The Voice of Prophecy, Lesson 36

This is an English translation (via GPT-5.4). Read the original Hebrew version.

This transcript was generated automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.

🔗 Link to the original lecture

🔗 Link to the transcript on Sofer.AI

[0:04] The controversy around Adolf Schwartz and the connection to Scripture
[2:21] Is a kal va-chomer a hypothetical inference?
[3:52] Logical inference and hypothetical inference – introduction
[4:59] Modus ponens and tollens – logical examples
[8:22] A complex hypothetical inference – example
[10:13] Examples of kal va-chomer in the Mekhilta and in Bava Kamma
[12:31] The structure of the classic kal va-chomer – three data points
[14:09] A kal va-chomer of “included in two hundred is one hundred” – simple deduction
[15:15] The connection between kal va-chomer and deriving punishments from logic
[29:52] Generalization and deduction in the process of kal va-chomer

Summary

General overview

The text presents a polemic with Adolf Schwartz סביב the question of whether kal va-chomer is a deductive-logical inference of the syllogistic type, or a method rooted in comparison, induction, and analogy. It tries to sharpen the point that kal va-chomer is not a binding deduction, and that is why it is open to refutation and subject to limiting rules such as dayo and the rule that punishments are not derived from logical argument. The speaker explains common logical terms such as categorical inference and hypothetical inferences, brings examples from the Mekhilta and Bava Kamma, and suggests that the crucial move in kal va-chomer is not in the final deductive step but in the stage of generalization that produces the “major premise.” From this he argues that the thirteen hermeneutical principles are authorized ways of reaching general premises, not a basic permit to use logic, and that perhaps the term “hypothetical inference” in the Nazir refers to the hypothetical-deductive model of science (Bacon and Hermann Cohen), not to modus ponens/tollens in formal logic.

Adolf Schwartz and the controversy over kal va-chomer

The speaker describes an earlier controversy with Adolf Schwartz, head of the Theological Seminary in Vienna, who wrote books on the hermeneutical principles by which the Torah is expounded and on kal va-chomer, and apparently died in the early twentieth century. The speaker says that in the past he argued against Schwartz’s claim that kal va-chomer is a hypothetical inference, and here he understands that the general direction of the text is to show that kal va-chomer is fundamentally based on comparison, as opposed to Schwartz’s view that kal va-chomer is a deductive-logical inference. The speaker points out a difficulty in that the continuation of the discussion uses logical terminology that usually belongs to deductive inferences, and so it is not always clear to him what exactly the thesis and antithesis are.

Logical terms: categorical inference and hypothetical inference

The speaker clarifies that a categorical inference is the classic syllogism in the form “All human beings are mortal; Socrates is a human being; therefore Socrates is mortal,” where a statement true of the whole necessarily applies to an individual case. The speaker then lays out two simple hypothetical inferences: if P then Q; P; therefore Q (modus ponens), and if P then Q; not Q; therefore not P (modus tollens), and explains that an inference of the form if P then Q; Q; therefore P is invalid. He adds that a complex hypothetical inference is a chaining of conditions: if P then Q; if Q then R; therefore if P then R, and emphasizes that the examples of rain and clouds are only illustrations and are not part of the logical structure itself.

Kal va-chomer as an argument that is not binding deduction

The speaker argues that the goal is not to analyze how the deductive inference is constructed, but to decide whether kal va-chomer is a deductive inference at all, because deductive inferences are necessary, like mathematical proofs. He proposes a principled practical implication: if kal va-chomer were a binding logical deduction, then punishments would be derived from it, because a deduction admits no refutations and there would be no reason to refrain from punishing on its basis. He adds that if kal va-chomer were simply the “interpretation of the verse” by means of necessary logic, there would be no need for it to be counted among the thirteen principles, and no room for a “law given to Moses at Sinai” permitting the use of logic, because logic is a foundational presupposition of all interpretation.

Types of kal va-chomer and the example of “included in two hundred is one hundred”

The speaker distinguishes between a “classic” kal va-chomer, in which there are three given laws and a fourth is inferred, and a kal va-chomer in which one law serves as the basis from which a second is learned. He demonstrates a classic kal va-chomer with a two-by-two table in Bava Kamma: tooth and foot in the public domain are exempt, tooth and foot in the injured party’s courtyard incur full damages, horn in the public domain incurs half-damages, and the question is horn in the injured party’s courtyard. He then brings a different kind of kal va-chomer from the Mekhilta at the beginning of Bava Kamma: “If for uncovering he is liable, then for digging all the more so,” and explains that this fits what the Pri Megadim in Ginat Veradim and the Maharsha call a kal va-chomer of “included in two hundred is one hundred,” where digging includes uncovering plus more, and therefore seems like a simple deduction with no “degree of freedom.”

“Punishments are not derived from logic” and the discussion in the Mekhilta and Tosafot

The speaker presents the accepted rule that punishments are not derived from logical argument, and the line of explanation offered by later authorities that because of possible refutation one does not rely on kal va-chomer in order to flog or execute. He also brings another explanation attributed to the Kesef Mishneh: sometimes when the case is more severe, the punishment of the lighter case is not necessarily “enough,” and so one cannot transfer the punishment even if one can learn the prohibition. He gives the example of one who passes his offspring to Molekh as opposed to all of his offspring to Molekh. He also suggests a direction according to which punishment is not always proportional to the severity of the offense, and so it cannot be inferred by simple logical transfer, though he hesitates about that and emphasizes that additional premises would be needed in order to derive a punishment.

The speaker cites the language of the Mekhilta: “If a man uncovers and if a man digs—if for uncovering he is liable, then for digging all the more so? Rather, this teaches you that monetary liability is not derived from logical argument,” and stresses that the Mekhilta presents a need for a verse even in a place where the kal va-chomer seems impossible to refute. He notes that there is a dispute among medieval authorities (Rishonim) in Bava Kamma over how the Babylonian Talmud relates to this matter, and comments that even if one accepts the explanation that the punishment of the lighter case is not enough for the more severe one, there would still seem to be room to punish at least for the “uncovering” component included in “digging,” as is also asked in connection with one who passes all of his offspring to Molekh.

Three forms of thought: analogy, induction, and deduction as stages

The speaker recalls an earlier distinction between analogy, induction, and deduction, and argues that there is no hierarchy here of strength, but rather three stages of one thought-process. He describes the order as follows: accumulated analogies lead to an inductive generalization, and once there is a general proposition, deduction is then applied to the particular. He argues that kal va-chomer works the same way: in the end there is always a deductive component, but the real sting and creativity lie in producing the general proposition.

Analyzing the kal va-chomer in Bava Kamma as the creation of a “major premise”

The speaker presents two possible directions in the kal va-chomer of horn in the injured party’s courtyard: one direction starts from the rules of the public domain and concludes that horn is more severe than tooth and foot “in every respect,” and from there one deduces that it must be liable in the injured party’s courtyard; another direction learns from the liabilities of tooth and foot that the injured party’s courtyard is more severe than the public domain, and from there concludes that in the case of horn, if in the public domain it incurs half-damages, then in the injured party’s courtyard it must incur at least half-damages. He explains that in the first stage one generalizes from the data to a general proposition, and only afterward does deduction apply the rule to a particular case. He connects this to Mill’s criticism of deduction, according to which the certainty of deduction depends on general premises whose source is induction.

Refutation as undermining the major premise, not the deductive structure

The speaker states that a valid deductive process cannot be refuted, and therefore the very existence of refutations in kal va-chomer shows that it contains a non-deductive component. He explains that a refutation does not mean that the conclusion does not follow from the premises, but rather that the major premise itself is not true, or that the generalization that was made is unjustified. He compares this to the claim “All human beings are mortal,” which can be undermined by an exception; in such a case what has fallen is the general rule, not the law of inference.

Dayo—“it is enough for what comes from the law to be like the source case”—as evidence for the structure of the inference

The speaker notes that in section 19 Adolf Schwartz brings proof from the rule of dayo that kal va-chomer is a categorical inference, because dayo parallels a logical rule according to which a conclusion cannot be “more” than the major premise. The speaker objects that even in deductive hypothetical inferences there is such a limit, and therefore the rule of dayo does not necessarily distinguish between different kinds of deduction. He cites the Nazir’s response that there are Tannaim for whom there is no dayo, such as Rabbi Tarfon, and concludes that it is enough that there exists a kal va-chomer without dayo to undermine identifying it with a binding categorical inference.

An attempt to understand “hypothetical inference” in the Nazir as the logic of science

The speaker suggests that “hypothetical inference” in the Nazir does not mean modus ponens/tollens, but rather the hypothetical-deductive inference used in science: if a certain law exists, then a phenomenon will occur, and when the phenomenon does occur, this confirms but does not prove the law, and the formal logical argument here is invalid. He connects this to Bacon and the “New Organon,” and to the view that induction is the tool of scientific progress, in contrast to deduction, which does not generate new knowledge. He points to the wording cited in section 21 in the name of Hermann Cohen: “The hypothetical judgment is the conscience of scientific thought, the soul of the new science,” and sees this as strengthening the idea that the Nazir’s terminology is aimed at that conception, even though the use of terms is confusing relative to standard logic.

Comparison, mah matzinu, and gezerah shavah as different frameworks for refutation

The speaker tries to understand how kal va-chomer is described as a comparison similar to mah matzinu, but has difficulty translating the principle that “similar cases should be equal in their law” to the kal va-chomer of dayo in Bava Kamma, where horn in the public domain and in the injured party’s courtyard are both set at half-damages. He notes that in gezerah shavah the comparison extends to all the laws, and therefore the place of refutation is more understandable, whereas in mah matzinu the analogy is limited to relevant aspects, and therefore many refutations are not relevant. He mentions the phenomenon in Tosafot, where they ask “Why didn’t they refute it in such-and-such a way?” and answer that a refutation that does not touch the relevant aspect does not undermine the comparison.

The thirteen hermeneutical principles and logic as a basic interpretive tool

The speaker argues that the simple tools of interpretation and plain common sense cannot “descend from Sinai,” because they presuppose understanding words and ordinary reasoning, and therefore there is certainly no need for special authorization to use deduction. He asks how one infers from the law of an ox to parallel laws regarding a donkey or the derivatives of horn, and argues that such inferences are made by interpretive reasoning and analogy that are no less than kal va-chomer in their use of reason. He concludes that the thirteen hermeneutical principles function as authorized ways of making generalizations and establishing general premises from which one later descends by deduction, not as a basic permission to activate logic.

Full Transcript

[Rabbi Michael Abraham] If you remember from where we started last time,

[Speaker B] there’s

[Rabbi Michael Abraham] some controversy here with the doctor—what’s his name—

[Speaker B] Schwartz, Adolf Schwartz.

[Rabbi Michael Abraham] I also just mentioned once in an article—Adolf Schwartz was, of course, the head of the Theological Seminary in Vienna, I think.

[Speaker B] Is he alive? Is he still alive? No, he died at the beginning of the…

[Rabbi Michael Abraham] Maybe in the twenties of the twentieth century. He published books on the hermeneutical principles by which the Torah is expounded, a book on kal va-chomer. No, no, I said he’s not alive, it’s not that I… I ran into this in an article I wrote on kal va-chomer, and I also argued against what he said—that kal va-chomer is a hypothetical inference. Okay, so here, to be honest, it’s not completely clear to me what the thesis and the antithesis are in our discussion here. I mean, I’ll tell you what I think; I’m not one hundred percent sure that this is what he intends. Basically, it’s pretty clear that he wants to show that kal va-chomer is a method rooted in comparison, and that’s meant to exclude the view of this Schwartz, who sees kal va-chomer as basically a deductive inference, a logical inference. That seems to me, broadly speaking, what he wants to show here. But the problem is that later on he uses all kinds of terms whose common usage in logic belongs to the realm of deductive inference. Meaning, the “hypothetical inference” he talks about here. His discussion is basically whether kal va-chomer is a hypothetical inference or what he calls a categorical inference, a syllogism. A syllogism is a logical argument.

[Speaker B] The translation—

[Rabbi Michael Abraham] of “syllogism” into Hebrew is “hekesh,” inference. So anyone working in the area of the Torah’s hermeneutical principles can’t use the Hebrew word “hekesh,” because people will immediately think of that specific Torah method of derivation called hekesh. So the Hebrew translation of the word syllogism is something like inference. In any case, the discussion he’s conducting here is whether kal va-chomer is basically a deductive inference, a logical argument, or whether it’s an inductive or analogical comparison. Now, his terminology isn’t entirely clear to me. Let me tell you what the accepted terminology is. In logic, the accepted terms—so a categorical inference, the first figure that he talks about here, it doesn’t matter which one exactly, there are several figures, but a large part of them are more or less equivalent—that’s the inference that accompanies us all the time with Socrates: all human beings are mortal, Socrates is a human being, and therefore Socrates is mortal. Basically, if a certain statement is true of the whole, then it is true of an individual member of that whole. That’s the standard logical inference. Now there are other inferences that still belong to logic, called hypothetical inferences. There are two simple hypothetical inferences and one complex one. The two simple hypothetical inferences are: if A, then B—that’s the first premise. The second premise is A. From that, you can infer B. If I know that there is a relation such that if A is true then B is true, and I also know that A is true, then of course I can infer that B is true. From those two premises, obviously I can infer that B is true. That’s one hypothetical inference. What? Shall we write it on the board? I once went over the disjunctive rule of form equivalence.

[Speaker B] You saw, I think, Uri, right? I wrote it on the board. What are you saying? Right, that rule is written on the board. No, you’re not allowed to write on the board—when studying Talmud, you’re not allowed to write down the Oral Torah.

[Rabbi Michael Abraham] So if P implies Q, that’s the first premise. The second premise is P, and then the conclusion is Q. Okay? This argument is usually called modus ponens. Ponens—that’s what it’s called in logic. The second argument is this one—this is a negation, okay? So if P then Q, the second premise is not Q, then the conclusion is not P. This argument—wait, let me explain for a second—this argument is, for example, not like this one: if P then Q, and I know Q, so therefore clearly P. That’s an invalid argument. Those are the two arguments usually called simple hypothetical inference. What does that mean? If, for example, P is “it’s raining,” then Q is “there are clouds,” okay? That’s a statement. If P is “it’s raining” and Q is—

[Speaker B] there are clouds, okay?

[Rabbi Michael Abraham] If there are clouds then it’s raining—that too you could say, but that statement is false. There can be clouds and no rain. But if it’s raining, then of course there are clouds, right? So let’s take that formulation. If I say like this: my first premise is that if it’s raining, then there are clouds. My second premise is that it’s raining. That’s a premise. Clearly I can infer that there are clouds, right?

[Speaker B] It’s a simple argument, just a simple argument.

[Rabbi Michael Abraham] Now here, if it’s raining then there are clouds, okay? I know there are no clouds, so clearly I can infer that it’s not raining, right? Why? Because if it were raining, if P were true, then it would follow that Q was true, but the premise is not Q. By way of negation you can prove it, so this too is a valid argument; it’s called modus—

[Speaker B] tollens. What a divine name.

[Rabbi Michael Abraham] Modus ponens and tollens. P and Q and R and whatever. Here’s an argument that people sometimes use, but it’s invalid. Meaning: if it’s raining then there are clouds; there are clouds; therefore it’s raining. That’s not right, is it? It’s not a valid argument. From those two premises you can’t infer that conclusion, okay? Now notice that the clouds and rain here are irrelevant to the structure of the argument. Meaning, this is true for any interpretation you put in. Whatever you put in place of P and Q, you’ll get that these two are valid inferences and this one is invalid. Okay? The clouds and rain are only for illustration. They’re just examples. Now these two are called—these two are called the simple hypothetical inferences. Complex hypothetical inferences, in logic, are usually just a doubled simple inference and nothing more. If P then Q, if Q then R, from those two you can infer that if P then R. Right? And that is the complex hypothetical inference. I’m going to use this a bit later, so I put it on the board, even though I don’t think that’s what he means by these expressions when he talks about conditional or hypothetical inference. Because it seems to me—again, from the context—it seems that his goal is to arrive at the point that kal va-chomer is a method that is not deduction. It’s not an argument that is mathematically valid, it’s not a logical argument. And these inferences, you understand, are deduction no less than any demonstrative proof. It’s exactly the same thing. It’s true in a necessary way. So I don’t think he’s bothering here to quibble over exactly how the deductive inference is built, but rather whether it is a deductive inference at all. What? What? Here, here, it’s just an example of deduction.

[Speaker B] Just an example of deduction. What? What? You can’t derive from a deductive inference.

[Rabbi Michael Abraham] Ah, now that already sounds much better. That sounds much better. Let me give you an example of a different kind of kal va-chomer just to sharpen things up. It’s a different kind of formulation; it’s a bit less the standard type of kal va-chomer, but there’s a kal va-chomer that appears in the Mekhilta, with extensive Tosafot, at the beginning of Bava Kamma: “If for uncovering he is liable, then for digging all the more so.” Someone who uncovers a pit or digs a pit—if for uncovering he is liable, then for digging all the more so. So how is that kal va-chomer structured? It’s not a regular straightforward kal va-chomer. A regular straightforward kal va-chomer has three data points, and from them we arrive at a conclusion, a fourth law. Right? For example: tooth and foot in the public domain are exempt; the famous Mishnah in Bava Kamma; horn in the public domain incurs half-damages; tooth and foot in the injured party’s courtyard incur full damages. Those are the three known laws. Now I ask: what is the law of horn in the injured party’s courtyard? So I make a kal va-chomer, and the conclusion is that it is liable—half or full, there’s always dayo—but I arrive at the conclusion that it is liable. But how is the kal va-chomer there structured? I have three given laws and the conclusion is a fourth law. Right? You can present this as a kind of two-by-two table. That was—

[Speaker B] that zero-zero one, right?

[Rabbi Michael Abraham] That was that zero-zero one, right? Good. This is the domain and this is the damager, okay? Let’s say the damager is tooth and foot, let’s say horn. And the domain is the injured party’s courtyard and the public domain. Okay? Now I’m interested in what the law is for horn in the injured party’s courtyard—that I don’t know. These three I do know, right? These three I know. Tooth and foot in the public domain are exempt, tooth and foot in the injured party’s courtyard incur full damages, horn in the public domain incurs half-damages, and now I ask: what is the law of horn in the injured party’s courtyard? Okay? So the classic kal va-chomer is what does this. It says, let’s learn by kal va-chomer—soon we’ll go into more detail and arrive at the conclusion of what this fourth law is. Now, “If for uncovering he is liable, then for digging all the more so” doesn’t fit that pattern. In that kind of kal va-chomer, there are three legal givens and the conclusion is a fourth law. “If for uncovering he is liable, then for digging all the more so” has one given datum for the kal va-chomer, one law that serves as the basis for the kal va-chomer, and the second law comes out of it as the conclusion, right? Someone who uncovers a pit—someone who uncovers a dug pit, a dug and covered pit, someone who removes its cover, that’s uncovering—he is liable. That’s the given. The conclusion is that someone who digs a pit is certainly liable, right? There aren’t three given laws here, there’s one given law here. Okay? That’s a somewhat different kind of kal va-chomer. Yes.

[Speaker B] Maybe the other two data points aren’t explicit because we simply know that digging is much more severe than uncovering.

[Rabbi Michael Abraham] More severe in terms of reasoning, yes—but those aren’t legal data points.

[Speaker B] The question is whether that’s… okay, but it serves in place of the two data points.

[Rabbi Michael Abraham] Yes, we’ll see in a second—but this point is very important. Very important. We’ll soon see why, and it will also connect to the issue of rejection.

[Speaker B] Here the kal va-chomer as deductive is built in. What? Digging a pit doesn’t have…

[Rabbi Michael Abraham] Here it’s from reasoning.

[Speaker B] So basically what are you saying?

[Rabbi Michael Abraham] You’re saying that the act of uncovering is included within it—the act of digging includes uncovering plus more, right? So it certainly can’t be less severe than uncovering, right? This is what is called, by the rule-writers in Ginat Veradim of the Pri Megadim—and the Maharsha writes this at the beginning of Bava Kamma—no, the Maharsha, I think, is in the later edition somewhere on the first pages there in Bava Kamma, I can look it up, I don’t remember exactly where. They call it a kal va-chomer of “included in two hundred is one hundred,” which is a different type of kal va-chomer. And a kal va-chomer of “included in two hundred is one hundred” is, at least on the face of it, a simple deduction, because here there’s no room at all, no degree of freedom. Meaning, someone who digs a pit certainly uncovers plus more. There’s uncovering here plus something else, right? So it’s clear that everything uncovering has, digging has at least that, if not more. This argument is a simple deduction. A practical implication, for example—on this kind of argument there can’t be… another practical implication, and of course a more important one than that one, is that in this kind of kal va-chomer it could be that punishments are derived from logic. The question is: why don’t we derive punishments from logic? There are several explanations. Why not derive punishment from something learned by kal va-chomer—we don’t derive punishment, right? At least that’s the accepted view. So what does it mean, why don’t we derive punishment from logic? Why indeed not? There are several explanations proposed by later authorities. I think later authorities suggest this; I don’t think the medieval authorities (Rishonim) do, but later authorities propose several explanations. There is a well-known Maharsha and others who say that perhaps there is a refutation of the kal va-chomer. Meaning, I can’t rely on it in order to flog or execute, because perhaps there is a refutation. Who says I was right? Kal va-chomer is simply something I do on the basis of my own reasoning. Who says I was right? Maybe there is a refutation. There is a second explanation, which says that since the second case is more severe, it could be that the punishment of the lesser one is not enough. The Kesef Mishneh says something like this regarding one who passes some of his offspring to Molekh, but not all his offspring to Molekh. Someone who passes all his offspring to Molekh is not liable to death, but one who passes some of his offspring to Molekh is. It’s a bit strange. The Kesef Mishneh explains that this is simply because someone who passes all his offspring to Molekh—who says that death would even be enough for him? I’m not prepared to atone for him with death at all; he deserves a punishment more severe than death, and that’s why he isn’t liable to death—not because it can’t be learned. Okay? They explain the case of conspiring witnesses this way too, for example, and others as well. Also the Kesef Mishneh—there’s a Kesef Mishneh like this in three places, here and three there, I don’t remember exactly where everything is. In any case, that’s a second direction for explaining why punishments are not derived from kal va-chomer. Although one can indeed learn that it is prohibited—and that certainly can be learned by kal va-chomer—one cannot transfer the punishment through a kal va-chomer derivation, because the punishment may be too lenient for the case if I transfer it; it may not be enough. A further direction—some say that this is learned simply from a scriptural decree. It’s some verse-based derivation, and therefore I don’t know exactly what that means or how it affects our understanding. Usually that appears as a third approach, though I don’t know—it could be that this verse teaches one of the first two ideas. And I think there’s yet another direction in this matter—I wrote something here for myself—that punishment is not always proportionate to the act. Therefore, even if you transfer the prohibition, it is not certain that you can transfer the punishment. Sometimes there are more severe transgressions whose punishments are lighter, or different—I don’t know if lighter, it depends how one ranks punishments. Paying one hundred shekels is certainly more severe than paying fifty shekels, but to die by stoning or to die by burning? I’m not sure the answer is so simple there—what is more severe? In the Talmud it’s obvious that stoning is the most severe, but why is it the most severe? Does it hurt the most? I don’t know—one second, let’s check. It doesn’t work, never mind. In any case, maybe punishment isn’t meant to cause pain, or something like that. Various directions one can examine, whose common conclusion—and there are nuances—is that there is no direct connection or direct proportion between the intensity of the offense, or the nature of the offense, and the nature of the punishment. And it could be that in order to cleanse this offense, you need specifically a punishment that addresses that aspect of the personality, even if that punishment is lighter. But since that is the damaged aspect, you need that punishment to cleanse that aspect. You follow? So it doesn’t necessarily have to be more severe. Now if you learn that that thing is prohibited by kal va-chomer from this thing, that still doesn’t mean that the punishment that addresses this is the same punishment that addresses that. Okay? That’s another possible direction to raise in this context. In any event, for our purposes: a kal va-chomer of “included in two hundred is one hundred,” at least according to the explanation that maybe there is a refutation—there is certainly no issue there. In a kal va-chomer of “included in two hundred is one hundred,” one could derive punishment from logic. In such a kal va-chomer, some commentators write this, and Ginat Veradim wants to say this, but in Tosafot in Bava Kamma it is proven not so. In Tosafot in Bava Kamma and in the Mekhilta. And behold, in the Mekhilta it is written—it’s difficult, because it implies that monetary liability is derived from logic in our first Mishnah in Bava Kamma. But in the Mekhilta it is taught: “If a man uncovers and if a man digs—if for uncovering he is liable, then for digging all the more so? Rather, this teaches you that monetary liability is not derived from logical argument.” So why do we need a verse teaching that one who digs a pit is liable to pay? That is exactly what the verse comes to teach. And this is a kal va-chomer for which there can be no refutation, right? Fine. But if we look according to the other explanations, then only according to the second explanation—of Rabbi Shimon. According to the second explanation, which says that maybe it’s more severe and therefore this punishment is not enough—even that I don’t understand why, but at least here there is a Mishnah that says this explicitly, as we said before. Because in practice, even according to that explanation, let’s say it is more severe—then punish him at least for that component, for what’s included within it. You can’t punish him for the rest? Leave that to the Holy One, blessed be He. But if within the act of digging, within that itself, there is uncovering plus more, then give him the punishment he deserves for uncovering. Now digging may be more severe, true, so the difference the Holy One, blessed be He, will deal with—but certainly you can give him the punishment for uncovering if he dug, right? Because within the act of digging there is uncovering.

[Speaker B] Right, he uncovered it. Can’t you split it up? What? Can’t you divide it?

[Rabbi Michael Abraham] Why? I don’t understand why. If he performed an act of uncovering here, that has a punishment—the uncovering within the digging.

[Speaker B] It’s not simple uncovering.

[Rabbi Michael Abraham] It’s an entirely different act, it—

[Speaker B] includes the uncovering within it, but—but it’s already something else. Why is it something else?

[Rabbi Michael Abraham] For uncovering he is liable; for the addition—the addition is something else that the Holy One, blessed be He, will take care of. So it’s not included at all. But again, if that weren’t true, then it also wouldn’t be true regarding one who passes all his offspring to Molekh. Because someone who killed all his offspring, one who passes all his offspring to Molekh—certainly first of all he killed his first son, right? At least execute him for that, and after that let the continuations be left for the Holy One, blessed be He, to deal with. So we see, at least in that direction, that perhaps there is room to say yes. The third direction that I mentioned, that the proportionality of the punishment is not always relevant to the proportionality of the offense—that too, I think, is not relevant here to the rule that punishments are not derived from logic. Because… again, because there is an act of uncovering here. As for uncovering, the punishment has already been stated—so give him that. Now if there is something else, less or more, let the Holy One, blessed be He, continue from there. But there was an act of uncovering here, physically there was. So why don’t you punish for that? Punish him with whatever one gives for uncovering. So that’s it. Fine. And this is a dispute among medieval authorities (Rishonim) there in Bava Kamma over the question whether the Babylonian Talmud accepts the—what? This—

[Speaker B] that the punishment is for the uncovering because of the digging, the punishment is for the fact that you killed a person.

[Rabbi Michael Abraham] For the fact that you uncovered it and through that killed a person.

[Speaker B] No, the question is whether that counts as intentional killing.

[Rabbi Michael Abraham] No, no, not intentional—but the punishment is for the uncovering.

[Speaker B] No, you caused it—the question is whether you caused it.

[Rabbi Michael Abraham] The fact is that they make such a kal va-chomer, that digging is more than uncovering, right?

[Speaker B] And that’s the question, but there’s no significance to the size of the punishment. The fact that I said you caused it—so there’s no significance to the size of the punishment, whether more or less. Because I’m not punished for… I’m punished for killing. No, because the fact that you died…

[Rabbi Michael Abraham] Fine, you’ve already put him there, so of course pay. I’m saying, even if it were more severe, you still should punish. And if it’s already the same thing…

[Speaker B] No, because the discussion here is whether you can impose a punishment that is connected to punishment.

[Rabbi Michael Abraham] Yes, and the Mekhilta too says that a verse was written—“if a man digs a pit”—in order to teach you that punishments are not derived from logical argument. So it seems to me that in such a kal va-chomer, one of the “included in two hundred is one hundred” sort, on the face of it, for example one practical implication is that punishments would be derived from logic. Punishments would be derived from logic because there is no concern that there may be a refutation, and all that we said before. Maybe according to the middle direction, they really still would not derive punishment even here, although in terms of reasoning I still don’t understand why—but I don’t know, who am I to say. Now if indeed ordinary kal va-chomer—someone asked earlier, what practical difference does it make that it is not a simple logical deduction? So there is a very simple practical difference: if kal va-chomer were a simple logical deduction, punishments would be derived from it.

[Speaker B] You wouldn’t treat it as a logical inference. Just, yes.

[Rabbi Michael Abraham] Fine, and in Tosafot here too it’s not clear what the conclusion is, in the end, in that final line in the Mekhilta.

[Speaker B] The Babylonian Talmud disputes this.

[Rabbi Michael Abraham] The analogy from both of them—

[Speaker B] they wouldn’t have known…

[Rabbi Michael Abraham] Right, although the analogy from both of them doesn’t speak about “punishments are not derived from logic.” It speaks about some very specific scriptural decree regarding one who passes some of his offspring, and not all his offspring, to Molekh. It doesn’t say this as the reason for the rule that punishments are not derived from logical argument. But in light of the analogy from that Mishnah, maybe one could say it there as well—although I don’t understand the reasoning,

[Speaker B] we don’t know.

[Rabbi Michael Abraham] Okay, thank you very much. So in any case, this could be a very big practical implication, yes? Meaning, one cannot say that kal va-chomer is a logical inference. If it were a logical inference, punishments would be derived from it. How is this different from any other act of interpretation that we do on verses in the Torah? When we read a verse in the Torah, don’t we use logic to interpret it? Right? And that is not called learning by the thirteen hermeneutical principles, right? That’s just called that it is written explicitly. The verse says, “If a man’s ox gores his fellow’s ox,” right? And what if a dog bit his fellow’s ox? So what? What is the law in such a case? Obviously you have to pay, right? Exactly the same as an ox that gores. Why? Never mind, the conclusion is yes. Why? That’s not even deduction, it’s not even comparison—it’s something stronger. And what about a binyan av? And with deduction, are you worried that maybe there’s a refutation? What? In the world of deduction there are no refutations. Why not do it there too? Anything that is simple reasoning—there is absolutely no reason in the world not to impose punishment on its basis. Anything that is simple reasoning is simply interpretation of the verse. Anything on which you do not impose punishment is where you are adding something beyond what is simply written in the verse. When you bring in your own interpretive reasoning, then we say punishments are not derived from logical argument. But where you simply grasp that the verse means this, and this is the interpretation you give as its straightforward interpretation, what is there to discuss? Why on earth? That’s the meaning of the verse—so why not punish on that basis? The same with kal va-chomer: if it is understood as a binding, necessary logical inference, then it is just part of interpreting the verse. It would not belong to the thirteen hermeneutical principles. It wouldn’t need to be one of the thirteen principles at all. What, do I need the first principle to descend from Mount Sinai to tell me that I’m allowed to use logic? If I didn’t use logic, I wouldn’t even understand that statement itself, the statement telling me that I’m allowed to use logic. Clearly, the use of logic is a foundational assumption of Torah interpretation. I don’t need permission from Sinai within the framework of the thirteen principles, because according to most commentators these principles are a law given to Moses at Sinai. I don’t need a law given to Moses at Sinai for

[Speaker B] the fact that one is allowed to use logic. That’s—

[Rabbi Michael Abraham] complete absurdity. I use logic every step of the way—what do you mean? It simply cannot be that this is a logical inference. One also has to explain why indeed it is not a logical inference. And I think it’s obvious why it isn’t a logical inference, because—

[Speaker B] there are propositions from two different things in an inductive way.

[Rabbi Michael Abraham] What do you mean?

[Speaker B] There are propositions from two things—let’s look at tooth and foot, for example. You could say that tooth and foot are simply entirely different kinds of damages. They’re two separate things for which there is no one single law in some unified sense. It could be that they have the same liability, but that doesn’t tell me anything—I’m just attaching them to other kinds of damages.

[Rabbi Michael Abraham] Yes, right. I think at the beginning of this discussion on the hermeneutical principles, we distinguished between three forms of thought: analogy, induction, and deduction. We said that apparently the discussion of the hermeneutical principles—and even the common view—implies that there is some kind of hierarchy among them, which is stronger than which.

[Speaker B] And then—

[Rabbi Michael Abraham] afterward, in the end, our conclusion was that this isn’t true. They’re simply three stages of thought that come one after another. There are three different stages of one thought-process. And every act of thinking is built through analogy, induction, and deduction. That is more or less the order. If I make analogies, then after I’ve accumulated many items that resemble this item, I make a generalization about that whole group that resembles this item. And after I have the general proposition, now I make a deduction and say: okay, once there is a general proposition, then the specific detail that belongs to that general proposition also has the property that all those particulars have. Okay? Now the question is how exactly we see this thought-process in kal va-chomer. So let’s take a look and see that in this kal va-chomer too we have exactly all these stages, like any ordinary thought-process. Kal va-chomer is just an ordinary thought-process. How do we do this derivation here, for example, in the kal va-chomer in Bava Kamma? Let’s choose one direction as an example, although both directions appear there in the sugya. One direction as an example: we assume from the laws of the public domain, within this column, that we arrive at the conclusion that since tooth—

[Speaker B] and foot and horn, it’s because that is more severe,

[Rabbi Michael Abraham] So from the laws of the public domain, we assume that horn is more severe than tooth and foot, right? And we have a conclusion: horn is more severe than tooth and foot in every respect. And especially regarding damage in the injured party’s courtyard, right? So in the injured party’s courtyard, if tooth and foot are liable, then horn, which is more severe than they are, certainly should be liable. And that of course will lead us to the conclusion that horn is liable for full damages in the injured party’s courtyard. But there’s another direction to make this argument. If we learn from the laws of tooth and foot that the injured party’s courtyard is more severe than the public domain, and then move over to horn and say: fine, in horn too, the injured party’s courtyard is more severe than the public domain, and therefore if for horn in the public domain one is liable for half, then in the injured party’s courtyard he certainly should be liable for at least half. Which leads us to half and not to one. Okay? But there are two kinds of a fortiori argument, and really what are we doing here if we analyze it? If we analyze it, then what we’re doing here is, at the first stage, taking the first two data points and making a generalization out of them. Right? Let’s say we look at the public domain and infer the conclusion: horn is more severe than tooth and foot in every respect. What does “in every respect” mean? If it says regarding damage in the public domain that this one pays half and that one pays nothing, from where can you conclude that this is more severe than that? That horn is more severe than tooth and foot in every respect? You’re making a generalization. Right? So really we have one stage of generalization. Once we have the stage of generalization, that horn is more severe than tooth and foot in every respect, then of course now it’s simple deduction. If it’s in every respect, then in particular in the injured party’s courtyard. That one is liable for full damages, and horn is certainly liable, right? So that is definitely deduction. But the punch of the a fortiori argument is not in that stage. The punch of the a fortiori argument is in the stage of generalization. When I take two specific laws and derive from them a general proposition. Once I have the general proposition, I can always derive all the specific laws from it by deduction. That’s obvious. But the question is how I arrived at the general proposition. And in every logical argument, like the syllogisms we spoke about earlier, all human beings are mortal—that’s the first premise. In logic that’s called the major premise, because it’s a general proposition. “All”—it speaks about some collection of particulars. Okay? Socrates is a human being—that’s the minor premise. There is a particular item that belongs to the class of human beings. And the conclusion is that Socrates is mortal. Socrates is mortal—that’s the conclusion, right? Now, in such an argument there is a major premise, a minor premise, and a conclusion. The major premise says that the entire collection of particulars of a certain type has a certain property. The minor premise says that there is a specific item that belongs to that collection. That is the minor premise. The conclusion is that that item has the property possessed by the whole collection. So: major premise, minor premise, and conclusion. Now, if that structure is the classical logical form from the standpoint of Aristotle’s first figure of syllogism—now, if I take all the arguments in every field from this stage onward, all the arguments will be deduction. The differences between the arguments come in at the question of how I arrive at that major premise. If you remember, that was exactly Mill’s challenge, right? We found Mill’s objection to deduction. He basically said: you tell me that this thing is necessarily valid, deductive, logical, mathematical, whatever. Very nice. But how do you know that all human beings are mortal? That’s one premise and that’s another premise. From those two premises it’s true that the conclusion certainly follows; the structure is brilliant. But how do you know that all human beings are mortal? From induction, right? How do you know that all human beings are mortal? You haven’t seen all human beings, you haven’t checked whether all of them died, right? Some of them haven’t even been born yet. Right? So how did you reach that conclusion? By induction. Which means that every deduction rests on induction. Deduction is simply the part that concludes the process of thought. But the creative part, let’s call it the synthetic part, as we called it then, of the thought process—that’s the part that enables us to arrive at the major premise. In science too it’s like this. Once I know that all objects fall toward the earth, all objects with mass fall toward the earth, then obviously I can conclude that any particular object standing before me will fall toward the earth. That’s simple deduction. But the whole sting in scientific work is to arrive at that conclusion that all objects fall toward the earth. How do I know that? I’ve seen only so-and-so many objects. How do I know that this is a general law? Here there sits some sort of scientific induction, right? So if you always look at the end of the thought process, you will always encounter deduction. Almost every thought process ends in deduction. The interesting question is how one gets to the major premise of one’s deduction. And that’s where the interesting processes are. So here, in science, it is by induction. I see one item, see two, see three, think a bit, and say: okay, let’s make a generalization like this. We’ll try it and see whether it works or doesn’t work. Okay? In an a fortiori argument too, it’s something like that. It’s some kind of generalization. It’s hard to call it exactly induction, but it’s some kind of generalization whose foundation here really is not in our own plain reasoning, but in the authorization the Torah gave us, in the thirteen principles. The Torah gave us thirteen principles. The thirteen principles are basically thirteen ways to arrive at the major premise of a deduction. Once I have that major premise, it will always end in deduction. If someone thinks that a fortiori is deduction, then as far as I’m concerned, so too “general rule, detail, and general rule” is deduction. Why? Because the detail contains only what is in the general rule. Infer a general conclusion that the detail and the general rule have the same rules, and consequently that this particular characteristic found in the detail is also found in the general rule. That’s already deduction, right? The only question is how I reached the conclusion that the detail has everything the general rule has, or that the general rule has everything the detail has. Because “the detail only…” So the difference between the principles always lies in the question of how I arrive at my general proposition. But once I have a general proposition, I can always descend to a particular proposition by deduction.

[Speaker B] Maybe it’s not…

[Rabbi Michael Abraham] Almost always, because even without checking it, since we already saw that analogy also works in this way. How does analogy work? After all, when I make an analogy—Socrates dies, so Jacob our forefather will also die. Because both are human beings. So what am I really saying? In the background I’ve basically said that what they share is that both are human beings, and if Socrates is a human being and he dies, then all human beings die—and now that’s induction—and now deduction comes and says: Jacob our forefather is also a particular within the group of human beings.

[Speaker B] Could be that this is the distinction between a fortiori and the other comparisons. That this is perhaps the refutation that is missing from all the other comparisons.

[Rabbi Michael Abraham] A direct comparison is a comparison that doesn’t go through my general proposition—everything regarding horn, or tooth, or foot. Maybe what you have here is a direct comparison between horn and foot and tooth, and it passes directly, not through the general rule. It could be that that really is what’s missing for him, because he keeps pointing to it as a comparison, and that’s in a

[Speaker B] common case or an a fortiori argument, and so on.

[Rabbi Michael Abraham] Leniency and stringency are the essential thing in every a fortiori argument. So that’s more or less the point, it seems to me, meaning…

[Speaker B] What? Your major premise doesn’t come from analogy. Exactly.

[Rabbi Michael Abraham] Meaning that a deductive process cannot be subject to refutation, which is what we already said earlier. There’s no such thing. In mathematics we haven’t found any refutation. There is no refutation in mathematics. Huh? Deductive always… there cannot be a refutation in mathematics. So how is there refutation in an a fortiori argument? Exactly because an a fortiori argument has a component that is not deductive. The component of generalization that leads me to the major premise—that is what stands here under the test of refutation. If there is a refutation, then what has fallen is not the derivation of this conclusion from these two premises—that can never fall. What has fallen is one of these two premises, meaning the major premise. It is not true that all human beings are mortal—look, Elijah the prophet is not. I have a refutation. What does that refutation say? A refutation does not say that if these two premises are true then this conclusion is not true—there is no such thing.

[Speaker B] If the two premises are true, the conclusion is certainly true. Refutation says that this major premise is simply not true. That it’s not the case that all human beings are mortal. Therefore there they brought another detail in horn and another proposition in a common case that they rely on.

[Rabbi Michael Abraham] No, there can also be a refutation of a common case.

[Speaker B] But they use a common case for refutation.

[Rabbi Michael Abraham] There can be a refutation that undermines the comparison.

[Speaker B] Well, maybe—

[Rabbi Michael Abraham] The discussion isn’t about analogy.

[Speaker B] Maybe it’s a verbal analogy?

[Rabbi Michael Abraham] So whoever said that that’s not right… so what? No, there can be a refutation that says to me: listen, maybe your comparison isn’t correct, it does not follow from the major premise of the generalization.

[Speaker B] You say it’s equal, and here is a refutation that it’s not equal. I’m making a comparison, I’m making a comparison between one detail and another.

[Rabbi Michael Abraham] No, but comparisons aren’t made on one specific detail; it’s a general rule. You have the verbal analogy of “to her, to her,” the exposition from slave to woman. So you don’t learn it regarding one specific law but for all the laws. Everything there is here, and everything here is there. You’re not learning it for one law only; it seems to me that it applies across the board. Now it’s true that analogy is not an inference like “to her, to her,” for example—it’s a comparison—but “a common case,” what we called a common case, that’s analogy. So there… now really it’s hard for me to understand why there is refutation.

[Speaker B] If I said this is similar—

[Rabbi Michael Abraham] and this is similar—it’s not true that it’s not necessary in the logical sense, but the similarity is a necessary similarity, that similarity is an absolute similarity. What I wanted to say earlier is that this common-case analogy—you don’t make an analogy for everything. When you make a verbal analogy of “to her, to her,” then these are laws. All the laws of a slave are the same for the slave and for the woman. But when you make a common case, meaning that there is an analogy between two things, then you do not make the analogy for every aspect of the matter, only for what is relevant.

[Speaker B] There, what you said is true—that it’s only for a certain clause and not for everything. But here, in a fortiori from ordinary analogy, where they tell you that for that reason a verse comes to tell you that there is something different here, here… no, it’s a comparison, it’s a verbal analogy. Ah, the comparison whose basis is comparison—that is a comprehensive comparison.

[Rabbi Michael Abraham] It’s not a comparison that rests on our own reasoning. Because it doesn’t rest on the relevant criteria of our thinking and understanding. Now, though, I think that if you continue this further, then it seems to me that simply the… it’s also not clear why there can’t be a refutation there. I mean, it’s clear to me that this is similar to that, so it’s clear to me that this is so—so what refutation can you offer? You have a problem, there’s something there that doesn’t fit with some law?

[Speaker B] Fine, it doesn’t fit, so let it. You understand?

[Rabbi Michael Abraham] I see that it’s similar. It’s not a matter of…

[Speaker B] It can’t be—we said deduction is guaranteed, that I won’t reach the wrong conclusion. Could there be an error?

[Rabbi Michael Abraham] There could be an error, but who said a refutation would reveal it? As we said earlier, analogy works only in those relevant directions in which it works. But it is certainly possible that the refutation you found points to an aspect in which these two things really are not similar. Fine—but who said they have to be similar in every respect? In a verbal analogy I understand why there needs to be and can be refutation, because in a verbal analogy it has to apply to all the laws. But in analogy, precisely because I’m making it myself, I make it in the respects where it is relevant to make it. But there may indeed be things that will not constitute a refutation. It could be that refutations really are only if they damage your analogy—meaning, if they also touch the very aspect that you think is similar between the source and the target. Okay? Fine, so this really requires deeper examination.

[Speaker B] It’s hard, hard to understand… we need to understand what exactly was going on here logically.

[Rabbi Michael Abraham] Certainly, certainly, yes, definitely. No, more than that. Many times they ask: why didn’t they bring this refutation or that refutation? Tosafot in many places asks: why didn’t they refute this way, and why not that way? And the answer is always on this plane—that this is an irrelevant refutation. It exists; it’s not that the law is incorrect. Sometimes the answer is that the law is simply incorrect—that it’s a mistake. They prove that the law is not correct. But many times the law is correct, and nevertheless this refutation is not relevant because it points to an aspect of a different kind.

[Speaker B] Okay, I think that the place of a scriptural decree has a role here… it could be that the Torah needs to give me authorization to use one of the tools in certain ways if I would have had an initial assumption not to use them. And when they establish something for me and it doesn’t override the other thing—then you said refutation—there’s something here that you don’t… grasp with the ordinary tools.

[Rabbi Michael Abraham] What do you mean? Deduction is not a matter of ordinary tools. Deduction… the Torah cannot tell me about deduction that it’s not correct. And even if it says so, I won’t listen to it. There are already amoraim who said: “By God, if Joshua son of Nun had said it, I would not obey him,” right? There are things that are so clear to you that even if Joshua son of Nun says it, you won’t…

[Speaker B] Yes, but here we’re talking about something called a fortiori. And a fortiori… as you said, what? No?

[Rabbi Michael Abraham] You’re really pointing out that a fortiori is not deduction. It is not necessary, and therefore I’m willing to listen if it comes from the Torah, obviously. But can the Torah say to me: listen, all human beings are mortal, Socrates is a human being, but know that Socrates is not mortal? Can the Torah tell you such a thing, as a scriptural decree? But there is no such thing. A scriptural decree like that—I do not accept.

[Speaker B] A scriptural decree—the Torah speaks about the punishment, about the law, how you need to act.

[Rabbi Michael Abraham] No, but there will always be… I don’t care, but there will always be a component that goes beyond deduction. Otherwise the Torah has nothing to say about it.

[Speaker B] After all, everything concerning conspiring witnesses, right? “As he plotted” and not “as he did.” And in that too there’s something that supposedly from every… I don’t know what sort of thought process to fit it into. No, I can give you other explanations for that.

[Rabbi Michael Abraham] There’s the explanation of Nachmanides, for example, that conspiring witnesses created a certain potential for destruction. The Maharal somewhere—I don’t remember exactly where—explains it more correctly. The conspiring witnesses create a certain destructive potential, and now that destructive potential has to be discharged. Meaning, it exists in the world. There is a destroying angel, you can call it by another name. You created here some death sentence that needs to be carried out. Now, if you did not kill… if you already killed the person, then you already killed him; you are merely guilty, but you already discharged it. There isn’t some destructive potential that still exists in the world. But if you didn’t kill the person, then now there is some destroying angel here that will kill someone.

[Speaker B] Meaning you did something, it’s something…

[Rabbi Michael Abraham] There’s no goal here of restoring. You created a destroying angel here, and now the question is what to do with it. So they say, fine—if you created it, let it kill you. Not as a punishment for what you did, but from an obligation inherent in the situation. Okay? No, I’m just showing you various directions.

[Speaker B] Fine, but there are also approaches that don’t explain it. What don’t they explain? And again, they don’t explain it—and as for deduction, how will you tell me that in principle…

[Rabbi Michael Abraham] No, never! Because every such explanation… I’m showing you these explanations only so that you understand that in order to reach a conclusion about punishment… you need something more than merely assuming that this is more severe than that. You need, for example, to assume that there are no side conditions about destructive potential, that there are no side conditions where the punishment is not severe enough for the act, all sorts of things like that. It shows you—I don’t need these explanations themselves. All I want to show you through them is that you need more premises in order to reach a conclusion about what the punishment is. Once that’s the case, I don’t mind receiving premises from the Torah, or from I don’t know where. You understand?

[Speaker B] So maybe according to that approach, for Schwartz an a fortiori argument really is a perfect inference, when he tells you that there are no all kinds of side factors here.

[Rabbi Michael Abraham] And that is the third direction in Avnei Shlomo, that the intensity of the punishment is not necessarily proportional to the intensity of the transgression.

[Speaker B] No, that’s Schwartz’s approach, that a fortiori reasoning is perfect deduction, that this is one of the thirteen principles. And what I asked about the thirteen principles is that it sounds to me like deduction that one can

[Rabbi Michael Abraham] punish based on it, but one cannot punish based on it.

[Speaker B] The Torah does not punish, even in—maybe even in warning. Not to tell me—I can assume that the commandment, the Torah, was given to me for reasons I don’t understand, and that it’s not true that if you don’t understand—then from here on I act.

[Rabbi Michael Abraham] Fine, but I still operate with the ordinary logical tools. One cannot, meaning, one cannot tell a person: listen, don’t use your logical tools.

[Speaker B] Yes, but I can say that commandments and prohibitions are not analogical. Or that they are decrees of the Holy One, blessed be He.

[Rabbi Michael Abraham] What do you mean? Then tell me—if a donkey, in a severe case, bites, is that also like an ox goring? Or not? In the Torah it says, “If one man’s ox gores another’s ox.” What about a donkey? Goring, biting, crouching, kicking—what about them? All the subcategories of horn? You assume as a simple matter that these are subcategories of—well, not as a simple matter, but that’s the Talmud’s conclusion—that these are subcategories of horn, right? Why? Because you have some reasoning that horn means intent to damage, and your property, and its guarding is your responsibility, and these too are intent to damage, and your property, and its guarding is your responsibility, right? That seems to you a weaker inference than a fortiori? Analogy. Yes. What do you mean, weaker than a fortiori in your eyes?

[Speaker B] Not simple. If it’s analogy, then it shouldn’t have a place in the Torah. Why?

[Rabbi Michael Abraham] It’s simple for him. Because that’s what I’m saying. Logic—even plain logic, I’m not even talking about mathematics, that’s certainly so—even beyond that, even ordinary, intuitive human logic, ordinary interpretive logic, that too is not something that could have descended from Sinai. It can’t be, because when I read the words this way, that’s how I interpret them.

[Speaker B] So what did the thirteen principles come for? Thirteen principles of induction because of them. Yes, they need to be explained.

[Rabbi Michael Abraham] That’s what I noted there, actually, that I really don’t understand. I noted there that I truly don’t understand why—I said there that I called it in the introduction

[Speaker B] what we today call the reasonings of the Sages.

[Rabbi Michael Abraham] At first I thought that every matter—so that comes to teach me that there is only one reason for every matter from the side of “what common factor.” But really, just to use my inductive tools or something like that, I don’t need these thirteen principles for that.

[Speaker B] Who says these thirteen principles are talking about analogical inference? What? Who says the usage is in statements about an ox?

[Rabbi Michael Abraham] What? Who really says that? How does the Talmud transfer it?

[Speaker B] What do you mean?

[Rabbi Michael Abraham] What if you intentionally damage with a car, or you damage with this—that isn’t written in the Torah, so you won’t pay?

[Speaker B] I don’t know, maybe different laws.

[Rabbi Michael Abraham] In any case, it’s not written in the Torah, no matter what. So how do you infer it? You infer it because you say: plain common sense says that if an ox, then a donkey too—what’s the difference? Right. So for that argument, isn’t it stronger than a fortiori?

[Speaker B] Maybe the Torah spoke about an ox? Maybe yes, maybe no.

[Rabbi Michael Abraham] Plain common sense says no.

[Speaker B] It says yes. Meaning, that it’s not only an ox. Fine, after all it’s a simple logical inference. What do you mean? Maybe if I hit with a manual car it’s more severe

[Rabbi Michael Abraham] than if I hit with an automatic car.

[Speaker B] With automatic it has nothing to do with…

[Rabbi Michael Abraham] They won’t pay damages—why? Because it’s a little different. What does that have to do with automatic?

[Speaker B] Never mind, we’re already drifting here into other things, it doesn’t matter.

[Rabbi Michael Abraham] But in any case we see that the simple means of interpretation, the means of common sense, do not require the thirteen principles. And notice, these things are much weaker than deduction. And even for them, I don’t need permission from anyone in order to use them. Right. So certainly for deduction I don’t need permission. I don’t know. Fine, now here—what time is it now? Here in section 18, I won’t even read it inside because basically we already discussed these things. So in section 18 he brings a proof that this is an inference—an inference not hypothetical but what is it called, a perfect inference, sorry, in 19, in 19. In 19 he brings a proof—this Adolf Schwartz—he brings a proof that it is a perfect inference and not a hypothetical inference from the law of “it is enough.” Yes, that same Talmud, that same Mishnah that learns horn in the injured party’s courtyard, it applies the rule of “it is enough,” and therefore horn is liable only for half in the injured party’s courtyard and not full damages—“it is enough for what is derived by law to be like that from which it is derived.” He says… the major premise. There it is, you see, the top line on page 62. That it is like “the derivative cannot be greater than the major premise in a perfect inference.” The major premise is what we said, yes, the general proposition that serves as the premise of a perfect inference. So he proves from the principle of “it is enough” that basically a fortiori is a perfect inference. From here I’m trying to think: what would a hypothetical inference be, one in which there would not be “it is enough”? What does the Nazir answer him?

[Speaker B] Why isn’t it an inference with

[Rabbi Michael Abraham] “it is enough”? Why what?

[Speaker B] The proof. After all, “what is derived by law is not to be more than that from which it is derived.” Why don’t we say “it is enough”? What does he say? Because it is impossible—

[Rabbi Michael Abraham] It cannot be that there is more in the conclusion than in the premises. If all human beings are mortal and Socrates is a very good human being—not merely a human being—that does not mean that he will be even more mortal. There won’t be more than in the premise. The premise says that all human beings are mortal.

[Speaker B] More than that you can’t derive. We say “it is enough” here like in Miriam? What? If the “it is enough” here is like in Miriam—that God shut her out seven days—then what’s the problem with saying

[Rabbi Michael Abraham] that if it’s a perfect inference then there is “it is enough”? That’s what you’re saying, and that’s what Rabbi Schwartz also says. If it’s really some kind of comparison, then what’s the problem with saying that if it’s the Holy One, blessed be He, then it should be fourteen days and not seven days?

[Speaker B] Another example: is tooth more severe than foot?

[Rabbi Michael Abraham] Yes, in the private domain—no, horn is more severe than tooth

[Speaker B] and foot, more severe than tooth and foot in the public domain, so in the injured party’s courtyard it also ought to be more severe. Why does it get reduced?

[Rabbi Michael Abraham] No, no, no, you’re talking here about the wrong direction of the a fortiori argument. The Talmud there learns an a fortiori argument—I said there are two directions—and the Talmud learns the second one. When I learn the injured party’s courtyard from the public domain, and not horn from tooth and foot. The injured party’s courtyard is more severe. Yes, and then I say: since in the public domain one pays half, then in the injured party’s courtyard too one pays half. More than that I don’t know. It is more severe, but okay, more severe is more severe—but how much more severe? I don’t know how much. So “what is derived by law is not to be more than that from which it is derived,” and therefore half. They ask why we don’t take the other side, of full damages.

[Speaker B] Here, here they discuss there—maybe there is a refutation of the a fortiori there.

[Rabbi Michael Abraham] Why would you say that it is a perfect inference and not…? Because he says that the basis of “it is enough” is that if you infer a conclusion from a premise, there cannot be more in the conclusion than in the premise. Now understand: if this is a hypothetical inference of the kind we discussed here, it too will have “it is enough.” Why wouldn’t it have “it is enough”? This doesn’t indicate one specific kind of deductive inference as opposed to another.

[Speaker B] The premise didn’t speak about the amount of liability or payment. It only said what is more severe, that this is always more severe than that.

[Rabbi Michael Abraham] No, the premise said that this is more severe than that, and the premise also said that horn is liable for half in the public domain. “What is derived by law is not to be more than that from which it is derived.” You learn from the public domain to the injured party’s courtyard, and you can go up to half; you can’t go beyond that. It seems to me that here one really sees—and the whole context says this too—

[Speaker B] that the derivative cannot be greater than the major premise.

[Rabbi Michael Abraham] The major premise in our case establishes the direction of the a fortiori. In this context you need to learn from the minor premise. The major

[Speaker B] premise is—

[Rabbi Michael Abraham] what determines the amount.

[Speaker B] Anyway, fine, there’s

[Rabbi Michael Abraham] a lot to go into in the details of a fortiori arguments and to see that they differ from one another. There are a fortiori arguments where the logic somehow says to learn specifically in one direction and not in the reverse direction, not the other direction. To learn one domain from another domain and not one damager from another damager. And that’s a separate discussion; I won’t go into it here. It seems to me that here the confrontation really is on the axis of an inference that is not deductive at all, as opposed to a perfect inference—not different kinds of perfect inference. The Nazir says—and in fact when the Nazir answers Shabt, he says that there are tanna’im who do not apply “it is enough,” for example Rabbi Tarfon in a fortiori. And besides that, afterward he says that “it is enough” is also something else; we’ll soon see what it is. But he really does have some understanding that “it is enough” does hint that this is a perfect inference. Why? Because apparently what is embedded in the phrase “hypothetical inference”—I’m just trying to support this, because I’m not completely sure I’m right, but it seems to me—I’m trying to explain to you why I think this—what he calls a hypothetical inference is not a deductive inference. It is some sort of analogy, some comparison. And there it may be that there would not be “it is enough.” Because he says that if you are really comparing things to one another, there is certainly room to say: look, this is twice that, so it too should be punished twice that. You are no longer bound by the formal framework of logic. You say: look, if your source case… it says pay half, but it cannot be that the target case pays full. You don’t have proof for that, but if you say that here you’re using the judgment of common sense, you say: look, this is twice as severe as that, that actually sounds plausible to me. So if so, then it pays twice as much too. Why not? That kind of argument one can hear. So why is there “it is enough”? And the proof, says this Schwartz, is that “it is enough” is evidence that this is a perfect inference and not some matter of comparison. So if on the other hand he claims that this is a comparison, first of all there are tanna’im who do not apply “it is enough,” so you see already that there are places without “it is enough” where they still make an a fortiori argument, yes? That is the sugya there in tractate Bava Kamma. It is enough that there are places where there is no “it is enough” and they make an a fortiori argument without “it is enough” to show you that it is not a perfect inference. It is enough that there are such places to show you that this is already not that. That is his first answer. Beyond that he says that even in places where they do say “it is enough,” “it is enough” also fits my conception, not only the conception of perfect inference. Why?

[Speaker B] The perfect inference comes earlier, and afterward they make a rule; then indeed the final stage may look like induction, but arriving at the rule—the deduction, arriving at the rule—we then use analogy.

[Rabbi Michael Abraham] Fine, but it could be that even at the end you’re not using deduction.

[Speaker B] Yes, so really—

[Rabbi Michael Abraham] if horn is more severe than tooth and foot by a factor of two, and therefore horn should pay twice as much; or the injured party’s courtyard is twice as severe as the public domain, and therefore it should pay twice as much in the injured party’s

[Speaker B] courtyard—it may be that if we arrived at the stage of analogy and not finally at deduction, but the earlier stage, everyone would still have to agree, is a stage of induction, and therefore—

[Rabbi Michael Abraham] So what you’re saying is that the major premise is really produced by induction, and “it is enough” derives from the deductive component of the argument, from its end. That’s one direction, but he doesn’t go in that direction. He says that “it is enough” also comes from the comparison, and that even according to the explanation of a fortiori as comparison, the principle of “it is enough” emerges. Now here I don’t entirely understand what he means, and what I do understand I don’t think I agree with. It seems to me that what he wants to say is that a fortiori is something like the “if it contains two hundred, it certainly contains one hundred” that we mentioned earlier. Meaning, when one thing is more severe than another thing, why do you learn the law from the lighter thing to the more severe thing? Because the more severe thing contains the lighter thing too, only it has more as well. But “it is enough” says that you learn the law only on the basis of what is common to the two. What lies beyond that is beyond; you don’t know what it is. But the principle of a fortiori is to learn, say, horn is more severe than tooth and foot, so it has tooth and foot in it plus something else. So it contains within it the laws of tooth and foot. Now what lies beyond that, I don’t know what lies beyond. But a fortiori basically allows me really to make a common-case argument. I think that’s what he means, because that’s also what he said at the beginning—that a fortiori is literally a common case. He said it in chapter 8 at the beginning and says that a fortiori is literally comparison, like a common case. It seems to me that that is how he understands the foundation of a fortiori, though I don’t think he is right about that. It seems to me he’s not right about that. How shall we learn tooth and foot as against horn? How do we say that horn is more severe than tooth and foot, or that the injured party’s courtyard is more severe than the public domain—that’s the a fortiori they make there with “it is enough.” That the injured party’s courtyard is more severe than the public domain, right? We learn that from the laws of tooth and foot, and now we move to the laws of horn and say that there too the injured party’s courtyard will be more severe than the public domain, and therefore in the injured party’s courtyard he will pay half. Now how can that be understood on the basis of comparison? What comparison? The injured party’s courtyard is like the public domain plus…? And in what sense and in what direction? Right, I agree, but they apply “it is enough” specifically in that direction. They apply “it is enough” specifically in that direction because in the end we want to arrive at half in the injured party’s courtyard. Right, I agree with your point; it’s an interesting point there in the sugya. But in any case the conclusion is that they make the a fortiori in that direction, and “it is enough” is applied to it. The question is how “it is enough” can be understood on the basis of comparison like this. I don’t see comparisons here. I also think that a fortiori—the meaning of a fortiori—does have the sense of comparison. But he says—I think he relied on “what is a fortiori”—he said it is literally a common case. No, no, no, I didn’t learn it from there; rather I learned it from the Nazir’s words here about “it is enough.” What does he mean to say? Here it’s clear that this is not a common case. So what is he saying here? That “it is enough” is fundamentally a law of comparison, that similar things should be equal in their law. Fine—translate that for me into tooth and foot and the injured party’s courtyard as against the public domain. Horn in the public domain pays half, and in the injured party’s courtyard it pays half. What does that mean? Horn in the injured party’s courtyard and in the public domain are similar, and therefore it pays half. And tooth and foot in the injured party’s courtyard and in the public domain are not similar? Why there does it pay nothing in the public domain, while in the injured party’s courtyard it does? What is going on here? How do you get comparison out of this? I don’t understand. I don’t see the comparison in this a fortiori argument. And in the a fortiori of “if it contains two hundred, it contains one hundred,” what are you really saying? There it’s classic. If one is liable for opening, then for tearing all the more so, right? What are you really saying? That someone who tears is someone who opens, plus something more. Now if you want to learn the law from opening, what will you learn? You really will learn the principle of comparison. So you’ll obligate someone who tears with the liability of opening too. What lies beyond that I don’t know, but at least the opening component within tearing, that I will learn from opening. So there really is an element of comparison here. But in an ordinary a fortiori I don’t see it that way. It’s clear that there are the same factors that generate liability in the public domain. At least what is additional. Why? What? No. Formally you can say that, but it has to be translated into actual reasoning—what are the factors of liability. In half-damages in the public domain there are factors of liability there. They are places. You have permission to walk, you don’t have permission to walk—that can perhaps make a practical difference for tooth and foot? No, that’s not the point. If you had told me, say, that I don’t go with tooth and foot in the public domain, but yes there is, there’s some… I’m allowed to walk there. It’s some condition of conduct in the public domain, and what is the condition of conduct in the private domain, yes? Fine, I don’t know, I… what exists here are conditions of conduct that are present in half-damages. So, the conditions of conduct exist in half-damages, they include— But they don’t include. In the public domain I’m allowed to walk, and in half-damages I’m forbidden to walk. It’s not this plus something else. It’s something… I don’t know. I’m not… I thought of such a formulation because it’s the natural formulation, but I can’t translate it. No, formally I can say it, but these are just words, I don’t understand it. Let me just finish with his terminology of hypothetical inference. It seems to me that what he means by the hypothetical inference of a fortiori is actually this inference. This inference is basically how science works. You say, if… it’s funny how science works. Why? Because it works like this. It works like this; I don’t understand. You have no other way. No other way gets you anywhere. By analytic paths you don’t get there. So what do you say? You say: if there is a law of gravity, then all objects will fall to the earth, right? That is the hypothesis I test in a scientific experiment. I test whether there is a law of gravity, and I say: if there is a law of gravity, then all objects will fall to the earth. What do I do? I drop an object and I see. If it falls to the earth, then I have confirmed the general claim that there is a law of gravity. Now notice: I certainly have not proved it. As a logical argument, it is an invalid argument. An analogical argument. Exactly. It is some kind of inductive argument, analogical argument, whatever we call it, but it is an argument whose basis is comparison and not deduction. On the other hand, the terminology the Nazir uses is hypothetical argument. It is a hypothetical argument, what is usually called hypothetical-deductive. It’s not ordinary deduction. I don’t think he meant that; therefore it seems to me that he meant this. And he speaks about logic, about the new inductive logic in section 20—we mentioned this—of Bacon, in Bacon’s “New Organon,” where he put great emphasis on… until then, logic was understood only as deductive reasoning. And Bacon noticed that by means of deduction you cannot progress. That’s what we discussed. You cannot really progress; you cannot build science on the basis of deduction. And therefore he constructed, as it were, a new inductive logic—that’s what he means; he himself called it that. He means Bacon here. He himself wrote this, I remember it from the beginning of the book. That basically its foundation is induction. And therefore it seems to me that that is the hypothetical inference to which he is referring. The inference by means of which science is established. That’s what he says—it is the soul of science, I think it says here somewhere, no? In the notes. The hypothetical inference is the soul of science—it says somewhere here in a quotation below in the notes. He is simply using terminology that in my opinion is not the common terminology. I’m trying here to examine what… Third? What? It has no name because it’s not valid. In logic it isn’t valid. Induction is not valid in logic; it simply is not a logically valid argument, but of course it is an argument we use. That’s how we learn altogether. It says somewhere here in the notes that it should be… yes, we started with this yesterday, but he himself points this out, so therefore—therefore this again confirmed for me that he means this, and that’s why it’s so important for me to see it, in order to understand what he is saying. It appears somewhere here; I’ll look for it more. Ah yes, here, in section 21, not even in the notes. Section 21 itself: “According to the logic of the pure religion of the new Jewish philosopher”—he means Hermann Cohen, yes—“the hypothetical judgment is the conscience of scientific thought, the soul of modern science.” Yes, so it also seems to me that he means this. Therefore I think that when he speaks about hypothetical inference, he actually means the third picture there; his terminology is just a bit confusing.

The Voice of Prophecy, Lesson 36

Table of Contents

Summary

General overview

Adolf Schwartz and the controversy over kal va-chomer

Logical terms: categorical inference and hypothetical inference

Kal va-chomer as an argument that is not binding deduction

Types of kal va-chomer and the example of “included in two hundred is one hundred”

“Punishments are not derived from logic” and the discussion in the Mekhilta and Tosafot

Three forms of thought: analogy, induction, and deduction as stages

Analyzing the kal va-chomer in Bava Kamma as the creation of a “major premise”

Refutation as undermining the major premise, not the deductive structure

Dayo—“it is enough for what comes from the law to be like the source case”—as evidence for the structure of the inference

An attempt to understand “hypothetical inference” in the Nazir as the logic of science

Comparison, mah matzinu, and gezerah shavah as different frameworks for refutation

The thirteen hermeneutical principles and logic as a basic interpretive tool

Full Transcript

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Table of Contents

Summary

General overview

Adolf Schwartz and the controversy over kal va-chomer

Logical terms: categorical inference and hypothetical inference

Kal va-chomer as an argument that is not binding deduction

Types of kal va-chomer and the example of “included in two hundred is one hundred”

“Punishments are not derived from logic” and the discussion in the Mekhilta and Tosafot

Three forms of thought: analogy, induction, and deduction as stages

Analyzing the kal va-chomer in Bava Kamma as the creation of a “major premise”

Refutation as undermining the major premise, not the deductive structure

Dayo—“it is enough for what comes from the law to be like the source case”—as evidence for the structure of the inference

An attempt to understand “hypothetical inference” in the Nazir as the logic of science

Comparison, mah matzinu, and gezerah shavah as different frameworks for refutation

The thirteen hermeneutical principles and logic as a basic interpretive tool

Full Transcript

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