Tetzaveh (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 — Erev Shabbat, Parashat Tetzaveh, 5766

Questions:

1. A fourth role of tzrichuta (showing why both source texts are necessary) in the process of the “common denominator.”
2. Is the common denominator a formal-textual hermeneutical principle, or a substantive, content-based one?
3. A further explanation of the process of the common denominator without tzrichuta.
4. Can the common denominator be built from two gezerah shavah inferences (verbal analogies)?
5. What hermeneutical principle would be created by combining two verbal analogies in this way?
6. Content-based forms of comparison, based on the kind of stringency, and quantitative forms of comparison, based on the degree of stringency.

The principles under discussion:

• binyan av (deriving a general rule from a paradigm) from one verse
• binyan av from two verses
• the common denominator
• verbal analogy
• “two verses that come as one do not teach”

A. Summary of Last Year’s Article

How is binyan av from two verses formulated? The section on the lamps is not like the section on the expulsion of the impure, and the section on the expulsion of the impure is not like the section on the lamps. The common denominator between them is that in both, the term “command” signifies immediate applicability and applicability for all generations. So too, every matter stated with the term “command” applies immediately and for all generations.

— Baraita of Examples, beginning of Sifra

The section on the lamps is not like the section on the expulsion of the impure, and the section on the expulsion of the impure is not like the section on the lamps. Had the section on the expulsion of the impure not been stated, I would have learned it from the section on the lamps. Why then was it taught here? Because many things can be taught from it. The common denominator between them is that in both, the term “command” signifies immediate applicability and applicability for all generations. So too, everything stated with the term “command” applies immediately and for all generations.

— Jerusalem Talmud, Bava Kamma 1:1

In last year’s article we dealt with the hermeneutical principle of the common denominator. We discussed its example in the Baraita of Examples, which is based on verses from our parashah. We noted that the medieval commentators disagree on the question whether binyan av from one verse also operates by way of the common denominator, or whether only binyan av from two verses does so. The logic of this principle was described in the sheet for Parashat Shemot, 5765.¹

The first derivation quoted above is taken from the Baraita of Examples. It lacks the elements of tzrichuta that are necessary for the structure of the common denominator, but the Ra’avad, in his commentary on the baraita, supplies them. In his opinion, then, this is a regular common-denominator derivation, and the problem is only a deficiency in the wording of the baraita.

The second derivation, quoted from the Jerusalem Talmud, seems different. The Jerusalem Talmud states that the section on the expulsion of the impure is not unique, and can be learned from the section on the lamps. Precisely because it can be learned from the other section, it is unclear why it is stated at all. From this the exegete concludes that it was apparently written so that we might learn from it, together with the section on the lamps, about the rest of the Torah.

We noted that usually such a situation leads to the opposite result. When the same element appears twice and one appearance is unnecessary, the conclusion is that these two verses come to teach only about themselves and not about the rest of the Torah, for if the purpose were to teach the rest of the Torah, one of them would have sufficed. This is the rule that states: “Two verses that come as one do not teach” (see the sheet for Parashat Toledot, 5765, part II).²

We noted that it is not clear why we would even think that other commandments do not apply for all generations. Is not the Torah, by its very nature, a body of commands for all generations?³ Put differently: do commandments in which the term “command” does not appear fail to apply for all generations? Normally, we do not treat the Torah’s commands in that way.

We saw two lines of explanation, both of which arise in the Ra’avad’s commentary on the Baraita of Examples:

1. Only with commandments stated using the term “command” could one raise the possibility that they were said only for the moment, because of some linguistic consideration. Therefore, only in those cases is proof needed that they were also said for all generations. As for the other commandments, it is obvious to us that they were said for all generations, even without a derivation.
2. In truth, with all commandments we might have entertained the possibility that they do not apply for all generations. But the conclusion of our midrash (rabbinic exegesis) teaches us that this is not so. According to this direction, this midrash is the source for the claim that the Torah’s commands are eternal; this is Maimonides’ ninth principle of faith.

The Ra’avad asks in his commentary why the baraita brings this derivation as an example of binyan av from two verses rather than of verbal analogy, since the midrash is based on the appearance of the word “command” in all the contexts. Here he assumes that the midrash really is using the word “command” itself, and therefore its conclusions concern only contexts in which the word “command” appears, as in the first explanation above. The Ra’avad offers two answers, corresponding to the two directions just mentioned. First, the word “command” is not mufneh (textually free, that is, superfluous for the plain sense), and therefore one cannot derive a verbal analogy from it. This leaves us with the first direction. His second answer is that the derivation is not in fact dealing only with commands phrased with the word “command.” That explanation obviously leads us to the second direction.

In note 1 on the sheet for Parashat Shemot, 5765, we assumed that the common denominator is always based either on qal va-homer (an a fortiori inference) or on binyan av from one verse, that is, analogy. We now see that the Ra’avad says this explicitly here. If this is indeed the structure of the common denominator, then clearly there is no verbal analogy here, and vice versa.

In the second part of the article we pointed to three different roles played by tzrichuta in the structure of the common denominator:

1. To prevent the application of the rule “two verses that come as one do not teach,” and thereby allow these sources to teach the rest of the Torah. This is how the Ra’avad and the author of Ha-Keritut explain our derivation.
2. To explain why the second source cannot be learned from the first, and why the Torah had to write it explicitly as well, even if it may not be needed in order to teach the general rule as such, as in the previous explanation.
3. In the Jerusalem Talmud’s derivation above, we saw that there is no tzrichuta, and yet the rule “two verses that come as one do not teach” is not applied. We explained that the two source cases are needed for another reason as well: diversity in the evidence required to ground the generalization. We also noted that one might understand the absence of tzrichuta in the Baraita of Examples in the same way as the Jerusalem Talmud, contrary to the Ra’avad just cited.

We discussed the connection between these conceptions and the question whether the eternity of the Torah is learned from this midrash or not. If it is learned from here, then we are dealing with a very fundamental principle of Jewish faith, and therefore as many proofs as possible are required in order to ground it, and the diversity of those proofs is also essential. But if this midrash deals only with contexts in which the word “command” appears, then we are not dealing with such a fundamental principle, and it stands to reason that tzrichuta would then be required only for the first two reasons.

We then discussed the difficulty of grounding the validity of generalizations, both in halakha (Jewish law) and in science. Because of this difficulty, diversity in the facts on which the generalization is based is required. We saw that the only way to validate the process of generalization, both scientific and Torah-based, is to understand it as the result of cognition and not of thought alone.⁴

In that discussion we presented two views in the philosophy of science that Ze’ev Bechler calls “actualism” and “informativism.” Actualism does not treat scientific generalizations as claims about reality, but as an efficient and convenient mode of collecting particular facts. Informativism, by contrast, treats generalizations as claims about reality. It regards the theoretical entities in scientific theory as real entities, and not as useful and convenient fictions, as actualism proposes. We pointed out that in halakha one cannot sustain an actualist position, because we base prohibitions and punishments on these generalizations. The halakhic generalization itself has consequences, and therefore it cannot be treated as merely a mode of presenting particular facts.⁵

We concluded the article by noting that the dispute among the authors who systematized the hermeneutical rules, over whether binyan av from one verse is also based on the logic of the common denominator, is likewise connected to the understanding of the roles of tzrichuta. According to the approaches that explain even binyan av from one verse as based on the logic of the common denominator, the difference between the two forms of binyan av lies in the question whether the source cases come from two different halakhic (legal) contexts or from the same context. If the two source cases belong to two contexts, a formal tzrichuta between them is not necessarily required. It is enough to point out that the principle being derived appears in two different halakhic contexts, so that we may regard this as diversity of evidence, and that is enough to ground the generalization made on their basis.

B. Another Possibility for Understanding the Jerusalem Talmud’s Derivation

Introduction

We saw that the Jerusalem Talmud assumes that the expulsion of the impure could have been learned from the section on the lamps, and that it is precisely the redundancy that leads us to learn from it to the rest of the Torah. We explained this by saying that we are dealing with a fundamental principle that requires a generalization based on as broad and varied a foundation as possible. In this chapter we shall propose a different line of explanation, based on Nahmanides’ remarks in the Babylonian Talmud, Makkot 4a, cited in the sheet for Parashat Shemot, 5766.

Nahmanides’ Remarks: A Fourth Reason for Tzrichuta in the Common Denominator

In the sheet for Parashat Shemot, 5766, we discussed a passage in tractate Makkot in which there appears the “objection from a stricter aspect.” In the structure of the common denominator, each of the two source cases has a unique property, and therefore there is tzrichuta between them. The objection from a stricter aspect argues that precisely these unique properties are what block the common-denominator derivation. Such an objection, as we explained there, undermines any derivation carried out in the form of the common denominator.

The discussion there concerns the question whether one receives lashes for a prohibition that involves no action. According to Rabbi Yehudah, one does receive lashes even for such a prohibition, while Rabbi Akiva disagrees, and the halakha follows Rabbi Akiva. Rabbi Yehudah learns this by means of the common denominator from conspiring witnesses and the slanderous husband. Conspiring witnesses are distinctive in that they are punished without prior warning, and the slanderous husband is distinctive in that he receives lashes and also pays money, something that generally does not happen in other halakhic contexts, where we hold that one does not receive lashes and pay monetary compensation.

The medieval commentators there ask about this Talmudic claim: if the objection from a stricter aspect really works, then there is no room at all for the common denominator anywhere in the Torah. By its very structure, this scheme always contains a unique feature, that is, a stringency, in each of the two source cases, and it is precisely for that reason that two source cases are needed. We cited several approaches of the medieval commentators in resolving this difficulty, and we even proposed an explanation of our own, which apparently also appears in the Ritva there in the name of his teacher, the Ra’ah.

One of the medieval approaches we cited was that of Nahmanides. He proposed a very novel explanation that completely changes the understanding of the common-denominator scheme as a whole. Nahmanides argued that the reason we usually do not raise the objection from a stricter aspect in the Talmud is that there is a stricter aspect in the target case as well as in the source cases. Each of the three has a different stricter aspect, and therefore they stand on equal footing and can still be compared. The passage in Makkot is unique because the target case has no stricter aspect, and therefore the fact that there are stricter aspects in the two source cases undermines the comparison to it.

It should be noted that, according to Nahmanides, there is a different reason, a fourth one, for why tzrichuta is needed in the common-denominator scheme: it is needed in order to equalize the standing of the source cases with that of the target case, since the target case has a stricter aspect, and thereby to make the comparison possible. Below we shall explain his remarks further.

Explaining the Jerusalem Talmud’s Derivation in Light of These Remarks of Nahmanides

If we accept Nahmanides’ novel proposal, we may perhaps also understand the course of the Jerusalem Talmud’s derivation in our case. According to Nahmanides, tzrichuta is needed in order to equalize the standing of the source cases with that of the target case, in a situation where the target case has a stringency. What happens when the target case is a halakhic context with no special stringency? In such a situation, it is quite possible that stringencies in the source cases are not needed either, for even without them their standing is equal to that of the target case. If so, in such a case there will also be no tzrichuta, since tzrichuta is based on the unique stringencies of the two source cases.

According to Nahmanides, it is entirely possible that the Jerusalem Talmud holds that in the present case the target case has no stricter aspect at all, and therefore the two source cases need not have stricter aspects either. If the two source cases did have stricter aspects, we could not derive from them to the target case, because the objection from a stricter aspect would refute the derivation. Therefore there is also no tzrichuta between them. As we have seen, according to Nahmanides, when the target case has no stricter aspect, it is specifically the absence of tzrichuta between the source cases that makes the derivation possible. When there is no tzrichuta between them, their standing is equal to that of the target case, and therefore the target case can be learned from them by means of the common denominator.⁶

The Main Difficulty in This Explanation

This explanation raises a major difficulty. According to our proposal in understanding Nahmanides, there are two situations in which the common-denominator scheme can be used:

1. When both source cases and the target case each have different stricter aspects. This is the normal case.
2. When none of them has any stricter aspect. This is the case in our Jerusalem Talmud.

By contrast, if the two source cases have stricter aspects and the target case does not, one can raise the objection from a stricter aspect, and therefore there is no possibility of deriving by the common denominator. This is the case in the passage in Makkot. And if the two source cases have no stricter aspect but the target case does have one, then obviously there is no need to derive by the common denominator, for one can derive from each source case separately by qal va-homer, by virtue of the target case’s stricter aspect.

But now the question returns: what is the relation between a common-denominator derivation and the rule “two verses that come as one do not teach”? Above we saw that the existence of tzrichuta between the source cases is what prevents the application of the rule “two verses that come as one do not teach,” because when there is tzrichuta, neither of them is redundant. The rule “two verses that come as one do not teach” applies only when one of the two verses is redundant.⁷

What happens in a case where the two source cases have no stricter aspect, that is, where there is no tzrichuta between them, as in the second situation above, exemplified by our Jerusalem Talmud? At first glance, one of them is redundant in such a case, and therefore the conclusion should be that they were written to teach only about themselves and not about the general rule. But according to our proposal in Nahmanides, even in such a case one can derive from their common denominator to the target case, provided that it too has no stricter aspect.⁸

A Possible Explanation in the Jerusalem Talmud

The Jerusalem Talmud itself addresses this difficulty, and says that the presence of the second source case does indeed require explanation, for it is redundant, since it can be learned from the first.⁹ But the explanation the Jerusalem Talmud offers is that the second source case is intended to teach about the rest of the Torah, and not about itself. If so, where are we to apply the rule “two verses that come as one do not teach”? Seemingly, in every case where there are two verses that are not needed, we could say, as here, that the need for the second verse is to teach about the rest of the Torah rather than about itself. Beyond that, in the Jerusalem Talmud it is still difficult to see why the second source case is needed, since we could have learned the generalization to the whole Torah from the first source case alone, namely the lamps, by binyan av from one verse, a one-from-one derivation.

We should first note that according to the Jerusalem Talmud it is clear that there is no stricter aspect in the lamps, since it writes that one can learn from them to the expulsion of the impure. If there were a stricter aspect in the lamps, that derivation would be refuted. By contrast, there is room to hesitate whether, according to the Jerusalem Talmud, the expulsion of the impure has a stricter aspect, or whether it too has none.

It is possible that the Jerusalem Talmud agrees that the expulsion of the impure has a stricter aspect, as the Ra’avad also wrote.¹⁰ If so, the expulsion of the impure by itself cannot teach the rest of the Torah, because if only that section had been written we would object: what is special about the expulsion of the impure is that it has a stricter aspect. Therefore Scripture needed to state the same law also in the section on the lamps, and from there one can learn to the rest of the Torah. According to this, it is clear why the lamps too were written.

The question, however, is why we should not learn directly from the lamps to the whole Torah, including the expulsion of the impure. Put differently: it is still not clear why there was any need to write the rule regarding the expulsion of the impure, since it could be learned by qal va-homer from the lamps. Beyond that, it is still unclear why we should not say that even if the expulsion of the impure was written, it was written only to teach about itself and not about the rest of the Torah, that is, to apply here the rule “two verses that come as one do not teach.”

The Relation to Verbal Analogy

We mentioned that the Ra’avad asks why we should not regard this derivation as a verbal analogy from “command” to “command.” In his first answer he says that the word is not mufneh. If so, in his view the word “command” in the sections on the expulsion of the impure and on the lamps is not mufneh. According to this, the question why we should not apply here the rule “two verses that come as one do not teach” does not arise at all. That rule is based on the fact that one of the two sources is redundant, since it could have been learned from the other. But if the word “command” is not mufneh, that means it needed to be written for the substantive law itself. If so, even had we not learned from it that throughout the Torah “command” means immediate applicability and applicability for all generations, it would not have been redundant. In that case the logic of “two verses that come as one” cannot be applied here. As noted, that logic is based on the fact that one source is redundant, and that redundancy teaches us not to generalize from these two cases to the rest of the Torah.

However, the Jerusalem Talmud writes that in the section on the expulsion of the impure there is redundancy, and that precisely because of this we learn from here to the whole Torah. It therefore apparently accepts the Ra’avad’s point only with respect to the lamps. It follows that according to the Jerusalem Talmud there is no special stringency in the lamps, but the word “command” there is necessary. In the section on the expulsion of the impure, by contrast, there is a special stringency, but the word “command” is redundant, that is, mufneh.

On that basis, it is possible that the Jerusalem Talmud intends a derivation by verbal analogy, as in the Ra’avad’s question. In the section on the lamps there is no stringency, and therefore a derivation from the lamps to the rest of the Torah would not be refuted. One might therefore have derived from the lamps to the whole Torah by verbal analogy, but the word “command” there is necessary and not mufneh. When the word is not mufneh, one does not derive a verbal analogy.

By contrast, in the section on the expulsion of the impure, the word “command” is indeed mufneh according to the Jerusalem Talmud, and it mentions this in order to establish the possibility of deriving from it by verbal analogy, since it is mufneh. But if we try to learn from there to all the occurrences of the word “command” in the Torah by verbal analogy, an objection will arise based on the special stringency found in the expulsion of the impure. We are assuming here that when a term is mufneh on one side only, one may derive but one may also refute; see the sheets for Parashat Chayei Sarah and Vayetze, 5766.

But when we notice that the law is written in both places together, the possibility opens of learning from both of them to the whole Torah by way of the common denominator. Of course, our present assumption is that one can make a common-denominator inference that is based on two verbal analogies. This is contrary to what appears from the Ra’avad’s remarks here, as we noted in last year’s article.¹¹

Below we shall see that this possibility exists only according to Nahmanides. But first we must examine his position more carefully.

A Difficulty in Nahmanides’ Approach

As we have seen, Nahmanides writes that the ordinary case of the common denominator in the Talmud is one in which each of the source cases has a special stringency, and the target case too has a special stringency. In his view, in such a situation one cannot raise the objection from a stricter aspect. His remarks imply that the unique stringency of each source case is not important to the law itself. What matters is only its overall level of stringency, that is, whether it has a stringency at all. Hence, according to Nahmanides, even when the two sides have different stringencies, there is still room to compare them.¹²

According to the other commentators, the situation is entirely different. The stringencies are unique, and therefore when there are different stringencies in the two source cases and in the target case, there is no room at all to compare them. Any such comparison can be refuted by the claim: what is true of the source cases is that they have unique stringencies, and perhaps those are what cause the law. Since the target case has different stringencies and not those, perhaps the law in question does not apply there. In the end, one denies the determining role of the two special stringencies in the source cases, and learns from the common denominator of both to the target case.

If so, according to Nahmanides the comparison is based on the level of stringency, whereas according to the other commentators the comparison is based on the quality and type of stringency.

At this point the question arises why, according to Nahmanides, a one-from-one derivation would not be enough. In the situation he describes, it would seem that one could take one of the two source cases and derive from it alone to the rest of the Torah. And if an objection were raised that it has a unique stringency found only there, we could answer that the various target cases also contain different but parallel stringencies that balance the picture. According to Nahmanides, then, there would seem to be no need to resort to the second source case or to the common-denominator derivation at all, except perhaps in a case with no stringencies whatsoever, as we suggested above regarding the Jerusalem Talmud.

According to the other commentators, this difficulty does not arise. In their view, a derivation from one source case would be refuted by the argument: what is true of the source case is that it has a unique stringency, and perhaps that is what causes the law. The fact that the target case has a different stringency is irrelevant, since one may attribute the law’s applicability precisely to the source case’s own stringency. But according to Nahmanides, in such a case the derivation cannot be refuted, since if the stringencies are at the same level, there is room to compare the two contexts despite their difference.

If so, according to Nahmanides, whenever we have two source cases between which there is tzrichuta, and we want to derive from them to a third target case, which must also have a stringency, for otherwise the objection from a stricter aspect would refute the derivation, there is also the possibility of deriving from each of them separately.

Clarifying Nahmanides’ Approach: The Difference Between Binyan Av from One Verse and Binyan Av from Two Verses

The conclusion is that according to Nahmanides this logic exists only in a one-from-two derivation, not in a one-from-one derivation. Put differently, in a derivation from one source case, if the source case has one stringency and the target case has a different stringency, we do not compare them. Here too Nahmanides would agree with the other medieval authorities that the derivation can be rejected by attributing the applicability of the law to the unique stringency found in the source case. Only in the common-denominator scheme does Nahmanides see the possibility of deriving on the basis of general levels of stringency, while ignoring the differences between the stringencies.

The conclusion, then, is that according to Nahmanides the common denominator is a formal principle and not a substantive comparison. It is not a generalization from particular cases to a general law, but the formal application of a textual hermeneutical principle, like verbal analogy. The comparison involved in the common denominator is based on levels of stringency and not on kinds of stringency. Therefore, according to Nahmanides, the only possible way to refute a common-denominator inference is by pointing to a difference in the levels of stringency, and not to a difference in the types of stringency.

By contrast, a one-from-one comparison is an ordinary analogical inference. In that case, even according to Nahmanides, we are making a substantive comparison, and when the source case and the target case have different stringencies, the comparison is refuted.

Can the Common Denominator Be Learned from Two Verbal Analogies?

As we mentioned, it is commonly thought that the common-denominator scheme must always be based on binyan av from one verse, that is, analogy, the “what do we find?” form of argument, or on qal va-homer. In other words, the derivation from the first source case is either binyan av or qal va-homer, and when an objection is found there the second source case helps us dismiss it. See the article for Parashat Shemot, 5765. By contrast, it is generally assumed that one cannot base a common-denominator derivation on verbal analogy. The Ra’avad above also assumes this.

Why indeed should one not derive in the form of the common denominator from verbal analogy as well? Presumably the reason lies in the logic of the common denominator. As we saw in the article for Parashat Mishpatim, 5766, this scheme is based on the fact that there is one shared idea, that is, a common denominator, in the two source cases, and it is that which causes the law. Therefore the same law will also apply to the target case, which is characterized by that same common denominator.

But verbal analogy, unlike binyan av and qal va-homer, is a formal principle. It is based on a hint arising from verbal similarity between two contexts, and not on a substantive comparison between them. If so, when we find the same word in two places, that does not mean that they have a shared substantive or conceptual basis. Therefore two verbal analogies cannot teach us by way of the common denominator.

But according to Nahmanides, even in the case of a common-denominator derivation based on qal va-homer and binyan av, the common-denominator scheme is not based on the existence of a shared conceptual foundation. Nahmanides bases the common-denominator inference on a certain level of stringency, and ignores the unique character of the source cases. In his view, all laws that have a certain level of stringency should be compared, and not because they share a common substantive feature. That is why Nahmanides accepts the objection from a stricter aspect as a legitimate objection. In his view, it is possible that the law is caused by two different reasons, and that in each source case it is caused by the special stringency that characterizes that case. If so, how can one learn from these two source cases to a third target case in which neither of those two stringencies exists? According to Nahmanides, this is possible only because a uniform basis for the applicability of the law under discussion is not required. It seems that Nahmanides does not accept the assumption that every law in the Torah has only one reason.¹³

If so, we can now understand that, according to Nahmanides, there is also no obstacle to making a common-denominator derivation by means of two verbal analogies. True, a shared word points only to verbal similarity, and not necessarily to substantive similarity as well, but as we have seen, according to Nahmanides that is enough to derive from those two source cases to the target case.

Comparison to the Logic of Qal Va-Homer

From our discussion above it emerges that there are two kinds of comparison: comparison on a substantive basis, meaning substantive and conceptual similarity, and comparison on the basis of stringency, meaning comparison between halakhic contexts that are at the same level of stringency even if they are of different kinds. We saw that binyan av from one verse is a conceptual analogy, that is, the identification of a shared basis. In binyan av from two verses as well, according to most medieval authorities, the issue is a substantive comparison between the common denominator of the two source cases and the character of the target case. According to Nahmanides, by contrast, the comparison in the common denominator is based on stringency and not on content.

What about the other principles? As for verbal analogy, we saw above that the comparison there is based on the text and not on content.¹⁴ It is commonly held that qal va-homer is a logical principle, not a formal one, and not a textual one either. But when we examine it more carefully, we find that the comparison there too is usually made on the basis of leniency and stringency, rather than on a substantive basis. Such a comparison is indeed logical, but it is a different kind of logic.

In a qal va-homer of the type “two hundred includes one hundred,” the inference is based on a substantive comparison. The source case is actually included within the target case, and therefore it is obvious that the law that applies to the source case also applies to the target case, for the same reason. For example, digging a pit includes opening its cover as well, that is, removing the upper layer of fill. Therefore all the laws that apply to opening a pit also apply to digging a pit, because the act of opening is included within the act of digging.

By contrast, in a reason-based qal va-homer, the comparison is usually based on leniency and stringency. For example, in the qal va-homer cited in the Baraita of Examples (see the article for Parashat Beha’alotekha, 5765), the Sages infer that if, had Miriam’s father spat in her face, she would have had to feel shame for seven days, then when the Holy One spat in her face she should feel even greater shame. Here there is a line of reasoning that compares the shame caused by her father’s spitting with the shame caused by the Holy One’s spitting, and this too seems to be a quantitative comparison, although the leniency and stringency are different levels of the same substantive kind.

In a gradational qal va-homer (see the sheet for Parashat Noah, 5765), the source case is lighter than the target case, and therefore we infer that the laws applying to the source case also apply to the target case. There the comparison is plainly quantitative.

According to Nahmanides There Is Only One Kind of Common Denominator

As we have already mentioned, the commentators point out that there are two kinds of common denominator: one based on qal va-homer and one based on binyan av. But according to Nahmanides, the common-denominator derivation deals with a situation in which each of the two source cases, A and B, and also the target case, C, has a different stringency, A, B, and C respectively. In such a situation, we are necessarily dealing with a common-denominator derivation that begins with qal va-homer: we derive by qal va-homer from source case A to target case C, since target case C has stringency C. After that we refute the qal va-homer by pointing out that source case A too has a stringency, namely A. We then raise the possibility of learning by qal va-homer from source case B to target case C in the same way. This qal va-homer too is rejected, because source case B has stringency B. We are thus left with a situation in which each of the source cases and the target case has a stringency, and finally we derive from the two source cases together.

In the parallel common-denominator scheme in which one begins with a one-from-one binyan av rather than a qal va-homer, one would be dealing with a case in which the two source cases have stringencies while the target case does not. But such a case is impossible according to Nahmanides, because in that situation the objection from a stricter aspect would refute the derivation. If so, according to Nahmanides the common-denominator scheme is always based on qal va-homer and not on binyan av. Above we saw that there is also a possibility of basing it on verbal analogy.

Another Possibility for Understanding Nahmanides

Perhaps this is the reason that Nahmanides bases the common denominator on quantitative comparison rather than qualitative comparison, that is, comparison of kind or content. The reason is that the structure here is of the type of qal va-homer, which by its nature is a quantitative rather than a substantive comparison. Only according to the other medieval authorities, according to whom the common denominator can be based on a one-from-one binyan av, is there room to see it as a substantive comparison rather than a quantitative one.

We should note that the assumption underlying this argument is that a common denominator based on two qal va-homer inferences retains the character of qal va-homer and does not become binyan av, that is, analogy. This assumption is disputed among the commentators; see Encyclopedia Talmudit, entry “Binyan Av,” near notes 59-61.

What happens in a common-denominator derivation where none of the three contexts has a stringency, as in our proposal above concerning the Jerusalem Talmud? In such a case, if it is possible at all, the common denominator begins with binyan av and not with qal va-homer, and therefore it may be that even Nahmanides would agree that this is binyan av and not qal va-homer.

Under what category should a common denominator based on two verbal analogies be placed? Presumably it would count as yet another kind of verbal analogy, but the matter still requires further investigation.

Footnotes