Vayakhel (5764)

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

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Mida Tova — With God’s help, eve of the Sabbath, Parashat Vayakhel, 5765

Questions

1. What is a hekesh (scriptural linkage or analogy)?
2. How many sin-offerings are required for each inadvertent violation of the Sabbath?
3. Why is hekesh not a binyan av (derivation from a paradigmatic case)?
4. Two kinds of hekesh: generalization and comparison.
5. Must we apply the rule “two verses that come as one do not teach” to generalizing forms of hekesh?
6. What do the two kinds of hekesh have in common?
7. In which of them is there a requirement that the particular and the general be similar in character?
8. The significance of the system of hermeneutical principles as part of the maturation of our civilization.
9. Postmodernism, New Age, and the hermeneutical principles.

Principles Discussed

• Hekesh.
• A matter that was included in a general category and then singled out in order to teach.
• Binyan av.
• Two verses that come as one do not teach.

A. What Is Hekesh?

Moses assembled the whole community of the Israelites and said to them: These are the things that the Lord has commanded you to do. On six days work may be done, but the seventh day shall be holy for you, a sabbath of complete rest to the Lord; whoever does any work on it shall be put to death. You shall kindle no fire throughout your settlements on the sabbath day.

— Exodus 35:1-3

It was taught in a tannaitic teaching: Rabbi Natan says, concerning the verse “You shall kindle no fire throughout your settlements on the sabbath day” — what need is there for this statement? For it is said: “Moses assembled the whole community of the Israelites… These are the things… On six days work may be done.” “Things,” “the things,” “these are the things” — these are the thirty-nine labors that were said to Moses at Sinai. One might think that if a person performed all of them in one lapse of awareness, he is liable for only one offering; therefore Scripture says: “In plowing time and in harvest time you shall rest.” Yet I would still say: for plowing and for harvesting he is liable for two offerings, but for all the others he is liable for only one. Therefore Scripture says: “You shall kindle no fire.” Kindling was included in the general category; why was it singled out? To establish an analogy to it, and to tell you: just as kindling is a primary category of labor, and one is liable for it separately, so too every act that is a primary category of labor carries separate liability. Shmuel followed Rabbi Yose, who said: kindling was singled out merely for an ordinary prohibition. For it was taught: kindling was singled out merely for a prohibition — these are the words of Rabbi Yose. Rabbi Natan says: it was singled out to divide the labors.

— Babylonian Talmud, Shabbat 70a

“For all of them, one [offering]” — because Scripture grouped them together as one category of labor and under a single prohibition. And as for the rule “a matter that was included in a general category and singled out in order to teach…” we do not apply it here, because the general category is stated as a prohibition, whereas the particular case is stated as a positive commandment, and we do not interpret such a general-and-particular in that way. Alternatively, plowing and harvesting are two verses that come as one, and they do not teach, since Scripture could have written only one.

“To establish an analogy to it” — namely, to all the other labors included with it in the general category, for this is a principle in the Torah: whenever a matter was included in a general category and then singled out in order to teach, it was singled out not to teach only about itself…

— Rashi to Babylonian Talmud, Shabbat 70a

Introduction¹

On this page we will deal briefly with the issue of separate liability for distinct labors on the Sabbath. It is accepted that sin-offerings are brought for inadvertent sin. The number of offerings is determined by the number of lapses of awareness. Calculating the number of such lapses is a complicated Talmudic issue, and the Sages disagree on several matters in this area. In practical halakha (Jewish law), however, we follow the rule that the number of sin-offerings corresponds to the number of lapses of awareness. Therefore, one who performed several different kinds of labor on the Sabbath, even within a single lapse of awareness, must bring a separate sin-offering for each labor. In Jewish law this is called the division of labors, meaning that different labors are treated separately with respect to sin-offerings.

As the Talmudic passage in Tractate Shabbat cited above states, there is a source for this law at the beginning of our parashah, in the command concerning the prohibition of kindling fire on the Sabbath. The background question is why the Torah chose to specify the labor of kindling in a separate prohibition, when in fact there are thirty-nine distinct primary categories of labor prohibited on the Sabbath, and these are not spelled out in the Torah but are derived through various interpretive methods.² The tannaim, Rabbi Natan and Rabbi Yose, disagree on the answer to this question in the baraita cited at the end of the passage above and in its parallels: Rabbi Natan holds that kindling was singled out in order to divide the labors, that is, to teach the principle of separate liability for distinct labors. Rabbi Yose, by contrast, holds that kindling was singled out in order to teach that on the Sabbath it is prohibited only by an ordinary prohibition, and not by the more severe prohibition punishable by stoning and karet (spiritual excision), like the other primary and derivative categories of labor on the Sabbath.

The Difficulties in Rabbi Natan’s Derivation

Rabbi Natan’s derivation begins by trying to learn the division of labors from the verse, “In plowing time and in harvest time you shall rest.” From there he infers that for plowing and harvesting one is liable for two sin-offerings, one for each labor separately. In other words, those two labors are distinct for purposes of liability. But he then raises the possibility that this distinctness applies only to those two labors, whereas for all the others one would be liable for only a single sin-offering. He therefore uses the derivation from kindling to teach that all the other labors likewise each carry separate liability.

There are several difficulties in Rabbi Natan’s line of reasoning:

1. It seems that the derivation from kindling does not replace the derivation from plowing and harvesting, but adds to it. Why is the second derivation not sufficient on its own?
2. If we indeed establish an analogy from kindling to the other labors, why could we not establish an analogous linkage from plowing and harvesting as well? And if we reject that linkage on the grounds that perhaps plowing and harvesting are unique, then why not say that kindling is likewise unique? More generally: in what way is the second linkage superior to the first?
3. What exactly is the nature of the linkage from kindling to the other labors? Is this an ordinary comparison between one labor and the others, or is it a comprehensive teaching about them all? We will elaborate on this point below.
4. Why does Rabbi Natan need the preliminary step in which he derives the number of labors prohibited on the Sabbath before he derives the division of labors? If that number did not emerge from our verses, but from tradition or some other source, would there be any difficulty here? Put differently: why is Rabbi Natan’s introductory formula, “since it is said,” necessary, when it seems merely to explain what follows?

What Is the Hekesh Here?

As noted, Rabbi Natan’s final conclusion derives the division of labors from the verse about kindling by means of a hekesh. But it is not clear what is being linked to what here. As we saw on the page for Parashat Vayigash, and also on the page for Parashat Vayechi, a hekesh usually appears where there is a list of items in the same verse. In such a case, the items in the list are linked to one another. But in our case there is no list at all, and the labor of kindling stands alone in the verse. The same difficulty exists with regard to the derivation from plowing and harvesting: what exactly is linked to what?

Moreover, the character of these derivations is somewhat different from that of an ordinary hekesh. In a standard hekesh, a feature of one item in the list is transferred, by rabbinic interpretation, to the other items. But here the relevant feature is not a property of kindling in itself. Rather, it is a feature that distinguishes kindling from the other labors: that one incurs separate liability for it. Imagine a person who inadvertently violated the prohibitions of kindling and trapping. Would he be liable for two offerings because the principle of divided liability was stated with respect to kindling, or perhaps liable for only one because that principle was not stated with respect to trapping? Seemingly, the principle of dividing the labors concerns the relation among the labors, not a property of each labor taken separately. If so, it appears that the hekesh here teaches a general principle that applies to all the labors, and is not an ordinary hekesh from one labor to others. This is not a property of kindling being transferred to the other labors, but a property of the relation that exists, or does not exist, among them.

These two considerations suggest that the hekesh under discussion here is not a comparison between two particulars, but a generalization from a particular to the general category that contains it. We will spell this out further below and examine its implications.

Rashi’s Approach

It seems that this very difficulty forced Rashi, in his comments on the Talmudic passage, in a direction that appears to depart somewhat from the plain sense of the text, as the citation above shows. Rashi sees these two linkages as instances of the special hermeneutical rule, “a matter that was included in a general category and then singled out in order to teach.” In his view, this is not a hekesh in the ordinary sense, but rather that distinct rule, because that is the rule responsible for learning from one specific particular to the whole from which that particular emerged. An ordinary hekesh is a comparison among items in a list, whereas “a matter that was included in a general category and then singled out in order to teach” is a rule by which we learn from a single item about the general category of which it is a part.

Rashi adds that the first linkage, from plowing and harvesting, is rejected for two reasons: first, because the rule of “a matter included in a general category” cannot be used when the general category, labor, is stated as a prohibition, whereas the particular case, plowing and harvesting, is stated as a positive commandment, namely “you shall rest”; and second, because plowing and harvesting are two verses that come as one, and therefore one cannot learn from them to all the other labors.³

What is the difference between these two possibilities? They seem to correspond exactly to the two possibilities we raised above. According to the first, there is no way to carry out a hekesh here at all, because the general category is formulated as a prohibition while the particular is formulated as a positive commandment. If so, the derivation from plowing and harvesting falls away entirely, and in the end we derive the division of labors only from kindling. This sits somewhat awkwardly with the wording of the Talmud, but conceptually it is the most spacious reading. In the end, after all, we truly derive the division of labors only from kindling, and the first two questions raised above disappear of themselves.

According to the second possibility, by contrast, there is no principled obstacle to learning from a particular of different character,⁴ but those two verses alone cannot teach because of the rule “two verses that come as one do not teach.” On this view, even in the final analysis they do teach the division of labors, but only with respect to themselves, not with respect to all the others. The others are learned from kindling, perhaps together with them.

Still, one may ask: why is this pair needed in addition to kindling? Why should kindling not teach even with respect to plowing and harvesting? And another difficulty arises: what does kindling help, given that it is a third verse, and three verses, by all opinions, do not teach either? Seemingly, we should conclude that the division of labors was stated only with respect to these three cases, and not with respect to the rest.

One might suggest that there is a relation of mutual necessity between plowing and harvesting on the one hand and kindling on the other, and therefore they are not treated as three verses; in that case one could learn from all three by binyan av, that is, by the rule of a common denominator. See, for example, the page for Parashat Mishpatim on learning from three teaching cases. According to this possibility, there is likewise no difficulty in the fact that the Torah mentioned plowing and harvesting and did not content itself with kindling, which would then have taught about them as well, because kindling could not have taught with respect to them. The obvious explanation for the uniqueness of plowing and harvesting is precisely that they are positive commandments rather than prohibitions, as we saw in the first possibility. Yet in the first possibility, this difference seemed to function as a formal limitation within the rule of “a matter included in a general category and singled out in order to teach,” not as a parameter that generates mutual necessity. And the second possibility does not accept the distinction between positive and negative formulations as relevant.⁵ Moreover, on Rashi’s view this explanation is difficult, because in his description of the second possibility he does not mention that distinction at all. His language suggests that the issue does not trouble him in the least.

Perhaps this can be understood differently, in light of the proposal we made on the page for Parashat Tetzaveh. As recalled there, we raised the possibility that even when there is no mutual necessity among several teaching cases, whether two or three, one can sometimes treat them as additional examples that come to reinforce the generalization and give it greater force. In such a case we may derive from them, by way of a common denominator, to other cases as well, even though there is no mutual necessity among them. In certain cases we will not apply the rule that “two verses that come as one do not teach.” As we are about to suggest, in our case this possibility seems almost compelled, in light of the distinctive character of the interpretive argument.

Between Generalization and Comparison: The Level of the Hermeneutical Principles

As we saw above, the hekesh here neither appears nor functions in the ordinary manner of hekesh. In ordinary cases, hekesh is a comparison among items in some biblical list, whereas here the hekesh seems to function as a generalization. A particular that departs from the general category teaches us something about the nature of the category as a whole, which includes that very particular. Put differently: the ordinary hekesh is an analogy, whereas the hekesh here is an induction. See the page for Parashat Noach, part II.

When one wishes to make an analogy from one particular to another, as in binyan av from one verse, or from two particulars to a third, as in binyan av from two verses or the rule of a common denominator, then there are rules requiring mutual necessity between the two teaching cases and the like. But in our case the particular does not teach about something external to itself; it teaches about the general category of which it is itself a part. In such a case, precisely the absence of mutual necessity between it and the other examples strengthens the generalization, and one may infer that throughout this category there is a principle of separate liability for distinct labors.

Indeed, this is precisely what the rule “a matter that was included in a general category and then singled out in order to teach” amounts to. What has been singled out does not teach by virtue of itself. Rather, its very emergence from the general category teaches about the category from which it emerges. In binyan av, the departure from the category has no significance at all; the particular stands on its own, and from it we draw conclusions about another particular that resembles it. In our case, the departure from the category is itself the teaching entity. Why did the Torah take the labor of kindling out of the general category of the thirty-nine labors? In order to teach a property of that whole group, namely that one is liable for an offering on each individual labor. What teaches is the departure from the category, not the particular as such. We do not learn the division of labors from the labor of kindling, but from the fact that the Torah extracted this labor and placed it by itself. Hence there is no significance to constructing mutual necessity between it and the other examples, plowing and harvesting, for we do not learn from each one of them, or from the combination, but from the very fact that the Torah took them out of the category and wrote them separately.

It follows, presumably, that according to this possibility as well, the fact that plowing and harvesting are positive commandments rather than prohibitions is unimportant. We do not learn from them as such, but from the very fact that the Torah took them out of the category and treated them separately. Therefore a refutation that singles them out by saying that they are positive commandments cannot undermine our derivation.⁶

This may also explain why Rabbi Natan prefaces the discussion with the derivation of the thirty-nine labors from the opening verse of our parashah: he must first present the general category from which the particular emerged. As noted, what teaches is the departure from the category, not the particular itself.⁷

What Is the Difference Between “A Matter Included in a General Category” and Binyan Av?

This may be the reason that the rule “a matter that was included in a general category” is defined as an independent hermeneutical principle, and not counted as a type of binyan av. At first glance, learning from a particular about the general category that contains it looks like an ordinary analogy, and there would seem to be no reason to define a special interpretive rule for it. But from our analysis it emerges that this is a different kind of rule.

If we take one item and infer from its own characteristics to the characteristics of the other items in the group to which it belongs, then we are dealing with ordinary binyan av. The teaching case is that specific item, and what is learned are the other items in the category. But in the rule “a matter that was included in a general category,” at least in manifestations of the type described here, the situation is different. We do not learn from a characteristic of the particular itself, but from the fact that the Torah took it out of the category. This is a textual rule, not a logical one. Beyond that, as explained above, in this rule we do not learn about a certain characteristic of the other particulars in the same category, but about a characteristic of the whole group itself. In binyan av, by contrast, we learn about the characteristics of each item, not about properties of the group as a whole.

Summary: Two Ways of Understanding the Interpretive Argument

We have seen in Rashi two ways of understanding the interpretive argument:

1. The hekesh in the argument functions like an ordinary binyan av, and therefore we learn from the examples to the general category that contains them. One cannot learn from plowing and harvesting because these examples differ in character from the general category about which we are learning. According to this approach, the conclusion seems to concern punishment rather than the transgression itself, and therefore one cannot use a particular of a different character, such as a positive commandment as opposed to prohibitions, in order to learn about the category.

According to this approach, the final derivation comes only from kindling. We have found no explanation for why the derivation of the thirty-nine primary categories of labor at the beginning of the parashah was placed before it.

2. According to the second possibility, the derivation concerns the transgression rather than the punishment, and therefore the different character of the particular does not interfere with the argument. The reason we do not learn from plowing and harvesting is that these are two verses that come as one. That is, they teach only about themselves, while kindling teaches us about all the rest. The reason all three teaching cases are needed is one of two possibilities: either there is mutual necessity based on the difference in character between the teaching cases, though as we saw this is a strained direction for several reasons; or, on this approach, we learn from all the teaching cases together even though there is no mutual necessity among them, since on this view there is no difference between a prohibition and a positive commandment. The teaching cases are simply the data that underlie the generalization, and therefore we do not learn from them as such, but from the fact that the Torah singled them out from the general category.

B. Hekesh as Synthetic Thinking

What Is Hekesh?

In the previous section we saw that there are two different patterns that go by the name hekesh; in fact, there are many more, as we shall note below. One is a comparison among items in a biblical list. The second is the emergence of one item from a general category in order to teach about the whole category. The question now naturally arises: what, then, is hekesh? What is common to these two patterns? Put differently: why do the Sages refer to a distinct rule such as “a matter that was included in a general category” by the name hekesh, instead of by its own name?

On the page for Parashat Vayigash we saw that the term hekesh does not necessarily designate one specific hermeneutical principle. It is a general expression meaning comparison or analogy. But if that is so, then the pattern we encountered here does not seem to fit the term, because, as we saw, it is based not on comparison but on generalization.

Between Comparison and Generalization: The Logical Level

On the page for Parashat Noach we presented three different forms of logical inference: from the general to the particular, deduction; from the particular to the general, induction; and from one particular to another, analogy. The relation between the latter two was discussed on the page for Parashat Va’era, where we saw that it is complex and can be approached in two different, indeed opposite, ways. One may understand comparison as tacitly presupposing a generalization, and one may understand generalization as tacitly presupposing many comparisons.

For example, if we compare frog A with frog B, and we assume nothing more than that both are frogs, then the conclusion is valid for all frogs. Seemingly, the conclusion regarding frog B is only an application of the general conclusion about the whole class of frogs. On such a view, analogy is based on induction. Conversely, one can ask: from where did we obtain the general conclusion about all frogs? Seemingly, it is only the accumulation of a collection of particular conclusions about each frog separately. But all those particular conclusions are analogical in character. If so, on this view induction is nothing but a collection of analogies.⁸

It is therefore difficult to draw a sharp distinction between analogy and induction, and they have much in common. Presumably, that common foundation, which is present both in comparisons and in generalizations, is precisely the foundation we are seeking as the basic content of the term hekesh.

Analytic Thinking and Synthetic Thinking

M. Avraham, in his book Two Wagons and a Hot-Air Balloon, addresses this question and defines two general modes of thought, which he there calls analytic thinking and synthetic thinking. Analytic thinking is logical-mathematical thought, whose conclusions follow necessarily from its premises. As he explains there, and see also the page for Parashat Noach, part II, this necessity stems from the fact that the conclusions are actually already contained in the premises. Put differently, analytic thinking tells us nothing essentially new. Its role is to uncover, sharpen, and clarify what we already know. Synthetic thinking, by contrast, is supposed to teach us something beyond what was already known at the beginning of the inference. That is why this kind of thinking is not based on necessary inferences.

This may be illustrated by the well-known joke about the hot-air balloon, cited at the beginning of Two Wagons and a Hot-Air Balloon. Two people were flying in a hot-air balloon and lost their way. When they saw a man plowing a field below, they asked him where they were. He answered: “Above my field.” One of them then said to his companion: “The man we just passed over is probably a mathematician.” Asked why he thought so, he replied: “For two reasons. First, what he said was perfectly precise. Second, it is of no use to us at all.”

These two characteristics of the mathematician depend on one another. Anything that is perfectly precise is of no use to us at all. As explained above, the reason a claim is perfectly precise and necessarily true is precisely that it contains nothing new, that is, that it is of no practical help whatsoever. In philosophy this phenomenon is called the emptiness of the analytic.

Hekesh as Synthetic Thinking

We can now identify the common feature shared by analogy and induction: both teach us something beyond what we knew in advance, that is, beyond what is contained in the premises of the inference. Both are forms of synthetic thinking, as opposed to analytic thinking. Our conclusion, then, is that hekesh is an expression of synthetic thinking.

As we saw on the page for Parashat Bereishit, the entire system of hermeneutical principles is a system of analogical, and perhaps more accurately synthetic, modes of thought. This is a unique addition to Greek mathematical logic, which alone is generally considered today entitled to the name logic. The hermeneutical principles are not a substitute for deductive logic, but an addition built on top of it. According to those who endorse the synthetic position, it is not enough to use analytic tools of thought, because we cannot learn anything if we focus only on them. Hekesh, or synthetic thinking, is what enables us to extend our knowledge into regions that are not yet known to us. These are the tools of expansion, creativity, and growth in human thought generally, in science, and also in Torah and halakha.⁹ That is why, in fact, it serves as a general name for the mode of thought that characterizes the interpretive methods. It is therefore no wonder that the term hekesh designates many different principles, and sometimes serves as a general name for interpretive inference, and even for inference in general.

The Two Parts of the Hermeneutical Principles

Several times in the past, see the page for Parashat Chayei Sarah and also the pages for Vayeshev-Vayechi, we have distinguished between the formal elements that characterize the pattern of a given hermeneutical principle and its substantive elements. The formal elements cannot by themselves lead to the result. There is always some dependence on the content involved in the interpretation. Even reconstructing the interpretive methods does not mean uncovering basic premises in the mathematical sense, from which halakhic conclusions could be derived in a wholly mechanical way, by means of a computer. There will always remain a unique human element here, perhaps also a somewhat subjective one.

Some infer from this that everyone interprets as he pleases, and that there is really no such thing as “interpretive methods” at all. Such conclusions assume that a defined interpretive system must be nothing other than an axiomatic system with mathematical unambiguity. See the end of the page for Parashat Bereishit. That is, for every problem there must be one correct solution, and it must also be possible to mechanize it. If no such solution exists, proponents of this view think that there is probably no defined interpretive system at all. Quite a number of readers of these pages have already told us that we are chasing the wind, meaning that there simply are no defined interpretive methods in halakha.

This conclusion is diagnosed in Two Wagons and a Hot-Air Balloon as an analytic stance. Such a stance assumes that only deductive axiomatic systems deserve the title of logical systems. Only within such systems do the notions of validity and invalidity apply to the conclusions obtained through them. Those who hold such positions accept as valid only claims that have been proven. By contrast, those who adopt synthetic positions are willing to recognize the validity, though not the necessity, of conclusions reached through synthetic inferences such as analogy and induction.

Two Paths of Maturation

The significance of these modes of thought can be understood by looking at a typical process of maturation in an individual person, which closely parallels the maturation of our civilization as a whole.

1. A person begins life as a small child, characterized by considerable dogmatism. Everything his parents or teachers tell him appears true to him, with no need for justification. This is also the early stage of our civilization, when myths held sway and superstitions guided the actions of many people without challenge and without explanation.

2. The next stage is adolescent rebellion. The growing youth challenges his parents and teachers: “How do you know? Prove it!” He senses that they are dogmatic, holding their beliefs without real justification or foundation, whereas he will be more rational than they are. He will do nothing without explanation and proof. This is an analytic stage, in which the youth believes that “valid” and “analytically provable” mean the same thing. This stage in the development of our civilization opened in ancient Greece, the cradle of Western rationalism.

3. A very important crossroads arrives at the end of adolescence, when the youth realizes that in fact he cannot prove any meaningful claim absolutely. As noted, the analytic is empty, and therefore no genuinely novel claim can be proven analytically. Put differently, every logical proof is a kind of begging the question.¹⁰ At that point two paths lie open before him. One is to continue assuming the youthful premise that only a proven claim is valid. In that case he moves into total skepticism and concludes that no claim is more valid than any other. This kind of maturation occurred in our civilization in the middle of the previous century, and it is called postmodernism. The second possibility is to abandon that premise itself, and adopt an approach willing to recognize the legitimacy and validity of unproven claims, provided that they have a synthetic grounding based on hekesh.

At times the distinction between these two paths is very difficult to draw. Together with postmodernism, many phenomena have grown up that stand somewhere between them. Their common name in Israel, as in the wider world, is New Age. Modern spirituality, sometimes even pagan in character, alternative medicine of varying degrees of seriousness, communication with entities from other worlds, and the like, all appear in our postmodern world and lay claim to certainty and rationality. With respect to a considerable number of these phenomena, it is very hard to know whether we are dealing with the first path of maturation or the second. Is this a renewed certainty, albeit without full logical justification, or charlatanism taking hold of postmodern skepticism, in which anything goes?

The Hermeneutical Principles

The main reason for all these phenomena is that we do not possess systematic tools for dealing with synthetic thinking. Deductive logic is a collection of well-defined and highly developed rules, but it does not help us at all, except in mathematics. Synthetic inferences, by contrast, which are the relevant ones in most contexts addressed by human thought, often look like speculations. If we lack a mathematical grounding, everything appears subjective. That is the essence of the analytic position.

This is where the hermeneutical principles enter the picture. As we mentioned on the page for Parashat Bereishit, the Nazir held that the system of hermeneutical principles is a kind of map of synthetic thinking, what he called “auditory logic.” It is a tool for dealing with phenomena that cannot be handled by logical-analytic means: a map of analogies and inductions, and a useful guide for using them.

If so, the renewal of the skill and capacity to use these principles takes on greatly increased importance and force in light of the picture described here.

Footnotes