Emor (5765)

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 of the portion Emor, 5766.

Questions

1. Does there exist a qal va-homer (a fortiori inference) of the type “two hundred necessarily contains one hundred”?
2. Can such an inference be refuted?
3. What is the difference between it and a reasoning-based qal va-homer?
4. On “blended composition” and “neighboring composition.”
5. Is the distinction between these kinds of composition made at the conceptual-logical level or at the normative level?
6. What does this have to do with Hume’s naturalistic fallacy?
7. What does “and they shall become one flesh” mean? Are man and woman one entity?

The Hermeneutical Principle

Qal va-homer.

He shall take a wife in her virginity. A widow, a divorced woman, a profaned woman, or a harlot—these he shall not take; rather, he shall take as a wife a virgin from his people. He shall not profane his offspring among his people, for I the Lord sanctify him.

— Leviticus 21:13-15

It was taught in a baraita: Scripture need not have stated the prohibition of a divorced woman with respect to the High Priest, for it could have been derived by a qal va-homer from the ordinary priest. For I would have said: if she is forbidden to an ordinary priest, is it even necessary to say that she is forbidden to a High Priest? Why then was it stated? Just as a divorced woman is distinguished from a harlot and a profaned woman with respect to an ordinary priest, so too she is distinguished with respect to a High Priest. Is that not obvious—should her status be made any less stringent? Rather, the point is this: just as a divorced woman is distinguished from a harlot and a profaned woman with respect to an ordinary priest, so too a widow is distinguished from a divorced woman, a profaned woman, and a harlot with respect to a High Priest. Why was “profaned woman” stated? Because there is no category of profaned woman except through a priestly prohibition. Why was “harlot” stated? “Harlot” is stated here, and “harlot” is stated elsewhere; just as here his offspring are rendered profane, so too there his offspring are rendered profane. Rav Ashi said: therefore, if a priest has relations with his sister, he renders her a harlot, but he does not render her a profaned woman; if he returns and has relations with her again, he thereby makes her a profaned woman.

— Babylonian Talmud, Kiddushin 77b

A. Summary of Last Year’s Article

Last year’s article was divided into three parts. The first dealt with the qal va-homer that appears in the Talmudic passage above, comparing the ordinary priest and the High Priest. In such a qal va-homer, one derives a prohibition—harlot, profaned woman, or divorced woman—that applies to the High Priest from the fact that the same prohibition applies to the ordinary priest. We saw there that this qal va-homer can be understood in two ways:

1. As a qal va-homer based on the reasoning that the High Priest is certainly more stringent than the ordinary priest.
2. As a qal va-homer of the “two-hundred-contains-one-hundred” type, which views the High Priest as composed of two layers: ordinary priest plus additional elements.

These two types of qal va-homer differ in the relation between the concepts involved. In the second type, we assume that the source concept is literally included, conceptually, within the target concept. In the first type, by contrast, the source is not included within the target; it is merely lighter than it—what we called an “external relation” between the concepts.

We pointed there to two differences between these two kinds of qal va-homer:

1. Degree of validity. The first qal va-homer is less solid, because it can be refuted by showing some halakha (Jewish law) that applies to the ordinary priest but not to the High Priest. The second, by contrast, is necessarily valid: one cannot refute the conclusion that whatever applies to the ordinary priest must also apply to the High Priest, who includes within himself an ordinary-priest dimension. Within two hundred, there is always one hundred.
2. Degree of novelty and amplification. On the other hand, there is also an inverse relation between the two. The first qal va-homer leads to the conclusion that the law in the target case should be more stringent than in the source case, and therefore it leads to what we there called amplification—an intensification of the source law when it is applied to the target case. The second qal va-homer, by contrast, leads to the conclusion that the two are equal, and therefore leaves no room for amplification. The reason is that, according to this second model, the law in the High Priest derives from the ordinary-priest component within him, and therefore it will be exactly equal to the law governing the ordinary priest.

We also briefly discussed how the Talmud can suggest that it would have been enough to state these prohibitions with respect to the ordinary priest and derive them by qal va-homer for the High Priest, when the rule is that punishments are not derived by inference. Had these laws not been stated explicitly regarding the High Priest, we could not have punished him for these transgressions.

To understand this, we cited the two standard explanations of why punishments are not derived by inference. Either: there may perhaps be a refutation of the qal va-homer; or: the punishment appropriate for the lighter offense may not suffice to atone for the graver offense. According to both explanations, it is clear that in a qal va-homer of the “two-hundred-contains-one-hundred” type one could, in principle, derive punishment by inference. In such a qal va-homer there is no concern about refutation. And the punishment must be relevant, since the lighter offense has in fact also been committed. When a High Priest has relations with a harlot, there is in actuality also an ordinary priest who has had relations with her. In this way we explained the Talmud’s suggestion that the laws of the High Priest could be learned by qal va-homer from the ordinary priest. If the derivation were of this type, one could also punish the High Priest. We shall elaborate and qualify this in this week’s article.

In the second part of last year’s article, we saw that these two characteristics are connected through what we there called “the principle of logical uncertainty”: a more far-reaching inference leads to more innovative conclusions, and is therefore less certain; by contrast, an inference that innovates less will generally be safer, that is, more valid. This relation resembles the familiar connection in economics between risk and return. We connected this with what philosophy calls “the vacuity of the analytic,” a topic we also discussed in the page for the portion Vayakhel, 5765.

In the third part of the article we discussed a case—later shown to have been a media hoax—in which the wife of a priest who had been raped was said to have been required to divorce her husband. We noted that such a case expresses a clash between opposing values: preserving the purity of the priesthood versus preserving the home and avoiding harm to people. Contrary to a widespread intuitive reaction, the obligation to divorce in such a case does not indicate contempt for the value of preserving the home and avoiding harm to the spouses—as some accused halakha of doing in that controversy—but rather the force that the Torah gives to the value of preserving priestly purity. From this we commented on the relation between emotion and intellect, and on the dominance of emotion in contemporary culture, due to postmodern despair of reason, which is what produced this misunderstanding.

B. Refutations of an Analytic Qal Va-Homer

Introduction

In last year’s article we assumed that a qal va-homer of the “two-hundred-contains-one-hundred” type cannot possibly be refuted. The reason was that this is a necessary logical argument, and, like any deduction, cannot be refuted. In this week’s article we shall try to show that the picture is not so simple. In fact, such a claim falls into Hume’s naturalistic fallacy—the is-ought fallacy.

The Example of the Vandervelde Law

In the page for the portion Acharei Mot, we gave an example from Belgian law of a refutation of a qal va-homer of the “two-hundred-contains-one-hundred” type. Belgian law contains the Vandervelde law, which permits the sale of alcoholic beverages only in quantities of two liters or more. At first glance, one could derive by qal va-homer that selling one liter should also be permitted. Strictly speaking, this is the reverse form of an a fortiori argument: if there is a leniency in the more serious case—selling two liters—then it certainly applies in the less serious case—selling one liter.

It should be noted that this is a qal va-homer of the “two-hundred-contains-one-hundred” type, since selling two liters is, among other things, also the sale of one liter. Therefore, it would seem impossible to challenge this valid logical consideration. From the opposite direction, one can prove this by contradiction, through an ordinary qal va-homer rather than the reverse form: if selling one liter of wine were forbidden, then selling two liters would certainly also be forbidden, since every sale of two liters is also a sale of one liter.

Yet, surprisingly, in practice this argument is not correct. Under Belgian law, it is forbidden to sell one liter of wine; only two liters and above may be sold. Thus both the reverse a fortiori argument and the ordinary qal va-homer fail in this case.

The reason lies in the purpose of the law. We discussed there the purposive interpretation of laws, what in halakhic jargon is called ta’ama de-kra—the reason or purpose of the text. The aim of the law was to prevent laborers from squandering their monthly wages on alcoholic drink. The law therefore did not permit sales below a quantity large enough to consume a significant portion of a monthly wage, on the assumption that in such a case the number of buyers would fall significantly. In light of that picture, it is understandable that selling one liter would remain prohibited. At first glance, then, we have here a refutation of a qal va-homer of the “two-hundred-contains-one-hundred” type: every two liters include one liter, and yet one liter is forbidden while two liters are permitted.

Explanation: Ta’ama De-Kra

Can one really refute a qal va-homer of the “two-hundred-contains-one-hundred” type? At first glance, this is an analytic and necessary consideration. In the article just mentioned, we explained this by saying that the refutation is based on purposive rather than literal interpretation. In truth, the wording of the law itself could not have been interpreted in such a way, because the inclusion consideration is analytic and necessary. But purposive interpretation effectively adds further dimensions of rationale to the law, and these dimensions do not necessarily preserve the hierarchy of leniency and stringency that appears in the law’s wording.

We added there that in halakha, purposive interpretation is generally not possible, since we do not usually derive law from the reason of the verse. One might therefore expect that a halakhic qal va-homer of the “two-hundred-contains-one-hundred” type can never be refuted. We shall now see, through several examples, that this picture is not exact, and we shall eventually try to explain and clarify why.

A Halakhic Example: Digging and Opening

In the page for the portion Acharei Mot, 5765, we cited the words of the Maharsha, in Mahadura Batra on Babylonian Talmud, Bava Kamma 49b (see also Ginat Veradim, no. 1), who writes that the Babylonian Talmud holds that in a qal va-homer of the “two-hundred-contains-one-hundred” type, liability is derived by inference—unlike the Mekhilta, a halakhic midrash (rabbinic legal exposition), cited in Tosafot, s.v. “ve-lo zeh ve-zeh,” Babylonian Talmud, Bava Kamma 2a. His example is the qal va-homer regarding a pit in the public domain: “If one is liable for opening, is one not all the more liable for digging?” If removing the cover from an existing pit creates monetary liability, then one who dug the pit certainly bears liability.

According to the Maharsha, the question that follows is: why, according to the Mekhilta, is liability not derived even in such a case? The Maharsha assumes that the rule that punishments are not derived by inference is based on the concern that perhaps there is a refutation. If so, according to the Mekhilta there is concern about a refutation even in a qal va-homer of the “two-hundred-contains-one-hundred” type. How can that be?

Two Halakhic Examples: Conspiring Witnesses and Passing One’s Offspring to Molekh

Halakha rules that conspiring witnesses are punished with the very punishment they sought to impose on the accused: “And you shall do to him as he schemed to do to his brother.” The Talmud determines that this rule applies only when the sentence has not yet been carried out. But once the court has already carried out the sentence, the witnesses are not punished; see Maimonides, Mishneh Torah, Laws of Testimony 20:2.¹

The Kesef Mishneh there connects this to another example in which one sees a similar phenomenon. The Talmud, Babylonian Talmud, Sanhedrin 64b, expounds concerning one who passes his offspring to Molekh that he is liable only if he passes some of his offspring, but not if he passes all of his offspring, in which case he is exempt: “From your offspring”—and not all of your offspring.

In both cases, says the Kesef Mishneh, the lighter case is punished while the more severe case is not. To sharpen the problem, we should note that in both cases we are dealing with a qal va-homer of the “two-hundred-contains-one-hundred” type. Passing all of one’s offspring to Molekh literally includes passing some of them to Molekh, not merely something more severe than that. Likewise, conspiring witnesses whose intended sentence was actually carried out have committed the same act of conspiracy that exists when the sentence has merely been issued but not yet executed.

The Kesef Mishneh explains the two cases in a similar manner:

It is possible to give a reason for our master’s words: we say “as he schemed,” and not “as he did,” only when they caused death by their testimony, because their punishment is too great to bear. It is therefore not fitting to give them a court-imposed death that would atone for them; rather, it is fitting to leave them so that after death they will be judged with terrifying punishments. An analogous case is one who gives all his offspring to Molekh, who is exempt. This cannot be said when lashes were administered on the basis of their testimony.

The Kesef Mishneh explains that the reason punishments are not imposed in these two cases is the concern that the more severe act may require a more severe punishment for atonement, and the punishment assigned to the lighter act may not suffice.

Usually, the Kesef Mishneh here is understood as offering an explanation of the rule that punishments are not derived by inference, one that differs from the Maharsha’s explanation mentioned above; see Encyclopedia Talmudit, entry “Ein Onshin Min Ha-Din,” and the sources cited there. But according to our approach, it is entirely possible that precisely because these two examples are of the “two-hundred-contains-one-hundred” type, the rule cannot be explained by concern for a possible refutation, since an analytic-deductive qal va-homer cannot, on the face of it, be refuted. Therefore the Kesef Mishneh proposes another explanation. But in cases of other types of qal va-homer, it is possible that he would agree with the Maharsha that punishments are not imposed because perhaps there is a refutation.

And Yet: A Refutation of an Analytic Qal Va-Homer

In any event, once we accept the Kesef Mishneh‘s explanation, it follows that these two are precisely cases of refutations of a qal va-homer of the “two-hundred-contains-one-hundred” type. What the Kesef Mishneh has explained is that one cannot, in fact, derive the target case from the source case, even though the source is included within it. It follows that this apparently analytic-deductive consideration is not correct. That is exactly the situation of a refutation. One can see this in the following argument: if we wish to derive some other law from the source case to the target case, using a qal va-homer of the “two-hundred-contains-one-hundred” type, we can refute it by saying: the target case is different, for no punishment is imposed there.

This is similar to what we saw in the Vandervelde law. There too we have a qal va-homer of the “two-hundred-contains-one-hundred” type, and yet it can be refuted, so that we cannot derive the target case from the source case. Thus such situations exist in halakha as well.

It should be noted that in these two halakhic examples, unlike the Vandervelde law, even after the “refutation” the hierarchy between the lighter and the more severe cases remains in place. In the Vandervelde law, once purposive interpretation is taken into account, selling two liters becomes lighter than selling one liter. In the halakhic examples, by contrast, the situation is different: passing all of one’s offspring is more severe than passing some and includes it, and false testimony that was actually carried out is more severe than testimony that did not yet lead to execution and includes it. And nevertheless, one still cannot infer the punishment from the lighter case to the more severe one, even though in these cases the lighter case is literally contained in the more severe one.

Sharpening the Difficulty: Is the Analytic Not Necessary?

How can one really refute a logical-analytic claim? A logical inference seems necessary and not open to refutation. Would anyone imagine that the following argument could be refuted?

1. Major premise: All human beings are mortal.
2. Minor premise: Socrates is a human being.
3. Conclusion: Socrates is mortal.

Clearly no refutation can be made against this argument, since it is logically necessary. Its logical necessity stems from the fact that the conclusion is literally contained in the premises, in the manner of “two hundred contains one hundred.” If all human beings are mortal, then Socrates, who is also a human being, is certainly mortal as well. In other words, the fact that there is a relation of “two hundred contains one hundred” is itself the reason for the necessity of this inference.

If so, how is the argument discussed above different from this logical syllogism? At first glance both are logically necessary. In both, the conclusion is logically included in the premises. What, then, distinguishes the Vandervelde case from this one?

We must also understand, in retrospect, what exactly was refuted here. As mentioned, the hierarchy of leniency and stringency remains in place even after the refutation. What other assumption of the qal va-homer could have been refuted? In the page for the portion Noach, 5765, we noted that only the generalization underlying a qal va-homer can be refuted, and no other component. Here, however, the “generalization”—which in this case does not arise from induction but from analytic reasoning—has not been refuted, as one would expect; analytic reasoning is not refutable. So what, then, has been refuted? What else is assumed in a qal va-homer of the “two-hundred-contains-one-hundred” type beyond the relation of leniency and stringency between the target and source cases?

A Preliminary Explanation: Back to the Ordinary Priest and the High Priest

The example from which we began was a qal va-homer that derives laws of the High Priest from the ordinary priest. At least according to some commentators, the assumption is that the ordinary priest is conceptually included within the High Priest. Can such a qal va-homer be refuted?

Quite clearly, yes. Theoretically, one can refute the very assumption that the relation between the High Priest and the ordinary priest is truly a relation of inclusion. Granted that if this is indeed the relation, the qal va-homer cannot be refuted. But if we find even one example of a stricter halakha that applies to the ordinary priest and does not apply to the High Priest, then we have refuted the inclusion assumption itself. The conclusion will be that the relation between them is what we earlier called an “external relation” rather than a relation of inclusion, and therefore there is no relation of “two hundred contains one hundred” between target and source here.

The conclusion, then, is that although one cannot refute a genuine qal va-homer of the “two-hundred-contains-one-hundred” type, one can refute the assumption that a given qal va-homer is indeed of that type.

This determination seems correct in relation to the ordinary priest and the High Priest. The reason is that the relation between them does not stem from the concepts themselves, since from a purely logical-conceptual standpoint the High Priest could be a completely different entity from the ordinary priest, rather than something that contains him. Their relation is halakhic rather than factual. By contrast, digging a pit necessarily includes opening it. Here the relation of inclusion is an analytic result of the conceptual-logical relation, or of the facts themselves, and apparently requires no additional assumption. Digging and opening are physical actions, whereas priesthood is a halakhic status.

If so, one would expect that the qal va-homer from opening to digging could not be refuted. But above we saw that, at least according to the Mekhilta, it can be. The same is true of the Vandervelde law: the relation there is analytic, and yet it can be refuted through purposive interpretation. So too with conspiring witnesses and passing all of one’s offspring to Molekh, as we saw in the Kesef Mishneh.

An Explanation of How the Refutation Works

We therefore arrive at the conclusion that in all these cases there are additional assumptions hidden beneath the surface. In other words: in all these cases it is possible to refute the assumption of inclusion itself, that is, the assumption that we are truly dealing with a qal va-homer of the “two-hundred-contains-one-hundred” type. How is this possible in cases where the relation of inclusion is the result of conceptual analysis—that is, an analytic result?

To understand this, let us look again at the examples we cited. On a deeper and more careful examination, one can see that in the qal va-homer of conspiring witnesses and of passing one’s offspring to Molekh, according to the Kesef Mishneh there is indeed an additional assumption beyond the factual inclusion relation. That assumption may be formulated as follows: punishment is additive. That is, if a person commits two offenses, one assumes that the punishment for them will be composed of the punishment for one plus the punishment for the other.

We can now understand the claim of the Kesef Mishneh: sometimes an act that contains two elements may require a punishment that is not the sum of the punishments but a single, more severe punishment. If passing two children to Molekh incurs death, and passing another two children also incurs death, it is not at all clear that passing four children to Molekh should incur the same death penalty—for there is no such thing as two death penalties.

What we see here are two different levels of discussion. On the factual plane, passing four children to Molekh indeed includes within it the passing of two of them, in the sense of “two hundred contains one hundred.” But the punishment imposed on these acts does not preserve that same relation. The punishment for passing four children to Molekh does not necessarily include the punishment for passing two of them. A different kind of penal liability may have arisen.

Is This Relation Located at the Conceptual Level?

At first sight, one might think that such a situation occurs where an act composed of two elements becomes something qualitatively different. It does indeed contain the source case, but once the unique supplement present in the target case is added, the result becomes something essentially different. Such a state would also require a new punishment, not necessarily the sum of the punishments for each element by itself.

Thus, if a person digs a cavity beneath a cover and afterwards removes the cover, he has performed an ordinary act of digging. That action is composed of opening a cover over an existing cavity, plus the act of creating the cavity beneath the cover. At first glance, such an act should incur the liability assigned to opening, perhaps with some further addition. But in any event it seems clear that the liability for opening ought also to be imposed for digging.

That, indeed, is the view of the Babylonian Talmud. But the Mekhilta maintains that even in such a case there is no necessity to infer that the liability for opening also applies to digging. The reason is that digging is not opening plus something else, but a new and unique act. The element of opening that is included within it is swallowed up in the renewed act of digging. Such an act may require a different liability—apparently a more severe one.

The situation is similar with the Vandervelde law. There too, at first glance, there is a conceptual-logical inclusion relation. But the legal prohibition or permission imposed on these actions always contains a further layer, normative in character. The normative layer determines that there is permission to sell two liters of wine. If so, then at the level of the actions themselves, selling two liters certainly includes the act of selling one liter, in the sense of “two hundred contains one hundred.” But the normative layer imposed on the action is not necessarily additive here either: it is not necessarily correct to infer from the fact that selling two liters is permitted that selling one liter is also permitted. Conversely, if the sale of one liter is forbidden, it does not follow that the sale of two liters is also forbidden.

Purposive interpretation merely exposes the fact that the normative dimension is not additive.²

Challenging the Very Definition of “Two Hundred Contains One Hundred”

As we mentioned, some later authorities define the qal va-homer of the “two-hundred-contains-one-hundred” type as a unique subtype of qal va-homer, and distinguish it from a reasoning-based qal va-homer or from the formal hermeneutical rule of qal va-homer. But the description we have suggested here actually undermines the very definition of a qal va-homer of the “two-hundred-contains-one-hundred” type. For every inclusion relation deals with facts and events that take place in the world. Yet the normative layer imposed on those facts and events can alter that logical structure. It therefore functions as an additional, hidden assumption of the qal va-homer, and that is what makes refutation possible. If so, a qal va-homer of the “two-hundred-contains-one-hundred” type seemingly becomes a reasoning-based qal va-homer, open to refutation.

It seems that only if we can ground some qal va-homer on an a priori conceptual relation can we still preserve the category of a qal va-homer of the “two-hundred-contains-one-hundred” type. In other words—to use the terminology of “blended” and “neighboring” that will be introduced below—if we know with certainty that the composite concept is a neighboring composition rather than a blended composition of its two components, namely the source case and the addition that together generate the target case, then we can still speak of a non-refutable qal va-homer of the “two-hundred-contains-one-hundred” type. In any case, it is quite clear that the certainty of such a qal va-homer is no longer purely logical-analytic, but depends on substantive reasoning.

Implication: Back to the Two Differences Noted Above

The conclusion from this analysis is that even if the conceptual relation is one of “two hundred contains one hundred,” it is still possible to refute the qal va-homer in a way that shows that this is not really the relation between target and source. If so, how can this qal va-homer still be characterized as belonging to the “two-hundred-contains-one-hundred” type?

Here we must return to the two differences between an analytic qal va-homer—namely, one of the “two-hundred-contains-one-hundred” type—and a reasoning-based qal va-homer, which we noted above. The first difference concerned their degree of validity. We saw that the analytic qal va-homer was wholly valid, like a deduction, unlike the reasoning-based qal va-homer. We now see that this is not correct, for it too can be refuted. It too is not logically valid in the strict sense.

The second difference, however, remains intact. In a qal va-homer of the “two-hundred-contains-one-hundred” type, as long as it has not been refuted, the inference is an equalizing inference rather than an amplifying one. We infer from the source case that the halakha applies also to the target case because of the source component present within it. Hence the transfer of the law from source to target takes place by way of equivalence, not amplification.

A possible implication is that even one who does not accept the principle of dayyo—that the conclusion of a qal va-homer may not exceed its premise—will nevertheless agree that one must not amplify the learned law when applying it to the target case. For example, he too would concede that the punishment for one who passes all of his offspring to Molekh is not necessarily more severe than the punishment for passing only some of his offspring.³

The Derivation from “He Has Uncovered the Nakedness of His Sister”

To conclude this chapter, let us recall that the source for the rule that punishments are not derived by inference is the prohibition of relations with one’s sister, whether she is one’s father’s daughter or one’s mother’s daughter:

It was taught in a baraita: “If a man takes his sister, the daughter of his father or the daughter of his mother”—I know only his father’s daughter who is not his mother’s daughter, and his mother’s daughter who is not his father’s daughter. From where do I know his father’s daughter who is also his mother’s daughter? Scripture says: “He has uncovered the nakedness of his sister.” Before Scripture said this, I could have argued as follows: if one is punished for his father’s daughter who is not his mother’s daughter and for his mother’s daughter who is not his father’s daughter, then all the more so for his father’s daughter who is also his mother’s daughter. From here you learn that punishments are not derived by inference.

— Leviticus 20:17

Here too, this is a qal va-homer of the “two-hundred-contains-one-hundred” type, since a sister who is both one’s father’s daughter and one’s mother’s daughter is, in particular, also one’s father’s daughter and also one’s mother’s daughter. Why, then, is an additional explicit prohibition needed? To teach us that punishments are not derived by inference. It would seem to follow from here that even in a qal va-homer of the “two-hundred-contains-one-hundred” type, punishments are not derived by inference.

In the page for the portion Acharei Mot, 5765, we explained this in a way very similar to the proposal offered here. In the terminology used here, a sister who is both one’s father’s daughter and one’s mother’s daughter is not merely the combined sum of one’s paternal sister and one’s maternal sister, but a third and new entity. The relation between her and them is not one of inclusion, but one of greater stringency, since the degree of kinship is greater.

C. External and Internal Relations Between Concepts: The Connection to Hume’s Naturalistic Fallacy

Introduction

In the previous chapter we pointed to three possible relations between the source case and the target case in a qal va-homer:

1. In a reasoning-based qal va-homer, the relation between target and source is one of greater stringency. For example: when her father spits in her face, she must be humiliated for seven days; when the Holy One, blessed be He, spits in her face, that is certainly more severe, and therefore it is conceivable that in such a case she should be humiliated for fourteen days, and certainly for seven days; see Babylonian Talmud, Bava Kamma 25a, and the page for the portion Beha’alotekha, 5765.
2. In a qal va-homer of the “two-hundred-contains-one-hundred” type, the relation between target and source is, on the face of it, one of inclusion. The target contains the source, and is not merely more severe than it.
3. In a qal va-homer that appears to be of the “two-hundred-contains-one-hundred” type but is nevertheless open to refutation—at least according to those views that allow such refutation—we revert from a relation of inclusion to a relation of stringency.

Conceptual Relations

The difference between the latter two types of relation between target and source lies in a conceptual question, that is, in the relation between concepts: does the inclusion of the source concept within the target concept leave the source concept intact and merely add something extra to it, or does it erase its independent identity, so that together with the added element it becomes a new entity—the target case?

In the terminology of the author of Tzafnat Paneach, this may be described as the question whether the composition between the source case and the additional element that together create the target case is a “neighboring composition”—that is, like neighbors standing side by side without affecting one another, a heterogeneous combination, a mere mixture, like two solids; in the terminology of the laws of mixtures, “dry with dry”—or rather a “blended composition”—that is, as though the two elements are poured into one another and form a new entity, a compound, like two liquids; in the terminology of mixtures, “wet with wet.” In that case a new blend is produced by the fusion of both, and the distinctive identity of the source case is erased.

When the identity of the source case is erased, the relation between source and target reverts to one of greater stringency rather than inclusion. There is indeed inclusion here, but one cannot compare target and source by isolating the source component within the target. If so, the target is more severe than the source. It has only an external relation to it, not an internal one.

Again, the Normative Layer

But it seems that these relations are not really located in the concepts themselves. Take the action of digging. One may understand its relation as a “blended composition” in two ways:

1. As a claim about the action itself, that is, about the concept: digging is not opening plus something.
2. As a normative claim, dealing only with the normative plane: conceptually, digging really is opening plus something. But on the normative plane, the norm that imposes tort liability on the digger is not additive. That is, the legal-normative meaning of digging is not the sum of the legal meaning of opening and the legal meaning of the additional element.

The second formulation seems more plausible, because the action itself apparently really does contain the act of opening. And similarly, a sister who is both paternal and maternal is, in particular, also a paternal sister. It is therefore reasonable to say that the “fusion” between the two elements occurs at the normative level rather than at the factual level. With regard to the prohibition of sexual relations, a sister who is both paternal and maternal is something new, not composed of kinship through each side separately. And with regard to tort liability, it is not correct to view digging as opening plus some further element.

Connection to Hume’s Naturalistic Fallacy

In the pages for the portion Bereshit, 5765-5766, we mentioned Hume’s naturalistic fallacy. This fallacy results from ignoring the normative layer and treating reality as though it itself determines the norm. For example, the conclusion that if the sky is blue then it is probably beautiful falls into precisely this error. The claim that the sky is blue is a fact. The claim that it is beautiful is a norm—an aesthetic one, in this case. A norm is never derived from facts. A further hidden assumption has entered here, linking the factual plane to the normative plane—for example: everything blue is beautiful. Only such an assumption can make the argument valid.

The same is true here. Treating the qal va-homer of the “two-hundred-contains-one-hundred” type as analytic and necessary falls into a similar error. It ignores the addition contained in a norm simply by virtue of its being a norm, as compared to bare facts.

A common human tendency is to treat facts as though they already carry value, and to think that values or norms can be derived from bare facts. This cannot be done. One must always seek the additional normative assumption hidden above the facts. That is the normative layer with which we have been dealing here.

Additional Halakhic Examples

We know of several additional halakhic examples of a blended composition of concepts; see the book Shtei Agalot Ve-Kadur Por’each, note 10.⁴ In a substantial number of them it seems clear that the blending occurs at the halakhic level, not at the factual-real level.

An entire range of examples appears in the book Tzafnat Paneach by Rabbi Menachem M. Kasher, which deals with the thought of the Rogatchover, author of Tzafnat Paneach, in chapter 8. There he discusses the concepts of “blended composition” and “neighboring composition,” and brings many examples and halakhic consequences. For example, there:

A mule that comes from a horse and a donkey has neither a horse side nor a donkey side; rather, it becomes an independent creature from both of them.

Precisely in this case, it seems that the blending occurs in reality itself. In the mule it is difficult to identify distinct horse and donkey components; there is resemblance to both parents, but their composition is “blended.” Hence here the blending is probably rooted at the conceptual level rather than at the normative level.⁵ As for twilight, which is a boundary between times, and a boundary between places—which is also regarded as composed of both, like twilight—it is open to discussion whether the blending there is conceptual or normative.

By contrast, with regard to the meal-offering of a suspected adulteress, Tosafot on Babylonian Talmud, Sotah 23a say that husband and wife are not considered partners, since a meal-offering is not brought in partnership. This too is understood by the author of Tzafnat Paneach there, no. 10, as a determination that husband and wife constitute a “blended composition.”

Here it is quite clear that the blending is normative, not factual. Before us stand two different people; only the family unit “melts” them, normatively, into a single entity.

This may perhaps help explain Rashi’s interpretation of the verse “and they shall become one flesh” (Genesis 2:24). At first glance, the meaning would appear to be, as in Tosafot, that they become one flesh only in a normative sense. But Rashi there explains that this exists only because of the children born to them; those children are what make the parents “one flesh.” In other words, Rashi is unwilling to treat this as a normative statement and wants to understand it as a factual one. By contrast, in the Tosafot just mentioned, it seems clear that this status does not depend on children, since the meal-offering of a suspected adulteress is brought even when there are no children. According to Tosafot, they are “one flesh” only at the normative level, not at the factual level.

A Possible Implication

There may be a difference between normative blending and factual blending. If there is factual blending, then the normative consequences must obviously be blended as well. For if act A and act B combine into a new act C, one cannot punish the person who performed C for act B, because he did not perform act B.⁶ The converse is not true: if there is normative blending, that does not mean that the concepts themselves are blended.

If so, when the blending is factual, there is no doubt that this is not a qal va-homer of the “two-hundred-contains-one-hundred” type, but at most an external relation of stringency. By contrast, if the blending is normative, then one may decide that it is not correct. That will probably depend on whether refutations of the qal va-homer are available.

Footnotes