Shoftim (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 of the Torah portion Shoftim, 5766

Questions

1. Is there such a thing as a formal kal va-homer?
2. More on relevance-based refutations?
3. What is the meaning of a “minimal refutation”?
4. Why is the hermeneutical rule of kal va-homer needed if it is just simple reasoning?
5. Is it possible for a kal va-homer to be refuted while the reasoning underlying it still remains?
6. What do defective hermeneutical derivations have to do with all this?

The Hermeneutical Principle

Kal va-homer (a fortiori inference).

“A single witness shall not rise up against a man for any iniquity or for any sin, in any sin that he commits; by the mouth of two witnesses, or by the mouth of three witnesses, shall a matter be established.”

— Deuteronomy 19:15

“What does Scripture teach by saying ‘a man’? It does not stand for iniquity, but it does stand in the case of a woman, to permit her to marry — these are the words of Rabbi Yehudah. Rabbi Yose says: it does not stand for iniquity, but it does stand for an oath. Rabbi Yose said: the matter follows by kal va-homer: if in a case where a person’s own admission does not combine with one witness for capital punishment, yet one swears on the basis of one’s own admission, then in a case where one witness combines with another witness for monetary matters, is it not all the more so that one should swear on the basis of one witness? No. What is unique about swearing on the basis of one’s own admission? That one also pays on the basis of one’s own admission. Will you say the same of swearing on the basis of one witness, when one does not pay on the basis of one witness? Therefore Scripture says, ‘for any iniquity’ — for iniquity it does not stand, but it does stand for an oath.”

— Sifrei to Deuteronomy, sec. 188

A. Summary of Last Year’s Article

In the first part of last year’s article, we dealt with the question whether the novelty in the verse cited above is that two witnesses are sufficient — that is, without the verse we would have required more — or whether the novelty is that at least two witnesses are required, meaning that without the verse we would have been satisfied with only one. The plain sense of the verse, and the exposition above, seem more compatible with the second possibility.

We also discussed the nature of the obligation to take an oath: is it a way of escaping monetary liability, or is it an independent obligation, whose nonfulfillment creates monetary liability? We considered these questions as well in light of the parallel passage in the Babylonian Talmud, Shevuot, and the differences between that passage and the exposition in the Sifrei.

In the second part of the article, we dealt with Rabbi Yose’s kal va-homer. Rabbi Yose learns from this verse that the Torah wishes here to exclude the obligation of an oath from the requirement of two witnesses. At first glance, this is a derivation of an exclusion from a verse, yet he also adduces a kal va-homer argument for that purpose — an argument that is ultimately rejected. Rabbi Yose’s line of thought is unclear, and even its wording is rather obscure; it is difficult to determine which is the source case and which is the derived case. In the end, we concluded that the source case is the oath imposed on a defendant who partially admits the claim, and the derived case is the oath generated by a single witness.

The kal va-homer is apparently as follows: one’s own admission is not effective in imposing capital punishment. It is not even effective when combined with one witness to impose capital punishment together with him, since capital punishment requires two witnesses. By contrast, one witness does combine with another witness to impose capital punishment. It thus follows that one witness is more stringent than one’s own admission. We may therefore derive from the oath of partial admission that if one’s own admission is sufficient to obligate an oath, then surely the testimony of a single witness, which we have seen to be stronger, should also obligate an oath.¹

The rejection of this kal va-homer may be understood in two ways, neither of which sits perfectly with the wording of the Sifrei:

1. A refutation based on lack of relevance. Partial admission, which generates an oath, does not operate directly. The admission itself is not what obligates the oath. Rather, the defendant’s admission regarding part of the money raises suspicion regarding the remainder of the money claimed, and regarding that remainder the defendant must swear. If so, what obligates the oath is not the strength of the admission, but the suspicion aroused by a partial admission.
2. A refutation of the generalization underlying the kal va-homer. Admission is not necessarily weaker than one witness, for it also has a stricter side: it obligates the one who admits to pay money just as two witnesses do, whereas one witness can never obligate payment by itself.²

We saw that according to both possibilities, this argument expresses a formal kal va-homer, that is, one not based on relevant reasoning. To illustrate this, we described the kal va-homer in the first Rabbi Hiyya passage (see Babylonian Talmud, Bava Metzia 3b), and in the course of that discussion several possibilities arose for understanding that kal va-homer similarly to ours — whether as a formal kal va-homer or as one based on relevant reasoning.

We then discussed the formal kal va-homer. Its basic schema appears as follows:³

• Premise A, the minor or particular premise: we find halakha (Jewish law) X in subject A.
• Premise B, the major or general premise: one can prove by generalization — usually from the existence of halakha Y in B but not in A — that subject B is more stringent than subject A.
• Conclusion: halakha X should apply to subject B as well.

Formal refutations can address only the generalization. If we find a stringent law Z that exists in subject A but not in B, then we have shown that A has a stringency relative to B, and the generalization is therefore invalid.

What about relevance-based refutations? In a formal kal va-homer there should be no relevance-based refutations, because we do not assume any relation of relevance between the derived case and the source case. If our kal va-homer is formal, then its refutation should be understood according to option 2 above. Option 1 is a relevance-based refutation, and it cannot attack a formal kal va-homer.

At the end of the article, we suggested a way to understand both of these kal va-homer arguments on a rational basis as well. That would allow us to remain with only one kind of kal va-homer, while continuing to assume that a relevant rationale always underlies it.

At the end of our discussion, we mentioned the claim brought in the Haggadah Mibeit Levi (Brisk),³ in its commentary on the liturgical poem “Who Knows One?,” in the section on the “thirteen measures,”⁴ where it is argued that kal va-homer is not a logical principle but a formal consideration, as one would expect from a Brisker approach. We shall elaborate on this in the present article.

B. Are There Formal Kal Va-Homer Inferences?

The Claim of Rabbi Yechiel Michel Feinstein

The Haggadah cited above brings the words of Rabbi Yechiel Michel Feinstein, the son-in-law of the Rabbi of Brisk. He discusses whether kal va-homer is a reasoning-based consideration or a mode of hermeneutical exposition received in the Sinaitic tradition like the other interpretive principles. In classic Brisker fashion, he adopts the second approach and offers several proofs.

One of his sources is Tosafot on the word “but,” in Babylonian Talmud, Bava Metzia 3b, which we discussed in last year’s article, and there we saw that no such conclusion is necessary. Another source he adduces is the kal va-homer of the grasses, which we discussed in our article on the portion Bereishit, 5765. There we saw the reasoning underlying that kal va-homer, and in light of that discussion his proof seems to be rejected. We shall now examine the third source he brings, from Babylonian Talmud, Berakhot 23, and we shall see that there too it is very difficult to accept his position.

The Proof from the Tefillin in the Lavatory — Berakhot 23

The Gemara in Berakhot 23b discusses the law of tefillin in a temporary and a permanent lavatory. On Berakhot 23a, a dispute between Beit Hillel and Beit Shammai is cited regarding entering a permanent lavatory with tefillin:

“It was taught in another baraita: One who enters a permanent lavatory removes his tefillin at a distance of four cubits, places them in a window near the public domain, and enters. When he comes out, he distances himself four cubits and puts them on. This is the view of Beit Shammai. Beit Hillel say: He holds them in his hand and enters.”

And there, on 23b, a baraita is cited that forbids entering a temporary lavatory with tefillin:

“The Sages taught: A person should not hold tefillin in his hand or a Torah scroll in his arm and pray; nor may he urinate while holding them; nor may he sleep with them, neither a regular sleep nor a brief doze.”

Immediately afterward, Rava in the name of Rav Sheshet rules that this baraita must follow Beit Shammai:

“Rava said in the name of Rav Sheshet: The halakha is not in accordance with this baraita, for it is the view of Beit Shammai. For if it were Beit Hillel — now if a permanent lavatory is permitted, is a temporary lavatory not all the more so?”

The Gemara then rejects that ruling and accepts the baraita as normative. But Rava’s argument remains difficult:

“In any case, the difficulty remains: now if a permanent lavatory is permitted, is a temporary lavatory not all the more so?”

An explanation is then proposed:

“This is what it means: a permanent lavatory, where there are no splashes, is permitted; a temporary lavatory, where there are splashes, they forbade.”

That is, in a permanent lavatory there is no concern about splashback, unlike a temporary one. Later the Gemara brings a tradition that the kal va-homer from temporary to permanent admits no answer, which does not fit the rationale of splashes:

“If so, why say that no answer can be given? That is an excellent answer!”

The Gemara concludes with the following cryptic statement:

“This is what it means: this matter should come by way of rationale and not by way of kal va-homer; for if it were to come by way of kal va-homer, this would be a kal va-homer to which no answer can be given.”

That is, there is indeed an explanation for why tefillin are permitted in a permanent lavatory and forbidden in a temporary one: because of splashback. But that is a rationale, not a kal va-homer. The Gemara says that if we had derived this law by kal va-homer from temporary to permanent, the splashback rationale would not have sufficed to refute it. The kal va-homer would have been unanswerable.

Rabbi Feinstein argues that the Gemara here explains that kal va-homer is not based on logic, and therefore if we had learned by kal va-homer, the logical rationale would not have helped us distinguish between a permanent and a temporary lavatory. Although his claim does seem to emerge from the plain wording of the Gemara, these words are very difficult on two principal planes: the interpretive and the logical. We will discuss them one by one.

The Interpretive Difficulty

The interpretive question that arises here is: why is this refutation different from every other refutation of kal va-homer that we find in the Talmud? If the relation between the lesser and the greater is indeed not based on logic and therefore cannot be refuted by logical tools, then how do we nevertheless find refutations of kal va-homer in the Talmud?⁵

It seems that this interpretive difficulty is not quite as severe as it first appears. Refutations that we find in the Talmud undermine the relation of leniency and stringency that exists between the source case and the derived case. Such refutations cut off the very branch on which the kal va-homer sits. For even if kal va-homer is not a rational consideration but a formal mechanism handed down from Sinai as a scriptural decree, it is still clear that it begins with relations of leniency and stringency between the source case and the derived case. Even the very name of this principle, kal va-homer, testifies to that. Therefore, if a refutation rejects the assumption that such relations exist between the source case and the derived case, it will refute a formal kal va-homer no less than a reason-based one.

But in the example before us, are we really dealing with a refutation that undermines the relation of leniency and stringency between the source case and the derived case? Apparently not. Even after the rationale of splashback is introduced, it remains clear that a permanent lavatory is a more degrading place than a temporary one. The rationale with which we are dealing is a different type of refutation: the relation of leniency and stringency remains intact, but the law under discussion depends not on the degree of degradation of the place, but on the concern about splashback. This is a relevance-based refutation, not a refutation of the relation of leniency and stringency. In last year’s article we distinguished between these two types of refutation.

It follows that the fact that we find refutations of kal va-homer in the Talmud does not necessarily contradict the claim that kal va-homer is a formal principle rather than a logical one. Yet in the Talmud we also find relevance-based refutations, not only refutations of the leniency-stringency relation. At first glance, such refutations are not to be expected if kal va-homer is formal.

One might therefore propose a distinction between two different kinds of kal va-homer, both of which appear in rabbinic literature. If so, the refutations in the Talmud would pertain to reason-based kal va-homer, whereas the case before us would involve a formal kal va-homer. But this distinction too is problematic, because if one could always move to a formal kal va-homer that is not vulnerable to refutation, then the Sages should have been able to dissolve every refutation raised against a reason-based kal va-homer simply by shifting to the formal track.

If so, the interpretive problem appears to remain.

The Logical Difficulty

Another difficulty regarding Rabbi Feinstein’s position lies on the purely logical plane. Kal va-homer considerations serve us in other contexts as well, and therefore it is clear that there is logic and rationale in them. It is self-evident, from a logical standpoint, that in a more severe context all the stringencies that apply in the lighter context should also apply. It therefore seems highly plausible that kal va-homer is based on reasoning rather than on a purely formal mechanism.

Let us sharpen the point further. Does Rabbi Feinstein mean that every law applying in the lighter context must also apply in the more severe context? For example, the Mishnah explains that the law of horn is more severe than the law of tooth and foot (see Babylonian Talmud, Makkot 24a). As is well known, the laws of horn in the case of a first-time offender are not adjudicated today, because we no longer have ordained judges. Does it follow from kal va-homer that today we should also refrain from adjudicating the laws of tooth and foot? Obviously not. Horn in the case of a first-time offender is a fine, and fines are not adjudicated today; payment for tooth and foot is ordinary monetary liability and is adjudicated today. The conclusion is that only laws relevant to the issue of stringency and leniency transfer from the lighter case to the stricter one. It is therefore clear that reasoning plays a role in the kal va-homer process. If kal va-homer were a purely formal consideration, it would operate blindly on all the laws that exist in the source case and transfer them to the derived case.

Still, this argument requires finer formulation. All the laws related to the axis of leniency and stringency do indeed transfer from the source case to the derived case, but not all laws without exception. If there are laws that are not themselves stringencies in the source case, but depend on local rationales rather than on its severity, they will not transfer from the source case to the derived case.

We must now ask what happens in our case. We saw that once the rationale is introduced, the leniency-stringency relation remains intact, and the refutation challenges only the relevance of the law under discussion to that relation. But now we may add that even the dependence of the law under discussion on the leniency-stringency relation is not wholly detached from the rationale raised here, namely splashback.

To be sure, the rationale of splashback gives us a reason to be stricter in a temporary lavatory than in a permanent one. But it still remains unclear why no weight is given to the degrading nature of the place itself, which is what defines the leniency-stringency relation between a temporary and a permanent lavatory, and why the only consideration is splashback. At first glance, one might well have thought that even where there is no splashback, one should still be strict because of the degradation involved in bringing tefillin into such a place.

If so, the splashback rationale not only fails to undermine the leniency-stringency relation, it does not even explain why one should not be strict for the independent reason of the disgrace of the place. Accordingly, this refutation is not really a refutation of the kal va-homer at all — neither of its basic reasoning nor of its relevance. It is therefore no surprise that the Gemara rules that this is a kal va-homer to which no answer can be given.

Explaining the Gemara

The conclusion that emerges from our discussion is that this kal va-homer is a reason-based kal va-homer, not a formal one. The rationale does not refute it; it merely points to an alternative explanation of the laws we find. We may therefore reread the Gemara and see that it should not be taken as making any claim that kal va-homer is a formal rather than a reason-based mode of inference.

We may now understand that the final sentence of the sugya does not mean to say that if we had learned by kal va-homer, we would have forbidden tefillin even in a permanent lavatory. Rather, the Gemara means that if the reason for the prohibition in a temporary lavatory had been the disgrace of the place, then the conclusion would indeed have been that a permanent lavatory too should be forbidden. But since the reason is the practical rationale of splashback, the law remains as it is — lenient in a permanent lavatory — despite the fact that the kal va-homer itself truly admits no answer on all the grounds we indicated above.

This may well be the very intent of Rashi there, who writes:

“It should come by way of rationale” — to permit in a permanent lavatory what is forbidden in a temporary lavatory, because of the rationale of splashback.

“For if it were to come by way of kal va-homer” — that is, to say: by right one should be lenient in the temporary lavatory, which is lighter, and stringent in the permanent lavatory, which is more severe, and one should follow not the particular rationale but rather the scale of leniency and stringency — whereas we in fact do the opposite — then I would have no answer to give, for I cannot find any respect in which a temporary lavatory is more severe than a permanent one, so that I could answer: if I permitted in the permanent one, which is lighter in that respect, then let us certainly permit the temporary one, which is more severe in it. But there is a rationale for what we do: here there is splashback and here there is not. And this matter is not kal va-homer at all — neither lighter nor more severe.”

“One Does Not Derive Punishments from Logical Inference”

In light of Rabbi Feinstein’s approach, one might have explained rather well the seemingly puzzling rule that one does not derive punishments from logical inference. If kal va-homer does not point to genuine relations of leniency and stringency but is merely a formal inference, then of course one cannot derive the punishment imposed on the violator of the source case and apply it to the violator of the derived case.

Precisely for that reason, however, it is important to note that the commentators offer many different explanations of this rule, and do not rest content with the claim that there is no real relation of leniency and stringency between the source case and the derived case.⁶ If so, this specifically proves that all of them understand kal va-homer as a tool based on the rationale of leniency and stringency.⁷

The Slides Model

In the article on the portion Shemini, 5765, we showed that kal va-homer operates in a formal way. One of the considerations that led us to that conclusion was that, at least according to Maimonides, the conclusion of a kal va-homer always undermines its main premise, namely the relation of leniency and stringency. The process is as follows: the law learned by the kal va-homer is not written explicitly in the Bible, and therefore according to Maimonides it has a lower halakhic status than the three other laws involved in the kal va-homer, because those are written explicitly in Scripture. If so, the law learned is lighter than the law from which it is derived, contrary to the premise of the kal va-homer, according to which the derived case is more severe than the source case.

The solution we proposed there was that kal va-homer is a textual principle that refers only to the biblical text. It should therefore not be tested, confirmed, or refuted in light of laws that are not written explicitly in Scripture. Those belong to the second “slide” — what is learned through the hermeneutical principles and is not written in Scripture — whereas kal va-homer is based only on laws found on the first slide, namely what is written in Scripture.

At first glance, if kal va-homer were indeed a reason-based principle, there would be no reason to ignore the fact that the derived case is lighter than the source case, since that fact really does refute the leniency-stringency relation between them.

But if this argument were correct, it would be a refutation of the kal va-homer even if we treated it as a formal consideration. As we saw above, the premise of the kal va-homer, even when it serves as the formal basis of the hermeneutical inference, still rests on relations of leniency and stringency between the source case and the derived case. If those relations do not exist, then even a formal inference cannot proceed on that basis.

We are therefore forced to conclude that the division into two planes, or slides, is indeed a formal dimension in the operation of kal va-homer, but the distinction between the slides is apparently not only a distinction of halakhic status; it is also a distinction of kind. The laws learned through the interpretive principles are not merely lighter than laws explicitly written; they constitute a different type. Therefore we assess relations of leniency and stringency only among laws of the same type, that is, laws belonging to the same slide.

The conclusion is that kal va-homer does indeed contain a formal component, yet within the plane on which we are operating — the biblical plane — its mode of operation is certainly based on the rationale of leniency and stringency.

C. The Arguments of the Author of Netiv Binah

Introduction

There is a long and illuminating essay by Rabbi Bunim Schreiber in his book Netiv Binah, sec. 48, dealing with the law of impurity conveyed by carrying and with the principle of kal va-homer. He too argues at length that kal va-homer is a formal principle and not the ordinary reasoning we use in other contexts. We shall briefly discuss several points from his essay and consider their implications for our topic.

Why Was the Rule of Kal Va-Homer Included in the Baraita of the Thirteen Principles?

At the beginning of chapter 2 of his essay, Rabbi Schreiber asks why it was necessary to teach the rule of kal va-homer at all, since it is simple human reasoning that serves us in every domain of thought.⁸ To sharpen the point, he cites Saadia Gaon’s commentary on the baraita of the thirteen interpretive principles. Saadia Gaon gives several examples of kal va-homer arguments that do not appear in rabbinic literature, as is his way there with respect to all the principles. All these are rational arguments, and we would make them even without the tradition that presents kal va-homer as one of the tools of exposition.

The Example of Unloading and Loading

For example, there is there a kal va-homer concerning the unloading and loading of another person’s donkey. The Torah commands with respect to “the donkey of your enemy,” and Saadia Gaon asks: from where do we know the case of “the donkey of your friend”? The answer is kal va-homer: if one is obligated to help an enemy, then all the more so one is obligated to help a friend.⁹

Rabbi Schreiber asks: but this is simple reasoning. Why, then, is a special hermeneutical rule required here? He adds that in the Talmud it is common to challenge a law derived from reasoning by asking, “Why do I need a verse? It is logical.” That is, if a law emerges from reason, there is no need for it to be written in Scripture.

He then suggests that perhaps the kal va-homer of the enemy’s donkey is not based on simple reasoning after all, because a distinction is made in Babylonian Talmud, Bava Metzia 32b, according to which there is a special value in helping specifically an enemy, in order to subdue one’s inclination — that is, to confront one’s hatred of the enemy, which is itself a halakhic prohibition. But he immediately adds that this cannot be the solution, because if that is the rationale, then that very rationale refutes the kal va-homer: it is now clear that a friend is not preferable to an enemy, since in the case of the enemy there is also the value of subduing the inclination.

The difficulty is therefore of the type: whichever way you take it. If the opposing rationale, that of subduing the inclination, exists, then there is no kal va-homer. And if that rationale is not correct, then the kal va-homer does stand — but then the question returns: why do we need the hermeneutical rule of kal va-homer if the reasoning itself is already present?

It seems that this case is very similar to the case of tefillin in the lavatory discussed above. Even after the rationale that ostensibly refutes the kal va-homer — subduing the inclination — the basic hierarchy between the source case and the derived case remains intact. More than that: even the relevance of the derived law to the leniency-stringency relation remains in force. In more concrete terms: even if there is a special value in subduing the inclination, the duty to help a friend — or the expectation that he be helped — is still stronger than the duty to help an enemy. The kal va-homer still appears valid.

“A Minimal Refutation”

Rabbi Schreiber notes that in the Talmud we find several refutations after which the rationale of the kal va-homer nevertheless remains intact; he refers to the sugya in Babylonian Talmud, Chullin 116a. From this he concludes that kal va-homer is not reasoning, and therefore one cannot derive by kal va-homer even where the reasoning remains valid.

The sugya in Chullin deals with what it calls a “minimal refutation.” The Gemara learns that meat cooked in milk is forbidden not only for eating but also for benefit, from the law of mixed planting in a vineyard or from orlah (fruit of a tree during its first three years). It then raises a refutation against both derivations, arguing that the source cases involve things that grow from the soil. The Gemara replies that a minimal refutation can undo a mah ha-tzad argument, that is, an argument from a common denominator, but not a kal va-homer.

Here, however, it should be noted that according to the conclusion of the sugya, one really does not refute a kal va-homer with a minimal refutation, and therefore one cannot infer from that sugya that the rationale remains in place even when the kal va-homer collapses. Beyond that, even a minimal refutation cannot be just any arbitrary point. Does anyone imagine refuting the argument by saying that mixed planting in a vineyard is written with one letter whereas meat and milk is not? Obviously the refutation must bear some relevance to the law learned by kal va-homer.

We must therefore say that a minimal refutation does not undermine the relation of leniency and stringency, but it can function as a relevance-based refutation. It raises the possibility that the law depends on some specific feature of the source case, even without explaining why that feature should matter, rather than on the stringency of the source case. If so, one cannot derive from it by kal va-homer to the derived case.

A Defective Kal Va-Homer

Later in his discussion, Rabbi Schreiber addresses the sugya in Babylonian Talmud, Yevamot 62a, and the parallel passage in Shabbat, concerning the three things Moses did on his own initiative and with which the Omnipresent agreed. The Gemara there cites kal va-homer considerations that underlay Moses’ reasoning, and Tosafot therefore ask why this is called something Moses did “on his own initiative.” After all, kal va-homer is one of the hermeneutical principles received together with the Torah itself.

Rabbi Schreiber proposes that the case involves a kal va-homer subject to refutations. The formal premise of the kal va-homer is therefore lacking, yet the rationale underlying it remains in force. The decision is thus considered Moses’ own initiative rather than a full-fledged hermeneutical exposition.

In our article on the portion Mishpatim, 5765, we dealt with this sugya at length and showed that according to Maimonides there is certainly no difficulty here, since for Maimonides even kal va-homer counts as something done “on his own initiative.” But even according to Tosafot, who assume a contrast between inference through the interpretive principles and acting “on one’s own initiative,” we explained that there is there a defective kal va-homer whose underlying reasoning nevertheless remains valid. There is something like a minimal refutation. There is a refutation of the kal va-homer, and it does indeed undermine it. Yet after that challenge, a hierarchical relation still remains between the source case and the derived case. The relation is less unequivocal, but one can still decide, by reasoning, in favor of that consideration.

This is very similar to what we saw above, where a refutation leaves the premise of the kal va-homer, and even its relevance to the law being derived, intact. The rationale remains valid, but the kal va-homer falls away. Yet this is not the reasoning of kal va-homer itself, but some other kind of reasoning.

For example, if the refutation proposes a stringency present in the source case but not in the derived case, the original stringency we posited at the start of the inference still remains. The result is that each of the two cases, source and derived, now has both a stricter side and a lighter side. In such a state, the kal va-homer is no longer valid, since one can no longer infer unambiguously that the derived case is more severe than the source case. Even so, one may still infer by reasoning that the law under discussion can be learned because of the aspect in which the derived case is more severe than the source case. Such reasoning can appear in two forms:

1. There is aspect A, in which the derived case is more severe, and aspect B, in which specifically the source case is more severe. The law under discussion depends on aspect A rather than aspect B, and can therefore still be learned despite the existence of an opposing aspect. This is the question of relevance: aspect A is the one relevant to the law under discussion.
2. Both aspects lie on the same axis of stringency and leniency, but they offset one another, and on the overall balance the derived case still emerges as more severe than the source case. Therefore everything can still be learned by reasoning as though no opposing aspect existed. We saw an example of this in the article on the portion Devarim, 5765, where we discussed the offsetting of opposing stringencies.

Main Conclusions: Is There a Formal Kal Va-Homer?

The main conclusion is that kal va-homer reasoning does indeed have formal dimensions. We saw one example of that in the slides model. On the other hand, the character of the inference is still the rational one in which this principle is usually understood.

At the end of our discussion, we saw that there are indeed situations in which the kal va-homer is refuted and yet a rationale remains. At first glance, that would seem to prove that kal va-homer is not built on the rationale of leniency and stringency. We noted that we had already encountered such examples in the past, such as cases where opposing refutations offset one another. In such situations the kal va-homer falls, yet the rationale remains. Does that mean that kal va-homer operates formally, in the sense that it is unrelated to the rationale of leniency and stringency, as Rabbi Feinstein and Rabbi Schreiber claim?

Quite clearly, it does not. The logic of kal va-homer is the ordinary logic. The point is only that for some consideration to count as a standard, proper midrashic kal va-homer, it must satisfy especially high standards. For example, the relation between the source case and the derived case must be general, and the source case must be capable of transferring all the laws that apply within it. When there is an opposing side — that is, when the stringency of the source case is only partial, or only from one angle, and therefore some laws cannot be learned from it — the kal va-homer is no longer standard. At that point a rationale may still derive those laws by one of the two mechanisms described in the previous section, but that is no longer a standard use of the principle of kal va-homer.

In any event, it is entirely clear that when kal va-homer is used in a standard way, its logic is the same logic that serves us in other circumstances. What differs is the threshold of generality and certainty required in order for a given consideration to count as a standard kal va-homer.

Thus, there can indeed be situations in which the kal va-homer is rejected and the underlying rationale still remains, but that is not because kal va-homer is unrelated to the rationale. It is because a very high threshold is required for a kal va-homer to be fully valid.

Footnotes