connection is there between the two? The gorings aren’t merely an indication—he became habituated. Right. Maharam of Rothenburg holds that the gorings too are habituation, not just evidence. Therefore he brings proof from gorings to “He causes the wind to blow and the rain to fall.” Meaning, he understands the process of an ox becoming forewarned differently from Rabbeinu Peretz. Rabbeinu Peretz understands that the gorings of the ox are only evidence of its nature, but that nature was already there from the beginning. You just need evidence, and for that you have to wait until it gores three times, and then you know that this is its nature, which was always its nature. Okay. Maharam of Rothenburg says: nonsense. Simply, after it gored three times, it became habituated to being a gorer. From now on it has a goring nature. He is not deterministic. Meaning, he does not say the nature of the ox is fixed from birth and the whole issue is merely how I know what the ox’s nature is. No. The nature of the ox is shaped by what actually happens to it. And if the ox gores three times, it gets used to being a gorer.

If that’s so, then now the proof is a good proof. Because regarding habituation one can argue whether ox and human being are the same, but now at least one can understand the proof: if with the ox, when it gets habituated over three days, then all the more so it would become habituated in three times on one day, then also for a human being’s habituation in “He causes the wind to blow and the rain to fall,” if thirty days works, then all the more so ninety times in one day. In short, what comes out is that the dispute between Maharam of Rothenburg and Rabbeinu Peretz is over the nature of an ox’s forewarned status. Is that forewarned status evidence? Is it a sign or a cause? Is it a sign that the ox is a gorer, or is it a cause that turns it into a gorer? Okay? That is basically how the later authorities usually explain the dispute between Rabbeinu Peretz and Maharam of Rothenburg.

And then the Rosh—that is, the Tur rules like the Rosh, like Maharam of Rothenburg. The Rosh was Maharam of Rothenburg’s student. So the Tur rules like that view, and then it comes out that an ox’s goring is habituation. Right? Because Maharam of Rothenburg brought proof from goring to “He causes the wind to blow and the rain to fall,” so he clearly understands that goring too is habituation. That’s the standard understanding. That’s always how they explain this in yeshiva classes on Bava Kamma; they always bring this Tur, and basically say that the dispute between Maharam of Rothenburg and Rabbeinu Peretz is whether an ox’s goring is habituation or merely an indication, evidence. Okay. And likewise for all presumptions based on three occurrences. They can all be discussed. If, for example, a woman saw her cycle three times on the same date… does her cycle become one that is tied to that date, or is that evidence that this was already her nature before, and I just need three times in order to have evidence? And so on. In all these cases of “three times,” the later authorities discuss whether it is a sign or a cause. There is a long Kehillot Yaakov on this in tractate Taharot, section 47 I think, where he goes into this at length across all the cases of threefold presumption and discusses whether it is habituation or evidence, and whether the cases can be compared at all. Because in principle you could say sometimes it’s habituation and sometimes it’s evidence, depending on the context. For a woman and her cycle it may work one way, for an ox another way, for the three-year land presumption another way—who says all contexts work the same way? Also with the ox, yes. It’s evidence that this is habituation and not a sign. Well, on the other hand, there are some proofs one way and the other. Anyway, that is the standard way they explain it.

Now the truth is that when you look, the Beit Yosef there brings various explanations of this matter, and you see that the earlier later authorities—those cited by the Beit Yosef, or really the medieval authorities, at least some of them—did not go in this direction. But among the later authorities, all the yeshiva heads always give this explanation. But this explanation cannot be right. It cannot be right. Not only is it not right—I will now prove to you that it’s exactly the opposite: that Rabbeinu Peretz holds that gorings are habituation, and Maharam of Rothenburg holds that gorings are a sign. Exactly the opposite of what all the later authorities say. And it’s clearly right—meaning, they clearly erred. This is not a matter of debate. Why? And here I return to Occam’s razor.

There is a question here that some later authorities raise, but for some reason somehow they ignore it. The halakhah is ruled like Rabbi Yehuda here, not Rabbi Meir. So why are you bringing proofs from Rabbi Meir? Rabbi Meir says: if spacing out its gorings makes it liable, then all the more so bringing them close together. So Maharam of Rothenburg brings proofs, and Rabbeinu Peretz rejects the proofs. Forget these proofs—Rabbi Yehuda disagrees with Rabbi Meir. This kal va-homer is Rabbi Meir’s kal va-homer. We rule in practice like Rabbi Yehuda, that there is no kal va-homer from spaced-out gorings to clustered gorings. So even if there were room to compare the forewarned status of an ox to saying “Give dew and rain for blessing,” from where you came, with regard to the ox itself it isn’t true that this is habituation. So what is going on here? Maharam of Rothenburg did something strange by bringing proofs from Rabbi Meir; what is even stranger is that Rabbeinu Peretz, who disagrees with him, does not ask him this. “Why are you bringing me proofs from Rabbi Meir, whose view is not accepted in practice?” Rabbeinu Peretz, when he says: don’t bring proof, because forewarning is a sign and saying “Give dew and rain” is habituation—why does he say that? Let him just say: you’re bringing proofs from Rabbi Meir, but Rabbi Yehuda directly disagrees on this very point, and the halakhah follows Rabbi Yehuda. What kind of proof is that? Meaning, even Rabbeinu Peretz, who disagrees with Maharam of Rothenburg—even he does not raise this argument. That is doubly strange.

And the root of the matter is Occam’s razor. Occam’s razor says the following. What I really need to do is understand how Rabbeinu Peretz understood the dispute between Rabbi Meir and Rabbi Yehuda, and how Maharam of Rothenburg understood the dispute between Rabbi Meir and Rabbi Yehuda. Then we can see what comes out for practical law, since we rule like Rabbi Yehuda, and then understand what the forewarning of the ox is, and see whether there is proof or not. That is the order in which the analysis has to be done.

Now let’s see what happens here. Look. We have to begin with the dispute between Rabbi Meir and Rabbi Yehuda, not with Maharam of Rothenburg and Rabbeinu Peretz. The tannaitic dispute. Because what does this question really mean? “Why are you bringing me proofs? The tannaim themselves disagreed over this very thing.” The tannaim disagreed over whether forewarning is habituation or evidence. And you’re bringing me proofs from Rabbi Meir, whose view is not the practical law, while Rabbi Yehuda says the opposite. If Maharam of Rothenburg brought proofs from Rabbi Meir, what does that mean? It probably means that he understands that Rabbi Yehuda’s disagreement with Rabbi Meir is not on that point. Right? Otherwise how could one bring proofs from a view that is not accepted in practice? Very often I can bring proof for practical law from a view that was not ruled in practice. When? If the view that was ruled in practice disagrees with that view not on this point but on another point. Or in other words, suppose there is a dispute between Rabbi Meir and Rabbi Yehuda. From Rabbi Meir I have proof that if spacing out gorings makes it liable, then all the more so clustering them. If I don’t have to, I have no reason to assume Rabbi Yehuda disagrees about that. It may be that Rabbi Yehuda disagrees with him about something else. So if I have proof from Rabbi Meir on this point, then even if Rabbi Meir is not the practical law, what do I care? I will explain Rabbi Yehuda as also accepting this principle, and whatever his disagreement with Rabbi Meir is, it is something else. Right? It has to be that way. Someone who brings proofs from a view that is not accepted in practice presumably understands that the dispute between that view and the one actually accepted is not on the point from which he brought the proof. Therefore his assumption is that Rabbi Yehuda agrees to that too.

Or in other words, Maharam of Rothenburg claims that, whether according to Rabbi Meir or according to Rabbi Yehuda, an ox’s gorings are habituation. That is not the point of disagreement between Rabbi Meir and Rabbi Yehuda. Because otherwise it would be impossible to bring proof from an ox’s gorings to “Give dew and rain for blessing.” So what is the dispute then? Rabbi Yehuda apparently says that an ox’s gorings… wait… they both agree that an ox’s gorings are… wait… no, sorry. The opposite. If Maharam of Rothenburg brings proof from Rabbi Meir to “Give dew and rain for blessing,” that means that both Rabbi Meir and Rabbi Yehuda agree that if spacing out gorings creates liability, then clustering them certainly does as well. Right? That is not their dispute. So why doesn’t Rabbi Yehuda accept it? Because Rabbi Yehuda claims that an ox’s gorings are evidence, not habituation. In habituation, you’re right: if spaced-out repetition creates a habit, then close repetition certainly creates a habit. Rabbi Yehuda agrees with that just as Rabbi Meir does. So why doesn’t Rabbi Yehuda accept this regarding an ox’s gorings? Because he thinks an ox’s gorings are not habituation but evidence. Therefore Maharam says: I can bring proof from Rabbi Meir’s words that when spaced out there is habituation, so when close together there is certainly habituation, to “Give dew and rain for blessing.” Because Rabbi Yehuda’s disagreement is only because, in his opinion, the gorings are not habituation but evidence. But in matters of habituation, Rabbi Yehuda also agrees that if spaced out it creates a habit, then brought close together it certainly creates a habit. And regarding “Give dew and rain,” everyone agrees that it is a matter of habituation.

So what comes out according to Maharam of Rothenburg? Is the warning of the ox habituation or evidence? It is evidence according to Rabbi Yehuda. According to Rabbi Meir, no. According to Rabbi Meir it is habituation. According to Rabbi Yehuda it is evidence. And halakhically we rule like Rabbi Yehuda. So if you ask me, according to Maharam of Rothenburg, is the warning of the ox habituation or evidence? The answer is: evidence. Because this is the dispute between Rabbi Meir and Rabbi Yehuda. Rabbi Meir says habituation, Rabbi Yehuda says evidence, and practical law follows Rabbi Yehuda. Against what the later authorities say. The later authorities say: if you brought proof from the forewarned ox to “Give dew and rain,” you must think the ox’s gorings are habituation. Mistake. The opposite. Not only is it a mistake—it’s the exact opposite. It is clear that the ox’s gorings are evidence and not habituation according to Rabbi Yehuda, whose view is accepted in practice. According to Rabbi Meir it is habituation. But that does not interfere with the proof, because Rabbi Yehuda also agrees that in matters of habituation, spaced repetition habituates less than clustered repetition. And that, after all, is what matters for “Give dew and rain for blessing.” So that overturns the later authorities regarding Maharam of Rothenburg.

Now I’ll overturn them for Rabbeinu Peretz too; they’re wrong there as well. What do they say about Rabbeinu Peretz? Rabbeinu Peretz says one cannot bring proof from the gorings of an ox to saying “Give dew and rain for blessing.” Why? So the later authorities explain: because the gorings of an ox are evidence, while saying “Give dew and rain” is habituation, so one cannot bring proofs from one to the other. And I ask: why doesn’t Rabbeinu Peretz ask Maharam of Rothenburg, “Why are you bringing proofs from there to here? The practical law follows Rabbi Yehuda and not Rabbi Meir—why are you bringing me proofs from Rabbi Meir?” Why does he bother making distinctions within Rabbi Meir’s view? Again the same point: because he thinks there is no dispute between Rabbi Meir and Rabbi Yehuda on this point. According to him there is no dispute between Rabbi Meir and Rabbi Yehuda on this point. Their dispute is over whether this is habituation or evidence. Okay? Before we said, according to Maharam of Rothenburg, they both agree that habituation works better when events are close together. They both agree. Their dispute is over whether this is evidence or habituation. Whether, yes, whether this is evidence or habituation. And Rabbi Yehuda holds it is evidence, and therefore according to Maharam of Rothenburg the practical law is that the ox’s gorings are evidence and not habituation.

With Rabbeinu Peretz it works the other way around. He doesn’t ask Maharam of Rothenburg why he is bringing proofs from Rabbi Meir, because he says that if there is a proof from Rabbi Meir, there would be a proof from Rabbi Yehuda too. Therefore he has to reject the proof from Rabbi Meir and not from Rabbi Yehuda. What does that mean? Essentially he is saying: after all, the ox’s gorings are habituation—they are evidence, sorry, right? But Rabbi Yehuda agrees with that too. It is evidence. Except that according to Rabbi Meir, evidence is built more strongly when things are close together, while habituation is not. Rabbi Yehuda says that evidence is not built more strongly by closeness, even though he too agrees it is evidence. What happens with “He causes the wind”? What? “He causes the wind”… wait, let me do the accounting one more time, just a second.

Suppose this way: according to Rabbeinu Peretz, everyone agrees that habituation does not work when the repetitions are close together, right? Because otherwise saying this in Rabbi Meir’s name would help nothing if Rabbi Yehuda thinks otherwise. So apparently Rabbi Yehuda too holds that habituation does not work when the repetitions are close together. Then why does Rabbi Yehuda say it does work? Why does Rabbi Meir say it does work? Because he thinks it is evidence, right? And on what does Rabbi Yehuda disagree with him? He thinks it is habituation. So what comes out now according to Rabbeinu Peretz? That the ox’s forewarning is habituation, according to Rabbi Yehuda, whose view is accepted in practical law. Meaning, the later authorities understood from this that according to Maharam of Rothenburg the ox’s forewarning is habituation and therefore one can bring proof to “Give dew and rain.” And according to Rabbeinu Peretz it is evidence, and therefore one cannot bring proof. The truth is the opposite. According to Maharam of Rothenburg it is evidence, and according to Rabbeinu Peretz it is habituation—but all this within Rabbi Yehuda’s opinion. Okay.

Rabbeinu Peretz should have asked: why don’t you simply follow Rabbi Yehuda? No, because that doesn’t help; according to Rabbi Yehuda too—Rabbi Yehuda also agrees. Right, exactly. Therefore there is no point asking, because Rabbi Yehuda also agrees with this. Rabbeinu Peretz’s question was: how are you using Rabbi Meir’s reasoning? It doesn’t belong here. Correct. But that reasoning doesn’t apply according to Rabbi Yehuda either. If that reasoning did apply according to Rabbi Yehuda, then what’s your problem that it doesn’t fit Rabbi Meir? Fine, I followed Rabbi Yehuda—what do you want from me? Rabbi Yehuda too agrees that this reasoning doesn’t work. In habituation, clustering the events does not help. That is agreed by everyone, both Rabbi Meir and Rabbi Yehuda, according to Rabbeinu Peretz. But if so, then why according to Rabbi Meir, in the case of gorings, does clustering help? Because it’s not habituation but evidence. And why according to Rabbi Yehuda does it not help? Because it’s habituation and not evidence. Then it comes out simply the opposite of what the later authorities say.

And why all this? Precisely because of this idea of Occam’s razor, which says that once we have a dispute between two tannaim, we need to understand what the point of dispute is, and the assumption is that on all other points there is agreement. There is no reason to assume that Rabbi Meir and Rabbi Yehuda disagree both on whether this is habituation or evidence, and also on whether in habituation clustering of events helps or doesn’t help. We do not multiply disputes. We do not enlarge the dispute beyond what is needed. Okay? That is the assumption behind the whole analysis. And once you assume that—and this is the accepted assumption in the halakhic world everywhere, we do not multiply disputes—then the conclusions come out exactly the opposite of what the later authorities say.

I’ll upload the column in which I spelled this out in more detail from my website; it comes from there. What, did the medieval authorities know this? So what? And all this just for this answer? Fine, then explain their position to me. What—why did they do this? After all, it isn’t correct. That’s not the principle of charity. The principle of charity is to present why what they say does make sense. If you present it as though they knew and still said it anyway, then you’re saying they just said something that makes no sense. Fine, I’ll upload it.