Eikev (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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With God’s help

Midah Tovah — Sabbath eve, portion Ekev, 5765

Questions

1. Is there a mitzvah (commandment) to study the holy tongue (classical Hebrew)? What is the scope of this commandment?
2. Is there value in precise speech?
3. Is the principle “from the negative you infer the affirmative” a logical rule?
4. Is the directive “from the negative you infer the affirmative” a hermeneutical principle, or is it simply an interpretive rule regarding ordinary human language?
5. Does this rule apply only to conditional statements, or to every statement?
6. What is its relation to the hermeneutical principle of restriction?
7. The two meanings of implication in logic.

The principles

• From the affirmative you infer the negative.
• From the negative you infer the affirmative.
• Restriction.

“You shall place these words of Mine upon your heart and upon your soul, and you shall bind them as a sign upon your hand, and they shall be frontlets between your eyes. You shall teach them to your children, speaking of them when you sit in your house, when you walk on the way, when you lie down, and when you rise. You shall write them upon the doorposts of your house and on your gates, so that your days and the days of your children may be multiplied upon the land that the Lord swore to your fathers to give them, as the days of the heavens over the earth.”

— Deuteronomy 11:18–21

“You shall teach them to your children — your children and not your daughters; these are the words of Rabbi Yosei ben Akiva. [From the words ‘speaking of them’] from here they said: when a child begins to speak, his father speaks with him in the holy tongue and teaches him Torah. And if he does not speak with him in the holy tongue and does not teach him Torah, it is as though he had buried him, as it is said: ‘You shall teach them to your children, speaking of them.’ If you have taught them to your children, then ‘your days and the days of your children may be multiplied’; and if not, then your days will be shortened. For thus words of Torah are expounded: from the affirmative, the negative; and from the negative, the affirmative.”

— Sifrei on Deuteronomy, piska 46:19

A. The Obligation to Teach and Speak in the Holy Tongue

Introduction

In the midrash (rabbinic exposition) cited above there is a novel halakhic (Jewish legal) ruling: a father is obligated to teach his son the holy tongue. In addition, the author of the midrash also derives a punishment for one who does not do so from the principle: “from the affirmative you infer the negative.” The midrash finds it necessary to state explicitly that this is an accepted hermeneutical principle in the Torah. Presumably the reason is that, according to some views, this rule is also used in interpreting ordinary human language. The midrash wishes to sharpen the point that, beyond that meaning, we are dealing here as well with an interpretive-midrashic rule for Torah verses.

The Course of the Midrash

The midrash opens with a close reading that also seems to be a derivation of the type “from the affirmative you infer the negative”: “your children, and not your daughters.” It is unclear why Rabbi Yosei does not already invoke here the hermeneutical principle “from the affirmative you infer the negative.” We shall return to this point at the end of the article.

After that comes a second derivation, which learns the new rule that the father is obligated to teach his son to speak in the holy tongue. In the third stage, they derive the punishment for one who does not do so from what is said in verse 21: if one who does this merits lengthened days upon the land, then one who does not do so is “as though he buried him” — that is, he shortens his days.

Two logical comments should be made here:

1. The positive side speaks of lengthening the days of both father and son, whereas the negative side seems to refer only to the son (“as though he buried him”). Perhaps the reasoning that speaks of shortened days is also intended to include the father.
2. The obligation is to teach the son both the holy tongue and Torah. From the wording of the midrash it appears that the punishment falls on one who fails to do both things. In practice, however, it is enough to judge one who fails to do even one of them. Perhaps the conjunction “and” here has the meaning of “or” — that is, one should read: “if he does not speak with him in the holy tongue or does not teach him Torah.”

The Obligation to Speak in the Holy Tongue

Let us begin with a brief discussion of the halakhic novelty regarding the obligation to speak with one’s son in the holy tongue. In this midrash, matters appear as though there are two independent commandments: one is learned from “you shall teach them to your children,” and the second from “speaking of them.”

In principle, however, one could view the obligation to teach him the holy tongue not as an independent obligation, but as a prerequisite for the commandment to teach him Torah. And indeed, in Torah Temimah it is written:

“The reason seems obvious: so that he will understand what he says in Shema and in Torah.”

Nevertheless, Torah Temimah goes on to wonder why the legal decisors omitted this rule obligating one to teach his son the holy tongue.

Maimonides, in his commentary to Pirkei Avot 2:1 (“Be as careful with a light commandment as with a grave one”), writes as follows:

“Afterward he said that one should be careful with a commandment that is considered light, such as the joy of the festival and the learning of the holy tongue, and with a commandment whose severity is clear, such as circumcision, fringes, and the slaughter of the Passover offering. The reason for this is that you do not know the reward assigned to them.”

From these words of Maimonides it emerges that he sees the obligation to learn the holy tongue as a full-fledged mitzvah, one that appears light and yet must not be treated lightly. He compares it to rejoicing on the festivals, which is a positive commandment included in the enumeration of the commandments. As Torah Temimah already noted, Maimonides himself does not bring this law in his code. Presumably he sees this law as a prerequisite to the commandment of Torah study, and therefore takes for granted that one who teaches his son Torah has already taught him the holy tongue as well; otherwise the son could not learn Torah. Perhaps this also answers the second logical difficulty mentioned above. One who does not teach his son the holy tongue has, by that very fact, also not taught him Torah, and therefore the punishment clearly applies to him as well. Learning the holy tongue is part of the commandment of Torah study.

Indeed, we find a parallel difference between two versions of a baraita. In Babylonian Talmud, Sukkah 42a, the baraita reads:

“Once he knows how to speak, his father teaches him Torah and the recitation of Shema. What is ‘Torah’? Rav Hamnuna said: ‘Moses commanded us the Torah, an inheritance of the congregation of Jacob’ (Deuteronomy 33:4). What is Shema? The first verse.”

Here the baraita does not present the ability to speak as an obligation upon the father; rather, it treats it as a condition, or prerequisite, for the obligation to teach his son Torah. By contrast, at the end of chapter 1 of Tosefta, Hagigah, a different version appears:

“Once he knows how to speak, his father teaches him Shema and Torah and the holy tongue; and if not, it would have been better for him not to have come into the world.”

Here it appears that we are dealing with two different obligations. Once the son knows how to speak — which is the condition for the obligation to teach him — there are two duties: to teach him Shema and Torah, and to teach him the holy tongue. The order here is even the reverse of what one would expect, since the obligation to teach him the holy tongue appears after the obligation to teach him Torah. Perhaps this reversed order is intended to emphasize the view that these are two independent obligations, and not a commandment and its prerequisite.

A Possible Halakhic Implication

One can perhaps suggest an interesting halakhic implication of the dispute over the obligation to teach the holy tongue. In Responsa Rema, no. 6, there is a responsum sent by Maharshal to Rema, in which he rebukes him for his involvement in secular disciplines. In the course of his remarks he notes that Rema is also not precise in his language, and writes:

“… With a thousand pardons, it would have been better for my master to study the science of grammar more carefully, for your writings are full of breaches in matters of second and third person, feminine and masculine, singular and plural. (See Yam Shel Shlomo, Chullin 1:15, where he writes that one of the things necessary for a Torah scholar is to write responsa, legal rulings, and even a letter of greeting in fine and elegant language.) Several times you wrote ‘what our master requested of us,’ which combines two opposites, singular and plural. You wrote ‘I was able to answer,’ speaking of yourself and another together, and much else besides. The earlier responsa wrote that when you are uncertain regarding one of the names — how to write it in a bill of divorce, whether in plene or defective spelling, or whether to end it with aleph or heh — you may rely on the earlier writings of the sages, even in a mere letter of greeting, and we presume that they were careful to write correctly. And on that very point I shall press my own claim: the master wrote Meshullam with a vav, whereas in Scripture it is written defectively (Nehemiah 8:4). There is also proof from Babylonian Talmud, Megillah 23a: ‘Why was he called Meshullam? Because he was perfect in his deeds’; and so too it is written in standard divorce forms…”

In no. 7 there, Rema replies to Maharshal concerning his involvement in the sciences; and regarding grammatical precision he writes:

“As for what my master wrote to me, that I erred in certain words grammatically, as my master has set down in writing, I say that I am not of the class of eloquent masters of language, for ‘I am heavy of mouth and heavy of tongue’ (Exodus 4:10). I am careful about the intended content, not about the words, for that neither adds nor detracts with respect to the law. I admit that I do not know my master’s refined idiom, but I say that this is a poor sort of grammatical nicety, and my master may pardon me. For every discerning person knows that such things happen to every great figure in Israel: when his thought ranges over some matter, error may creep into his words. All the more so can he not be careful about plene and defective spellings, as my master noted that I wrote Meshullam in full spelling — for this is not a Torah scroll, to be invalidated on that account.”

Thus Maharshal holds that there is importance in precise language, even when writing a letter of greeting, and even in a matter unrelated to the law itself. Rema, by contrast, holds that linguistic precision has no great importance, beyond accuracy of content, except in a Torah scroll, which may be invalidated because of inaccuracy.

Perhaps the root of the difference lies in the question whether the obligation to speak in the holy tongue is an independent obligation. According to Maharshal, there is an obligation to learn to speak the holy tongue, and therefore one must always speak precisely; otherwise, this is not truly the holy tongue. According to Rema, this obligation is only an instrument that enables Torah study, and therefore what matters is understanding and conveying the content, not necessarily grammatical precision.

True, one might have explained the dispute in terms of the question whether the holy tongue is an ordinary conventional language or not; see the page on portion Balak. In any event, even without Rema and Maharshal, it seems that if there is indeed an independent obligation to learn and speak the holy tongue, then there is also a demand for precise speech.

B. “From the Affirmative You Infer the Negative”: Between Linguistic Interpretation and a Hermeneutical Principle

Introduction

We saw in the previous chapter that the midrash brings a derivation by means of the principle “from the affirmative you infer the negative,” and states explicitly that this is one of the principles by which the Torah is expounded.

In fact, this rule itself is disputed in the Talmuds, and there it is not presented as a hermeneutical principle but as an interpretive principle for statements or ordinary human speech — in the contexts of vows and oaths, and in contracts. As we have seen, the emphasis in our midrash is apparently meant to sharpen the point that this rule also constitutes a hermeneutical principle. In this chapter we shall try to examine these two contexts and see whether a connection exists between them.

Examples from the Talmud: Linguistic Interpretation

In Mishnah Shevuot 4:13, discussed in Babylonian Talmud, Shevuot 36a, the discussion concerns one who adjures a witness to come and testify by using a formulation that blesses him if he comes to testify, such as: “May He not strike you, and may He bless you, and do you good.” According to Rabbi Meir, this is an oath that entails the sacrifice for a false oath of testimony — the offering brought by someone who swore that he did not know testimony and was later shown to have lied — because from the affirmative we infer the negative. According to the Sages, the oath does not entail liability, because from the affirmative we do not infer the negative. In Babylonian Talmud, Nedarim 11a–14a, several statements are brought that discuss different formulations of vows, and the Gemara makes the question whether a vow exists depend on whether from the affirmative we infer the negative or not.

In all these contexts there appears a dispute concerning the principle of inferring the unstated opposite from the stated clause, and in all of them the context is the interpretation of a person’s speech, not the interpretation of biblical verses. Thus, in these discussions, the rule does not appear as a hermeneutical principle but as a logical or linguistic basis that helps interpret human speech.

The Talmud links this dispute to Rabbi Meir and Rabbi Yehudah, who disagree in the mishnah discussed in Babylonian Talmud, Kiddushin 61a, regarding a double condition. According to Rabbi Meir, one must double the condition, and from this it follows that he holds one does not infer the affirmative from the negative; otherwise there would be no need at all to double the condition. Rabbi Yehudah, who disagrees with him, apparently is satisfied with either the negative or the affirmative clause, because in his view the other side can be inferred from the wording. Here too we are dealing with linguistic interpretation.

“From the Negative You Infer the Affirmative” in the Interpretation of Scripture

In Babylonian Talmud, Shevuot 36b, the conclusion emerges that Rabbi Meir indeed holds: “from the negative you do not infer the affirmative,” but that is only in monetary cases, not in matters of prohibition. In matters of prohibition, he holds: “from the negative you infer the affirmative.”

The source for this rule in matters of prohibition is Babylonian Talmud, Sotah 17a, where the Gemara derives from the verse “And if no man has lain with you, be cleared,” that if a man did lie with her, she will not be cleared. The Gemara says that according to Rabbi Meir, who derives the opposite clause from what is stated, one should read “be cleared” without the yod, and then the fact that if she did lie with a man she will not be cleared is learned by exposition. There are contradictions among the passages on this point, but this is not the place to discuss them.

The discussion in Sotah of the principle “from the negative you infer the affirmative” is exceptional. There it takes place in the context of interpreting Scripture — the meaning of the word “be cleared” — and not in relation to the interpretation of ordinary human language. The Talmud links these two issues to one another, which implies that it understands them as one and the same dispute and one and the same issue.¹

The Connection between This Rule and the Laws of Logic

At first glance, the dispute between Rabbi Meir and Rabbi Yehudah is a logical dispute: how should conditional propositions be interpreted? Does a stipulation in one direction include within its meaning the opposite direction as well, or not? If this is indeed the basis of the two views, then there seems to be no difference here between ordinary human language and the language of the Torah. According to Rabbi Yehudah, one may infer from a positive statement the opposite with respect to the opposite case; according to Rabbi Meir, one may not.

It would then follow that Rabbi Meir, who does not accept the principle “from the negative you infer the affirmative,” should reject it in the interpretation of Scripture as well. If so, our derivation — which learns a punishment for one who does not teach his son to speak in the holy tongue — was stated only according to Rabbi Yehudah, whereas Rabbi Meir would dispute it. This is somewhat puzzling, since the derivation appears without dissent, while in practice the law follows Rabbi Meir, who requires a double condition.

On Logic and Science

Let us now try to understand more deeply the foundations of the dispute regarding the principle “from the negative you infer the affirmative.” For this we must define a logical relation called implication. When we say “if X, then Y,” our intention is not univocal. For example, when we say a sentence such as, “If you give me money, I will be very happy,” does this mean that if no money is given to me, I will not be happy? It is certainly impossible to infer from this that if no money is given, I will therefore be sad. But even with regard to the question whether I will not be happy, the answer is not so clear. From the standpoint of pure logic, this is not necessary. Such a sentence may also be said by someone who is cheerful under all circumstances. In that case, he will be happy if you give him money, but he may certainly still remain happy even if the money is not given.

Nevertheless, the plain meaning of the sentence does seem to imply that the giving of money is a cause that actually produces the happiness. Therefore, it is plausible that in the absence of the giving, there will be no happiness. Here we have already introduced the relation of causation into the picture. One who interprets implication as causal production will tend to see the implication statement as something symmetrical. By contrast, one who interprets implication as a purely logical condition has no reason to assume symmetry. Symmetry is of course possible, but not necessary. Therefore it cannot be inferred from the implication statement alone.

It is important to note that causation is not a logical relation but a factual one, sometimes scientific or physical. “A causes B” is a factual claim. By contrast, “If A, then B” is a logical claim. True, a causal relation between two events does entail the existence of a logical relation between them: if A is the cause of B, then one may infer the logical relation “if A, then B.” Even so, the two relations are not identical.²

The Asymmetry of Material Implication

In logic, it is customary to define implication in a “material” way. This means that an implication statement is false only in the case where the antecedent (X) is true but the consequent (Y) is false. Under this definition, implication is called “material implication.” The following truth table presents the material implication marked by an arrow, where T = true and F = false:

X	Y	X -> Y
T	T	T
T	F	F
F	T	T
F	F	T

It is easy to see that under the material interpretation of implication one cannot infer the affirmative from the negative. If we know the statement “if X, then Y,” we can infer only that it cannot be the case that X holds and Y does not. But certainly not the statement “if not X, then not Y,” whose meaning is that it cannot be the case that X does not hold and Y does. That is a different meaning, and these two implication statements cannot be derived from one another.

This seems to be precisely Rabbi Meir’s formalization of implication. How, then, should we formalize implication according to Rabbi Yehudah? We must allow a broader family of relations that could count as implication, and choose a non-material option that will reflect the symmetry of implication according to Rabbi Yehudah.

We wish to define an implication that satisfies both directions at once. With a little attention, one can see that the reverse statement — “if not X, then not Y” — can also be written as “if Y, then X.” In fact, we need to look at the third row of the table, which describes a situation in which the cause is absent but the effect is present. According to Rabbi Meir, such a situation does not contradict implication, but according to Rabbi Yehudah, such a situation is impossible. Therefore, in order to obtain Rabbi Yehudah’s formalization of implication, we must change the truth value of that row in the table. Let us mark this relation with a double arrow:

X	Y	X <=> Y
T	T	T
T	F	F
F	T	F
F	F	T

It is easy to see that the implication relation in this formalization satisfies the condition of symmetry: if “X <=> Y” holds, then necessarily “Y <=> X” also holds. This is easy to verify by switching the columns of X and Y and rewriting the column of truth values; it will come out identical to the one before us. This table expresses what logic calls “equivalence,” and therefore also the statement “not X <=> not Y.”

In everyday language, Rabbi Meir’s material implication is expressed by the word “if” — a sufficient condition — whereas the symmetrical implication according to Rabbi Yehudah can be stated as “if and only if” — a necessary and sufficient condition.

It should be noted that this relation too does not necessarily express physical causation. It is a logical expression of a symmetrical relation, wholly located on the logical plane. A relation of causation between X and Y is only one possible basis for the emergence of such a symmetrical logical relation, but it is not itself the concern of logic.³

C. Double Condition and Logic⁴

The Relation between the Principle “From the Negative You Infer the Affirmative” and Double Conditions

Up to this point we have assumed that the dispute between Rabbi Yehudah and Rabbi Meir lies on the logical plane: each of them formalizes the relation of implication differently. For that reason, it is clear that the dispute exists both on the plane of interpreting human language and on the plane of interpreting biblical verses; and indeed, as we saw, the Gemara itself does not distinguish between these two contexts. Logic is always relevant.

However, later authorities — see, for example, Kovetz Shiurim, Bava Batra, sec. 438, and part 2, no. 42 — note that the picture emerging from Maimonides’ rulings is different. On the one hand, Maimonides rules like Rabbi Yehudah that “from the affirmative you infer the negative” — see Maggid Mishneh and Lehem Mishneh on Maimonides, Laws of Divorce 10, and at the end of chapter 1 of Laws of Vows in the gloss of Raavad and the commentaries there, and elsewhere. On the other hand, when Maimonides discusses conditional clauses, he rules that one is obligated to double the condition — see Laws of Marriage 6:2 and elsewhere.

The author of Kovetz Shiurim explains there that there are two different laws involved in the requirement of a double condition. On the one hand, Rabbi Meir requires a doubled condition because “from the negative you do not infer the affirmative.” On the other hand, he requires it because, like all the other laws of conditions, it is learned from the condition of the tribes of Gad and Reuven. Maimonides rules like Rabbi Meir only with respect to the second factor — the derivation from Gad and Reuven — but not with respect to the logical principle. There he rules that from the negative we do infer the affirmative. See there how he resolves all the contradictions in Maimonides’ rulings on the basis of this distinction; that discussion lies beyond our scope.

In any event, Maimonides’ rulings show that although, according to Rabbi Meir, the requirement of a double condition also stems from a logical understanding — namely, that from the negative one does not infer the affirmative — as a matter of practical law we require it for a different reason. It is a formal halakhic rule, like all the other laws of conditions: that the affirmative must precede the negative, that the condition must precede the act, and so on.

An Implication

According to this Maimonidean view, there are important implications for the principle “from the negative you infer the affirmative” in the interpretation of Scripture. With respect to biblical interpretation, there is obviously no room to derive the matter from the laws of conditions. Scripture is not formulating a legal stipulation. On the other hand, Rabbi Meir’s logical premise was not accepted as law, and therefore in interpreting Scripture we may indeed infer the affirmative from the negative. Our midrash would then seem to support Maimonides’ rulings. Although Maimonides rules like Rabbi Meir that a condition must be doubled, he nonetheless rules “from the negative you infer the affirmative.”

Our difficulty above is now resolved very smoothly: one may rule in practice like Rabbi Meir that the condition must be doubled, and nevertheless hold “from the negative you infer the affirmative,” as in our midrash. Thus our derivation can also accord with normative halakha, though not with Rabbi Meir’s own reasoning.

More on the Relation between “From the Negative You Infer the Affirmative” and Logic

Even so, Maimonides’ view requires clarification. Why, in fact, must a condition be doubled if as a matter of law we interpret implication in a non-material way? If implication is interpreted symmetrically, as Rabbi Yehudah maintains, then conditioning a legal act in one direction already includes the opposite direction as well. If so, why must the condition be doubled explicitly? What is the meaning of the principle learned from Gad and Reuven?

As we have seen, it is clear that stating one direction — for example, the negative — does not include, in a logically necessary way, a statement in the other direction — the affirmative. It is possible to interpret the statement that way, but that is a context-dependent linguistic judgment, not a matter of logical derivation. From the standpoint of strict logic, an implication statement does not mean equivalence. In certain linguistic contexts, however, implication statements may be understood as though they were equivalences.

We can now understand what happens in the case of a legal condition. For a condition to operate, the intention of the stipulator must be expressed with complete clarity. Even if his intention is reasonably expressed and known to us to a considerable degree, that is not enough for the condition to take effect. A condition takes effect only if the intention is absolutely clear from the language itself, beyond all doubt.⁵ Therefore, even if in ordinary situations the negative clause alone is enough for us to infer the affirmative, in order for a legal condition to take effect it must be formulated in a completely unambiguous way, and therefore a doubled condition is required.

What Happens When a Condition Is Not Doubled

We can see this by examining a case in which someone made a condition but did not double it. The Gemara rules that when a person makes a condition but does not satisfy one of the laws of conditions, the act remains valid in any event, and only the condition is nullified. For example, consider a man who divorced his wife on condition that she give him one hundred silver coins, but did not double his condition. The law is that in such a case the woman is divorced regardless, whether she gives him the money or not. At first glance this is astonishing: after all, he plainly did not intend to divorce her if the condition was not fulfilled. How can the divorce take effect against his will? One would have expected the law to say that in such a case the divorce is void in any event, and that if he wishes he must divorce her again — this time with a properly formulated condition.

If the basis for the requirement of a doubled condition were the principle “from the affirmative you do not infer the negative,” then when he states only the affirmative clause, we do not know what he intends if the condition is not fulfilled. If so, it is difficult to assume that the woman should be divorced in any case, when his intention is unclear. It would seem that from here alone it is already proven that the principle “from the negative you do not infer the affirmative” is not a logical principle, but a formal halakhic requirement.

According to Maimonides, the problem becomes even sharper. If we rule that “from the negative you infer the affirmative,” then when a person states a condition in only one direction, that should apparently suffice to make clear to us that his intention is that if the condition is not fulfilled — if, for example, the woman does not give him the money — he does not want the act, namely the divorce, to take effect. If so, how can we impose the divorce upon him against his will? It would seem that from here it is proven that even Rabbi Yehudah’s claim, according to which one may infer the affirmative from the negative, is not a claim on the plane of logical meaning.

A Note from the View of Ri in Tosafot

Tosafot, s.v. “Harei Zo,” on Ketubot 56a, raises this question and brings two opinions in resolving it: that of Ri and that of Rabbenu Tam. Ri’s view is that a condition is not a suspension of the legal effect itself. When a person attaches a legal act to some condition, the act takes effect in any case, and the condition — if properly formulated — can cause the act to be uprooted if the condition is not fulfilled. Ri adds that this uprooting cannot be carried out unless the condition is formulated in accordance with the laws of conditions. Without satisfying those laws, this is merely speech, and speech cannot come and nullify an act that has already taken effect. But if the laws of conditions are satisfied, the Torah innovates — in the passage of the tribes of Gad and Reuven — that speech of this sort can indeed uproot the act. For that reason, Ri explains, when the condition was not stated in the correct form, the act nonetheless takes effect, and the condition has no power to uproot it even if the condition was not fulfilled.

At first glance this is a technical-formal explanation, and it disconnects the question of whether the condition takes effect from the meaning of the stipulator’s words. However, that is not necessary. At first glance, Ri tacitly assumes that the stipulator does not truly intend to make the effectiveness of the act depend on the fulfillment of the condition, for otherwise it is still not clear how the act takes effect in any event.

Yet it seems that according to Ri our remarks are not necessary. The taking effect of the act does in fact accord with the stipulator’s intention, for otherwise the act could not take effect at all. The discussion there deals with a condition that takes effect retroactively — a clause of “on condition that,” not a clause of “if.” Ri holds that a legal effect cannot come into being before the conditions for its creation have been fulfilled. Therefore, the stipulator is compelled, whether he likes it or not, to proceed by a mechanism in which the act takes effect in any event and is accompanied by a condition that allows it to be uprooted if what the stipulator demanded is not fulfilled. Hence, although this is not the stipulator’s most basic desire, in practice, for the mechanism of condition to function at all, he is forced to choose a mechanism in which the legal effect takes place regardless, while the condition remains as a mechanism of retroactive uprooting.

If so, according to Ri it is indeed possible to interpret the principle “from the negative you infer the affirmative” as referring to the logical meaning of the statement under discussion.

D. Three Concluding Remarks

1. The Relation between “From the Negative You Infer the Affirmative” and “From the Affirmative You Infer the Negative”

From all that we have said thus far it emerges that these two inverse rules are based on the same principle. Whoever accepts one should accept the other, and vice versa. And indeed, on the purely logical plane there is no difference between these two directions. However, as we saw above, these rules are not necessarily located on the logical plane. They may instead reflect an understanding of the meaning of such statements in ordinary spoken language, and not necessarily a logical rule.⁶

If these rules are indeed based not on logical derivation but on an understanding of the meaning of such statements in spoken language, then it becomes possible to separate them. When a person makes something contingent upon the existence of something else, one may say that the legal effect will come into being if the condition is fulfilled, and therefore, if the condition is not fulfilled, the legal effect will not come into being. This is an explanation based on causation, as we saw above. But if a person says that a certain legal effect will not come into being if something does not occur, that does not mean that if the condition does occur, the legal effect will necessarily come into being.

For example, Reuven tells Shimon that if he gives him one hundred silver coins, he will show him a certain book. It seems that the right to see the book is created by the payment of the money. Hence, if the money is not given, the situation remains as it was, and Shimon will not be able to see the book. But if Reuven tells Shimon that if he does not give him one hundred silver coins, he will not be able to see the book, there is no mechanism of causation here. There is only a logical indication, and not a relation of causation — or, put differently, there is here a necessary condition, but not a sufficient one. If so, the inference about what will happen if he does give him the money is not necessary.

If so, there may perhaps be room to separate these two rules.⁷

2. Is the Principle “From the Negative You Infer the Affirmative” Specifically Connected to Conditions?

It is not clear whether, for the purpose of the rules discussed here, there is any difference between a conditional sentence, which has two parts, and an ordinary sentence. One might say that these rules concern only conditional statements, and ask whether a stipulation stated in one direction also teaches us about the intent in the opposite direction, or not. But in a sentence that has only one part, the inference is not connected to these rules.

Let us recall the midrash with which we began. The midrash opens with the wording “you shall teach them to your children,” and infers from it “and not your daughters.” Here the rule “from the affirmative you infer the negative” is not mentioned. We asked why it is not invoked already at this stage. Later in the midrash this rule is indeed brought, but it is applied to a two-part proposition that appears in the verses, according to which if we teach Torah and the holy tongue, our days will be lengthened. Here the rule comes and teaches us that if we do not do so, our days will not be lengthened. Perhaps the reason for this difference lies in the suggestion we made above. The rule “from the affirmative you infer the negative” may apply only to conditional statements, and not to one-part statements.

The exclusion of teaching daughters from the commandment to teach sons is an instance of the principle of restriction, not of “from the affirmative you infer the negative.” The rule “from the negative you infer the affirmative” is stated only with respect to conditional statements, and it is a different rule. This point requires further examination, both in the interpretation of Scripture and in the interpretation of ordinary human language, but this is not the place.

3. Another Side Remark on Our Midrash

The Torah says that if we teach our children Torah and the holy tongue, our days will be lengthened. The midrash derives from this the opposite meaning, that if we do not teach them Torah and the holy tongue, our days will be shortened. In any event, this inference is not necessary, since all that can be inferred is that our days will not be lengthened, not necessarily that they will be shortened. Beyond that, how do we know at all that in the language of the Torah one may in fact make even this inference, even with respect to the “correct negative”? Perhaps the Torah means to say that if we teach them, our days will be lengthened, and if we do not teach them, then it is not necessarily the case that they will be lengthened. From the standpoint of pure logic, that conclusion too is possible.

We are therefore forced to conclude that the principle “from the affirmative you infer the negative” is a principle handed down to us by tradition with respect to the interpretation of the language of Scripture. According to this, it is not necessarily connected to the interpretation of ordinary human language. It is therefore possible that everyone agrees to this interpretive-midrashic rule, and yet a dispute arises concerning it as an interpretive rule regarding ordinary human language.

From here we may perhaps understand why this rule can be regarded as a hermeneutical principle, and not merely as a plain interpretive principle.

We have seen that this rule is not logically necessary, and that it depends on the structure of the language of Scripture. We have seen that it may concern only conditional statements, and not every sentence in Scripture. If so, we are dealing here with a unique structure of the holy tongue, and there is therefore room to understand it as a hermeneutical principle transmitted to us at Sinai.⁸ Moreover, it may be that this rule is not connected to the structure of the holy tongue itself at all, but is rather a midrashic rule that creates an additional layer of meaning beyond the plain linguistic one; see an example of this on the page for portion Vaetchanan.

At first glance, our midrash treats this principle as a kind of interpretive exposition — “for thus words of Torah are expounded.”⁹ On the other hand, the authors of the collections of hermeneutical rules did not include this principle as one of the formal hermeneutical principles. Usually it is treated as an interpretive principle regarding ordinary human language. Therefore, for us, its status as a hermeneutical principle remains unresolved.

Footnotes