Midrash and the Principles of Interpretation – Lesson 8

Table of Contents

• Words of the Sages, derashot, and the continuum of connection to the text according to Maimonides
• The Sages as interpreters and as legislators, and judicial legislation
• The impossibility of objective translation and the parallel to the discussion in the laws of the Shema
• Derrida, deconstruction, and the boundary that has no boundary
• Derashot as soft inferences rather than deduction: analogy, induction, and abduction
• The thirteen hermeneutic principles as a logical toolbox: Rabbi HaNazir, auditory logic, and the distinction between logical and textual principles
• A response to the criticism that “it’s all made up”: soft logic that is neither necessary nor arbitrary
• A formalization of methods of interpretation and its demonstration from Talmudic passages and Tosafot
• Kal va-chomer, “punishment is not derived by legal inference,” and the distinction between “two hundred automatically includes one hundred” and a kal va-chomer of stringency
• A refutation even of “two hundred includes one hundred”: Perelman, the wine law, and refuting the application rather than the mathematics
• Mathematics, physics, and refutation: “two plus three” and vector forces
• Quantum theory and logic: rejecting the claim that quantum theory “refutes” the laws of logic
• Intuition, Kant, and the claim of “cognitive thinking” between empiricism and rationalism
• Soft logic, systematicity, and the planned continuation
• Opening a series on Rabbi Shimon Shkop: the new Lithuanian analytic method, sources, and obligation and ownership

Summary

General Overview

The claim is that according to Maimonides, the classification of a law as Torah-level or Words of the Sages is not a catch-all concept with automatic consequences such as leniency in cases of doubt or setting aside rules for the sake of human dignity, but rather a collection of distinctions in which each halakhic consequence must be examined on its own terms according to the degree of connection to the biblical text. The Sages function both as interpreters and as legislators, and Maimonides points to an intermediate realm in which derashot are a kind of judicial legislation: they are not deductions that uncover what was already “inside” the verse, but soft inferences such as analogy, induction, and abduction. From here a response is built to criticisms in the style of Derrida or to criticism of judicial legislation, according to which every interpretation is an arbitrary “invention,” and the position is established that there is in fact a system here, and a non-deductive logic that can even be formalized. At the end, a new series is opened on Rabbi Shimon Shkop, as someone who formulated a philosophy of the new Lithuanian analytic method, and a first axis for discussion is presented through the concepts of obligation and ownership.

Words of the Sages, derashot, and the continuum of connection to the text according to Maimonides

Maimonides sets up a scale of levels of connection to Scripture that determines whether a law is Torah-level or Words of the Sages, and the boundary is not binary but a continuum that illustrates the “sorites paradox.” The idea is that “Words of the Sages” does not require one fixed set of consequences, and there are situations in which a law derived from interpretation will be classed as Words of the Sages and its doubt treated stringently, while by contrast a law given to Moses at Sinai will be classed as Words of the Sages and its doubt treated leniently. The distinction between Torah-level and rabbinic is not understood as a uniform bundle of accompanying laws, but as a classification from which one cannot automatically infer punishment, doubt, or override, and every implication requires independent clarification.

The Sages as interpreters and as legislators, and judicial legislation

The accepted division is that when the Sages interpret, the product is Torah-level, and when they legislate, the product is rabbinic, and Maimonides argues that there are actions that mix the two poles and resemble judicial legislation. The example from Israeli law is the supermarket ruling, in which the High Court allows local authorities to decide about opening supermarkets on the Sabbath, creating the impression that the judges’ rulings reflect different worldviews. The claim is that there is no “clean” interpretation, because every interpretation includes values, experience, and inner inclinations, and therefore principled criticism of judicial legislation as a violation of mandate rests on the illusion of an interpreter-computer.

The impossibility of objective translation and the parallel to the discussion in the laws of the Shema

Maimonides rules that the Shema may be recited in any language, provided one articulates its letters carefully, and the Raavad objects that all languages are interpretation, and who can be exact about his own interpretation, and what does precision of letters even mean in translation. The claim is that translation is not one-to-one but bound up with subjectivity, and therefore pure interpretation without any legislative component is impossible. From this follows the claim that too sharp a distinction between interpretation and legislation misses the actual structure of interpretation in practice.

Derrida, deconstruction, and the boundary that has no boundary

Deconstruction is presented as a caricatured philosophy that takes a correct point—that the interpreter inserts himself into the interpretation—and pushes it all the way to the claim that the text has no meaning beyond the interpreter himself. The demand to “draw a boundary” is presented as impossible, because the boundary itself will also invite new interpretations, and therefore the discussion cannot be closed by one principle that determines what counts as “an interpretation that fits the words.” Legal positivism, which imagines a judge deriving a ruling deductively from statute, is presented as unworkable because law and science are not mathematics.

Derashot as soft inferences rather than deduction: analogy, induction, and abduction

The claim is that derashot are not deductions, and therefore do not uncover a conclusion already contained in the premises, but activate soft inferences in which the interpreter adds an element beyond the text. The example “You shall fear Hashem your God” including Torah scholars is presented as an analogy in which the text provides a trigger (“et” comes to include), but does not determine the outcome, and the choice of what to include depends on the reasoning of the interpreter. Abduction is defined as an inference from particulars to an explanatory theory from which the generalization also emerges, and the example of the force of gravity is brought as an explanation that unifies isolated observations, alongside the example of the green frog, to show that inference is not objective even though that does not make all conclusions equally valid.

The thirteen hermeneutic principles as a logical toolbox: Rabbi HaNazir, auditory logic, and the distinction between logical and textual principles

Rabbi HaNazir in Kol HaNevuah is presented as arguing that the thirteen hermeneutic principles are the basic toolbox of logic, an “auditory logic,” as distinct from Greek-mathematical visual logic. A division is proposed between logical principles such as kal va-chomer and binyan av, and textual principles such as general and particular, and gezerah shavah, where the difference lies in the trigger for interpretation: logic as opposed to a stylistic phenomenon in the text. Every interpretation contains reasoning, and the principle does not dictate the result but directs an act of expansion, exclusion, or comparison, and after the trigger the inference is determined by the interpreter’s logic.

A response to the criticism that “it’s all made up”: soft logic that is neither necessary nor arbitrary

The argument against Derrida and against criticism of judicial legislation is that it is true there is a subjective component, but it does not follow from this that everything is a rigged game of positions. A distinction is drawn between uncertainty and arbitrariness, using the image of a teenager who demands proofs and concludes that the absence of certainty means it is all invented, as against the “synthetic adult” who argues that there is probability and common sense even without deductive necessity. The claim is that one can show an orderly method and even a formalization for this logic, so this is not random improvisation but a regulated mode of inference.

A formalization of methods of interpretation and its demonstration from Talmudic passages and Tosafot

It is claimed that a formalization has been written describing how the hermeneutic principles operate in a way that connects scientific, legal, and Talmudic thinking, and that the model makes it possible to reach results mechanically even without extraordinary talent. An anecdote is brought about Tosafot that had not been understood in the yeshiva, and a presentation by means of tables and formulas showed that the conclusion “has to come out this way,” alongside the claim that Tosafot and the Sages reached their conclusions without modern mathematics. The passage in tractate Kiddushin 5a about whether a bridal canopy effects acquisition is presented as a complex test case involving kal va-chomer, refutations, binyan av, and a common denominator, and the model is built so that it can analyze even very complex structures out of those building blocks.

Kal va-chomer, “punishment is not derived by legal inference,” and the distinction between “two hundred automatically includes one hundred” and a kal va-chomer of stringency

The example is brought of “If a man opens a pit, or if a man digs a pit,” and the claim in the Mekhilta that the additional verse comes to teach that punishment is not derived by legal inference, whereas the Babylonian Talmud derives something else from it, and the Maharsha explains that the Babylonian Talmud holds that in monetary law one may indeed derive punishment by legal inference. Another kal va-chomer is brought: “Behold, the children of Israel did not listen to me, so how will Pharaoh listen to me?” in order to distinguish between a kal va-chomer of stringency, which contains an assumption of similarity that can be refuted, and “two hundred includes one hundred,” in which the more severe case already contains the lighter one within it. The example is brought of “from his seed, but not all his seed” regarding Molekh, and the Kesef Mishneh understands this as a kal va-chomer of the type of “two hundred includes one hundred,” in order to emphasize the intuition that someone who did “everything” also did “part.”

A refutation even of “two hundred includes one hundred”: Perelman, the wine law, and refuting the application rather than the mathematics

It is argued that even a kal va-chomer of the type “two hundred includes one hundred” can be refuted, and the example is brought from Chaim Perelman of a Belgian law forbidding the sale in a pub of more than three liters of wine, where a judge ruled that it was permissible to sell fifty liters because the law was intended to limit the wasting of one’s weekly salary, not to prohibit commercial investment. The claim is that the refutation does not refute the mathematical truth that three is included in fifty, but refutes the assumption that this mathematical model correctly describes the legal meaning of the statute. From here it is inferred that in Jewish law as well, the mathematics of inclusion is not the deciding point, but rather the question of applying the model to norms, punishments, and purposes.

Mathematics, physics, and refutation: “two plus three” and vector forces

It is argued that “two plus three equals five” is not a scientific claim subject to refutation, because an experiment of “two oranges plus three oranges” will never lead one to give up mathematics, but at most to give up its suitability as a physical description of the situation. An example is brought from mechanics in which “five plus five” in perpendicular forces yields a resultant of 5√2, and the inference is that mathematics was not refuted, but rather the assumption that combining forces is described by arithmetic addition rather than vector addition. In this way it is explained that the mechanism of refutation in reality always strikes the fit between a formalism and the world, and not the mathematical truths themselves.

Quantum theory and logic: rejecting the claim that quantum theory “refutes” the laws of logic

It is argued that quantum theory cannot refute logic because it itself uses logic in proofs, including proofs by contradiction, and therefore anyone who claims otherwise is confusing a physical model with the conditions that make analysis of it possible. It is explained that a quantum particle is an extended wave function and not a classical little ball, so there is no logical contradiction in the fact that its description is spread out in space, while in measurement one obtains one point-result and not “in two places at once.” The conclusion is that logic and mathematics are not tested in the laboratory, and scientific discussion concerns only their application to reality.

Intuition, Kant, and the claim of “cognitive thinking” between empiricism and rationalism

A question is raised about what intuition is and how we know logical and mathematical truths, and this is linked to Kant’s problem of the synthetic a priori and to criticism of the dichotomy between rationalism and empiricism. The claim is that the solution is that generalization and theory are not “pure thinking” detached from the world, but a continuation of observation through an additional faculty of cognition, and that this is what is called intuition. The argument is that science “works” because generalizations are not arbitrary constructions, and it is maintained that there is truth even in definitions, and that a dispute about a definition points to an assumption of truth and not to a pluralism in which “everyone is right.”

Soft logic, systematicity, and the planned continuation

It is argued that the goal is to show how a logic operates that is not deductive and yet is still systematic and precise, thereby strengthening the legitimacy of “judicial legislation” in the world of interpretation, which is not necessary but also not arbitrary. It is proposed that the tools will be defined in a way that matches intuition and afterward will stand as an independent mechanism, and it is said that the systematic application will begin next time through analysis of kal va-chomer and then binyan av. It is said that this logic can be called non-deductive logic or “soft logic,” but the main thing is the practical construction of the tools.

Opening a series on Rabbi Shimon Shkop: the new Lithuanian analytic method, sources, and obligation and ownership

A series of five units is opened on the figure of Rabbi Shimon Shkop as an attempt to analyze his legal and logical theory and his innovation in the world of Torah analysis, not as a biography. Rabbi Shimon Shkop is presented as an important representative of the new Lithuanian analytic method, born in 1860 and died in 1939, a student of Rabbi Chaim of Brisk and of Rabbi Itzele of Ponevezh, and as someone who gave a “philosophy of Torah analysis” in contrast to the more positivist-legal Brisker method. The foundational sources are defined as the introduction to Shaarei Yosher and the books Shaarei Yosher and Chiddushei Rabbi Shimon Yehuda HaKohen, together with scattered philosophical remarks, and the first discussion is set around the basic concepts of obligation and ownership through the Talmudic text in Bava Batra 175b about the meaning of debt—whether it is a personal obligation or a connection to property.

Okay, last time we talked about the explanation according to Maimonides: what is the meaning of this status of laws that emerge from exegetical derivations, that these are rabbinic laws. So I said this is not some sweeping statement that comes with one automatic package of consequences. If it’s rabbinic, then in a case of doubt we rule leniently, human dignity overrides it, and so on, and you don’t punish for it, and all kinds of things like that; and conversely for Torah-level law. The claim is that no, that’s not right. There is a collection of consequences, and each consequence has to be examined separately. There is, first of all, a collection of categories of rabbinic laws, a whole range of levels of connection to Scripture. That’s what determines whether something is Torah-level or rabbinic according to Maimonides: the stronger the connection, the closer it is to the content of the verse or verses. And each such category of rabbinic law can have different halakhic consequences. One might be rabbinic law where doubt is treated stringently—we spoke about that regarding laws derived through exegetical readings. A law given to Moses at Sinai, for example, is rabbinic law where in a case of doubt we rule leniently. I even tried to suggest explanations for why. In other words, there is no single broad categorical statement here; rather, there is a collection of distinctions. And the concept of Torah-level and rabbinic is not some umbrella concept. Meaning, it’s not that it has a whole package of many consequences that all automatically go together. Each such consequence has to be examined on its own terms.

But for our purposes, if we return now to the main line of the discussion, the basic claim is that whether a law is Torah-level or rabbinic depends on its connection to the text. If it is really inside the written text, then it is Torah-level; if it is not in the text, then it is rabbinic law. But what does “not in the text” mean? There are different degrees of not being in the text. We talked about the heap paradox, we talked about the fact that many times it is wrong to use binary logic of yes-no, black-white; rather, there is some kind of continuum. And I brought a set of examples illustrating that point.

By the way, alongside this distinction of Maimonides—which really appears here—well, maybe not alongside; first I’ll sharpen it further. We talked about the fact that the sages basically have two kinds of roles, or two hats: legislators and interpreters. When they function as interpreters, the product is Torah-level law; when they function as legislators, the product is rabbinic law. Okay? That’s the standard division. Maimonides claims that there are certain functions of the sages that actually mix both poles. They have an interpretive dimension and a legislative dimension. In our language today this is called judicial legislation. And there are endless polemics and arguments about this, not only in academia but also in public discourse: when a judge reaches some decision and it’s obvious that his worldview affects it. It’s not just dry interpretation of the law, which ostensibly is what he’s supposed to do.

In our system, for example, there is ostensibly a very clear division. Members of parliament are the legislators and the judges are the interpreters. In Jewish law, the sages do both things, or the rabbinic authorities do both things. In the legal world there’s a division: the legislator is the legislator, meaning the legislative institution is responsible for legislation, and the courts are responsible for interpretation and application. Okay? So what happens? Sometimes a judge gives a ruling that isn’t just a simple interpretation of the law. The proof is that another judge would rule differently. So where does that difference come from? Apparently they have different worldviews. And those worldviews affect the way they interpret the law. And that’s what is called judicial legislation. In other words, this is a judicial act, but it has a legislative dimension. You are actually creating a new law; you’re not merely interpreting the existing law. And then comes the criticism: “That’s not your mandate; you can’t do that.”

There’s a great example of this. Not many years ago there was the supermarkets ruling—opening supermarkets on the Sabbath. Can local authorities decide whether to allow stores to open on the Sabbath, or should this be done by the Knesset, or on a national level? So it reached the High Court, and there they allowed the local authorities to make that decision, each municipality according to what it saw fit. There were, I think, five judges on the panel. The two religious ones were against it, the three secular ones were in favor. And Miriam Naor, who was then president of the court—it was her farewell ruling—wrote this decision, and she says: just so you know, this is completely professional, it has nothing at all to do with worldviews. And they keep repeating this all the time. But the two religious judges ruled one way and the three secular judges ruled the other way. There’s a kind of impression here that is very hard to wrap in those funny words. Yes, it depends on the judges’ worldviews. And by the way, that’s how it is. It’s not anyone’s fault. There’s nothing to be done. There is no such thing as purely neutral interpretation. There is no such thing. Whenever you interpret something, you bring with you your world, your values, your understandings, your experience. That’s just the way it is. No human being is a computer.

Right, exactly. Today even a computer is no longer a computer—ChatGPT. So as we know, ChatGPT is left-wing. Yes, ask it questions and you’ll get left-wing answers. People often bring this as proof that the left is right: look, the computer, which is supposedly objective, says so. And that’s nonsense. Who fed that computer? Silicon Valley—everyone there is left-wing, and they are the ones feeding it. So of course if you let a computer read only Haaretz articles, you’ll get opinions out of it according to what you’ve stuffed into it. That proves nothing at all about what is true. In any case, yes, the paradigmatic computer—not today’s computers—really is clean. Give it the data, it’ll do the calculation and tell you the answer. But human beings are not computers, and interpretation of law always includes components of the interpreter’s worldview, his understandings, his inclinations, all kinds of things.

And therefore there is really no interpretation that lacks a legislative dimension. There isn’t. It’s a mistake. This somewhat recalls the dispute between Maimonides and the Ra’avad in the laws of the Scroll of Esther—no, in the laws of reciting the Shema, sorry. Maimonides says that one can recite the Shema in any language, provided one articulates its letters carefully. The Shema can be said in all languages, not only in Hebrew; that’s a Mishnah in tractate Sotah, at the beginning of chapter seven, listing things that may be said in any language, and one of them is the Shema. You can translate it into English and say “Hear, O Israel, our God is…” whatever. The claim is that you can say it in any language, but you have to be precise. So the Ra’avad asks him: but all languages are just interpretations—who can be precise about an interpretation? What is there to be precise about in an interpretation? The letters of the interpretation? The interpretation merely expresses some content. What meaning is there to precision in the letters? In Hebrew, you can say maybe there is significance to this exact wording and not another, because the wording is binding. But when you translate, one person chooses these words, another will choose somewhat different words—the main thing is that the content is preserved. So what is there to be precise about in the letters?

Yes, that’s the point. There is no translation that is just translation… If there were an objective translation, then you could also be precise about the letters of the translation, because then the translation would be one-to-one with the original. But there isn’t. It always involves a lot of subjective matters, personal factors, biases, whatever. And so the illusion that one can interpret something in a completely clean way—that’s an illusion. There is no such thing. Therefore the claim that legislative interpretation or judicial legislation is illegitimate is nonsense. You can argue about degrees; you can say here you went too far, there you exaggerated. But to think that in principle a judge should be a computer and is forbidden from bringing himself into it—even if he tried, he couldn’t succeed. It can’t be done. That claim is disingenuous. It’s disingenuous, but it also cannot be true.

What this means is that the distinction we make between legislation and interpretation is too sharp. There is no such thing as pure interpretation. Every interpretation has a legislative dimension. It contains an element that goes beyond the interpreted text. When I interpret the text, the interpretation contains something that expresses not only the text but also something of me. To such an extent that in the hermeneutics of the last several decades—deconstruction, Derrida, all those things—they basically say: forget it, there is nothing besides this legislative act. Meaning, only the interpreter is there. There is no real significance to the content of the text; everything is subjective. Which is nonsense on stilts. But he takes a correct point too far. It’s like a caricature: if someone has a mole here, in a caricature that mole suddenly becomes half the picture. A caricature does that justly because it wants to illustrate a point it wants to draw your attention to. But when you do caricatured philosophy—caricatured—then that’s what it looks like. Deconstruction is caricatured thought.

Okay, you just walked in—we were talking about Derrida and deconstruction. So, the Frenchman, the French-Algerian Jew. Tunisian? Tunisian? Not Algerian? I thought he was Algerian. In any case, the claim is that you can’t—yes. How should one relate to all of this…? I’m asking where to draw the line. There isn’t—I don’t know where to draw the line; that’s exactly the point. That’s a childish demand; you can’t draw a line. From now on and onward? I don’t know. There are no lines. The moment you draw a line, the line itself will be subject to interpretation. If I establish the principle that is supposed to be the line—okay, the line is that you should only interpret in a way that fits the words of the text, something like that—okay, what counts as fitting the words of the text? Again there will be arguments. You can’t close this issue off. There is no such thing. It’s an illusion.

Yes, in the legal world there are approaches called positivism. Really in philosophy generally, but in the legal world there is legal positivism. Legal positivism consists of several elements; one of them is this illusion that says the judge is supposed to be merely an interpreter, to derive the ruling deductively from the law. Okay? Complete nonsense. There is no such thing. You can’t do it, even if you want to. Even if in principle you hold such a view, it’s not workable. It can’t be done; this is not mathematics. Okay? Therefore, even if one can argue in principle whether one ought to proceed that way, one cannot argue in practice that it’s practical, because it isn’t. It simply isn’t. Anyone who says otherwise just doesn’t understand what he is talking about.

So the claim is that what Maimonides is really saying is that when we derive a law by means of an exegetical reading, what we are doing is judicial legislation. It is something between legislation and interpretation. It is interpretation with a dimension that comes from the interpreter and not from the text. Therefore you cannot say that he uncovered something that was inside the text. That would be deduction; deduction uncovers what was in the text. We talked about this, right? In a deductive argument, the conclusion was already inside the premises. That’s why the conclusion follows necessarily from the premises. Therefore a deductive argument is a revealing argument. That is the positivist’s dream: that the judge should be a deduction machine. In other words, you simply expose what is already in the law, and that’s it; you add nothing of your own.

But science, law, all fields that are not mathematics, really involve analogies and inductions and softer forms of inference. And what does it mean that they are softer? It means there is something that you add to the facts or the premises from which you begin, and only thus do you reach the conclusion. The conclusion contains not only the facts or only your premises. There is something you added beyond the facts and the premises, and that apparently comes from you. And someone else, built differently, may reach a different conclusion because he adds different things. Okay?

By the way, this does not mean everyone is right. For example, in an analogy about reality. Someone comes and says: “This frog is green; that’s also a frog, so it too is green.” That’s an analogy, right? And someone else says: “Why are you assuming that all frogs have the same color? Maybe there are pink frogs too. You can’t be sure. Maybe yes, maybe no.” So there may be someone who makes that inference and says, “This frog is green,” and someone else says, “No, that’s not right. I don’t think this frog has to be green.” At the end of the day, you can look and see whether the frog is green or not. What I just said does not mean they are both right. That’s an important point. What it means is that the process is not objective. One will do it this way, another will do it another way. That does not mean they are both right. It only means that we have no other way. We have no way to be certain of our conclusion. And therefore it is possible that we will make a mistake, and possible that we will be right.

The postmodernist or pluralist will say: “That also means everyone is right, that there is no truth in this context.” But that is not true. There is truth in this context, in my view. There is truth. It is true that we have no clear or certain way of reaching it, because these are softer routes, not rigid routes, not unambiguous routes. Analogy and induction—and we talked about these things. What this really means is that the methods of exegesis, and now I’m continuing to the next part, are ultimately not deductions from the verses. They do not extract what is inside the verse; rather, they are analogies or inductions. In other words, I take “You shall fear the Lord your God,” and I say: “Let’s make an analogy—so also Torah scholars.” If one must fear the Holy One, blessed be He, then one must also fear Torah scholars. So I’m making some kind of analogy. Now, “et” comes to include something, so it helps me say, it tells me, perform an analogy here. It does not tell me what the result of the analogy is, right? We talked about this. And the result of the analogy depends on what I think resembles the Holy One, blessed be He. I think Torah scholars. Someone else will think, I don’t know, Torah scrolls. Someone else will think chairs. I don’t know. There could be several things.

So the fact that I’m making some inference from the Torah does not mean that the result is something I uncovered inside the Torah. The result is not in the Torah. I added to what is in the Torah itself further things that are from me, my own. Therefore this inference is not a deduction but an analogy, induction, or some softer kind of inference. In science too we deal with softer inferences. That is what distinguishes science from mathematics. Mathematics is deductive inference; science is analogies and inductions and abductions. What is abduction, Rabbi? Abduction means—the idea is this: induction is moving from particulars to the general rule. Abduction is moving from particulars to a theory that explains them, and therefore also, of course, to the generalization. That is what underlies induction.

Let’s say you say: all objects with mass fall to the earth. How do you know? Because I saw several such things fall, and I assume that this is true for all objects with mass. Right? That’s induction. If instead I say there is a law of gravity, every two masses attract each other, and as a result the objects I saw fell to the earth—that is an explanation of why they fell to the earth, because there is a force that every two masses exert. And from that there will of course also emerge the generalization that every object with mass will be drawn toward the earth. But notice that moving from the cases to the theory is not the same thing as moving from a few cases to the whole set of cases. The second move, what is called induction, is on the phenomenological level, the level of facts: from a few facts to a larger body of facts. The move called abduction includes an intermediate step: trying to formulate a theory, from which the generalization will then emerge. From the theory a generalization will emerge because the theory basically says that all objects with mass will fall.

What underlies induction is really abduction. Very often we don’t even put that on the table, but it’s there. The claim is that the color of the frog, say in the analogy I gave earlier, probably follows from its body structure. And since all frogs have a similar body structure, they will probably have the same color. So I have some assumption here that serves as a theory explaining my claim that the color is always green, and it’s not just a bare claim that the color is green. Because saying the color is green is only a move from a few facts to many facts. But behind this there is supposed to be some rationale, some theoretical explanation. The move to the rationale is what is called abduction. Peirce defined that inference as abduction.

So these inferences we make from midrash are really softer inferences. Therefore they are not legislation, because legislation has nothing to do with verses at all. Ordinances, decrees, and so on have nothing to do with verses. They are not interpretation in the simple sense either, because they do not extract what is in the verse itself. Rather, this is something that expands what is in the verse, does induction or analogy with it or something of that kind. And therefore it is something between legislation and interpretation, something in the middle. That is the character of the world of exegesis. That is basically the summary of everything we said about Maimonides, and from here I continue onward. That’s the picture.

Now I want to explain a bit more the meaning of this matter. What does it mean that this is really judicial legislation, or something between legislation and interpretation, something in the middle? What I want to do now is try to show you how this logic works when it is not deductive logic. Deduction is classical logic; that’s what you study in logic courses in mathematics or philosophy, doesn’t matter, but that’s what you study in logic courses. I want to try to show you how soft logic works, the logic of analogies and inductions, not the logic of deductions. And there too there is logic.

Where is this idea taken from? Rabbi HaNazir, in his book Kol HaNevuah and in other writings, claims that the thirteen hermeneutic principles are really the basic toolbox of logic—what he calls auditory logic, as distinct from visual logic. Visual logic is the classical Greek or mathematical logic, whatever you want to call it. And he claims that in the world of Torah, what rules is auditory logic, some different kind of logic. And its basic building blocks are not the basic logical rules we know from logic, but the hermeneutic principles. He claims that the hermeneutic principles are the basic building tools of Semitic logic.

Now, you can argue about what exactly he means. I had all kinds of arguments about this with different people; that doesn’t matter right now. So for now I’m saying what I’m saying. Fine? Whether this is really what HaNazir meant or not—you can argue, but who cares? The question is what is correct, not what HaNazir said. So I want to claim that this is correct. I don’t care whether he said it or didn’t say it.

I’ll divide the hermeneutic principles into two types. The hermeneutic principles are basically divided into logical principles and textual principles. Logical principles are principles where the inference I make is based on logic. For example, argument a fortiori, an archetype built from one verse, an archetype built from two verses, and so on. Those are the logical principles. Actually not “and so on”; that’s more or less it. Maybe two verses that contradict one another. Logical principles are argument a fortiori, an archetype from one verse, an archetype from two verses. What exactly is an archetype? An archetype from one verse and from two verses is basically analogy and induction. Analogy and induction, yes. And argument a fortiori too, as we’ll soon see, is a kind of analogy. There is no deduction in the world of hermeneutic principles, contrary to what some have thought. No deduction? None.

Deduction is not a hermeneutic principle. Now, according to what I’ve said so far, you understand that this must be the case. Because if there were a deductive inference, it wouldn’t be called exegesis. Then I would be interpreting what is in the Torah itself; I would simply be extracting more and more things that were already inside the Torah. That cannot be exegesis. Maimonides would not call that rabbinic law. That would be revealing what is in the Torah itself. Therefore by definition, in the world of exegesis there cannot be deduction.

Now, there is a scholar of the hermeneutic principles named Adolf Schwarz, from the rabbinical seminary in Vienna—this was a hundred years ago or so. He published books on some of the hermeneutic principles, in German; I think two of them were translated into Hebrew. He, for example, claims that argument a fortiori is deduction. So I’ll explain shortly why he is wrong, but here I’ll say why he cannot be right. He cannot be right, because if so, argument a fortiori would not have been a hermeneutic principle. Fine? You don’t need a law given to Moses at Sinai telling me the hermeneutic principles in order to use deduction. I use deduction everywhere, in every context. Obviously. You don’t need a law given to Moses at Sinai to tell me to use deduction. Fine? That would be like saying: use your brain. Okay? So it cannot be right. Later I’ll explain why it’s also actually false—where exactly he misses the point.

So these are the logical principles. Still, they are logical principles. Not deduction, but logical principles. The textual principles are principles that are not based on logical rules but on textual rules. For example, the principle of general statement and specific detail, or the principle of verbal analogy. General and specific, general and specific and then general again—all these are textual principles. What does that mean? Let’s say the Torah says, “You shall spend the money on whatever your soul desires: cattle, sheep, wine, or strong drink.” Fine? So what is “whatever your soul desires”? That is a general statement. “Cattle, sheep, wine, or strong drink” is a specific detail, right? Those are specific examples. “Whatever your soul desires” is the general statement. So from here we derive an interpretation of general and specific, general and specific and general, because there is a general statement again at the end.

What does that mean? The style the Torah chooses is a style that moves from a general formulation to examples and then back to a general formulation. And that means I am supposed to do something here. In other words, what moves me to action is a textual phenomenon, a formulation the Torah chose, and from that I am supposed to draw some conclusion. That is why I call these textual principles. By contrast, in an argument a fortiori, the Torah says that tooth and foot are liable in the damaged party’s courtyard, therefore all the more so horn is liable in the damaged party’s courtyard. That has nothing to do with the Torah’s style; it is not because the Torah phrased the liability of tooth and foot in one way or another. My logic simply tells me that horn is more severe than tooth and foot, so I make an argument a fortiori. It doesn’t begin from some stylistic textual phenomenon; it follows from logic. Therefore I call that a logical principle, and this I call a textual principle.

All the textual principles, and we already talked about this, begin from a textual phenomenon, from the Torah’s wording, and from this I draw some halakhic conclusion. The way from the text to the halakhic conclusion always includes reasoning. Because otherwise how do I know what to include under general-and-specific, or in the case of “et” which comes to include—“You shall fear the Lord your God”—to include what? How do I know what to include? But here reason is already at work. What is most similar to the Holy One, blessed be He? Presumably Torah scholars. Someone else could come with a different reasoning and make the same type of derivation. What do both share? That “et” comes to include something. But include what? That depends on your reasoning. So what does that mean? It means the hermeneutic principle does not tell me what the result is. It gives me a trigger for exegesis. It says: here you must perform an expansion, here a limitation, here a comparison. Okay? That’s what the hermeneutic principle instructs me to do. From that point on, the exegete’s reasoning comes in: how to compare, what to compare, what to generalize, what to exclude. That is already your own decision based on your own reasoning.

So there is reasoning in every derivation. The difference between the logical principles and the textual principles is the question: what is the trigger for the derivation? In the logical principles, the trigger is logic. In the textual principles, the trigger is the text. In the end, once I have the trigger, I use reason to derive the conclusion. That is true in both contexts.

Now I want to begin analyzing the logical principles. We probably won’t get beyond the logical principles, but I want to deal a bit with them. And I will try to show you that this is basically a defense against Derrida—we mentioned him earlier. It is a defense of the fact that we have the ability to do judicial legislation and that this is not just an arbitrary matter. It is not necessary, but the fact that it is not necessary does not mean it is arbitrary; that would just be speculation. The criticism of judicial legislation, or Derrida’s criticism of classical interpretation, says this: you understand that what enters into your interpretation contains subjective dimensions of your own, and therefore what you are doing is an invention, not an interpretation. And then Derrida turns this into an ideology: okay then, so it’s an invention, that’s what interpretation is—let’s call it invention. Okay?

Likewise the criticism of judicial legislation: after all, you the judge inserted your conceptual world—like the supermarkets ruling I mentioned earlier, where they allowed local authorities to open supermarkets on the Sabbath, or to decide to open them. The religious judges objected, the secular judges favored it. Meaning, it is obvious that the judge’s world of values took part in his ruling. That is obvious; hard to deny. Right? So what? Then they say: fine, so it’s all speculation. It’s just invention. Don’t tell me stories that you function as a judge; you function as a person with an agenda, with a position. That is the criticism of judicial legislation, and it is very similar to the criticism of deconstruction against classical interpretation, which tries to strive toward the meaning of the text or of the author of the text. There are all kinds of nuances there. Okay?

But that criticism is not correct. Not here and not there. Why? True, there is a subjective element in interpretation. But it is not true that this makes it equivalent to invention. It is not true that this is just arbitrary invention and everyone does whatever he wants. No. Even a religious judge will have cases where he rules in the secular direction, because he understands that it can’t be otherwise. There are situations that can bear both this interpretation and that interpretation, and then he will presumably lean toward the religious interpretation and the other toward the secular one. That doesn’t mean it is always like that. It doesn’t mean all these stories are merely a collection of agendas and inventions and everyone basically does whatever he wants. That leap is what I do not accept.

The criticism is correct in the sense that you should not present this as pure interpretation. It is not pure interpretation. You inserted something from your world. But the conclusion people draw from this criticism—that if so, everything is a fixed game, all games of position—not true. Simply not true. There is logic behind these things, even if it is soft logic and not unambiguous, not yielding one mathematical result and no other. But it is not true that this is invention.

Remember when I spoke about maturation—the child, the adolescent, and the adult? I talked there too about this sort of criticism. The adolescent says to the adult: listen, you accept things without proof, so they are inventions. I accept only proofs. And what does the adult answer him—the synthetic adult, as opposed to the fundamentalist; we talked there about three models—the synthetic adult says: you’re right that there’s no proof, it’s not certain; you’re wrong that these are inventions. There is something in between. There is something that is common sense, common wisdom, something that is… yes, it is reasonable. It is not certain. But don’t tell me it is just arbitrary invention, a position, or whatever. If you are a Marxist, then every invention becomes a position. But that is all the same thing. Okay? No, it is not the same thing. There is common sense, and there is something that is not common sense.

Now what I will try to show you is that behind what I call common sense there is a logic that I can even formalize mathematically. Even though this is not deduction, not mathematics, I can show you how the thing works and thereby answer the criticism that says, listen, you’re just inventing things. Not true. I’ll show you: I have a very orderly method for how I do this. Fine? Even though people think that if there is an orderly method then it must be deduction—mathematics or ordinary logic. No. I claim that even the softer parts, analogy and induction, have logic behind them. And I can even formalize it, and make a formalization of that logic.

We once wrote a book about this formalization. I think it really is the formalization of how science works, how law works, and it all really comes out of the hermeneutic principles, just as Rabbi HaNazir says. Again, not that they learned it from the hermeneutic principles, but in the hermeneutic principles one can see how this thing works. And it is quite surprising to discover, by the way, that the sages reached conclusions that at first glance seem illogical, and when you do the mathematical analysis you see that they hit the mark. It’s quite amazing.

After we made this model, I gave a lecture on the subject—not here, actually at Tel Aviv University, in computer science. We gave a seminar there in computer science on this logic of hermeneutic methods. The Sabbath before that lecture, my son came to me—he was then studying at Merkaz—and said: listen, there’s a Tosafot that we don’t understand. Nobody in the yeshiva understands it. What is this thing? The conclusion makes no sense. It was some argument a fortiori with a refutation and then another refutation and so on, and the question was how Tosafot ultimately reaches its conclusion. I told him, okay, wait till after the Sabbath. After the Sabbath I sat down with the charts and formulas and showed him that this is the result. It has to come out that way. Afterward you can also understand the logic behind it. But you need the logic in order to understand. And it’s amazing that Tosafot did this without it. Meaning, they—and the Talmud too—reached these conclusions without the mathematics of the matter. No, I don’t imagine for a moment that they used this mathematics. This mathematics is simply an attempt to imitate their modes of thought in more modern tools. And by the way, this allows less talented people to reach the correct conclusions, as always in logic. Even if you are less talented, you can reach the right conclusions because you have tools that do it mechanically. You don’t need to be a genius for this. In the past you had to be a great genius to reach the right result. But it’s interesting that they did reach the right results. In most cases, almost all cases, they reach the right results. It’s amazing.

Now we built that book in such a way that we took the sugya in tractate Kiddushin on page 5, the sugya about the bridal chamber—“if you wish, say that the bridal chamber acquires,” and so on. This is one of the most complex sugyot in the Talmud. There is an argument a fortiori, then a refutation of the argument a fortiori, then they build an archetype, then a refutation of the archetype, then they make a common denominator, then they refute the common denominator, add something else, refute that, combine the two and create a larger common denominator, refute that common denominator, do something else, and in the end they make some refutation that is of an entirely different kind, and finally reach some conclusion.

Wait, a common denominator is an archetype built from two verses. Meaning, there are two teaching cases—we’ll see this later. There are two teaching cases from which they derive the conclusion. That’s induction. No no, it’s all logical. It’s all logical. It’s a combination of all the building blocks of logical reasoning: argument a fortiori, an archetype from one verse, an archetype from two verses, and refutations. And you can combine them into more and more and more complex structures, infinitely. You can see that scientific induction is there and legal reasoning is there—everything is there. Everything can be built out of those building blocks. And we showed a systematic way to analyze every structure, however complex, from these building blocks and arrive at the result. You can see how this works—the inductive logic of Francis Bacon, what is called scientific logic today, is really a special case of this. Okay? So in the end this gives you the results in a wonderful way, and the amazing thing is that the sugya each time gives the correct answer. It really gives the answer that follows from the matter.

Now, that is not so surprising, because after all, we built the logic on the basis of the sugya. Meaning, how did we build the logic? We saw that the sugya reaches such-and-such a result, and we tried to understand it. And we couldn’t find any explanation for the sugya’s conclusion. It didn’t fit in any way. We tried ad hoc assumptions and changing things—nothing helped. Two days we racked our brains, thinking this would collapse the whole model. Okay? And then suddenly we discovered that we had simply copied something incorrectly. In one of the tables there was a one instead of a zero in one of the cells. We had simply copied the data incorrectly. And once we put in the correct data, everything worked out.

Now, that was very nice, because we didn’t do it intentionally. It was very nice because suddenly it showed us that you can’t make just anything work. It’s not “give me a table, and if this is the answer, I’ll build you a mechanism that gives that answer—what’s the problem?” No. If it’s not right, you won’t be able to build such a mechanism. In any way. Otherwise we would start thinking maybe, well, if you tailor everything to fit the sugya, then of course everything works—you’re building it so as to explain what the sugya says. No. It turns out to be very internally consistent. And if you try to tailor something untrue, you won’t succeed in tailoring it. In any form. And did you build the table? We’ll get to that. I’m just giving the motivation. I hope we’ll get there. Fine? I’m giving the motivations.

So this will really be a part that is a bit more, let’s call it, formal. Not really mathematics, but a bit more formal. There are also mathematical aspects to it. Someone did a master’s thesis on it, a student of mine, one of my students here from the kollel. He did a master’s in mathematics, and he worked on this. He proved various theorems about the matter. He didn’t manage to solve the problem completely, but he proved a few theorems about the topic.

In any case, let’s begin. Fine? That’s where I’m heading. Okay, let’s start from the beginning. Now I want to begin with argument a fortiori. After that we’ll move to archetype and onward. Let’s begin with argument a fortiori. What is argument a fortiori? At first glance it is a necessary inference. It says: if the lighter case is forbidden, then the more severe one is certainly forbidden, right? So ostensibly that is a necessary inference. Therefore it is deduction. So says Adolf Schwarz, whom I mentioned earlier. He says, “Argument a fortiori is deduction.” Okay?

Now let’s take an example. The Talmud says—the Torah says—“If a man opens a pit, or if a man digs a pit.” A pit in the public domain, right? So if the pit causes damage, you have to pay. It says whether you opened the pit or dug it. Meaning, whether you removed the cover from an existing pit or dug a new pit. The midrash asks: if one is liable for digging, then for opening it all the more so; if one is liable for opening it, then for digging it all the more so. If there is an existing pit with a cover and you remove the cover, you are liable. Then obviously, if you dug the whole pit yourself, you should be liable. So why does it need to say, “if a man digs a pit”? Let it just say, “if a man opens,” and I would learn automatically that one who digs a pit is liable. The midrash says: to teach you that one does not punish on the basis of a legal inference. What does that mean? There is an argument a fortiori from opening to digging, fine? But you cannot punish by the force of an argument a fortiori. Therefore, if I want to punish someone for having dug a pit, I must write it explicitly. Because if I learned it by argument a fortiori from opening a pit, that would not be enough in order to punish him. To punish him, it has to be written. Argument a fortiori cannot serve as a sufficient basis for punishment. One does not punish based on legal inference.

Now, that’s an example of argument a fortiori. And this really looks like deduction, right? If there is liability for opening, then for digging all the more so. If you impose liability for opening, then of course you impose liability for digging. Right? Can one argue with that? Can anyone dispute such a thing? Isn’t that a necessary inference? Isn’t it included there? Seemingly yes.

Let’s take another argument a fortiori in order to understand the matter better. “Behold, the children of Israel did not listen to me, so how will Pharaoh listen to me, and I am of uncircumcised lips,” Moses says. The midrash brings this as one of the ten arguments a fortiori that appear in Scripture. There are several. “If her father had but spit in her face, would she not be ashamed seven days”—Talmud Bavli, Bava Kamma 25 and elsewhere. One of them is: “Behold, the children of Israel did not listen to me; how then will Pharaoh listen to me?” If the children of Israel did not listen to me, will Pharaoh listen to me? That’s what Moses says. That too is an argument a fortiori, right? What is he assuming in that argument? That Pharaoh is of course less obedient than the children of Israel, and if even the more obedient ones did not listen to me, then will Pharaoh listen to me? That too is an argument a fortiori, right? Is that the same thing as the argument a fortiori of opening and digging? No. Why? What’s the difference between them?

Because I would say that… exactly, exactly. There is a big difference between these two arguments a fortiori. In the language of the later authorities, they call this one a fortiori argument of “if the greater amount contains the lesser amount,” and an ordinary a fortiori argument. What? An argument a fortiori of “if the greater amount contains the lesser amount,” and an ordinary argument a fortiori. “If the greater amount contains the lesser amount”? Yes. What does that mean? One maneh is included within two maneh. If you say something about one maneh, then certainly you have also said something about two maneh, right? Actually it’s the reverse: if you said something about two maneh, certainly you also said it about one maneh, because it is included within it. Okay? So that is the language of the later authorities to describe a deductive, necessary argument a fortiori. Meaning, one where the conclusion is embedded in the premise.

In “the children of Israel did not listen to me, so how will Pharaoh listen to me,” this is not an argument a fortiori of “if the greater amount contains the lesser amount.” I estimate that the children of Israel are more obedient than Pharaoh. It’s not as though inside Pharaoh there sits a little Israel, right? Rather, Pharaoh is simply more stubborn than Israel. It is more severe than that, but it is not contained within it. So an a fortiori argument of the kind of severity is called simply an argument a fortiori. An a fortiori argument of the kind of inclusion is called “if the greater amount contains the lesser amount.” Fine?

Now, when the Talmud speaks about an a fortiori argument of “if the greater amount contains the lesser amount”—opening and digging—it does not learn as the Mekhilta does. It asks: why was digging written? It could be learned by an argument a fortiori from opening. So the Talmud derives from this some other source, in Bava Kamma page 51, I think; they derive something else from it. Fine? The Maharsha asks: why not learn like the Mekhilta, that from this we derive the rule that one does not punish on the basis of legal inference? He says: because the Babylonian Talmud thinks that one does punish on the basis of legal inference. The Bavli thinks that monetary liability can indeed be imposed on the basis of legal inference, and therefore it derives something else from it.

Now let’s try for a moment to understand: why can one not punish on the basis of legal inference? Why, if there is an argument a fortiori, is that not enough to punish? Let’s say I have a lighter transgression, and it carries the punishment of lashes. Then I have something more severe—fine, then surely lashes should apply all the more so. More justly. Right. So there are two possible explanations. There are more, but let’s take two that are commonly brought by the later authorities. One explanation: perhaps there is a refutation of the a fortiori argument. The second explanation: perhaps the more severe matter deserves a more severe punishment, and the lighter punishment is not enough. Fine—those are two explanations.

Let’s go with the first explanation: perhaps there is a refutation, therefore you cannot punish. A refutation of what? A textual refutation? No, a refutation. It may be that it isn’t similar. Maybe it is more severe in one respect but not more severe in another. Exactly. That’s what I mean. Maybe I missed something, maybe I didn’t think of it, but there is some refutation and I missed it. Therefore I say I cannot be certain of the a fortiori argument, and that’s why it is not enough to punish. Perhaps there is a refutation. Fine?

Now, if indeed—let’s assume this—that the reason one does not punish on the basis of legal inference is the concern that maybe there is a refutation. Okay? The Maharsha says: in an a fortiori argument of “if the greater amount contains the lesser amount,” one does punish on the basis of legal inference. Therefore the Bavli disagrees with the Mekhilta. Why? Because there can be no refutation there; it is deduction. If there is liability for opening, then for digging all the more so. Let’s say it had written only opening and not digging, and someone dug a pit in the public domain and someone fell in and was injured. Should the owner of the pit, the one who dug it, have to pay? Obviously yes. Why? Not only because it is more severe than opening. Something much stronger: because included in digging there is also opening. After all, when you dug the pit, among other things you also dug the top layer. So the act of digging includes the act of opening plus more. Therefore punish him on account of the opening that is in it. I don’t care now whether digging is more severe than opening; there was opening here. Forget it—punish him as one who opened, not as one who dug. That is the force of an a fortiori argument of “if the greater amount contains the lesser amount.” Such an argument cannot be refuted, because it is not that I assume this is more severe than that and then you say, wait, maybe in another respect it is not more severe. No, I punish for the lighter case, not for the severe one.

If there is a transgression—say, one who passes some of his children through to Molech, but not all of his children to Molech. There is a Kesef Mishneh on this; Maimonides rules it as halakhah and it appears in the Talmud. One who passes some of his children to Molech is liable to death. One who passed all of his children to Molech—not. How can that be? So the Kesef Mishneh says because it says “of his children,” and the Talmud says: “of his children,” not all of his children. The Kesef Mishneh says, what do you mean? That is an argument a fortiori. Yes, but one does not punish on the basis of legal inference. The Kesef Mishneh says: what do you mean one does not punish on the basis of legal inference? This is an a fortiori argument of “if the greater amount contains the lesser amount.” There can be no refutation of it.

Let’s say I passed all ten of my children through to Molech, okay? And they tell me: look, if you had passed through two or five, we would kill you. You passed ten, so we don’t kill you. I don’t understand. Included in the ten is also two. Punish me for that. Forget the extra eight I passed—leave them aside—but after all I certainly passed two. Punish me for passing two. That is the idea of an a fortiori argument of “if the greater amount contains the lesser amount.” It’s not that ten is more severe than two; rather, within ten there is also two, and something extra besides. Right? The same with opening and digging. When you dig a pit, of course you also opened it. Besides opening, you did more things—but you also opened. So if I don’t punish for digging, fine, don’t punish for digging; punish me as one who opened. After all, I opened it. That is called “if the greater amount contains the lesser amount.” I stole two maneh—perhaps two maneh are not liable, but within two maneh I also stole one maneh, so punish me for that. This is not the same as Israel and Pharaoh, because when Pharaoh does not listen to me, that does not mean he is Israel plus something. He is more severe than Israel—meaning there is less chance he will obey me than Israel, so he is more severe. But maybe in fact Pharaoh would obey you more for some other reason—because he wants to show that he is very humble. Fine? He wants to show that even as king he obeys you, although really he owes you nothing because he is a great bully. Fine? So there is another respect in which Pharaoh might obey more than Israel. Therefore in principle such a thing can have a refutation. And even if you didn’t think of it, maybe you simply didn’t think of it—but the refutation still exists.

Wait, what does the Talmud say about this? Wait, wait, one second, I want you to understand the idea. The idea is that an a fortiori argument of this kind can have a refutation; an a fortiori argument of “if the greater amount contains the lesser amount” cannot have a refutation. Okay? If this reminds me—I’ll tell you—there is an Israeli scholar named Amotz Zahavi, a professor of evolution and biology. He came up with the idea called the handicap principle. What does that mean? A peacock has that huge tail and it’s very colorful and stands out tremendously. That is not helpful for survival. You stand out from far away; everything around will see you and prey on you. On the contrary, if you had colors that blend into the environment, that would be much better for survival. So how do you explain the fact that the peacock has such conspicuous colors? Isn’t that bad for survival? He explained it in the book in topological terms too. Yes.

So he says: the handicap principle. What does it mean? The peacock is trying to project self-confidence. It says to you: look, here I am with all these colors and I’m not afraid of anyone. Now whoever sees such a peacock says: this peacock must be such a thug, I’m not going near it. It allows itself to be so colorful, spread its tail and wings all over the place, and it isn’t afraid of anyone. All the lions immediately flee in panic. Okay, because it is so full of self-confidence.

Now you understand that this idea of the handicap principle may be true and may not be true, but it means that the theory of evolution cannot be refuted. Why? Because if you have a good trait—good, you survived because you have a good trait. If you have a bad trait, you also survived, because people see that you have a bad trait and you’re not afraid of anyone, so that too helps your survival. So what would not help survival? Is there anything that might not help survival? Basically you turn evolution into a theory that cannot be refuted. Well, I discussed this in some book I once wrote. I’m not saying it isn’t true, by the way. I’m only saying that because of this it is not scientific. Not that it is false. Mathematics is not scientific, and it is true. That’s a different claim. Many say—Mathematics is not scientific? No, certainly not. It’s not refutable. Yes. And it is true, on the contrary. Why is it not… why is it not scientific? Because it is true with certainty, not because it is false. Science is never true with certainty. In science I conjecture something, I have support for it, but I may be wrong. Something about which you cannot be wrong is not scientific, if we use Popper’s criterion. Okay. People disagree with him. What? Not really. They disagree only on… He took it too far. About the post-scientific? No, he took it too far. He claimed that a scientific theory can only be refuted, not confirmed. On that they disagree. They argue that it can be confirmed. But nobody claims that a theory that can neither be refuted nor proven or confirmed is scientific. On that everybody agrees. Yes, but if I can refute it but I can also confirm… that’s another discussion. I’m talking only about the minimal aspect on which everyone agrees. Okay?

Wait, but if I can confirm, can I confirm mathematics? No. Why not? Because it makes no claim whatsoever about reality. How would you confirm it? You can’t refute it. What you can’t refute, you also can’t confirm. What does it mean to confirm? To put it to a test of refutation and see that it withstands the test, then you confirm it. If it can’t face any test of refutation because nothing refutes it, then nothing confirms it either. If, say, every fairy has three wings—now there is no way to see fairies, so you can’t refute that. Can you confirm that thesis? How would you confirm it? You’d have to look at a fairy and see. But there aren’t any; you can’t. For the same reason you can’t refute it, you also can’t confirm it. Maybe you’re talking about the intuition that mathematics also behaves accordingly? Mathematics behaves? One plus one equals two. If you proved it, you proved it. If not, then not. There is no such thing as confirming. What does it mean to confirm? If you proved it, no confirmation is needed—you know it’s true. If you didn’t prove it, no confirmation will help. Mathematics does not deal with the world at all—soon I’ll talk about this because it’s relevant to us. That is the a fortiori argument of “if the greater amount contains the lesser amount.”

So what emerges from here, says the Maharsha in his second version there in Bava Kamma 51, is that an a fortiori argument of “if the greater amount contains the lesser amount” is not open to refutation. There is no refutation of an a fortiori argument of “if the greater amount contains the lesser amount.” Therefore there, certainly one punishes on the basis of legal inference, he claims. But he is mistaken. An a fortiori argument of “if the greater amount contains the lesser amount” can also be refuted. I’ll give you an example. This example is taken from a book by Chaim Perelman. He was a professor of law, a Belgian Jew, and he wrote books on legal rhetoric, legal logic, and so on. He gives the following example.

There was a law in Belgium, in a place called Vandervelde—I don’t know if I’m pronouncing it correctly, but something like that—and the law said that one may not sell a person in a pub more than three liters of wine. They didn’t want a person wasting his whole weekly salary on wine; they wanted him to bring it home to support the family. So they said: more than three liters, we don’t sell. Fine? I don’t remember if it was three liters; I’m just giving this as an example. There was such a law. A man comes and wants to buy fifty liters of wine. The seller says to him: I can’t. More than three liters is forbidden to sell. Right—three is forbidden, but I want fifty. But if the greater amount contains the lesser amount—what do you mean? If you sold me fifty, you sold me three too; except that besides that you sold me forty-seven more. You violated the law. If three is forbidden, then certainly fifty is forbidden. This is really an a fortiori argument of “if the greater amount contains the lesser amount,” right?

They went to court—again, judicial legislation—and the judge said that the buyer is right. The buyer is right: fifty is allowed, three is forbidden, and fifty is allowed. Now before I get into the reasoning, understand what this means. It basically means that an a fortiori argument of “if the greater amount contains the lesser amount” turned out to be incorrect. Meaning, there is a refutation of an a fortiori argument of “if the greater amount contains the lesser amount.” If you convince me. Yes. But that’s what the judge in fact argued. And what did he say? He said like this. Why is it forbidden to sell you three liters of wine? Because they want your weekly salary—workers there received salary every week, not every month like in Israel—and the weekly salary was apparently something like, I don’t know, the cost of five liters of wine. They said: three liters you can buy; beyond that, bring the money home. Okay?

If a person decides to go into the wine business and wants to invest in fifty liters of wine, keep it, sell it, I don’t know, host guests over the course of a year—is that allowed or forbidden to buy? There is freedom of occupation, freedom of commerce, whatever you want to call it. How could such a thing be forbidden to him? How can the bartender bring fifty liters of wine into his pub if it is forbidden to buy it? Okay? Therefore, clearly, if I want to enter the wine business, that is permitted. The judge says: what is at the scale of a weekly salary—up to three liters. You want to invest your savings in this? That’s your right. The law cannot prohibit it, or does not prohibit it. It is permitted.

You can accept that and you can reject it. But it is an argument one can hear. Does it not really refute the principle of…? We’ll come back to this. Right, every refutation is like that. We’ll see in a moment: every refutation is like that. But the deduction remains. No, the deduction does not remain. No. I’ll explain in a moment. You’re right, but I’ll explain it more fully.

Look at what we actually saw here. What we saw is that clearly, when you sell fifty liters, you also sold three. That is obvious. Meaning, if you stay on the mathematical level—mathematics cannot be refuted—three is contained in fifty. That is a mathematical statement. And we said mathematics cannot be refuted. Mathematics is certain. But whenever you take mathematics and apply it to the world—in law, in physics, in anything—you have turned it into a claim that can be refuted. Not the mathematics itself, but its application in the world can be refuted.

Then the claim is as follows: you sold fifty, you sold in particular three. At the mathematical level that cannot be refuted. But whenever you speak about law, or physics, or something like that, you are speaking about the world, not mathematics. Mathematics does not deal with the world. You are speaking about the world. In the world itself there can always be interpretations that show you that three is forbidden but fifty is permitted. That is what is called refuting an a fortiori argument. To refute an a fortiori argument is not to refute the mathematics of the a fortiori argument. Mathematics is not refutable. It is always true, necessary. But whenever you speak about an a fortiori argument, this is not a statement in mathematics. An a fortiori argument comes to talk about Jewish law, or law, or physics, or whatever. And here there are always additional assumptions, and those assumptions can be refuted. The assumptions, for example, that explain why three is forbidden: because you want him to bring his weekly salary home. If so, then maybe fifty is allowed. The refutation does not say that three is not included in fifty—that is mathematics. The refutation says that although three is included in fifty, from the standpoint of the law that does not suffice to forbid fifty. Because your assumption that this mathematical model is the right description of the law is not correct. That is what the refutation shows.

Now I’ll give you another example that is not a refutation of an a fortiori argument, but it explains this issue better. This happened to me personally. Rabbi, but is that only in law and judgment and things like that? In everything. In everything that relates not to mathematics but to some application. Here, I’ll give an example from physics. Fine? When I arrived here in the physics department, because of my sins they assigned me—since I came from engineering, I had done a bachelor’s in electrical engineering—straight to the lab. That is exactly why I had run away from engineering to physics, because I didn’t like labs. Doesn’t matter. In my second year I was already teaching mechanics. Mechanics deals with forces—you learned a bit of mechanics? vectors, forces, velocities, accelerations, and so on.

So I opened the first tutorial and said to them: is the statement two plus three equals five a scientific statement, a scientific claim? The criterion for a scientific claim, as I said earlier, according to Popper, is whether it is refutable. Okay. So let’s see: is it refutable? Propose to me an experiment that would subject the statement two plus three equals five to scientific refutation. Is that possible? If you find a case where two and three, when combined, do not come out as five. Meaning, for example, let’s take a bowl, put two oranges in it, then take three more oranges and put them in the bowl and count. If the result is minus twelve, then we have refuted the law that two plus three equals five. Right? If it comes out five, then we have confirmed the law, or not refuted it, according to Popper. Okay, so it seems we have an experiment.

Now I’ll ask you a hypothetical question. Suppose you put in two oranges, add three more, and get minus twelve. You counted and got minus twelve, minus pi oranges. Okay. Would you give up the statement that two plus three equals five? No. Then you have not refuted it. So don’t tell me it can be refuted. That’s not true. Even if this happened, you would not give up that statement. Why? Because that statement is certainly true. It is not a matter of an experiment succeeding or failing. What would you say at most? That there was an error in the experiment. Or you might say: perhaps when you add oranges to a bowl, the mathematical model that describes this is not arithmetic addition but something else. Meaning, two plus three equals five is a statement in mathematics, and it is certainly true. If you want to use it to describe adding oranges into a bowl, maybe you are wrong, because that is already physics, not mathematics.

Mathematics is the numbers: two plus three equals five, completely abstract. The moment you apply it to the world, you are really saying that this arithmetic, mathematical model describes adding oranges into a bowl. If in experiments you discover consistently that this is not so, the conclusion will not be that two plus three does not equal five. It remains equal to five. It’s just that two plus three equals five is not a good theory for explaining adding oranges into a bowl, and you need to look for something else. So you have refuted the statement in physics that two plus three equals five describes adding oranges into a bowl. That is a statement in physics, not in mathematics. The statement two plus three equals five is a statement in mathematics, and that cannot be refuted. Because every time you perform an experiment showing that it is not correct, what you will say is not that the mathematics is wrong, but that its application to the physics involved in that experiment is probably wrong. You refuted the physical dimension of the matter, not the mathematical one.

What is the moral of the story? Why is this the first lesson in mechanics? Because in mechanics, what we do is this. Look, I’ll refute for you the statement five plus five equals ten. Fine? We take a body and apply to it a force of five newtons northward and another force of five newtons eastward. What is the net force? The total force acting on the body? Five root two—seven point something, right? That’s the parallelogram rule. Fine? So we’ve seen: five plus five equals seven point something, not ten. We’ve refuted the statement five plus five equals ten. Here is a counterexample. What is the mistake? The mistake is that we did not refute five plus five equals ten. That is certainly true. What we refuted is the assumption that the addition of forces is described by arithmetic addition. It is not. It is vector addition. In order to add forces, you have to add the vectors, and then of course you get the diagonal, depending on how the vectors are combined.

Meaning, we did not refute the mathematical claim that five plus five equals ten. We refuted the claim in physics that arithmetic addition, five plus five, is suitable for describing the addition of forces. It is not. You have to look for a different mathematical theory. The attachment of a certain mathematical theory to certain factual circumstances—that is a claim in physics, not in mathematics. And that stands open to refutation if an experiment shows it to be false. Then you must abandon it and look for another mathematical theory. The mathematical theory itself cannot be refuted.

Now, this is exactly the same as Vandervelde. Because what did we see there? We refuted the a fortiori argument from three to fifty—three liters to fifty liters. And clearly we did not refute the fact that fifty is made up of three plus three plus… and forty-seven. Okay? That is certainly true. No experiment will refute it. So what did we refute? We refuted the claim that this mathematical theory—that three is included within fifty—describes the legal rule forbidding the sale of liters of wine. Not so. That law is described by a different mathematical theory. So we refuted a claim in law, not a claim in mathematics.

And that is how refutation always works. Therefore the Maharsha is wrong: an a fortiori argument of “if the greater amount contains the lesser amount” is indeed refutable. Certainly it is refutable. Its mathematical dimension is not refutable, but its legal, halakhic dimension is. Let’s take the pit. What are you telling me? That this a fortiori argument is not refutable, because when you dug, you also opened; you only did something else in addition. How could such a thing be refuted? Very easily. I can say, for example, that the punishment given for opening is too light. Digging is more severe. The second explanation of why one does not punish on the basis of legal inference. Not because of “what can you refute it by,” but because perhaps the punishment is not severe enough. The second explanation is a refutation of the first explanation. Because clearly there can be another explanation. It may be that the punishment appropriate for digging is so severe that I will not give you the punishment for opening, because it is not severe enough.

Now, does that not mean that included in digging there is also opening? And still, I will not give the punishment of opening to someone who digs, because perhaps it is not severe enough. Now, without entering at the moment into the dispute over this matter, the very fact that I can raise such an argument means that although this is an a fortiori argument of “if the greater amount contains the lesser amount,” in principle it can be refuted. It is not true that if this a fortiori argument is of “if the greater amount contains the lesser amount,” then it is immune to refutation. No, one can refute even an a fortiori argument of “if the greater amount contains the lesser amount.” Never the mathematics or the logic itself—you will never refute that. But the assumptions underlying the application of the mathematics to this case—those can be attacked by refutation.

Basically, the fact that it is forbidden by legal inference cannot be refuted, but the practical dimension can, because the practical application… Look at the actual law of Molech, of one who passes all his children through to Molech. I don’t remember… The Kesef Mishneh. Only the Kesef Mishneh. Yes, yes. That it is so severe that one cannot punish him with… Right. And that itself is a refutation of an a fortiori argument of “if the greater amount contains the lesser amount.” Because if I passed ten of my children through to Molech, then punish me for having passed two. One cannot dispute that I passed two. Mathematics is not refuted in any way. But here exactly what I said about the pit—that is what the Kesef Mishneh says there about passing one’s children through to Molech. And that itself is a refutation of an a fortiori argument of “if the greater amount contains the lesser amount.” It does not refute that two is included in ten, or that one maneh is included in two maneh. Obviously, if you gave two maneh, then you also gave one maneh within that. Yes, but sometimes the legal consequences can be refuted, because they do not necessarily follow the mathematical model. And if there is a refutation, the refutation shows that it does not follow the mathematical model.

And that is the reason Adolf Schwarz is wrong. Argument a fortiori is not deduction. Even an a fortiori argument of “if the greater amount contains the lesser amount” is not deduction. Even that can be refuted. Mathematics cannot be refuted. If the proof is correct, then it is correct—you cannot refute it. Two plus three equals five: no example, no refutation in the world will move us from that. But I have a question about this. I’m not so familiar with physics in general. There’s the thought experiment of Schrödinger’s cat, where the idea behind it is supposedly that one thing can be in two places at once. No, not in two places but in two states—alive and dead. Two states. But I also understood that later there was some sort of discovery regarding particles, right? In quantum theory, yes. That they can be in several places at once. Correct.

So we have the logic that it’s impossible—everything is in one place, not in two. There really is a whole issue here that requires getting more into physics. A lot of physicists are mistaken about this, and a lot of philosophers even more so. In the context of quantum theory, people think it refutes the laws of logic. That cannot, first of all, be true, because quantum theory itself uses the laws of logic. When you prove a theorem in quantum theory, in the mathematics of quantum theory, you use the laws of logic. There are proofs by contradiction. Now if you refuted the law of contradiction or the law of the excluded middle, then how can you use quantum theory, when it itself is built on them?

All the many-valued logics—for example Łukasiewicz, a Polish logician, maybe you don’t know him. Poland is a logical superpower, you know. There is a Polish school of logic. There is a form of notation in logic called Polish notation. The Poles are a logical superpower. So one of the famous logicians—I’m not talking about now, I mean the early twentieth century—was Łukasiewicz. Łukasiewicz devised a three-valued logic, a logic that is not yes or no but yes, no, or something third. Okay, likewise fuzzy logic—we talked about this in the heap paradox and so on.

Now clearly this is not an alternative to our logic, as many philosophers want to claim. Nonsense. After all, he himself performs his analysis with binary logic. He proves his results by contradiction. How? If you’ve only ruled out this possibility, that still doesn’t imply the other one, because there are two other possibilities. So how can you prove theorems by contradiction? You ruled out this option—that doesn’t mean that option is true, because maybe there’s a third possibility. In three-valued logic you cannot prove things by contradiction. But the theorems of three-valued logic itself are also proved by him by contradiction. That means it does not really replace our logic. Rather, there is a certain domain in which you can build another formalism called three-valued logic. It does not really say anything about our thinking. Our thinking still operates with the same logic, and that is the correct logic, and there is no other.

And the same in quantum theory. The same mistake made by interpreters of quantum theory. A particle in the classical sense cannot be in two places. A particle in the classical sense is a tiny grain of matter, yes, pointlike, located in a certain place. If it is here then it is not there, and vice versa. There is no such thing. Rather, the world is not made of classical grains; it is made of quantum grains. Quantum grains are what are called a wave function. This is not a point object; it is a spread-out object. Where is a wave in the sea located? Look at a wave in the sea. A wave is the whole sinusoidal form, not just one crest as we mistakenly say. That entire sine curve is called a wave. Where is it? In the whole space. There is such a function of time and space, right? You cannot talk about where it is. That is what is called a wave function. An electron, from the perspective of quantum theory, is a wave function, not a little ball. The wave function is in all of space; there is no logical problem in that. It is not a point element.

A point element cannot be in two places; that is a logical contradiction. But there is no problem at all for a wave to be in many places. However, when you check it, when you measure where it is, sometimes it turns out to be here, sometimes it turns out to be there. Why? Because measurement turns it into a little ball. That is why we always think it is a little ball—but that is a mistake. When we look at it, it is a little ball. But ordinarily it is a wave. Now when we measure it, it is either here or there. It is not in both places at once. True, we don’t know—it may be here, it may also be there. It is not in both places at once. If I measured in two places at once, what would I see? You would see it in one of them. Not both? No. A particle is in only one place, not in two places. There is no such animal. Those are legends of popular science. There is no such thing. As long as you haven’t measured it, yes, as long as you haven’t measured it, it is a wave. But when you haven’t measured it, it isn’t a point particle at all. Why is there a problem if it is in two places? The wave is in all of space. Okay, so what? And measurement somehow changes it—not entering into that now; this too is a huge scientific-philosophical debate unresolved to this day. But it doesn’t matter. Somehow in observation something happens; it collapses. Fine.

The important point—this really does concern our issue—is where all those people go wrong. They think you can measure logic in the laboratory. That a laboratory experiment can tell you what the correct logic is. There is no such thing, because the experiment itself is based on a certain logic. Logic is a condition for conducting the experiment and analyzing it. Logic cannot be the result of the experiment. There is no such thing. You presuppose all the logic when you perform the experiment. If it turns out that the logic was not correct, then you can throw the whole experiment in the trash. All the mathematics of quantum theory is based on classical logic; they prove things there by contradiction. So how can you say that quantum theory refutes logic? This is nonsense. Okay? It’s simply philosophically mistaken.

Okay, so this relates to what I said earlier, because what I said earlier was that logic and mathematics and deduction do not speak about the world. Quantum theory deals with the world; therefore a measurement in the world will not prove to us what the correct logic is. The correct logic is always correct; it has nothing to do with measurements in the world. It is not refutable. Logic is not a scientific theory. The application of logic to reality is already a claim in physics. Perform an experiment and check whether it can be applied to reality or not. That is another discussion. That can be refuted, confirmed, whatever you like, because that is the world of physics, the physical sphere of claims, not the logical or mathematical sphere of claims. Logic and mathematics are completely pure, completely Platonic; nobody can touch them. They are eternal. No experiment will change anything about them.

But then one should ask: how do I really know they are there, that they are true? I know because I have such an intuition. That’s all. Intuition? Excellent question. It relates somewhat to what I talked about in the previous lesson, but I won’t get into it here. I wrote books about it: Two Wagons and a Balloon, Truth and Not Stability—those are the two main books that deal with that question; those two books are devoted to it. What is intuition? Yes. How do I know? But what is intuition? One has to understand. This connects exactly to what we discussed here.

Because my claim is that intuition—we always look at the world and have two ways to deal with it: observation and thought. Observation is empirical, observing the world; that’s science. Thought—say mathematics, philosophy, or something like that. Rationalism versus empiricism? Exactly, rationalism versus empiricism. And I claim—and the whole history of philosophy shows this—that rationalism and empiricism are fictions. What Kant said? Basically that is what Kant claims, but one has to understand very well how to interpret him. This is his synthetic a priori. What is the claim? The claim is that when we function, we really function with cognizing thought, or thinking cognition if you like, which is exactly judicial legislation. Exactly the same thing. That is Kant’s synthetic a priori and Maimonides’ exegetical derivations.

In the book I wrote on Maimonides’ exegetical derivations—I also published a book on Maimonides’ first and second roots, rabbinic laws from derivations or rabbinic laws from enactments—I explain there this idea of connections, the continuum of connections to the text. And there I parallel it to Kant’s synthetic a priori and to judicial legislation in the legal world, and it is all the same thing. It all comes from the mistake of this dichotomy of either thought or cognition. We have some ability to think cognitively.

One of the great problems—maybe the problem—in philosophy of science is: how do I extract the general rule from the facts? Yes, Hume’s problem of induction, and so on. Everything circles around this question in one form or another. How do I derive it? My answer is: I simply see it. I simply see that the general theory is this one and not that one. Not with the eyes. I have some cognitive ability that is not sensory. I look at the facts and I understand that this is the correct theory that explains them. Not with certainty—I may be wrong—but I understand that this is the correct theory. I have some sort of sixth sense—not one of the usual five senses—that sees that this is so. And my claim is that what we call intuition is this sense. It is a sense. Not one of the ordinary five senses, but it is cognition, not thought.

Because if intuition were thought—the standard empiricist claim is that observation is done with the senses. Everything beyond observation is thought; it happens in the head. And what happens in thought has no reason at all to fit reality. The fact that you think in a certain way does not mean reality owes you anything. As Mark Twain said, it was here before you. The world owes you nothing; it was here before you. What was the exact quotation? It was here first. Yes. So the claim is: because you think in some way, does that mean the world behaves that way? What, does it owe you something? If you saw it, then you know the world behaves that way. Therefore the empiricists reject rationalism. They say: what is the product of thought is not a legitimate tool for understanding what happens in the world. To understand what happens in the world, you need observation. And of course they are wrong. Why? Because observation too is done through thought. No, the opposite: because thought too is a kind of observation.

When I generalize from facts, the generalization is not a purely mental process detached from the world. I look at the world and I see that this is the right generalization and not that one. I claim that this too is observation. There is a book by Hugo Bergmann called Introduction to the Theory of Knowledge. In chapter nine of that book he calls this “the world’s rationality,” from the word intellect. How does the world behave according to our intellect? It’s a miracle. Many have written about this. How can it be? Why does mathematics fit physics? Why in physics do we succeed in using mathematical techniques? Why does that happen? There are various explanations, but the claim is—he is basically asking Kant’s question: how can thought correspond to what happens in the world? How can a synthetic judgment be a priori? A priori, meaning prior to observation, yet able to say something about the world; synthetic, not analytic. It makes a claim. How can there be a claim that is the product of thought? That is really Kant’s problem of the synthetic a priori. How can thought give us something about what happens in the world? Observation can tell us what happens: I look and see what happens. But the fact that I think in a certain way—so what? Aristotle thought that objects fall to the earth at a speed proportional to their mass. A heavier object falls faster. That is what Aristotle thought. So he thought that—but the world owed him nothing. It turned out not to be true. All objects fall at the same speed. Mass doesn’t matter. The fact that you think in a certain way does not mean the world behaves that way. There is no reason at all to assume so. Not just that maybe you are wrong—of course maybe you are wrong. No, there is no reason at all to assume you are right. You are built in a certain way—so what? What does that say about the way the world behaves?

My claim is that what you call thought is not thought; it is cognition. It is a kind of observation of the world; therefore I am right. When I make generalizations, the generalization is not a procedure in which I take the facts from observation, which are private facts, and then make a generalization in my head. No. The generalization is a continuation of the observation. I look at the world and understand that this is the right generalization. Okay? And this is the only solution to Kant’s problem of the synthetic a priori. Hugo Bergmann surveys—I don’t remember how many methods throughout the whole history of philosophy that tried to answer this problem, and in the end he says none succeeded. One has to say it is a methodological necessity or something like that. But that is not correct. There is one solution that does succeed—and only one. And it is the solution that says that the distinction between thought and cognition is not dichotomous. What we call thought has a cognitive dimension. We simply see that it is true. And the proof is that it works. Science works. After all, the greatest miracle, the one impossible to explain, is how science works. Science is built on the generalizations we make. If our generalizations are just conventional things or the result of our structure, how do we send spaceships to the moon? How does this whole thing work? That is the very thing that needs explanation.

My claim is: it works because it is not an invention occurring in our heads. We simply see. And this has enormous implications for countless contemporary disputes in our world. Enormous. Almost any dispute you can think of depends on this. Postmodernism, LGBT issues, everything you want. Everything depends on this. Because the question always is: how can one define? After all, it’s all definitions. You define man this way, I define man that way. But if you say no, it’s not a definition—I observe the world and tell you that a man is this and not that. Maybe I’m wrong; one can argue. One can be wrong in science too. But don’t tell me that it is all arbitrary, or social constructions according to Marxist notions of power and motivations and agendas of one kind or another. No. It is simply the result of observation. Now, maybe I am not observing well; maybe I should hear you out and maybe you’ll correct my observation—that’s perfectly fine. But don’t say… I’m not saying I am certainly right. All I am saying is that I am not certainly wrong. It is not true that everyone can define whatever he likes and remain intellectually alive. Definitions, contrary to what logicians and philosophers think, are not arbitrary. Definitions are the result of observation.

When I define democracy, it is not because I decided to gather these characteristics and say that this is called a democratic state. I simply observe the world and see that the concept of democracy is defined this way. That is the Platonic conception. It means I observe the idea and say: democracy, the idea says this and this and this. How did you put it—understanding the full concept? Something like that. I observe the world and understand that those are the correct characteristics of the concept. Don’t tell me you define it differently. It’s not a matter of defining; it’s a matter of who is right. If it’s all definitions, then there is no right and wrong—you define one way, I define another. I claim there is right and wrong even in definitions.

Whenever we argue about definitions, by the way, you should ask yourselves: there is a dispute about who is a Jew. What’s the problem? You define Jew one way, I define Jew another way—what is there to argue about? Definitions! One does not argue about a definition; define whatever you want. The moment we argue, it means that both sides agree on one thing: that there is a right and a wrong, and we are arguing over what is right. But we both agree that it is not just a matter of definitions; there is right and wrong here. Otherwise what is the argument about? And in that, both sides agree. Important point: notice that the dispute shows not that there is no truth, but that there is truth, because otherwise what is the dispute about? People often understand it the other way: there is a dispute, which means there is no truth and everyone defines it differently. The opposite! Why are we arguing? We are arguing because we both agree that one side is right and the other is wrong. We argue over who is right and who is wrong, fine. But if the dispute really showed pluralism, that everyone is right, then there would be no need to conduct the dispute. You define it one way, I another, all is fine, everyone goes his own way in peace.

I went rather far afield here, but all these things really relate to the one point I’m talking about here: that there is something in between thought and cognition. And that something means cognizing thought, thinking observation. Okay? And this is what in another context I call intuition; if you like, this is HaNazir’s auditory logic. I claim that the hermeneutic principles are a way of looking at the verses through these lenses and drawing conclusions from them by way of analogy. But that analogy is not an invention. It is a certain mode of observation of the verses and the spirit of the verses, what emerges from them. The product, of course, is not what was inside the verse, but it is also not detached from the verse. Rather, it is something I understand to be similar. How do I understand? Is that just my invention, a speculation inside my head, a thought? No. It is not thought; it is cognition, interpretation.

It is not legislation—which parallels thought, legislation, done inwardly without connection to the text. Interpretation parallels observation: I look at the text and interpret it, trying to understand what is in it. Okay? And my claim is that here there is cognizing thought, or interpretive legislation, what is called judicial legislation. All the issues I discussed today all emerge from this one single point. And that is why this logic I am talking about here is so important. Because this logic is the logic of intuition. I will show you how to work systematically in order to reach intuitive conclusions. To reach conclusions that are neither pure thought nor pure cognition, but thinking-cognition, or something softer that can be mistaken. Unlike mathematics, it is not certain. But it is not true that it is just speculation, that everyone does whatever he wants. There is a system here, there is a way to do it precisely, and there is a way to advance with it in a grounded manner. That is really my goal, and that is what we will begin to do next time.

Wait, is there an English expression for this soft logic? Is this something you’re taking from somewhere, or are you formulating it in your own words? I assume there is, but I don’t know. I’m not… Maybe I’d try to translate it into French, but in French… In English, “soft logic”? Yes, you could say that, but I don’t know if anyone uses it. Maybe “non-deductive logic”; everything that is not deductive is soft. That exists. We said that we recognize the logic in use by intuition, right? We recognize in… No, I define the logical tools by their fit with intuition. That will help me formulate these logical tools, but now they will stand on their own. It’s simply the way I’ll try to conceptualize them. We will do it, so there’s no point discussing it in the abstract. We’ll simply do it next time. Fine? Good, thank you very much. Next time we’ll break for about a week and then come back. There are recordings; you can look at them too.

Today we’re beginning a series of five units in which we’re going to discuss the thought of Rabbi Shimon Shkop. Not his personality in the biographical sense, but rather an attempt to analyze his legal and logical theory and understand what he tried to innovate in the world of Talmudic analysis. Rabbi Shimon Shkop is seen as a classic representative—perhaps the most significant representative—of the new Lithuanian style of learning. He was born in 1860 and died in 1939. A student of Rabbi Chaim of Brisk, at least that’s how he defines himself, and of course Rabbi Itzele of Ponevezh, and in some sense he was the one who provided the philosophy of this mode of learning. Unlike the Brisker method, which is more positivist or legalistic, Rabbi Shimon Shkop tried to give it a somewhat deeper philosophical expression.

We’ll try to understand what he was trying to innovate and basically why he did it. In other words, what was his aim when he approached the task of organizing Talmudic learning in this way? I’ll also send you a short reading list for anyone who wants to go deeper, but in broad terms our main sources will be the introduction to Sha’arei Yosher, of course, and the books Sha’arei Yosher and Chiddushei Rabbi Shimon Yehuda HaKohen. Maybe also some of his reflective writings that were published in various places.

What I’ll try to do is take fundamental concepts in Lithuanian Talmudic learning and, through them, try to understand what exactly he is doing. So today we’ll talk about the concept of obligation and acquisition, which is perhaps the most basic concept in the world of Talmudic analysis and the hardest to define. Let’s begin with the first source I handed out. It’s a Talmud in tractate Bava Batra 175b. The Talmud there discusses the question of what it means when a person owes money to someone else. In other words, when I owe someone money, what does that mean? Does it mean that I have a personal debt toward him, or that he has some kind of share in my property? The Talmud there brings the statement of Rav Huna.