Mishpatim (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. Mida Tova — Friday eve of Parashat Mishpatim, 5766

Questions

1. Four understandings of how the principle of the common denominator operates.
2. What is “conceptual construction”?
3. Is there a connection between conceptual construction and the common denominator?
4. Can conceptual construction be presented as a common denominator, and vice versa?
5. Why do we not find subcategories in Shabbat derived by the principle of the common denominator, unlike the subcategories in the laws of damages?

The Hermeneutical Principles

Binyan av (derivation from an archetypal source), the common denominator, conceptual construction.

A. Summary of Last Year’s Article

“Whoever curses his father or his mother shall surely be put to death.”
Exodus 21:17

“He shall surely be put to death—by stoning… We have heard the punishment; from where do we know the warning? Scripture says: You shall not curse a judge. If your father is a judge, then he is included in You shall not curse a judge; and if he is a leader, then he is included in You shall not revile a leader among your people. If he is neither a judge nor a leader, but merely an ordinary person, then you may derive by binyan av from the two of them: a judge is not like a leader, and a leader is not like a judge; the common denominator between them is that they are among your people, and you are warned against cursing them. So too your father, who is among your people, you are warned against cursing him. But perhaps the common denominator between them is that they are eminent people among your people, and it is their eminence that caused the warning against cursing them; would you say the same of your father? Therefore Scripture says: You shall not curse the deaf. Scripture is speaking of the most wretched among human beings. Thus you derive by binyan av from the three of them: a judge is not like a leader, and a leader is not like a judge, and neither of these is like the deaf, and the deaf is not like these two; the common denominator between them is that they are among your people, and you are warned against cursing them. So too your father, who is among your people, you are warned against cursing him.”

Mekhilta de-Rabbi Ishmael, Mishpatim, Tractate Nezikin, Parashah 5, s.v. “He shall surely be put to death”

The midrash (rabbinic exposition) cited above seeks a warning—that is, a scriptural prohibition—for the offense of cursing one’s father or mother, whose punishment is stoning. In the end, the warning is found by means of a binyan av built from a combination of three sources: judge, leader, and deaf person. The structure of this exposition is complex: it is a case of the common denominator derived from three verses, not from two, as is usually the case.

At the beginning of the article, we dealt with the term “warning” and with the rules that one does not derive warnings and one does not derive punishments from logical inference. We saw several explanations of the rule that punishments are not derived from logical inference, and applied them as well to the rule that warnings are not derived from logical inference. We saw that even one who disagrees and holds that punishments may indeed be derived from inference would still agree with the rule that warnings are not derived from inference.

We noted that the accepted interpretation of the term “inference” in this context is an a fortiori argument. Maimonides, however, in the Second Root, maintains that the term refers to all the hermeneutical principles by which the Torah is interpreted; according to him, one never derives warnings from exposition at all. Nahmanides, in his glosses there, disagrees.

We saw that according to most views, the very existence of a prohibition can certainly be learned by inference. The rule that warnings are not derived from inference concerns only punishment. In other words, both punishment by inference and warning by inference deal, in one way or another, with punishment. We noted, however, that Maimonides’ view on this issue is different, because according to him, even the prohibitions themselves that are learned from the thirteen hermeneutical principles are not of Torah status but rabbinic enactments. The conclusion is that, according to Maimonides, the rule that warnings are not derived from inference does not concern a condition for punishment, but the prohibition itself.

We also saw that the midrash cited above served Maimonides as a source for the claim that a warning derived from inference—that is, from exposition—is valid when the punishment for it is written explicitly in the Torah.

In the second part of the article, we dealt with the midrash itself, and saw that it can be understood in four different ways:

1. One can understand the derivation as built from two structures of the common denominator, one layered upon the other,¹ each based only on two teaching sources: we learn from the common denominator of judge and leader, and that entire result then becomes one side that joins the side of the deaf person, and together they teach through a further structure of the common denominator.
2. We may learn that the father has two different legal aspects: he is both an authority of a quasi-governmental sort and another ordinary citizen. Two prohibitions apply to him simultaneously: the prohibition against cursing governmental authority and the prohibition against cursing another person. According to this direction, the exposition is not a common denominator at all, but two independent derivations.
3. One can construct a more basic common denominator out of these two foundations—for example, the duty not to harm aspects of the social order, whether toward the wretched or toward authorities.² The language of the midrash, however, does not suggest that this is its intention.
4. The exposition contains three verses, each of which is needed for a different reason, yet all of them together teach one principle. They all operate on the same level.

In the end, we noted that we are dealing here with a case in which we need a warning for a punishment that already appears explicitly in Scripture. In such a situation, the essential character of the law plays no role at all. When the punishment is explicit in Scripture, we seek only some source that will establish the sheer fact that there is a prohibition, not necessarily one that serves as the source of the prohibition itself, since that can be inferred from the punishment. Therefore, it is possible to say that there really are several different foundations here—for example, authority and wretchedness—and the father’s case rests on a third foundation, different from both.

In light of this, we can now see that these two structures are equivalent. The derivation from two distinct foundations—the first structure, in which two common-denominator derivations are layered on one another—and the fourth structure, in which one level derives the father from all three together, are both merely disclosures that teach only the fact that a prohibition exists. In the end, it is clear that even judge and leader already rest on two distinct foundations; certainly the prohibition in the case of the deaf person is different from both of them; and the prohibition of cursing one’s father defines a fourth foundation, different from all the others.

B. Conceptual Construction³

Introduction

In last year’s article, we mentioned the process of “conceptual construction” and connected it to the third way of understanding the midrash above. Here we shall try to describe in greater detail the logic of conceptual construction, and discuss its connection to the logic of the common denominator. At the end, we shall return to comment on the hermeneutical principle employed in this midrash.

The “common denominator” in the primary categories of damages and of labor

At the beginning of Tractate Bava Kamma (Babylonian Talmud, Bava Kamma 2a, 3a), the Talmud discusses the relationship between primary categories and subcategories. It determines that with respect to Shabbat, the subcategories are equivalent to their primary categories, whereas with respect to damages it concludes that some are equivalent to their primary categories and some are not.

Against that background, let us note a puzzling phenomenon in the relationship between primary categories and subcategories in the laws of Shabbat. In the context of damages, the Mishnah at the opening of Bava Kamma states that there are subcategories learned by “the common denominator” from two primary categories: “the common denominator between them…” And the Talmud there (Babylonian Talmud, Bava Kamma 6a) gives several examples, such as one’s stone, knife, or load that he left on his rooftop; they were blown down by a normal wind, he did not renounce ownership of them, and they caused damage. This is learned by the common denominator from pit and fire. See there for several additional examples.

By contrast, with regard to Shabbat, we do not find any derivation at all by the common denominator. That is, we do not find subcategories learned jointly from two primary categories through the procedure of the common denominator. The question is why we do not find such a derivation in the context of the labors prohibited on Shabbat.

At first glance, one might attribute this to the fact that with respect to Shabbat the rule is that the subcategories are equivalent to their primary categories, and therefore every subcategory is learned only from the primary category to which it is similar. By contrast, subcategories learned from two primary categories are not similar to their primary categories. But this cannot be the explanation, for two reasons:

1. This is not an explanation but only an indication: because there is no derivation by the common denominator, therefore on Shabbat the subcategories are equivalent to their primary categories. But the matter still requires explanation: why indeed do we not find, with respect to Shabbat, a derivation of a subcategory from two primary categories?
2. With respect to damages, the Talmud there says that the subcategories are equivalent to their primary categories, except for half-damages in the case of pebbles propelled by an animal’s walking; see Babylonian Talmud, Bava Kamma 3b. Yet there we do find a derivation of a subcategory from two different primary categories, in the discussion in Babylonian Talmud, Bava Kamma 6a. If so, the fact that subcategories are equivalent to their primary categories does not contradict a derivation of a subcategory through the procedure of the common denominator.

Two proposed explanations and their rejection

In a conversation with a well-known Torah scholar, two explanations were suggested:

The common denominator is a hermeneutical principle for interpreting the Torah. The primary categories of damages are written explicitly in the Torah, and therefore they can be expanded by means of the hermeneutical principles through which the Torah is interpreted. The labors of Shabbat, however, are not written explicitly in the Torah. Rather, the Sages defined them in light of the analogy between Shabbat and the Tabernacle, and perhaps also on the basis of the derivation that there are thirty-nine primary categories from the fact that the word “labor” appears thirty-nine times in the Torah; see Babylonian Talmud, Shabbat 49b. Therefore, it is not relevant to expand them by any hermeneutical principle, and especially not by the common denominator.

The Sages define thirty-nine distinct primary categories of labor on the basis of the analogy between Shabbat and the Tabernacle. If there were some additional labor learned by the common denominator from two primary categories, it would have to count as another primary category, the fortieth. But it is known that there are only thirty-nine primary categories of labor, and therefore it is clear that they exhaust all the fundamental possibilities of labor.

It seems, however, that these explanations are insufficient. As for the first explanation, throughout the Torah we do learn from material that was itself learned, with the exception of sacrificial law; see Babylonian Talmud, Zevahim 50a and the surrounding discussion. That is, everywhere in the Torah except the realm of sacrifices, one may use the hermeneutical principles even with respect to laws that were themselves generated through exposition. If so, why should we not be able to use the common denominator in relation to labors that were themselves learned through exposition?

As for the second explanation, one can say that here we are speaking of a subcategory, not a primary category. The labor that would be learned by the common denominator from two different primary categories of labor would be a subcategory of both, not a new primary category. There is no reason to define it as a primary category, since it can be learned from the existing primary categories, even if two of them are required for that purpose. In the laws of damages there are subcategories of two primary categories, and they are still classified as subcategories, for the Mishnah there lists only four primary categories. The reason they are classified as subcategories is precisely this: they can be learned from the existing primary categories. Primary categories are fundamental modes of labor or damage that cannot be learned from the other primary categories, even from a combination of several of them, had the Torah not introduced them explicitly.

Spitting on Shabbat

We do find one case in which it seems that something like this exists in the laws of Shabbat as well. In the Jerusalem Talmud, Shabbat, chapter “Kelal Gadol,” halakha 2, it says:

“One who spits and the wind disperses it is liable because of winnowing, and anything that is completed through the agency of the wind is liable because of winnowing.”

This was ruled as halakha (Jewish law) in Or Zaru’a (part 2, no. 59), Rokeah (no. 62), and by the Rema (Shulhan Arukh, Orah Hayyim, toward the end of section 319). In the words of the Rema there:

“One who spits into the wind on Shabbat, and the wind scatters the spittle, is liable because of winnowing.”

Some commentators explained that the case is one in which the wind breaks the spittle into small pieces; see, for example, Korban HaEdah on the Jerusalem Talmud there. But others noted—see Nishmat Adam, rule 15, section 1; Rabbi Akiva Eiger, responsum 20; and also Menuchat Ahavah, part 2, chapter 7, note 13—that our own Talmud makes it clear that the whole idea of winnowing is separating food from waste, like selecting, for the Talmud asks (Babylonian Talmud, Shabbat 73b): “Is not winnowing the same as selecting, and the same as sifting?” The labor of winnowing is tossing grain into the wind so that the chaff is blown away and the kernels fall to the ground. That labor separates the kernels from their husks, like selecting.

For that reason, some emended the text and explained that the liability is because of throwing, not because of winnowing. See the glosses of Erekh Lehem by Maharikash, toward the end of section 319, and Yehaveh Da’at, part 6, no. 25. The labor of throwing is related to the labor of transferring, and it means throwing an object four cubits in the public domain.

In Bi’ur Halakha, however, the words of Rabbi Menashe of Ilya, a disciple of the Vilna Gaon, are cited there, toward the end of section 319, s.v. “scatters”:

“And in the book Alfei Menasheh he explained that the intention of the Jerusalem Talmud is a case in which the wind carries it four cubits in the public domain, and the reference to winnowing is only by way of example. That is: just as in winnowing, even though the wind assists him, he is nevertheless liable, so too in the case of spitting, where its movement is caused by the wind, he is likewise liable; and this is correct.”

It thus appears that Rabbi Menashe of Ilya interprets the Jerusalem Talmud as imposing liability for spitting specifically in the public domain, and presumably also from private domain to public domain and vice versa. In this respect he agrees with the later authorities who explain the liability as because of throwing. However, unlike them, he retains the reading “winnowing” in the Jerusalem Talmud rather than “throwing,” and explains that the labor of winnowing serves as the model for the case of spitting.

Conceptual construction in the labors of Shabbat: winnowing plus conveying equals spitting

From his words it emerges that spitting is a subcategory of both primary categories together: both of winnowing and of conveying four cubits in the public domain. The explanation seems to be as follows: the Talmud in Babylonian Talmud, Bava Kamma 60a explains that the labor of winnowing is exceptional, because the person uses the wind in order to perform his labor. Even so, one is liable for this labor just like for any other labor prohibited on Shabbat.

If so, from the labor of winnowing we can learn that a prohibited labor performed by means of the wind is regarded as though the person performed it entirely on his own. The assistance of the wind does not exempt him from liability. If so, the conveying of an object four cubits in the public domain, which is certainly a prohibited labor, remains prohibited even when it is done by the wind.⁴ It should be noted that this also appears to be the conclusion of the Mishnah Berurah itself, as is evident at the end of its discussion there.

What we have here is the creation of a new labor through the combination of two different labors. The labor of winnowing and the labor of conveying in the public domain each contribute one part to the construction of the new labor of spitting. Building a new concept out of two previous concepts, when each of them contributes or constitutes part of the new concept, is what is called here “conceptual construction.”

The common denominator

We have already discussed the principle of the common denominator several times in the past; see the sheets for Parashat Shemot and Tetzaveh, 5765, and elsewhere. For purposes of comparison with conceptual construction, let us cite again the example brought by the illustrative baraita:

“How does one derive a binyan av from two verses? The section of the lamps is not like the section of sending away the impure, and the section of sending away the impure is not like the section of the lamps. The common denominator between them is that both are introduced by the word command, and they apply immediately and for future generations; so too, anything introduced by the word command applies immediately and for future generations.”

This is a structure with two teaching sources: the lamps and sending away the impure. From these two teaching sources—that is, the primary sources—we derive the various secondary cases, namely that they apply immediately and for future generations. In this formulation, one crucial component that usually appears in derivations by the common denominator is missing: the explanation of why each of the two sources is needed. The Raavad, in his commentary on the illustrative baraita, supplies what is lacking:

“The lamps of the Sanctuary have a stricter feature, for they are regular and part of the inner service, and therefore one cannot learn from them anything that is not part of the inner service. Sending away the impure has a stricter feature, for it involves excision, and therefore one cannot learn from it anything that does not involve excision. But we learn from the common denominator in both, since in both the word command is stated, and they apply immediately and for future generations.”

That is, sending away the impure has a unique characteristic in that it involves excision—that is, an impure person who remains in the sacred precincts is liable to excision—and the Sanctuary lamps have the unique characteristic that they are regular and part of the inner service. Each of these unique characteristics prevents us from learning from that source alone to other cases that also apply immediately and for future generations, and therefore the combination of the two teaching sources is required.

In the past we pointed to several ways of understanding this logical inference from the two teaching sources to the derived case. See illustrations A-D in the sheet for Parashat Shemot, 5765, where the different possibilities are explained in more detail:

1. One can learn from the first source, and use the second source—in which the first source’s unique characteristic is absent—as evidence that the unique characteristic of the first is not the reason for the law in the first source.
2. One can learn from the second source, and use the first in the same way.
3. One can use both to show that neither of these two unique characteristics causes the law. Rather, the common denominator that characterizes both sources—in our case, that the word command is used—is what causes the law. From there we learn to every case in which that common denominator appears, namely every place where the word command is used, that the law applies there as well—that is, in our example, that it applies immediately and for future generations.
4. One can also learn from the two teaching sources themselves, and not from the common denominator of the two.

[Insert Figure X4 from Parashat Shemot here.]

Conceptual construction and the common denominator

The procedure of conceptual construction creates a new concept out of the combination of two existing concepts. At first glance, this is exactly what happens in a derivation by the common denominator. There too we create a derived case out of two primary sources. For example, in the discussion in Babylonian Talmud, Bava Kamma 6a, a new kind of damager is created—such as one’s stone, knife, or load that he placed on his rooftop and which caused damage—out of two primary categories of damages, fire and pit. Are these really the same logical procedure?

In the construction of spitting out of conveying and winnowing, we did not go through the process of showing why each source is necessary—that is, finding a unique stringent feature in each of the teaching sources and bringing the other source in order to neutralize it. The impression is that we are dealing here with a different kind of inference.

The distinction that emerges from examining the two types of inference is this: in the procedure of the common denominator, we do not actually combine the two teaching sources. Either we use only one of them as the real source and the other serves merely to neutralize a difficulty, or we use the common denominator of the two sources—not the sources themselves—to teach the derived case. By contrast, in conceptual construction there is no common denominator at all.

What is the common denominator between conveying four cubits in the public domain and winnowing with the wind? Nothing. We combine the two concepts themselves, rather than searching for a common denominator between them. The combination creates a third concept built as a composite of the two components. More precisely, we take some component of winnowing, namely the involvement of the wind as an external factor, and a component of conveying, namely its basic definition as moving an object four cubits in the public domain by hand, and combine them into a third concept: spitting, which is the straightforward sum of the two.

In the common denominator, the essence of the inference is abstraction: stripping away the secondary properties and retaining the common components. It is an act of removal. By contrast, in conceptual construction the essence lies in exposing the significant components, which are not shared by the two teaching sources, and combining them into one structure. In the end, each teaching source contributes a different component, whereas in the common denominator both contribute the same component itself—namely, their common denominator.

A challenge to the distinction above

At first glance, in a derivation by the common denominator there is room to view one source as the actual teacher and the other as merely removing possible objections. In the article for Parashat Shemot, 5765, we saw that there are medieval authorities who indeed understand the derivation by the common denominator in this way. The reason is that at the end of the process, the two teaching sources contribute the same contribution, for both contain the common denominator that teaches the law of the derived case. If so, nothing prevents us from treating only one of them as the principal source. By contrast, in conceptual construction we combine two different components in order to create the new concept. Here, seemingly, one cannot learn from only one of the teaching sources, because each contributes a different component to the combination.

However, when we look at the conceptual construction we carried out in the case of spitting, specifically there it seems that one source is dominant: conveying. One who spits in the public domain is very similar to the labor of conveying four cubits in the public domain. The problem is that he does so with the assistance of the wind and not with his own hands. Therefore, the contribution of winnowing is required, for it proves that in the laws of Shabbat a labor performed through the agency of the wind also incurs liability. If so, this is a process very similar to the common denominator.

On the other hand, let us look at the common denominator involving primary categories of damage in the discussion in Babylonian Talmud, Bava Kamma 6a. There we learn the liability of a person who placed objects—a stone, knife, or load—on the roof, and they were blown down by a normal wind and caused damage after they fell. The derivation is from fire and pit. Here too, apparently, one could view the case as conceptual construction, for the new damager can be presented as the sum of two distinct components from fire and pit: fire contributes the fact that one can be liable for damage caused through the agency of the wind, and pit contributes the fact that my object lying in the public domain, when it causes damage, obligates me to pay. If so, a case usually classified as the common denominator can be understood as conceptual construction.

Moreover, just as in the case of spitting, here too it is reasonable to view pit as the principal source, while fire merely proves that the assistance of the wind does not exempt one from payment for the damage.

At first glance, there is no common denominator between winnowing and conveying, whereas between pit and fire there is a common denominator—namely that both are considered one’s property and their safeguarding is one’s responsibility, as the Mishnah at the opening of Bava Kamma states.⁵ If so, there is still a certain asymmetry between the two cases: spitting must be viewed as conceptual construction and not as the common denominator, whereas placing objects on the rooftop can be viewed in both ways.

But this too is not correct. The common denominator of fire and pit is not embedded in their specific definitions. In those definitions they are not similar in any way. The common denominator identified by the Mishnah is that both are considered one’s property and their safeguarding is his responsibility.⁵ In the same sense one can say—at least according to some medieval authorities—that winnowing and conveying four cubits also have a common denominator: both are significant forms of productive activity and are therefore forbidden on Shabbat.⁶ If so, the symmetry between the two cases is complete.

And yet the common denominator is not conceptual construction

If we look at the example in the illustrative baraita, we can see that there is no way at all to view the combination there as conceptual construction. The lamps and sending away the impure each have no unique component that can be combined with the other to create a third concept. Here it is clear that this is only the common denominator, not conceptual construction. The common denominator is that in both cases the word command is used, and its meaning is that the law takes effect immediately and for future generations. From there we learn that wherever we find the word command, the meaning is immediate and for future generations.

If so, there are cases in which it is clear that we are dealing with the common denominator and not with conceptual construction. No wonder, then, that the illustrative baraita chose precisely this example in order to demonstrate the principle of binyan av, that is, the common denominator.

If so, the example in the Mishnah in Bava Kamma is also apparently not really a case of the common denominator, even though the terminology used by the Mishnah and by the Talmudic discussion on 6a is identical to the terminology used in derivations of the common denominator. According to what we have said, this case, like the case of spitting, is really one of conceptual construction and not of the common denominator. The terminology is indeed confusing, but authors of methodological works have already written that at times similar terminology is used with different meanings.⁷

Summary: the distinction between conceptual construction and the common denominator

In conclusion, let us note that conceptual construction can usually also be presented as a common denominator, but a genuine common denominator cannot be presented as conceptual construction. Above we saw four different understandings of how the principle of the common denominator operates. We can now see their significance:

1. In the first two, there is a dominant teaching source, and the second source serves only to remove objections. According to what we have now learned, these are mechanisms of conceptual construction, not of the common denominator. The construction is such that there is one principal source—as conveying four cubits in the public domain is in relation to spitting—and an additional component is needed to complete the derivation. That completion can be understood either as the removal of a side difficulty—winnowing proves that the fact that the wind assists does not interfere with liability—or as the addition of another component to the new concept that is formed—the component of the wind’s assistance is added to conveying four cubits in order to create spitting.
2. There may perhaps also be a construction in which the two teaching sources have equal standing; see examples in M. Avraham’s aforementioned article in Meisharim 2. This is probably the fourth mechanism among those described above in explaining how the common denominator works.
3. A genuine common denominator, like the one brought in the illustrative baraita, is always symmetrical. This is the third mechanism described above.

Our conclusion, then, is that the only accurate description of a genuine common denominator is the third of the four mechanisms. The other mechanisms are different forms of conceptual construction. When the medieval authorities present these four conceptions in the discussion in Babylonian Talmud, Bava Kamma 6a, they are not dealing with the common denominator at all, but with conceptual construction, despite the confusing terminology of the Mishnah and the Talmud there.

Application to the exposition above

As we saw in last year’s article, our exposition is a certain kind of complex common denominator, and we proposed several schemata for it. Some of them are based on layering two common-denominator derivations one on top of the other. We can now ask whether the entire derivation, or each of its two components, is a case of the common denominator, or whether we are dealing here with conceptual construction.

A simple look shows that this is indeed the common denominator and not conceptual construction. First, there is a common denominator among the teaching sources, as we saw there: injury to governing authorities, to the wretched, and to other people, all combine into the prohibition of injuring any person. The teaching sources have equal standing; none is preferred. Above all, there is no assembling of different components into an inclusive concept, but rather the extraction of an inclusive prohibition from the shared basis of the teaching sources.

Back to the primary categories of labor and damages

Above we asked why, in the labors of Shabbat, we do not find subcategories learned from two primary categories through the principle of the common denominator, unlike the subcategories in the laws of damages. We can now see that even in the laws of damages there are no such subcategories. What we do find there are subcategories created through conceptual construction, not through the common denominator. Such a phenomenon exists in the labors of Shabbat as well, at least in the example of spitting. To be sure, one must still discuss why this is so rare, and apparently also not universally accepted—for this is only the view of Alfei Menasheh and the Mishnah Berurah—in the context of the labors of Shabbat. It is possible that the large number of primary categories of labor is what causes this; there is not enough “space,” that is, not enough distinction, between them.

Thus, the relationship between primary categories and subcategories is structured through the mechanism of conceptual construction, not through the mechanism of the common denominator.

Footnotes