Chukat (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 — Friday eve, Parashat Hukat, 5766

Questions

1. The relation between the principle of “an item singled out from a general category” and generalization-specification-generalization.
2. What happens when the general category and the item singled out from it appear in the same verse? “An item singled out from a general category” as hekesh (juxtaposition-based analogy).
3. Principles that deal with defining groups and principles that deal with laws.
4. Is there an essential difference between the two?
5. Phenomenological theory and essential theory.
6. Definition by extension and by content.

The hermeneutical principles

• An item that was included in a general category and then singled out to teach about itself.
• An item that was included in a general category and then singled out to teach about the general category.
• Generalization, specification, and generalization.
• Hekesh.

“And whoever touches, in the open field, one slain by a sword, or a dead body, or a human bone, or a grave, shall be impure seven days.”
— Numbers 19:16

“‘By one slain with a sword or by a dead body’ — even a dead body is included in ‘one slain,’ yet Scripture singled it out from its category in order to make that which has separated from it like it. These are the words of Rabbi Yoshiyah. Rabbi Yonatan says: a dead body is not included in ‘one slain,’ for we find that Scripture taught about a dead body on its own and about the slain on its own. From where, then, do we know to make that which has separated from it like it? You say: it is an a fortiori inference. If carrion, which is the lighter case, makes that which has separated from it like it, then a corpse, which is more severe, should certainly make that which has separated from it like it. No: if you say this regarding carrion, whose impurity until evening is more extensive, will you say the same regarding a corpse, whose seven-day impurity is more limited? But where is it more extensive? Is it not the corpse that is more extensive, since a corpse imparts seven-day impurity whereas carrion imparts impurity only until evening…'”
— Sifrei Bemidbar, piska 127, s.v. “by one slain with a sword”

A. Summary of Last Year’s Article

In the verse cited above appears the halakha (Jewish law) that “a sword is like the slain.” According to this halakha, a sword by which a person was killed is itself regarded as an ultimate source of ritual impurity, and not merely as a primary source of impurity, and one who touches it becomes a primary source of impurity.

The Sages explain this halakha from the fact that, with respect to corpse-impurity, the law does not distinguish between one who died from a sword blow and one who died in any other way. All of them have the status of an ultimate source of impurity. If so, it is unclear why the Torah specifically says “one slain by a sword.” From this the Sages derive that a sword is like the slain. According to this, the verse should be read as follows: whoever touches a sword that made someone slain, that is, killed him, or the corpse itself, or a bone, or a grave, shall be impure for seven days.¹

Other midrashim (rabbinic interpretations) on this verse deal with the ordinary laws of corpse-impurity, and treat the term “slain” as though it referred to an ordinary corpse. According to these midrashim, the corpse appears twice in the verse: once in the word “slain” and again in the word “dead body.” It seems that the Sifrei cited above also proceeds from that same assumption.

The midrash above opens by asserting that the concept “slain” includes the concept “dead body.” We explained this by suggesting that “slain” is a kind of dead substance: life has been desecrated by death; its holiness has become profane. A whole dead body is a specific reality composed of this type of “substance,” and therefore the “dead body” counts as a specification singled out from the general category, namely, “slain.” Such a conception naturally directs our attention to the hermeneutical principle of “an item that was included in a general category and then singled out to teach.”

Rabbi Yoshiyah, at the beginning of the midrash, learns that the singling out of the specification is intended to make that which has separated from it equivalent to it. This does not appear to be an application of the principle of “an item that was included in a general category,” for in that principle the item singled out teaches about the general category, not about itself, whereas here the inference concerns the item that was singled out.

In this context we cited principle 24 in the baraita of the thirty-two hermeneutical principles of Rabbi Eliezer son of Rabbi Yose the Galilean: “An item that was included in a general category and then singled out from that category to teach about itself was singled out.” For example, see Sefer Keritut, section Netivot Olam:

“‘Joshua sent men to spy out the land and Jericho’ — but was not Jericho included in ‘the land’? Why, then, was it singled out? To teach about itself that in strength it was equivalent to the whole land.”

This is a structure very similar to what we have here. The specification was singled out from the general category in order to teach that it is equivalent to the entire category. Rabbi Samson of Chinon notes there that this principle characterizes aggadic exegesis only, and it may not even be accepted by Rabbi Ishmael. For on his view, the item singled out from the general category was singled out to teach about the entire category and not about itself. If so, it is unlikely that this is the principle at work in our midrash.

We raised two possibilities for understanding the meaning of the expression “that which has separated.” It may refer to textual separation, that is, to the specification that separated, meaning was singled out, from the general category. It may also refer to physical separation, that is, to a limb that separated from the corpse. We saw that these are opposite interpretations in content, and that the difference between them also affects our understanding of the hermeneutical principle employed by the midrash. According to the first possibility, this appears to be a derivation based on the principle of “an item that was included in a general category” and then singled out to teach about the general category. According to the second possibility, this is a comparison between the detached limb and the corpse from which it separated, a comparison apparently based on hekesh; we saw that the parallel sugya in Nazir seems to have understood the derivation in this way. Both are treated as ultimate sources of impurity. This brought us back to the aggadic principle cited above. In the end we also proposed a possibility that combines these two options.

We noted that hekesh and the principle of “an item that was included in a general category” are very close to one another. In both cases, we compare the specification to the general category, whether this comparison is created by hekesh or by the singling out of the specification from the general category in order to teach about the general category. Usually, however, the singling out from the general category occurs in a passage entirely separate from the passage in which the general category appears, whereas hekesh operates between two items that appear in a list within the same verse. Our case is exceptional: the specification and the general category both appear in a list in the same verse, and therefore they can be compared both by means of the principle of “an item singled out from a general category” and by means of hekesh.² This was the basis for the proposal that unified the two possibilities mentioned above.

We pointed out several differences between these two principles, even when we are dealing with a biblical instance in which the specification and the general category appear in the same verse. One of those differences will also concern us in this year’s article.

We then turned to Rabbi Yonatan’s approach. We saw that the difference between Rabbi Yoshiyah and Rabbi Yonatan does not begin with the interpretation of the verses, but rather with a difference in their conception of the term “slain,” rooted in their understanding of what it means for a person, or for life, to be desecrated. According to Rabbi Yoshiyah, the “dead body” is included in “slain,” because for him “slain” is a kind of substance. Every dead person is a “slain,” and so is a limb from a living person or from a corpse. If so, according to Rabbi Yoshiyah, every lifeless person is a desecrated person, and the desecration is the very absence of life. By contrast, according to Rabbi Yonatan, “slain” means only one killed by the sword, and not every dead person. In other words, what counts as desecration is not the absence of life, but specifically murder by the sword. The problem lies in the mode of death, not in death as such.

From there we moved to a brief discussion of deontological morality, a morality of will and action, and teleological morality, a morality of end or result. Rabbi Yoshiyah sees death as a negative state, and killing as immoral because it leads to a negative state. This is teleological morality. By contrast, Rabbi Yonatan seems to uphold specifically deontological morality, in which the negativity lies in the act of murder itself.³

From there we discussed the concept of the sanctity of life, and we saw that life is tied to holiness, while impurity is tied to the absence of life. We pointed to two examples that express this: cases of uncertain impurity in the public domain, and the rule that impurity is permitted for the community. Both of these laws express the fact that a community does not die, and therefore impurity does not apply to it. In light of this, we cited the explanation of the Avnei Nezer to the sugya in Babylonian Talmud, Bava Kamma 11a, regarding the rule that “there is no part of a placenta without a fetus.”

B. More on the Relation Between Hekesh and “An Item Singled Out from a General Category”

Introduction

In last year’s article we encountered two principles of “an item singled out from a general category.” In Rabbi Ishmael’s system there is the rule: “Any matter that was included in a general category and then singled out to teach, was not singled out to teach about itself, but rather to teach about the entire category.” In the system of Rabbi Eliezer son of Rabbi Yose the Galilean there is a parallel rule, except that the item singled out teaches about itself. We saw that both of these principles are certain kinds of hekesh between two halakhic contexts.⁴

We pointed to two differences between hekesh and Rabbi Ishmael’s principle of “an item singled out from a general category”:

1. An item singled out from a general category teaches about the general category in such a way that it “transfers” its unique properties to the general category. The characteristics of the specification define the characteristics of those items in the general category to which the law applies. This concerns defining the situation to which the law applies, or the scope of its application, and not the law itself. By contrast, hekesh compares the laws of the two items under discussion, and does not define situations. On this, see the essay for Parashat Shelach, 5765, where we saw a midrash whose entire purpose is to clarify spheres of application and not laws. See also the essay for Parashat Tzav, 5765, toward the end, and the essay for Parashat Vayakhel-Pekudei, 5766.
2. The principle of “an item that was included in a general category” teaches us some specific feature of the general category. By contrast, hekesh is not expounded by halves. This rule has two meanings, at least according to some of the medieval authorities; see the essay for Parashat Vayechi, 5765-6, and for Parashat Beshalach, 5766:
3. Hekesh has no special direction, for example from the specification to the general category, as in the principle of “an item that was included in a general category.” Hekesh is bidirectional.
4. In hekesh, one must compare the two items with respect to all their relevant properties. By contrast, in the principle of “an item that was included in a general category,” we learn only particular laws, and there is not necessarily a full comparison. There is also directionality in the inference: from the specification to the general category.

In the essay for Parashat Vayakhel-Pekudei, 5766, we pointed out an additional difference, concerning the methodology of the inference:

1. The inference in the principle of “an item that was included in a general category” is founded on the very fact of its singling out from the general category. That is what creates the motivation to expound the verse. The inference in hekesh is based on the fact that the two items appear in the same list within a verse.⁵

In this year’s article we will focus on the first distinction, and on its implications.

Does the Principle of “An Item Singled Out from a General Category” Not Teach Laws?

The first distinction assumes that the principle of “an item that was included in a general category” does not teach laws, but rather characterizes halakhic contexts. Is that always true? We will now examine the examples of this principle in rabbinic literature.

The first example is the one that appears in the baraita of examples, and which also appears in Babylonian Talmud, Yevamot 7a, and Keritot 2b, regarding karet for eating sacred things in impurity. We learn from the fact that the peace offering was singled out from the category of sacred things that the sacred things under discussion are altar-sanctities. In this example, the singling out from the general category indeed teaches about the character of the items in the general category to which the law of karet applies, and not about the law of karet itself.

A second example appears in Babylonian Talmud, Menahot 55a-b, where it is learned from the fact that baking meal offerings as leaven was singled out from the general category of all the acts involved in preparing a meal offering, that one is liable to punishment for each act separately, and not only for all of them together. This exposition resembles derivations such as “kindling was singled out to divide,” and the like, which learn from the specification that was singled out, and for which one is liable, that one is separately liable for each specification within the general category. See on this the essay for Parashat Tzav, 5765, and elsewhere. Here too one can see that the inference does not deal with the laws themselves, but with defining the act to which the law applies, for example liability to stoning or to a sin offering on the Sabbath.⁶

The same is true of the exposition in Bereishit Rabbah 3, s.v. “Pekod et,” cited in the essay for Parashat Pinhas, 5765. There we learn from the singling out of Eleazar from the general category that the decree of death in the wilderness was not imposed on Eleazar’s entire tribe. Admittedly, this is a different kind of exposition; see our comments there.

But in the sugya in Babylonian Talmud, Bekhorot 6a, there is a derivation based on “an item singled out from a general category” which learns, from the singling out of the firstborn donkey from the general category of firstborns of impure animals, that just as the firstborn donkey is redeemed only with a sheep, so too every firstborn of an impure animal is redeemed only with a sheep. This is an inference of a law, and not an inference dealing with the scope of application of the law, or with the character of the items to which the law applies.

Likewise, in Babylonian Talmud, Pesahim 120a, it is learned from the singling out of the seventh day of Passover from the first six days, that just as eating matzah on it is optional, so too eating matzah on the first six days is optional.

Is There a Difference Between Scope of Application and Laws?

Until now we assumed that the question whether the comparison concerns laws or scopes of application is a clear and well-defined one. But the matter is not so simple.

Let us take as an example the redemption of the firstborn of an impure animal. From the course of the discussion there it emerges that the inference does not introduce an obligation to redeem firstborns of impure animals other than donkeys, such as horses or camels,⁷ but deals only with the question of what one redeems them with. The initial assumption was that they might be redeemed with anything, and the inference from the singling out of the item teaches that they are redeemed with a sheep. In other words, here too there is a determination of the scope of application: not the scope of the law of redemption itself, but the scope of the law concerning the redeeming object.

The comparison of the seventh day of Passover to the first six days seems more problematic. We learn that just as eating matzah on the seventh day is optional and not obligatory, so too on the first six days it is optional. Is this a characteristic of the days or of the law that applies on them? We assumed that it concerns the law, but it can also be seen as a comparison dealing with application, though not with scope of application. The law of eating matzah applies to the seventh day with the force of optionality, and so too to the first six days. In any case, it seems that there is no innovation here concerning the law itself, the obligation to eat matzah, but rather concerning the degree of obligation. Still, this seems to be an exceptional case.

Comparison to the Principles of Generalization and Specification

A similar characteristic can also be seen in the principles of generalization and specification. Many times, the comparison there concerns the scope of application and not the laws themselves. But there too there are exceptions, and they usually lie in the intermediate domains presented in the previous section.

In Babylonian Talmud, Moed Katan 3, the types of labor for which one receives lashes during the sabbatical year are learned from generalization-specification-generalization, that is, the scope of application of the prohibition of agricultural labor during the sabbatical year. Likewise in Sotah 16a, regarding the characterization of the relevant places for the shaving of a sotah, that is, the scope of application of the law of shaving; and in Kiddushin 24b, regarding the defects for which a slave goes free through tooth and eye, that is, the scope of application of the law of emancipation through tooth and eye; and in Bava Kamma 54a, it is learned that only animals are included in liability for damages caused by a pit, that is, the scope of application of the law of damages caused by a pit.

In Babylonian Talmud, Eruvin 27b, it is learned regarding the redemption of second tithe that it may be redeemed with anything that is “fruit from fruit and produce of the ground.” At first glance this is the derivation of a law, but in fact it is precisely parallel to the description of the objects by which one redeems second tithe, learned through the principle of “an item singled out from a general category.” It characterizes the scope of application of redemption, not what is redeemed, but with what one redeems. Similarly, in Sukkah 50b it is learned from the specification that all service vessels must be made of metal. At first glance this too is a law, but in fact it can be seen as an innovation concerning the scope of the sanctity of service vessels, which can take effect only on metal vessels.

This comparison between the principles of generalization and specification and the principle of “an item singled out from a general category” should not surprise us. We already noted in the essay for Parashat Tzav, 5765, that every case in which there is a general statement followed by a specific statement that serves as its elaboration should, in principle, be expounded by means of generalization and specification. However, the Talmud in Menahot 55b states that the principle of “an item that was included in a general category” is used in situations where the specification is distant from the general category, where we do not expound by means of generalization and specification because of the principle that there is no chronological order in the Torah. See on this the essay for Parashat Ki-Tissa and the sugya in Pesahim 6.⁸ The Raavad writes similarly in his commentary to the baraita of examples.⁹ See also Rashi on Shevuot 7a, s.v. “one for the general category.”

Updated Definition

If so, the more refined definition of the first difference between the principles of singling out from a general category and hekesh is that these principles, and likewise the principles of generalization and specification, deal with defining halakhic categories. These categories are relevant to the applicability of laws, but are not themselves laws. Hekesh, by contrast, deals with halakhic comparisons, that is, with transferring laws from the source text to the derived text.

The Inference in Pesahim 120a

As stated above, the inference we cited regarding the eating of matzah is exceptional, because it does not deal with defining any category. One could think of defining the category of days on which eating matzah is optional, but that would be the result of the inference and not the nature of the inference itself. We compare the seventh day to the first six days with respect to the intensity of the obligation, but we certainly do not learn from the seventh day some characteristic of those days themselves as the objects of the law under discussion. If so, this is an exceptional case, and probably a unique one.

Now, in the essay for Parashat Vayakhel-Pekudei, 5766, we already pointed out that this instance of the exposition is an exceptional use of the principle of “an item singled out from a general category,” because the general category and the specification appear in the same verse, as in our example of “a sword is like the slain.” We saw there that the general category also does not contain the specification as part of it, for the six days do not contain the seventh day. These are two characteristics of hekesh, and not of the principle of “an item singled out from a general category.” Here too, the motivation of hekesh is present, and not only the motivation of singling out from the general category that stands at the basis of the exposition.

Indeed, our conclusion there was that the inference there is not a regular application of the principle of “an item singled out from a general category,” but is closer in character to hekesh.¹⁰ If so, the picture that emerges here fits very well with what we argued there: this exposition is not a regular instance of the principle of “an item singled out from a general category,” but a different manifestation of it, one that resembles hekesh in character. We should therefore not be surprised that the content learned there resembles hekesh more than it resembles the ordinary principle of “an item singled out from a general category.”

Conclusion: The Exception Testifies to the Rule

We saw two exceptional cases in which the general category and the specification appear in the same verse. In both of them, the inference has the character of hekesh in several respects: in the motivation for performing the exposition, and in the character of the exposition itself. In both, laws are learned from the source to the derived case, and halakhically relevant categories are not being defined.

If so, these are two derivations with the character of hekesh. Must they also satisfy the other rules of hekesh, namely that hekesh is not expounded by halves, which includes symmetry in the directions of inference and a full comparison between source and target? It seems that this is not relevant in our case. After all, we are dealing with a situation in which the two sides of the hekesh are a general category and a specification contained within it. In such a case, there is nothing to learn in the opposite direction, that is, from the general category to the specification, for the specification is included within it by definition.¹¹ Therefore the conclusion is that the direction of inference here is like that of the principle of “an item singled out from a general category”: from the specification to the general category. This is thus an inference that combines elements of the two principles.

These, then, were the exceptional cases. As for the ordinary use of the principle of “an item singled out from a general category,” the conclusion is that the exception testifies to the rule, though not in the sense of the principle of “an item singled out from a general category,” for here the inference from the exception to the rule is by contrast and not by comparison. The conclusion is that the ordinary derivations based on the principle of “an item singled out from a general category” serve to define halakhic categories, and not to transfer laws. As we saw, derivation by means of the principles of generalization and specification has a similar character, and the difference is only the question whether the specification and the general category are adjacent or appear in different places, in which case the principle that there is no chronological order in the Torah becomes relevant. See on this the essay for Parashat Tzav, 5765, and elsewhere. The exceptional cases occur when there is a general category and a specification singled out from it that both appear in the same verse.

In the next chapter we will discuss the nature of the relation between defining halakhic categories and learning concrete laws, and we will view this from the perspective of the philosophy of science.

C. Characteristics and Categories

Introduction

In the previous chapter we distinguished between expositions that teach us the definitions of halakhic categories, such as generalization and specification and the principle of “an item singled out from a general category,” and expositions that teach us laws, such as hekesh. The categories in question are categories to which various laws apply.

This distinction leads us to examine the relation between those categories and the laws that apply to them. In other words: is the fact that law X applies specifically to group A accidental, or essential? For example, is the determination that the punishment of karet for eating consecrated food in impurity applies only to altar-sanctities grounded in chance, or in the very meaning of the prohibition? Apparently not. It is reasonable to assume that there is a good reason why the prohibition against eating consecrated food in impurity, and the punishment attached to it, are relevant only to altar-sanctities and not to sancta dedicated to Temple maintenance.

It is true that there is no logical contradiction in saying that there is a prohibition, and even a punishment of karet, for eating sancta dedicated to Temple maintenance in impurity. But once that law has been stated, we infer from the meaning of the law of eating in impurity that the category relevant to this law is specifically altar-sanctities.

If so, the question arises what the difference is, if there is one at all, between defining halakhic categories and introducing a law. If some exposition were to teach us the law of karet for eating sacred things in impurity, and if we understood the meaning of that law, we would understand that it can apply only to altar-sanctities. If so, de facto a halakhic category would have been defined here. The definition of the category to which a certain law applies is, in a certain sense, equivalent to the legal determination itself. One who understands the rationale of redeeming second tithe, or a firstborn animal, will be able to infer that the redemption can be carried out only with certain objects. Is this a legal determination, or a determination of the definition of a halakhic category? Is there any difference at all between these two?

Definition by Extension and Intension¹²

The problem we raised above can be formulated through the distinction between definition by extension and definition by intension. In the essay for Parashat Korah, 5765, we presented two ways of defining a category, or a term: definition by extension, which describes the category by listing the items included in it, and definition by intension, which describes the category through the shared characteristics that distinguish the items included in it. For example, the term “democratic state” can be defined by enumerating all the democratic states that exist in the world. That is a definition by extension. But the term can also be defined in an essential way, through the meaning of democracy as the set of shared characteristics that distinguish all those cases. For example: states in which the government is elected by all the citizens once every few years, and in which there is separation of powers, civil rights, and the like.

It is clear that behind the extensional definition there stands some intensional definition. How do we know to include a certain state in the list of democratic states for the purpose of an extensional definition? Presumably by considering its essential characteristics. Even so, there are times when it is more convenient to use definition by extension rather than definition by intension. For example, when the term is intuitively clear to us, but it is difficult to characterize it explicitly. In such a case, it is convenient to use examples in order to explain it to someone else, or to define it by extension.

In this terminology, we can formulate the problem raised in the introduction by saying that there is no difference between an extensional definition of the situations to which the law under discussion applies and a definition of that law itself. If so, the hermeneutical principles that deal with defining situations are in fact defining laws, except that they do so by extension rather than by intension. The halakhic characteristics are what stand behind the categories we have defined, and therefore what we are really doing here is defining halakhic contents indirectly.

In the example we discussed above, the definition of the category to which the punishment for eating sacred things in impurity applies, that is, the set of objects that are altar-sanctities, reflects some feature of the prohibition itself, and that feature is what underlies the definition of the category to which the prohibition applies. It is the same reason for which the punishment is imposed only on one who eats altar-sanctities in impurity, and not on one who eats sancta dedicated to Temple maintenance in impurity.

The reason, however, is not always clear to us, and it is certainly difficult for us to define it explicitly. Therefore the route of definition by extension is convenient. The principle of “an item singled out from a general category” helps us bypass the problem of giving explicit definitions to laws, by directly defining the category to which those laws apply. Once that is done, we may perhaps search for the essential definition that underlies the extensional category.

The mechanism that links the category with the essential characteristics is the search for ta’ama de-kra, the rationale of the verse. If we knew the reason for the law, we would be able to define clearly the category of situations or objects to which it applies. Since we do not generally expound ta’ama de-kra, definition by extension is a more convenient and efficient alternative.

A Parallel Picture in the Methodology of Science¹³

A similar mechanism can be seen in the process of scientific progress. We are confronted by phenomena that we do not understand, and we search for the general law that lies behind them. There is an inherent problem in this search, because before we know how to divide the phenomena and situations into relevant categories, we cannot look for a general explanation for them. For example, imagine that we are faced with the whole range of physical phenomena in the world, and suppose that we still know no general physical law at all. We now begin to look for general laws. The basic question is: what is the category of phenomena that stands behind a given general law? For example, do the falling of bodies to the ground and the phenomenon of the tides belong to the same category? Is the same general law behind them, or do they belong to different scientific laws? And perhaps there is some general law that links the falling of bodies downward with the color of the surrounding trees?

As noted, as long as we do not know the laws, we cannot define the relevant categories. But the converse is also true: as long as we do not know the division into categories, we cannot arrive at the general laws, because we will not know which categories of phenomena belong to the same law.¹⁴

Karl Hempel, in his book Philosophy of Science, published by the Open University, gives an example of this phenomenon in Dr. Semmelweis’s search for the causes of puerperal fever. Before he knew that one must connect such diseases with infection and infectious agents, the question whether the doctors and midwives washed their hands might have seemed like a question better suited to magicians. Today, after we know the connection between infection and disease, the question seems relevant to us, and even obvious.

Phenomenological and Essential Theories

In scientific research it is customary to divide progress into two successive stages. From the raw facts one forms a phenomenological theory, that is, a descriptive theory. Such a theory does not explain the facts; it merely describes them. Only afterward can one look for an explanation of that set of facts.

For example, if one has a phenomenological theory according to which there is an attraction between bodies that possess mass, then one can connect the phenomenon of falling bodies with the tides. Once such a connection has been made, one can look for an essential theory that explains the nature of the connection and the precise description of the attraction between those bodies. At that point one can also investigate whether stars have mass, and whether seawater has mass, and attribute the paths of the stars, or the tides, to the same gravitational force that is found on earth.

Another example is scale laws that link different phenomena mathematically. Zipf’s laws are well known for showing similarities between the distribution of population sizes among cities in the world, the distribution of planetary orbits, and so on. All these behave according to power laws. For example, the number of cities with a given population size is proportional to some power of that population size. We see that the distributions of different phenomena are similar, and therefore infer that they are related to one another in some way. Thus we group them into categories, even before we have any real understanding. Afterward we seek an explanation of that shared phenomenon by studying the characteristics of all the items that belong to the relevant category. What is shared by population sizes in large cities and planetary orbits? If we find such an explanation, we will have an essential theory, that is, an understanding of the phenomena.

The phenomenological theory is nothing but a grouping of phenomena into categories according to their visible and external characteristics. The essential theory is an attempt to trace the deeper roots of those phenomena. Clearly, if we possess an essential theory, we can in principle derive the phenomenology from it. But the reverse is not true. The way from phenomenology to essence is neither simple nor univocal, for there may be several essential explanations for the same phenomenology.¹⁵

Application to Halakhic Midrashim

In this terminology, principles such as “an item singled out from a general category,” or generalization and specification, are principles that deal with phenomenology. They group halakhic phenomena into categories. Afterward, one can perhaps also try to think about the essence, within the limits of expounding ta’ama de-kra.

As we have already mentioned more than once, the same methodological problem described above exists in the halakhic context as well. We have a structure of generalization-specification-generalization. We know that the conclusion is an expansion of the domain of the specification, that is, to things similar to the specification. But along which axes are we to expand it? The same is true regarding expansion based on the principle of “an item singled out from a general category.” For example, the specification is the peace offering, and we conclude that karet for eating sacred things in impurity applies only to that which resembles the peace offering within the general category. A similar exposition could have been made on the basis of generalization-specification-generalization, with the peace offering as the specification singled out and then generalized.

But the expansion to a category that includes the peace offering is not unambiguous. In what sense of similarity? Does it include all objects that begin with the same letter as the peace offering? Or perhaps everything that expresses joy, as the peace offering does? As long as we do not know the meaning of this prohibition, we cannot guess along which axes we should expand the specification that was singled out from the general category.

Therefore we must develop a phenomenological theory. Even before we possess an essential understanding, it seems reasonable to us that this prohibition ought to be connected to degrees of holiness. Therefore technical expansions based on similar names, or on expressions of joy, do not seem relevant. The conclusion is that we should probably extend the punishment to all altar-sanctities. That is the natural category to which the law can be extended.

This expansion stems from an intuitive sense that this is the relevant category, despite the fact that we still do not have an explicit definition of the meaning of the prohibition that would yield the correct category. Such a definition does not exist even after the exposition, for that would amount to nothing other than ta’ama de-kra. This intuitive sense is what underlies phenomenological theories, both in halakha and in science. It is an intuition that anticipates full understanding.

The Analytic Character of Scientific Equations

We asked above whether there is a necessary relation between the law under discussion and its scope of application. Would someone who fully understands why there is a punishment of karet for eating sacred things in impurity be able to derive from that understanding that such a punishment is imposed only for eating altar-sanctities? Apparently yes. It is reasonable to assume that there is a good reason why the punishment is imposed only for eating altar-sanctities, and that this probably follows from the very nature and meaning of that punishment.

A similar question exists with respect to scientific laws and equations. For example, Newton’s second law establishes a direct relation between the force acting on a body, F, and the acceleration it develops, a: F = m*a. The coefficient of proportionality is the mass, m.

We may ask whether the equation that describes Newton’s second law is an analytic definition of the concept “force,” or whether it is a statement with empirical content. One can understand the equation as setting a relation among three concepts that are defined independently: force, mass, and acceleration. In that case, it is a statement with empirical content. One can test whether that relation in fact obtains in reality between the concepts. By contrast, one can understand the law as a definition of the concept “force.” Since we have no independent way of defining force except through acceleration, the equation is then nothing more than a definition lacking empirical content. It is not open to independent empirical testing.

Put differently, one might say that a person who fully understood what mass is ought to have inferred that if a body possessing mass accelerates, then this can also be described in terms of force, which is nothing other than a different verbal description of the fact that the body accelerates. According to this approach, our treating this equation as a statement with empirical content stems from the fact that we do not yet know the full meaning of the concept “mass,” or of the concept “force.” Experience helps us uncover definitional relations among scientific concepts.

In both cases, the Torah case and the scientific one, we are saying that a proposition that does not appear necessary turns out to be a necessary analytic claim that follows from the definitions of the concepts contained in it. The appearance that leads us to think that the claim is not necessary is simply lack of knowledge: either a full understanding of the concept “mass,” or a full understanding of the concept “eating sacred things in impurity.” For one who had such understanding, these propositions would follow from it necessarily.

If that is indeed the situation, then defining the relevant category and defining the law itself are completely identical processes, with the very same content. Once we know and understand the law, we can derive from it the relevant category, and vice versa. In the realm of science, this approach does not appear to be correct; see Et Asher Yeshno ve-Asher Eineno, Gate Two. In the realm of halakha, by contrast, it seems more plausible that it is true.

In any case, in a situation of lack of knowledge, whether halakhic or scientific, there is no avoiding the creation of phenomenological theories before understanding emerges, even if that understanding may later turn out to be an analytic result of the definitions of concepts. This intuition arises from that same implicit grasp of the meaning of the concepts. At least in the Torah realm, it seems that our ability to create a phenomenological theory without explicit understanding derives from our intuitive understanding of the concepts involved in the subject, from which we derive the appropriate conclusions.

Of course, this claim does not render the various hermeneutical principles superfluous. There are principles that approach a biblical-halakhic topic in a phenomenological way, and others that approach it in an essential way. Each of these paths could in principle have been replaced by the other, but so long as there is a lack of knowledge, which is essential to human beings as such, there is room for both.

Footnotes