Bereshit (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 — Sabbath eve, Parashat Bereshit, 5766

To all our dear readers: may God be with you, and best wishes for a good year.

This issue of Midah Tovah opens its second year, and our aim this year is to expand upon points that arose in the corresponding essays last year. In each essay we will begin by presenting several principal points from last year’s essay, and then we will broaden some of them as far as space permits.

The primary aim of the Midah Tovah Association is to arrive at a systematic study of the hermeneutical principles, and afterward also of the rest of the Written and Oral Torah, and even beyond that. At the present stage, we see this as one further step toward that goal.

As always, we will be happy to continue receiving readers’ responses. The feedback gives us strength to continue our enterprise. Various suggestions, comments, and objections will likewise be warmly welcomed.

The questions:

1. What is the relation between qal va-homer (a fortiori inference) and binyan av (inference from a paradigm case)?
2. Is qal va-homer a comparative inference or an amplifying inference? Is there a difference in this respect among the various types of qal va-homer?
3. What is the relation among the three types of qal va-homer, and why are they all called qal va-homer?
4. If all the hermeneutical principles are forms of comparison, then what distinguishes them?
5. Why is the grasses’ first line of reasoning a qal va-homer?

The principles:

• Qal va-homer
• Binyan av
• Gezerah shavah (verbal analogy)
• Im eino inyan (reassigning a verse when it is unnecessary in its immediate context)

A. Summary from Last Year

And God said: Let the earth bring forth vegetation, seed-bearing herbs, fruit trees bearing fruit according to their kind, whose seed is in them, upon the earth. And it was so.

And the earth brought forth vegetation, seed-bearing herbs according to their kind, and trees bearing fruit whose seed is in them according to their kind. And God saw that it was good.

— Genesis 1:11–12

Rabbi Hanina bar Pappa expounded: “May the glory of the Lord endure forever; may the Lord rejoice in His works” (Psalms 104:31). This verse was spoken by the Prince of the World at the moment when the Holy One, blessed be He, said “according to its kind” concerning the trees. The grasses then drew a qal va-homer on their own: if the desire of the Holy One, blessed be He, were for mixture, why did He say “according to its kind” regarding the trees? And another qal va-homer: if, in the case of trees, whose way is not to emerge intermixed, the Holy One, blessed be He, nevertheless said “according to its kind,” then we, all the more so. Immediately each and every one emerged according to its kind. The Prince of the World then began and said: “May the glory of the Lord endure forever; may the Lord rejoice in His works.”

— Babylonian Talmud, Hullin 60a

In last year’s essay on Parashat Bereshit, we focused on two general points: the need for command, and the approach of midrashic Platonism.

In the first part, we saw that command is what grants the commandments their normative significance; without command, they would be mere statements of fact. In philosophical terms, one may say that we argued that command is meant to circumvent the naturalistic fallacy identified by Hume, which prevents the emergence of a norm out of factual claims. According to Hume’s argument, if the Torah had confined itself to revealing that a certain act is harmful or beneficial, no normative obligation would thereby have arisen either to perform it or to refrain from it. That is precisely why command exists: to instruct us to pursue what is beneficial and avoid what is harmful.

In the second part, we presented a conception of the hermeneutical principles as forms of conduct built into creation itself. We saw this through the example of inanimate entities that, as it were, perform qal va-homer reasoning. Our claim was that the hermeneutical principles are existing Ideas, not arbitrary interpretive rules. From such a conception it follows that their validity and applicability pertain to reality as such, and not only to biblical interpretation.

As for the content of the midrash (rabbinic exposition) cited above itself, we discussed two aspects:
1. the difference between potentiality, which is amorphous and uniform, and actuality, which is varied and complex;
2. a brief remark on the grasses’ own qal va-homer argument.

The topic of qal va-homer itself was hardly discussed directly in that essay, and it requires expansion. After several essays dealing with this foundational hermeneutical principle, we can now return and examine the grasses’ qal va-homer reasoning as part of a discussion of the principle of qal va-homer.

B. The Qal va-homer Reasoning in the Midrash

The Grasses’ Reasoning

The midrash presents two lines of reasoning used by the grasses, and both are described as qal va-homer arguments. We will try to examine these two arguments and determine their character.

The First Reasoning

The first qal va-homer begins from the premise that the Holy One, blessed be He, did not command the grasses to emerge according to their kinds. Apparently, then, He wants them to emerge intermixed. But now the grasses wonder: if the desire of the Holy One, blessed be He, is for mixture, why did He command the trees to emerge according to their kinds? From this the grasses learn that, even though He did not command them explicitly to emerge according to their kinds, His desire is nevertheless for differentiation and distinction among species, and therefore they too must emerge according to their kinds.

Already last year we noted that this reasoning is unclear, for two reasons. First, from the fact that the Holy One, blessed be He, did not say this with regard to them, it may be that His will concerning them is different. Second, it is not clear what sort of qal va-homer is involved here. This is a conceptual argument, built at most on a comparative analogy, not on learning from the lesser to the greater, as we know from the standard use of qal va-homer. The grasses compare the obligation of the trees to their own obligation. There is no “lighter” and “more severe” here. As a comparison, one may contrast it with the second argument, which really is based on learning the more severe from the lighter.

The Second Reasoning

The second qal va-homer looks more like an ordinary qal va-homer. The grasses compare themselves to the trees and argue as follows: if the trees, whose natural way is to emerge separately, were commanded to emerge that way, then the grasses, whose natural way is not to emerge separate and distinct, all the more so should emerge that way.

Yet this qal va-homer too is not free of difficulties. If the trees, in their initial condition, already possess a formed character, namely, to emerge distinctly and not intermixed, why does the Holy One, blessed be He, need to command them at all to emerge in that manner? On the other hand, the grasses are not built from the outset in that way, since their natural tendency is to emerge intermixed. If so, how do they infer that the obligation of differentiation is imposed on them as well? Seemingly, that command is meant only for the trees, for whom this is their natural way, and not for the grasses.

The Solution We Proposed Last Year

Last year we proposed a solution that viewed the entire movement of the midrash as one single qal va-homer argument. The grasses engage in a two-stage qal va-homer. First, if the Holy One, blessed be He, commands the trees “according to their kind,” then He evidently wants distinction in the world, not mixture. Second, the trees are by their very nature such that their natural emergence is already distinct and not intermixed. Therefore, if the Holy One, blessed be He, nevertheless finds it necessary to command them to emerge distinctly, this must be something very important to Him. If so, in the case of the grasses, whose natural mode of emergence is not distinct by their very essence, all the more so does the Holy One, blessed be He, expect them to separate and differentiate from one another.

This solution too is not perfect. First, the wording of the midrash makes it seem that there are two different arguments here, both of them of the character of qal va-homer. Second, if this is indeed the overall logic of the midrash, then the first argument recorded there is superfluous. Everything needed is already contained in the second.

And third, the formulation of the opening argument seems somewhat problematic. That argument infers from the fact that the Holy One, blessed be He, commanded the trees to emerge separately that He evidently does not desire mixture. But on our approach here, the emphasis should be that emerging separately is evidently very important to Him, not merely that He wants them to emerge separately.

Put differently: the formulation of the midrash implies that had the Holy One, blessed be He, not commanded the trees to emerge separately, they would have emerged intermixed. But according to our proposal that is incorrect, since even without command they would have emerged according to their nature, namely, separately. The superfluous command addressed to them is meant to show us that distinction and individuation are very important to the Holy One, blessed be He. From this the grasses learn that, even though no such explicit command was addressed to them, they too are meant to emerge separately. In fact, the command is meant for the grasses and not for the trees, for the latter would have emerged separately even without any command. There is here something like im eino inyan. If the command is not meant for the trees, since they would have emerged separately anyway, then it is evidently meant to express a general policy, and therefore the grasses too are supposed to implement it.

We shall therefore nevertheless try to understand these two arguments separately. The second argument is apparently the one we proposed above and elaborated in last year’s essay. But the first argument is truly puzzling, and above all it is not clear why it is classified as a qal va-homer.

Explaining the First Reasoning: Qal va-homer and Comparative Reasoning

As we have seen, the first argument looks like comparative reasoning rather than qal va-homer. The question is what exactly distinguishes qal va-homer from comparative reasoning.

Let us take as an example the qal va-homer brought in the illustrative tannaitic teaching discussed in the essay on Parashat Beha’alotekha:

“If her father had but spit in her face, should she not be ashamed seven days?”

If her father spits in her face, she must be secluded for seven days. Then all the more so, if the Shekhinah (Divine Presence) spits in her face, she should be ashamed for seven days. The Talmudic discussion adds here that from the qal va-homer we ought to infer that when the Shekhinah spits in her face she should be secluded for fourteen days. However, the principle of dayyo — “it is sufficient for what is derived by inference to be like the source case” — reduces the conclusion and sets it at seven days, like the source case, namely her father. See Babylonian Talmud, Bava Kamma 25a, and parallels.

In the essay on Parashat Beha’alotekha we presented several rationales and explanations for the limitation imposed by dayyo in qal va-homer. In any event, once dayyo is applied, the derived case turns out to be equal to the source case, not more severe than it. This state of affairs can be understood in two possible ways:

1. The derived case really is more severe than the source case, but because of a technical problem — for example, the lack of a criterion that tells us where to stop the amplification produced by the qal va-homer — we place the derived case at the same level as the source case.
2. The derived case is not more severe than the source case. Qal va-homer is an indirect way of revealing an analogy, or comparison, between the derived case and the source case. Dayyo teaches us that there is no hierarchy of severity between them.

To sharpen the second direction, let us say the following. If the derived case really were more severe than the source case, and in truth ought to have been more severe in law as well, but for a merely technical reason we place it at the same level as the source case, then the Torah ought to have written the derived case explicitly and not relied on a qal va-homer that will not yield the correct result. If the Torah leaves the derived law to emerge from qal va-homer reasoning, then apparently the derived law is indeed equal to the law of the source case. This argument shows that the comparison between the derived case and the source case is not accidental but essential. The technical limitation of dayyo is the tool that helps us extract the comparison out of the apparent amplification.

Let us recall that in the essay on Parashat Shemini we noted that, at least according to Maimonides, a law explicitly written in the Torah is more severe than a law derived through one of the hermeneutical principles by which the Torah is expounded. There we asked how this could fit with the very assumption underlying qal va-homer, namely that the derived case is more severe than the source case. According to the second possibility, the force of the question is substantially reduced, for in truth we are not dealing with an argument from lesser to greater severity, but with comparison.

Formal, Rule-Based Qal va-homer

In the essay on Parashat Noach we distinguished between a qal va-homer based on ordinary reasoning and a formal, rule-based qal va-homer. The reasoning-based qal va-homer rests on one datum, together with a reasoned assumption that another context is more severe than the given one, and therefore what we find in the given case must apply there as well. A formal, rule-based qal va-homer, by contrast, rests on three data points. Two of them are used to create a generalization, and when that generalization is applied to the third datum it yields the conclusion of the qal va-homer.

The qal va-homer arguments found in Scripture are all reasoning-based. For example, the qal va-homer of Miriam and the Shekhinah mentioned above rests on one datum — that if her father spits in her face she must be ashamed for seven days — and on a piece of reasoning, namely that the Shekhinah is more severe than her father. By contrast, the qal va-homer arguments used by the Sages are mostly formal and rule-based. Such a qal va-homer is not based on an independent piece of reasoning but on a generalization from two data points; precisely for that reason, it is easier in this type to discern the comparative dimension between the derived case and the source case.

For example, the Mishnah in Bava Kamma 24b–25a brings a formal qal va-homer concerning liability for horn-damage in the injured party’s courtyard. There are three biblical data points:

1. Horn that caused damage in the public domain incurs half-damages.
2. Tooth and foot that caused damage in the public domain are exempt.
3. Tooth and foot that caused damage in the injured party’s courtyard incur full damages.

There are two ways to construct a formal qal va-homer in such a case:

1. From the first two data points, create the generalization that horn is always more severe than tooth and foot. Apply that to the third datum: tooth and foot are liable for damage in the injured party’s courtyard. Then infer the conclusion: horn too is liable in the injured party’s courtyard.
2. From the last two data points, create the generalization that damage in the injured party’s courtyard is more severe than damage in the public domain. Apply that to the third datum: horn is liable in the public domain. Then derive the conclusion: horn is liable in the injured party’s courtyard.

If we examine each of these two formulations, we see that no independent reasoning is present. What we have here is a formal generalization, generated by the relation between two specific data points. For example, in the first formulation the generalization is that horn is more severe than tooth and foot. Yet after applying the limitation of dayyo, we discover that in all contexts other than those specific data, horn will be equal to tooth and foot. If so, only in the public domain do we have a specific case in which horn turns out to be more severe than tooth and foot, whereas in all other contexts horn will be equal to them. Thus the qal va-homer served as an indicator that there is a comparison between the category of horn-damage and the category of tooth-and-foot damage. We have no reason to assume that horn has a severity beyond that of tooth and foot, for the case of the public domain is an exception, evidently dependent on a unique parameter.

Rabbi Isaac Alfasi (the Rif), at the beginning of Tractate Bava Kamma, and following him other medieval authorities, explain the uniqueness of the public domain by noting that every person has permission to lead his animal there, and therefore one cannot obligate him for damage it causes in its normal manner — that is, damage of tooth and foot. But what about damage it causes in a place where it has no permission to walk, such as the injured party’s courtyard? There it would seem that there is no difference between damage caused by horn and damage caused by tooth and foot. We thus have a case in which the qal va-homer is only an indicator of comparison and does not truly express a hierarchical relation of severity between the derived case and the source case.

Analytical Qal va-homer: “A Hundred Is Included in Two Hundred”

So far we have seen that a formal, rule-based qal va-homer can indeed express comparison and not a hierarchical relation of severity. But what about a reasoning-based qal va-homer? Can the same be said there as well?

At first glance, no. If we take as an example the qal va-homer of Miriam and the Shekhinah, it is obvious there that the Shekhinah is more severe than her father. That is precisely the reasoning on which the qal va-homer rests. If so, there dayyo would apparently express a technical limitation and not an essential one. It would seem that we are not dealing there with comparison, but with a clear hierarchy. Yet it turns out that the matter is not so simple.

We have already noted several times בעבר, for example in last year’s essay on Parashat Noach, that reasoning-based qal va-homer is itself divided into two kinds:
1. a qal va-homer based on ordinary reasoning;
2. a qal va-homer of the type “a hundred is included in two hundred.”

We illustrated ordinary reasoning-based qal va-homer above through Miriam and the Shekhinah. An example of the “a hundred is included in two hundred” type is the inference regarding liability for one who digs a pit, from the liability of one who removes the cover of a pit that then injures someone who falls into it. See Tosafot on Babylonian Talmud, Bava Kamma 2a, s.v. “And not this and this”; the discussion in Babylonian Talmud, Bava Kamma 49b; and Maharsha, second recension, ad loc. In this example the derived case is literally included within the source case, for whoever digs a pit necessarily also performs the act of removing a cover. The act of digging concretely includes the act of uncovering. As we have often noted, this is indeed a piece of reasoning based on the greater severity of the source case relative to the derived one, but it is a compelled piece of reasoning, since one is literally included in the other.¹

As we explained in the essay on Parashat Noach, the necessity of the reasoning at the basis of this kind of qal va-homer stems from the fact that the conclusion is already contained within the premises. There we noted that this is the analytic necessity present in every deductive argument. For example, consider the following argument:

• General premise: all human beings are mortal.
• Particular premise: Socrates is a human being.
• Conclusion: Socrates is mortal.

The conclusion is necessary, because it was already contained in the general premise that all human beings are mortal.² Is there anything in Socrates beyond what is found in every other human being? Of course there is. He has all sorts of unique traits that no other person has. But are those traits relevant to the conclusion that he is mortal? Certainly not. His being human, and not any other unique characteristic of his, is what leads us to the conclusion that he is mortal. If so, the conclusion is already contained in the premise, since the premise already determines that every human being is mortal.

Let us now return to the qal va-homer case. The conclusion that we obligate one who digs a pit may be understood in two different ways:
1. We obligate him as a digger, who is more severe than one who merely uncovers.
2. We obligate him as one who uncovers, for every digger is also an uncoverer.

The difference between these two possibilities is exactly our issue. According to the first possibility, there is a hierarchical relation between the digger and the uncoverer, and the digger is more severe. According to the second possibility, there is no hierarchical relation of severity at all. There is indeed a relation of inclusion, but the derived law is based on comparison, since the digger is equal to the uncoverer: both are, in essence, instances of uncovering, and both are liable by virtue of uncovering. All the additional content that the digger has beyond the uncoverer is irrelevant to the conclusion that he is liable for tort damages, just as in the deductive argument about Socrates.

Back to Reasoning-Based Qal va-homer

What about an ordinary reasoning-based qal va-homer, one not of the “a hundred is included in two hundred” variety? At first glance it surely seems to express hierarchy rather than comparison. Yet that too is not necessary. In light of everything we have seen, there is room to say that even such a qal va-homer is nothing but a comparative inference. To understand this, let us return once more to Miriam and the Shekhinah.

That qal va-homer as well can be understood in two ways:
1. The Shekhinah is more severe than her father, and therefore she ought to be secluded for fourteen days, were it not for the technical problem created by dayyo.
2. The Shekhinah is not more severe than a father in the relevant respect. The fact that the Shekhinah requires seclusion stems from the “father” component that also exists within the Shekhinah. In other words, the obligation of seclusion when the Shekhinah spits in her face stems from there being in the Shekhinah something that fully parallels her father, in addition to other characteristics.

Here too, then, the relation is one of inclusion; but the conclusion follows from comparison, not from a hierarchical relation of severity.

If so, what distinguishes this qal va-homer from the “a hundred is included in two hundred” type? It appears that in the case of an ordinary reasoning-based qal va-homer, extracting the identical component is not as straightforward as in the case of “a hundred is included in two hundred.” In the second case this is an analytic operation, whereas in the first case it is a more complex and non-necessary inference.³ Such an argument can be refuted by showing that the Shekhinah does not in fact include a “father” component, something that is impossible in the case of digging and uncovering.

It should be noted that in the case of Miriam and the Shekhinah it is less plausible to view the matter as a comparative qal va-homer, since the Shekhinah is more severe than her father and the additional dimensions of severity also seem relevant to the obligation of seclusion. The excess content present in the Shekhinah beyond the father does seem relevant to the duty of seclusion. In our present terminology, the relation between them is therefore not only one of inclusion but also a hierarchical relation of relevant severity. The existence of such a relation would indeed require amplification, were it not for dayyo, which limits it. In any event, we do find a number of reasoning-based qal va-homer arguments that can certainly be interpreted in the comparative manner.

Back to the Midrash of the Grasses’ Qal va-homer

We can now return to the grasses’ first argument and understand why the authors of the midrash call it a qal va-homer. As we have seen, all types of qal va-homer can be understood as varieties of comparative reasoning. The comparison is grounded in a relation of inclusion, but the additional content present in the derived case is irrelevant to the law being inferred. What generates the inferred law is only the identical component shared by the derived case and the source case. If so, in the final analysis we are indeed dealing here with comparative reasoning. We should therefore not be surprised that the comparison between the grasses and the trees is called a qal va-homer in the midrash. The grasses find a similarity between themselves and the trees, and therefore infer that they too must emerge according to their kinds, just like the trees.

The Relation Between the Three Types of Qal va-homer and Binyan Av

As we have seen so far, it is possible to understand the three types of qal va-homer as arguments of comparison based on a relation of inclusion, rather than on a hierarchical relation of severity. Inclusion means that within the derived case there is a component identical to the source case, and it is that component that causes the relevant law to apply, both in the source case and in the derived one. The rest of the additional content found in the containing case beyond the contained one is irrelevant to the law under discussion.

The difference between an ordinary reasoning-based qal va-homer and the “a hundred is included in two hundred” type was clarified above. It lies in the degree of certainty we have concerning the relation of inclusion. In the case of “a hundred is included in two hundred,” the inclusion is explicit, salient, and clear. There the inference is analytic-deductive. In the case of ordinary reasoning, extracting the included component is a matter of comparative reasoning, that is, analogy rather than deduction.

The formal, rule-based qal va-homer is of a completely different type. True, according to this proposal it too ultimately ends in comparison, but the indicator of comparison is altogether different from that in the other two types. Two similar laws direct our attention to the possibility that there is a similarity between the two contexts, or some kind of inclusion relation between them; on this more will be said below.

If so, why is qal va-homer a distinct hermeneutical principle at all? Why is it not included under binyan av, which is the basic principle of comparison among the thirteen hermeneutical principles?

We have already noted that all the principles are different forms of comparison. The difference among them lies only in the question of what serves as the indicator for making the comparison. For example, the principle of gezerah shavah leads us to comparison by virtue of verbal similarity between two contexts. The inference from juxtaposition is based on textual adjacency. Binyan av rests on a reasoned perception of similarity. Thus all the principles are nothing but different indicators for carrying out comparison.

Accordingly, there is no difficulty in saying that qal va-homer too is a comparative principle. What distinguishes it from the other principles is the indicator that triggers the comparison: the existence of a relation of inclusion between the derived case and the source case. As we saw above, there are three subtypes of indicators for such a relation of inclusion. It stands to reason that if these three types are all manifestations of the hermeneutical principle called qal va-homer, then they all rest on one and the same basic logic and character. It therefore seems plausible that all of them indeed express, in different forms, comparison grounded in a relation of inclusion, as we proposed above.

What Is the Inclusion Relation in the Case of the Grasses?

We must now return and ask ourselves why the first argument made by the grasses was a qal va-homer. It is not enough to say that it is a comparison, for all the hermeneutical principles are different kinds of comparison, and what distinguishes them is only the indicator that licenses the comparison. Was the indicator for the comparison between trees and grasses a relation of inclusion? Which of the three kinds of relation we encountered here, if any, appears in the grasses’ first argument?

The verse states: “vegetation, seed-bearing herbs, fruit trees bearing fruit according to their kind.” The Rif, in his commentary printed in Ein Yaakov, explains that the grasses did not know whether the phrase “according to their kind” referred to everything listed in the verse, or only to the trees. In the end they understood that it referred to all of it. It may be that this itself is the relation of inclusion that forms the basis of the qal va-homer: textual inclusion. The grasses are included among all the species listed in the verse, and therefore the command “according to their kind” refers to them as well. This would be a pure deductive argument, exactly like the Socrates argument cited above. Even so, it is difficult to view this as qal va-homer. The only type of qal va-homer that is deductive is the “a hundred is included in two hundred” type, and that requires a relation between the derived case and the source case. But who here is the derived case, and who is the source case? It is strained to say that the collection of details listed in the verse is the source case, and that one of those details — the grasses — is the derived case.⁴

Perhaps the grasses inferred from the command to the trees that the desire of the Holy One, blessed be He, is that every creature emerge according to its kind, and not in mixture. On this understanding, the command does not arise from the special character of the trees; rather, it is a command addressed to all vegetation to emerge according to its kind. If so, the grasses too are plants, and therefore they contain the component from which the obligation to emerge according to their kinds is derived. The other characteristics of the trees, which differ greatly from the grasses, are irrelevant to the command to emerge according to their kinds. Therefore it was clear to the grasses that the obligation applies to them as well, since they too are plants. Their being plants is the shared component they have with the trees, and it is the basis of the obligation to emerge according to their kinds. Animals were not commanded in this way, and the reason for that still requires investigation. According to this, we are dealing here with a reasoning-based qal va-homer, though it still remains not entirely clear why this is not simply an ordinary binyan av.

It should be noted that, on our approach, it may in the end be true that the phrase “according to its kind” does indeed refer to everything itemized in the verse — both grasses and trees — because all of it belongs to vegetation, and the command was directed to all vegetation.

The Dispute Between Rabbi Tarfon and the Sages in Bava Kamma

In the essay on Parashat Beha’alotekha we pointed to the possibility of understanding the dispute between Rabbi Tarfon and the Sages precisely along this axis: whether qal va-homer is comparison or amplification. According to our proposal there, Rabbi Tarfon understands qal va-homer as an amplifying inference, and dayyo as a formal limitation. Therefore the discussion in Bava Kamma 25a states that when dayyo would undo the qal va-homer, Rabbi Tarfon does not apply dayyo. By contrast, according to the Sages, dayyo teaches us that the principle of qal va-homer is a comparative inference. If our words are correct, then the accepted ruling follows the Sages, and therefore qal va-homer is a comparative inference, not an amplifying one. That was our conclusion here as well.

Let us look again at the two formulations of the qal va-homer cited above, and see this through an analysis of the relation between them.

The Two Directions of Qal va-homer and an Explanation of the Sages’ View: the Formal Qal va-homer as Comparison

According to the first formulation, the generalization states that horn is always more severe than tooth and foot. If we apply this to the third datum, namely that tooth and foot incur full damages in the injured party’s courtyard, the conclusion is that horn too incurs full damages in the injured party’s courtyard. In this formulation, horn in the injured party’s courtyard is learned from tooth and foot in the injured party’s courtyard, and therefore we must compare them. By contrast, in the second formulation the generalization is that the injured party’s courtyard is always more severe than the public domain. Therefore, if we apply this to the third datum, namely that horn is liable for half-damages in the public domain, then in the injured party’s courtyard it will certainly also be liable for half-damages by force of dayyo. In this formulation, horn in the injured party’s courtyard is learned from horn in the public domain, and therefore we must compare those two.

From the course of the discussion in the Mishnah it emerges that Rabbi Tarfon and the Sages disagree over whether to apply dayyo and set the liability of horn in the injured party’s courtyard at half-damages, or to disregard dayyo and set it at full damages. At first glance, this would seem to depend on which formulation of the qal va-homer we use. But the fact is that both formulations are valid, and therefore we must take both into account.

Accordingly, Rabbi Tarfon would seemingly be correct in obligating full damages, since it is enough that one valid formulation yields such a conclusion in order to impose full damages. The second formulation would teach us only half-damages, but it has no power to reduce the legal result that emerges from the first formulation. If so, from the fact that according to the Sages we do apply dayyo and obligate only half-damages, it follows that they apply the limitation of dayyo to the first formulation as well, and therein apparently lies the root of the dispute between them.

How can we understand the view of the Sages — which is also the accepted law — who apply dayyo even to the first formulation? Seemingly, if horn in the injured party’s courtyard is learned from tooth and foot in the injured party’s courtyard, the result should be that horn incurs full damages there, not half. Why should the fact that in the public domain it incurs only half-damages interfere?

Apparently, the Sages understand qal va-homer as a comparative argument and not as a formal hierarchical one. From the first formulation it emerges that there is a similarity between the public domain and the injured party’s courtyard, and therefore the level of liability should be similar in both. As we noted above, the exemption of tooth and foot in the public domain is precisely the exceptional case, and it does not testify to the general rule. If so, the required conclusion is that the public domain is similar to the injured party’s courtyard and their laws should be equal. Consequently, horn in the injured party’s courtyard is liable only for half-damages and no more. Why not full damages? Presumably because there is some characteristic of horn-damage that causes it to incur only half-damages. See the discussion in Bava Kamma 15a regarding whether half-damages are a penalty or compensation, and the medieval commentators there.

The necessary conclusion is that even if we examine the formulation that learns horn from tooth and foot, we still arrive at the conclusion that horn is liable in the injured party’s courtyard, but only at the level of half-damages. The reason is that according to the Sages there is a substantive similarity between horn in the public domain and horn in the injured party’s courtyard. That similarity remains in force even when we examine the other formulation, and therefore it limits the result to half-damages.

We thus see that, according to the accepted ruling that follows the Sages, qal va-homer is indeed a comparative inference and not an amplifying one. As we noted above, if the formal, rule-based qal va-homer has a comparative character, it is plausible that the other types do as well. These are three subtypes of the hermeneutical exposition called qal va-homer, and they should therefore be based on a similar idea.

Footnotes