Noach (5764)

From the book Mida Tova: Articles on the Hermeneutical Principles by Rabbi Michael Avraham. Translated from Hebrew using gpt-5.4 (reasoning_effort=high, batch API).

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With God’s help

Midah Tovah — Eve of the Sabbath, Parashat Noah, 5765

A. Three Types of Kal Va-Homer (A Fortiori Argument)

“In his generations. Rabbi Yohanan said: In his generations—but not in other generations. Resh Lakish said: In his generations—and all the more so in other generations. Rabbi Hanina said: To what may Rabbi Yohanan’s view be compared? To a barrel of wine that was placed in a cellar of vinegar. In its place its fragrance spreads; out of its place, its fragrance does not spread. Rabbi Hoshaya said: To what may Resh Lakish’s view be compared? To a vial of perfume that was placed in a filthy place. In its place its fragrance spreads, and all the more so in a perfumed place.”

— Babylonian Talmud, Sanhedrin 108a

“In this generation. Rabbi Yohanan said: In this generation, but not in the generation of Abraham, Isaac, and Jacob. Rabbi Shimon¹ says: If in a generation that was entirely wicked he was found righteous, then had he been in a generation that was entirely righteous, all the more so.”

— Midrash Ha-Gadol, Parashat Noah

“These are the generations [of Noah; Noah was a righteous man, blameless in his generations]. What does in his generations mean? Some expound it favorably, and some expound it unfavorably. Righteous in his generations—but not in other generations. To what may this be compared? If a person places one silver coin among a hundred copper coins, the silver one appears beautiful; so Noah appeared righteous in the generation of the Flood. Some expound him favorably. How so? Like a young woman who lived in a marketplace of prostitutes and remained chaste: had she been in a marketplace of chaste women, all the more so. Or like a jar of balsam that was placed in a grave and yet gave off a good fragrance: had it been in a house, all the more so.”

— Midrash Tanhuma (Buber), Parashat Noah, sec. 6

The Dispute between Rabbi Yohanan and Resh Lakish

These passages in the midrashim (rabbinic homiletic interpretations) are well known, and in the last of the above formulations they also appear in Rashi at the opening of the portion. The dispute between Rabbi Yohanan and Resh Lakish may revolve around the question whether one should evaluate a person for what he is, or for what he could have been. Rabbi Yohanan examines the matter in light of what Noah could have been: if in a wicked generation he managed to be righteous, then clearly in a righteous generation he would fare even better. Resh Lakish, by contrast, examines Noah’s current condition: this condition counts as righteousness relative to the present generation, but in a righteous generation such a state would not be considered a great virtue.

Of course, one can suggest other interpretations of the dispute as well. For example, it may be that Resh Lakish is arguing not only that Noah’s current state would not count as a virtue in a more righteous world, but also that Noah himself would be unable to rise to a higher level even in a more righteous world. Understanding the dispute is certainly relevant to the way we evaluate people and actions performed against a given background, and to our ability to predict what people would do under different circumstances. This has implications as well for giving others the benefit of the doubt, and more. The different parables offered in these midrashim also call for analysis. Here, however, we will focus mainly on the logical aspect of the arguments.

Does Rabbi Yohanan Use a Kal Va-Homer?

At first glance, Rabbi Yohanan’s reasoning about Noah is a kind of kal va-homer: if in a wicked generation Noah succeeded in being righteous, then all the more so in a righteous generation he would have been righteous. Resh Lakish’s reasoning, by contrast, can be interpreted in several ways. Under the first interpretation we suggested above, Resh Lakish’s view can be understood as independent of Rabbi Yohanan’s, so that both are correct: one may read the verse unfavorably in one respect and favorably in another. Under the second interpretation, Resh Lakish’s claim may sound like a refutation of Rabbi Yohanan’s kal va-homer, or as a rationale for the opposite position. Any refutation of a kal va-homer is, after all, a possible argument for the opposing view.

Whether this is a refutation or merely a counterargument depends on whether Resh Lakish is convinced by his own claim, or only raising it as a possibility. It seems that if we understand it as a refutation, we in fact return to the view that both sides are right: there is reasoning in both directions, and therefore the verse can be expounded both unfavorably and favorably.

The Ordinary Three-Premise Kal Va-Homer

What is the character of Rabbi Yohanan’s kal va-homer? It is not the ordinary kal va-homer found in the Talmud, for the ordinary kal va-homer, which is one of the thirteen hermeneutical principles through which the Torah is interpreted—Rabbi Hayyim Hirschensohn, in his Birurei Ha-Middot, calls it a “hermeneutical” kal va-homer²—contains three premises, and from them derives a fourth law. Here, by contrast, there is only one premise, namely that Noah was righteous in his generations, and from it we infer the conclusion that in Abraham’s generation Noah certainly would have been righteous.

To sharpen the point, let us present an example of a “hermeneutical” kal va-homer. In the Mishnah in Babylonian Talmud, Bava Kamma 24a, liability for damage caused by horn—an ox that causes damage with its horn, that is, in an aggressive manner—is derived, in the case of the injured party’s courtyard, from the liability for damage caused by tooth and foot. In this argument there are three legal premises; for simplicity we shall ignore the amount of payment. Damage caused by horn in the public domain entails payment. Damage caused by tooth and foot in the public domain is exempt. Damage caused by tooth and foot in the injured party’s courtyard entails payment. From these premises we infer by kal va-homer the conclusion that damage caused by horn in the injured party’s courtyard entails payment.

As the Mishnah indicates, this can be done in two different ways:

1. If damage caused by tooth and foot, which is exempt in the public domain, is liable in the injured party’s courtyard, then damage caused by horn, which is liable in the public domain, is certainly liable in the injured party’s courtyard.
2. If in the public domain, where damage caused by tooth and foot is exempt, damage caused by horn is liable, then in the injured party’s courtyard, where damage caused by tooth and foot is liable, damage caused by horn is certainly liable there as well.

In both forms we need all three premises in order to derive the conclusion. Yet these are two different lines of reasoning. In the first, we rely on the assumption that horn is more severe than tooth and foot. In the second, we rely on a different assumption: that the injured party’s courtyard is more severe than the public domain.³

The Kal Va-Homer of the “Two Hundred Includes One Hundred” Type

At first sight, Rabbi Yohanan’s kal va-homer seems to be what the authors of the rules call a kal va-homer of the “if two hundred is included, one hundred is certainly included” type.⁴ For example, we learn that it is forbidden for a person to have sexual relations with his sister who is both his father’s daughter and his mother’s daughter, by kal va-homer from the prohibition against his sister who is his father’s daughter or his mother’s daughter. The kal va-homer here is based on the fact that a sister who is both his father’s daughter and his mother’s daughter is, in particular, also his father’s daughter. Therefore every rule that applies to his father’s daughter certainly applies also to one who is both his father’s and his mother’s daughter. Whereas in a “hermeneutical” kal va-homer we assume that the derived case is more severe than the source case, here the basic assumption is not that the derived case is more severe, but that it is actually included within the source case. Put differently: one who has relations with his sister by both father and mother thereby violates the prohibition of relations with his father’s daughter. By contrast, the liability to pay for horn damage in the injured party’s courtyard is not generated by the liability for tooth and foot there, nor by the liability for horn in the public domain. It is a new liability, whose existence we prove from the liability of tooth and foot by means of kal va-homer.

Thus, the ordinary kal va-homer is based on a non-necessary, “hermeneutical” logic, whereas the kal va-homer of the “two hundred includes one hundred” type is one whose logic is necessary. The logical kal va-homer rests on one premise, not on three as the “hermeneutical” one does, and the conclusion is already contained within that one premise. Clearly, such a logical kal va-homer cannot be refuted, since no argument can show that someone who is his father’s and mother’s daughter is not also his father’s daughter. The “hermeneutical” kal va-homer, by contrast, rests on three premises, and the conclusion is not contained in any one of them, nor even in all of them together. It is learned from them through a non-necessary, non-analytic consideration. Therefore, refutations are possible against a “hermeneutical” kal va-homer.

Rabbi Yohanan’s Kal Va-Homer: A Third Type

At first glance, it seems natural to say that Rabbi Yohanan’s kal va-homer is logical rather than “hermeneutical.” It too assumes only one premise, and its conclusion seems to be contained within it. But the picture is not so simple. As we have seen, the logical kal va-homer cannot be subject to any refutation. A refutation shows that the derived case is not necessarily more severe than the source case. Yet, as we have already noted, in the logical kal va-homer that is not the assumption on which the argument rests. The argument that one’s sister by both father and mother is in fact also one’s sister by father is analytic, and therefore necessary; see below in Part B. No refutations can arise against it.

By contrast, Rabbi Yohanan’s kal va-homer can certainly be refuted. As we saw above, Resh Lakish’s own reasoning can be understood as a refutation of Rabbi Yohanan’s kal va-homer. Even if that was not Resh Lakish’s intention, such an argument is, in principle, a possible refutation of the kal va-homer. If so, Rabbi Yohanan’s kal va-homer cannot be of the “two hundred includes one hundred” type, since it is open to refutation. In fact, a careful look at Rabbi Yohanan’s reasoning immediately shows that it is not of that type. Righteousness in a more righteous generation is not actually included in righteousness in a wicked generation. This is merely a consideration of greater and lesser difficulty, not genuine inclusion.

On the other hand, Rabbi Yohanan’s kal va-homer is apparently not an ordinary “hermeneutical” kal va-homer either, since it rests on only one premise. The conclusion, then, is that this is probably a third type of kal va-homer: one that is based on a single premise, but is not analytic and is nevertheless open to refutation.

Kal Va-Homer as Part of the System of Hermeneutical Interpretation

A troubling problem raised by the various types of kal va-homer is this: why is kal va-homer included in the system of hermeneutical principles at all? At first sight, it is simply a straightforward logical consideration of the sort every person uses in different contexts. It is not specifically tied to Torah interpretation, and there seems to be no need for God to grant us permission to use it, or to reveal to us the secret of how to use it.

Moreover, Rabbi Yohanan’s very formulation does not look like the use of a formal hermeneutical rule. The expression “some expound it favorably” does not necessarily mean scriptural exegesis in the technical sense. It means an interpretive or evaluative argument. Likewise, the disagreement between Rabbi Yohanan and Resh Lakish—if there is indeed a disagreement here; see above—does not look like a debate about methods of interpretation, but rather a rational-moral dispute of the sort that can take place between any two human beings on any subject. Rabbi Yohanan’s reasoning is not analytic, but it is certainly a form of ordinary human reasoning.

One might have suggested that only the ordinary “hermeneutical” kal va-homer belongs to the system of hermeneutical principles. Although it is also quite clearly a kind of reasoning that can be used in many contexts, there are some rabbinic examples of this type of kal va-homer that really do look like purely formal procedures. It therefore makes sense to require divine authorization before applying it to the Torah. For example, in the realm of punishment we have no license to apply it, and the halakha (Jewish law) is that punishment may not be imposed on the basis of inference.⁵

Yet even this solution is not simple. In many rabbinic sources, considerations of these other types are also called kal va-homer. The example of kal va-homer brought in Rabbi Ishmael’s baraita of the hermeneutical principles, at the opening of Torat Kohanim, is itself of this kind: “If her father had but spat in her face.” Nearly all the kal va-homer arguments in the Bible are of these two types.⁶ A particularly striking example appears in the sugya in Babylonian Talmud, Bava Kamma 24a, where the rule that what is derived by inference may be no more stringent than its source—a rule belonging to kal va-homer—is discussed, and it is applied there to these types as well. Indeed, it is derived from a case of that sort.

B. The Vacuity of the Analytic

Deduction, Induction, and Analogy

The questions we encountered in Part A are connected to the logical classification of the different kinds of kal va-homer reasoning. In logic one distinguishes among three main kinds of inference: deduction, induction, and analogy.

Deduction is an inference from the general to the particular, and it is the central concern of logic. For example:

Premise A (the general, or major, premise): All windows are transparent.

Premise B (the particular, or minor, premise): Object X is a window.

Conclusion: Object X is transparent.

Induction is an inference of generalization, from the particular—or from several particulars—to the general:

Premise A: Window Y is transparent.

Premise B: Window X is also transparent.

Conclusion: All windows are transparent.

Analogy is a parallel inference from one particular—or general case—to another particular—or general case:

Premise A: Window Y is transparent.

Premise B: Object X is also a window.

Conclusion: Object X is transparent.

The first inference is necessary, that is, its conclusion follows necessarily from the premises on which it rests. Of course, the premises themselves need not be true, and neither need the conclusion. The necessity concerns only the way the conclusion follows from the premises. The other two kinds of inference are of a different character.⁷ In both of them, the conclusion does not follow necessarily from the premises, yet it would be hard to say that its derivation is arbitrary. The conclusion follows from the premises with some degree of probability, varying from case to case, but not with necessity.

The Necessity of Deduction Derives from Its Vacuity

From what does the necessity of deductive inference arise? In such an inference, the conclusion is already contained in the premises from the outset. If we know that all windows are transparent, then the particular window under discussion is transparent as well. This sort of reasoning presupposes what it seeks to prove, and therefore anyone who accepts the premises is committed to accepting the conclusion contained within them.

In Kantian terms, deductive inference is an analytic consideration. Nothing beyond what is already contained in the premises is needed.⁸ By contrast, in the other two forms of inference the conclusion is not contained in the premises, and therefore they are not necessary. Induction and analogy are ways of expanding our knowledge beyond what was known at the outset of the discussion. Deduction, by contrast, is concerned with analyzing existing knowledge, not with expanding it.

Let us conclude this brief survey with John Stuart Mill’s critique of deduction. Mill argues that deduction is valueless, because in order to derive the conclusion we must assume at least one general premise. But how do we know that this general premise—such as “all windows are transparent” in the previous example—is correct? Apparently it must itself be the result of induction, that is, a generalization based on the windows we have seen. If so, the warrant for the conclusion of a deductive argument cannot be stronger than the warrant of the induction on which it rests.⁹

The Character of Kal Va-Homer Arguments

Some interpreters of the hermeneutical principles commonly assume that kal va-homer, unlike the other principles, is a necessary inference—that is, a deductive one. What this means is that the conclusion of a kal va-homer follows necessarily from its premises, and indeed, as we have seen, is contained within them.

But this is a mistake. First, the very fact that a kal va-homer can be refuted proves that it is not a necessary inference. Clearly there is a component in kal va-homer that is not analytic-deductive. And indeed, if we examine the reasoning carefully, we can immediately locate it. For that purpose, let us return to the example presented above in Part A, where we learned by kal va-homer the law of horn damage in the injured party’s courtyard.

The “Hermeneutical” Kal Va-Homer as a Two-Stage Process Based on Generalization

We saw there that in this “hermeneutical” kal va-homer there were three premises: damage caused by tooth and foot in the public domain is exempt; damage caused by horn in the public domain is liable; and damage caused by tooth and foot in the injured party’s courtyard is liable. From these premises, in either of the two forms we presented, one can reach the conclusion through a two-stage process. In stage A, one infers an intermediate general conclusion by generalizing from two of the premises. In stage B, one uses the remaining premise together with that intermediate generalization in order to reach the conclusion.

Let us demonstrate this through the first form of the kal va-homer in the example above; see Part A. The first form uses the two premises concerning the public domain—horn is liable, whereas tooth and foot are exempt—to infer the intermediate conclusion that horn is more severe than tooth and foot. Once this intermediate conclusion has been drawn, one uses the third premise, which was not used in the generalization, namely that tooth and foot in the injured party’s courtyard are liable, together with that general conclusion. The argument from these two premises is indeed a simple deduction, constructed as follows:

Premise A (general): Horn is more severe than tooth and foot. This is the intermediate conclusion.

Premise B (particular): Tooth and foot in the injured party’s courtyard are liable. This is the third premise.

Conclusion: Horn in the injured party’s courtyard is liable.

The conclusion follows necessarily from the premises, and therefore this stage is indeed deductive, moving from the general to the particular.¹⁰

But, as stated, this stage in the kal va-homer is stage B. Before it, a stage of generalization is required—stage A. What kind of inference is such a generalizing inference? It is induction. From a comparison between horn and tooth and foot with respect to one particular law, namely their law in the public domain, we infer that in every respect horn is more severe than tooth and foot. Such a generalization is possible, but by no means necessary. It is not arbitrary, as we noted above regarding all induction, but the intermediate conclusion is not swallowed up in the two premises from which it was inferred. It is an ampliative argument, and therefore not a necessary one.

Here we can see Mill’s critique of deduction very clearly. We have seen how the deduction that constitutes stage B of the kal va-homer rests on a general premise, but that general premise is itself the result of an inductive generalization. If so, one may perhaps formally describe kal va-homer as a deductive argument, but, as Mill already established, it is not a necessary argument. Since it contains a hidden element of generalization, the kal va-homer is not a necessary form of reasoning. The generalization is what determines the logical force of the entire argument; the strength of a chain is only as great as the strength of its weakest link. The failure to notice this stage stems from the fact that in the formulation of kal va-homer it is difficult to detect the stage of generalization, since it is not stated explicitly.

The main implication of the existence of such a hidden stage concerns the understanding of refutations, where they exist. In cases where a refutation is raised against a kal va-homer, it always attacks the background generalization, and never the deductive component of the reasoning, namely stage B. As stated, deduction is a necessary form of inference and therefore cannot be refuted.

We may illustrate this by means of a theoretical refutation in the example above: What comparison is there to horn, which, where it is liable, pays only half damages? Would you say the same of tooth and foot, which pay full damages? Such a refutation attacks the generalization that horn is always more severe than tooth and foot, that is, the intermediate conclusion. It obviously does not touch any of the legal premises of the kal va-homer, nor the final deduction of stage B.

The Character of the Other Two Types of Kal Va-Homer

We can now examine the other two types of kal va-homer. The “two hundred includes one hundred” type is composed of one premise, from which a conclusion is inferred. As we have already seen, this is a clear case of an inference in which the conclusion is explicitly embedded in the premise; that is the meaning of the expression itself. Thus, such a kal va-homer is an analytic argument, that is, a necessary deduction.

By contrast, the third type of kal va-homer is indeed based on one premise, but its conclusion is not contained in that premise. That is also why we saw that it can be refuted.¹¹ In what, then, does it differ from the “hermeneutical” kal va-homer? It seems that the difference lies in stage A of the inference. In the “hermeneutical” kal va-homer, stage A is an inductive generalization based on two of the premises. In this third type, however, the nature of stage A is different. It is not a generalization from two premises, since we do not have two additional premises from which to proceed. The “intermediate conclusion” is not the result of an inferential process at all, but an independent piece of reasoning, sometimes genuinely a priori.

We can see this in Rabbi Yohanan’s kal va-homer, discussed in Part A. The inference there was this: if Noah is righteous in a wicked generation, then all the more so he will be righteous in a righteous generation. There is one premise here: Noah is righteous in a wicked generation. The major premise of the deduction—the only explicit inferential step here—is this: righteousness in a righteous generation is more plausible, or easier to attain, than righteousness in a wicked generation. This is an independent rational intuition, not a conclusion derived from data.

Of course, it does not follow that this claim is necessary. Counterconsiderations may be raised that refute it. For example, as we saw, Resh Lakish’s argument, according to one of the interpretations, says that Noah’s capacities might not have sufficed for him to reach the level of “righteous” even in a righteous generation, since there more would be demanded of him in order to count as such. This is a counterconsideration that undermines the force of Rabbi Yohanan’s reasoning, and therefore the force of the entire kal va-homer.

Summary and Conclusions

Our conclusion from combining the two parts of the discussion is this: an ordinary “hermeneutical” kal va-homer is built on a general premise that arises from generalization. A kal va-homer of the third type is built on a general premise that arises from independent reasoning. In both types there is logic, but they are not necessary inferences, and therefore they are open to refutation. In both cases, the refutation always targets the general premise. By contrast, the “two hundred includes one hundred” type is a necessary deductive inference, and therefore it is a kal va-homer that cannot be refuted at all.

An ordinary “hermeneutical” kal va-homer probably does belong to the system of hermeneutical principles. By contrast, it is reasonable to think that the “two hundred includes one hundred” type is not part of that system, since it is hard to suppose that one needs permission or revelation from Sinai in order to make a deductive inference. The third type likewise appears to be an ordinary interpretive consideration, of the sort we use in various contexts, and it is plausible that here too no authorization from on high is needed. The fact that it is nevertheless treated as part of the system of principles indicates that the entire principle of kal va-homer is exceptional. There is no special inference here that was introduced at Sinai. Rather, what we have is an ordinary human form of thought, shaped and bounded by certain restrictions—such as the rule that punishments are not derived from it, the rule that what is derived by inference may not be more stringent than its source, and the like. We will return to this point, God willing, in the coming weeks.

Footnotes