Ki Teitzei (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 of Parashat Ki Tetze, 5765

Questions

1. What is the difference between kal va-homer (a fortiori reasoning) and homer va-kal (reasoning from the more severe case to the lighter one)?
2. Is there an asymmetry between prohibitions and permissions?
3. Is there a prohibition against relations with an unmarried woman?
4. What is a kadesh, the biblical term for a man designated for sexual promiscuity?
5. More on “from the positive you infer the negative” as a hermeneutical principle.
6. On content redundancy and verbal redundancy in the Torah.
7. Are there superfluous degrees of freedom in creation? And in the Torah?

The Principles

• Kal va-homer.
• Homer va-kal.
• From the positive you infer the negative.

“There shall not be a kedeshah, a woman designated for sexual promiscuity, from among the daughters of Israel, and there shall not be a kadesh, a man designated for sexual promiscuity, from among the sons of Israel.”

— Deuteronomy 23:18

“There shall not be a kedeshah from among the daughters of Israel” — you are not warned about her among the nations. “And there shall not be a kadesh” — you are not warned about him among the nations. For this could have been derived by logic: if, with respect to kedeshah, which is less severe, you are warned in Israel, then with respect to kadesh, which is more severe, is it not a fortiori that you are warned in Israel? Or the reverse: if, with respect to kadesh, which is more severe, you are not warned about him among the nations, then with respect to kedeshah, which is less severe, is it not all the more so that you are not warned about her among the nations? What then does Scripture teach by saying kadesh? It had to say it, for if it had said kedeshah and had not said kadesh, I would have said: if, with respect to kedeshah, which is less severe, you are warned in Israel, then with respect to kadesh, which is more severe, is it not a fortiori that you are warned about him among the nations? Therefore Scripture says: “There shall not be a kedeshah from among the daughters of Israel” — you are not warned about her among the nations; “and there shall not be a kadesh” — you are not warned about him among the nations.

Another interpretation: “There shall not be a kedeshah” — this is a warning concerning a woman who makes herself available, as it is said, “No kedeshah was here.”

— Sifrei Devarim, section 260¹

A. The Prohibition of Kadesh and Kedeshah in Israel and Among the Nations

Introduction: The prohibitions of kadesh and kedeshah

The verse cited above forbids kadesh and kedeshah among Israelites. The Sages understand from here that the prohibition applies only to a Jew, and not to someone from the other nations.

The very meaning of the terms kadesh and kedeshah is not clear from the verse itself. Various midrashim (rabbinic interpretive texts) offer different explanations of this verse, some understanding it as dealing with male homosexual intercourse, bestiality, and more.

And indeed, among the halakhic (Jewish legal) authorities as well, opinions are divided on this matter. Maimonides and those who follow him — see, for example, Sefer HaHinnukh, commandments 209 and 570 — understand the prohibition of kedeshah as a negative commandment against relations with an unmarried woman. In negative commandment 355, Maimonides defines the prohibition of kedeshah as the prohibition against relations with a woman without a marriage contract and without formal betrothal. In negative commandment 350, Maimonides counts the prohibition, from the end of Parashat Aharei Mot, against male homosexual intercourse, and writes that this warning is repeated in the verse “there shall not be a kadesh.” He does not count this prohibition independently, because, as he himself states in the ninth principle, two negative commandments with overlapping content are not to be counted separately.

Sefer HaHinnukh there cites another approach in the name of the Targum, but that need not detain us here.

Nahmanides, in his glosses to Sefer HaMitzvot, negative commandment 355, and in his glosses to Maimonides’ fifth principle, pages 116-120 in the Frankel edition, as well as in his commentary to the Torah in our parashah and in Aharei Mot, disputes Maimonides’ understanding of these prohibitions. His remarks are also cited in Sefer HaHinnukh. There are differences among Nahmanides’ various discussions, and here we will present the picture that emerges from them taken together.

Nahmanides holds that the prohibition of kedeshah is a commandment directed to the bet din (rabbinical court) to prevent intercourse with one with whom formal betrothal cannot take effect, and likewise to prevent any Israelite from being available for promiscuity: a woman available for ordinary promiscuity, and a man available either for ordinary promiscuity or for male homosexual intercourse. According to Nahmanides, the prohibition does not apply to the participants in the act of promiscuity, nor is it tied to the act itself. The prohibition concerns the very existence of an ongoing state in which an Israelite man or woman is available for promiscuity.²

Nahmanides writes that this state must be prevented because it may lead to forbidden sexual unions. When a person is available for promiscuity, there is no control over with whom he or she has sexual relations, and such relations may therefore involve incest or another prohibited union. Beyond that, such a state can lead to marriages between close relatives who do not know they are related. The same woman may conceive by some man whose identity is unknown, and thus a situation may arise in which a person marries his sister, and so on.

The meaning of the word kadesh

As noted, Nahmanides understands the prohibition of kadesh as an obligation on the bet din to prevent someone from being available for promiscuity. According to this, kadesh is a term of designation. And indeed, he brings support for this from several biblical passages, as well as from Ibn Ezra and Rabbi David Kimhi, who interpret it that way. We find the same in Midrash Aggadah (Buber), Deuteronomy 23, on the words “there shall not be”:

“There shall not be a kedeshah” — there should not be an unmarried woman who makes herself available in the land, so that anyone who wishes to come to her may lie with her. Thus one will not come into forbidden sexual unions, as the nations do. Likewise, “there shall not be a kadesh” — there should not be a male who makes himself available for male homosexual intercourse, as the nations do. And kadesh is only a term of designation, as it is said: “Prepare yourselves for tomorrow” (Numbers 11:18).”

If so, the definition of kadesh is someone designated for promiscuity.

We should note here that even within Maimonides’ view, quite a few commentators understood him as meaning that the prohibition under the heading of kadesh or kedeshah applies only to a state in which someone is available for promiscuity, and not to an occasional private act — see Kesef Mishneh on Mishneh Torah, Laws of Virgin Maiden 2:17; the novellae of Maharit on the Rif at the beginning of tractate Kiddushin; and the Vilna Gaon’s commentary, Even HaEzer 26:8. Still, this reading is very forced in the language of Sefer HaMitzvot, where it appears that anyone who has relations with a woman without a marriage contract and formal betrothal violates this prohibition. In any case, Maimonides’ view should not be identified with Nahmanides’, for according to Maimonides the prohibition applies to the participants in the act itself and not to the bet din, and on his view the act itself must clearly take place in order for there to be a prohibition here.

Nahmanides, in his commentary on our verse, offers an additional interpretation of the term kadesh, deriving it from the root of holiness: anyone who abstains from promiscuity is called holy, and therefore one who joins himself to promiscuity is called kadesh.³ According to the straightforward understanding of Maimonides, under which no prior designation for promiscuity is required in order to violate the prohibition, we probably must explain the term as Nahmanides suggests.

The view of our midrash

Nahmanides himself, both in the principles and in his commentary on our verse, cites our midrash and proves from it that his own view is correct. The midrash states that this prohibition does not exist among the nations, whereas the prohibition of male homosexual intercourse certainly does exist for gentiles, for which they are stoned.⁴ True, according to Nahmanides as well, the prohibition of kadesh speaks of male homosexual intercourse, which is indeed forbidden to gentiles; but on his view this is an obligation on the bet din to prevent a state of designation for promiscuity, and such an obligation exists only in Israel and not among the nations.⁵

We should note that Maimonides’ view is in fact very difficult. If the prohibition of kadesh really concerns male homosexual intercourse, it is obvious that this is forbidden to gentiles as well. A solution that says this midrash was not accepted as halakhah by Maimonides does not answer the difficulty, because the exclusion of gentiles from this prohibition is explicit in the verse itself, in the phrase “from among the children of Israel.” Thus not only the midrash but the verse itself points against Maimonides’ interpretation.⁶

Two additional proofs may be brought that the view of our midrash follows Nahmanides and not Maimonides:

1. There is another difficulty in the midrash: the prohibition of male homosexual intercourse carries karet, spiritual excision, and stoning, whereas the prohibition of intercourse with an unmarried woman, or with one designated for promiscuity, is at most a mere negative commandment. If so, how can kadesh in Israel be learned by kal va-homer from kedeshah?⁷ According to Nahmanides, this is not difficult, because the prohibition is directed to the bet din’s duty to prevent a state of being designated for promiscuity, and we are not speaking of a prohibition on the act of promiscuity itself. The kal va-homer teaches that the bet din must prevent a situation in which people are designated for promiscuity.

2. It is also difficult, according to Maimonides’ interpretation, how the midrash can suggest learning these prohibitions from one another by kal va-homer, given that punishments are not derived from logical inference. Again, according to Nahmanides the matter is clear, because we are not speaking of offenses that incur punishment, but of the bet din’s duty to prevent a state of being designated for promiscuity.

The conclusion is that in any event this midrash seems to fit Nahmanides’ view, namely that the basis of the prohibition is designation for promiscuity, as we saw above in Midrash Aggadah.

The basic structure of the midrash

Rabbinic literature contains an entire family of midrashim with the same structure as this one. In all these cases, the Torah contains two commands, or two examples of a given command, where one can be learned from the other, usually by kal va-homer. In such a situation, one of the examples is redundant, and we must ask why it was nevertheless written in the Torah. In other words, we must examine what it teaches us beyond its simple sense, that is, beyond serving as just another example of the command.

One example among many appears in the Mekhilta on Parashat Mishpatim, which discusses the prohibition against opening or digging a pit in the public domain and the obligation to pay for the damage it causes. The Mekhilta writes as follows — section 11, on the words “and if a man shall open”; it is also cited in Tosafot on Babylonian Talmud, Bava Kamma 2a, s.v. “ve-lo zeh”:

“Another interpretation: ‘And if a man shall open’ — I know only one who opens; from where do I know one who digs? Scripture says, ‘or if a man shall dig.’ But even before Scripture said this, I could have reasoned: if one who opens is liable, is one who digs not all the more so? Yet if you say so, you would be imposing liability on the basis of logical inference; therefore Scripture says, ‘or if a man shall dig,’ to teach you that punishments are not derived by logical inference.”

If a person who opened a pit is liable to pay, then it is obvious that someone who dug the pit is liable as well. The statement about the one who dug is therefore redundant, and it is clear that it is meant to teach us something beyond its simple sense, namely beyond the simple obligation to pay for the damage caused by a pit that I dug. In this case, the redundancy teaches us a general halakhic principle: even in monetary law, punishments are not derived by logical inference.

Our midrash assumes that the duplication of kadesh and kedeshah contains redundancy, and therefore one of the two examples must be intended to teach some additional law. The assumption is that kedeshah is less severe than kadesh, and therefore kadesh is obviously redundant, so we must ask what it comes to teach.

Why is kadesh more severe than kedeshah?

First we must ask why the Sages assume that kadesh is more severe than kedeshah. In the example of digging a pit in the public domain, the answer is simple: every act of digging in fact includes opening, and therefore if one is liable for opening, one is certainly liable for digging. In the past we cited this kal va-homer as an example of the type called in the literature of interpretive rules “a maneh included within two hundred.” With respect to kadesh and kedeshah, however, there is no such simple relation between them. As noted, the kal va-homer from kedeshah to kadesh is not of the “maneh included within two hundred” type, but neither is it a quantitative kal va-homer — that is, one based on a generalization from two legal data points concerning kadesh and kedeshah. See the page on Parashat Noah. Clearly, then, we are dealing here with a kal va-homer based on reason.⁸ But what is that reasoning? Why is kadesh more severe than kedeshah?

If we are speaking of a kadesh who is available for ordinary promiscuity, then one could have thought that such a man might encounter a married woman, and then a forbidden sexual union would occur, whereas a kedeshah who is unmarried, even if she encounters a married man, does not thereby create an incest prohibition. But according to the explanation we gave above, the kadesh is designated for male homosexual intercourse, so this cannot be the basis of the greater severity here.⁹ Still, it may be that this itself is the severity of kadesh: the sexual relation for which he is designated is male homosexual intercourse, whereas kedeshah is designated for a sexual relation that is not inherently bound up with forbidden unions.

The course of the midrash in the Sifrei

The midrash in the Sifrei begins by stating that kadesh and kedeshah are forbidden only in Israel and not among the nations.¹⁰ It then presents a double line of reasoning based on the assumption that kadesh is more severe than kedeshah: in Israel it would have been enough to write that kedeshah is forbidden, and we would have learned by kal va-homer that kadesh is forbidden as well. Among the nations it would have been enough to write that kadesh is permitted,¹¹ and then we would have learned by homer va-kal — that is, if the more severe case is permitted, then surely the lighter one is permitted¹² — that kedeshah too is permitted among them. In light of this, it is clear that we cannot adopt a solution according to which the duplication is intended to teach something about the permission among gentiles rather than about the prohibition among Jews. If so, the difficulty now appears with respect to both kadesh and kedeshah. One is redundant with regard to Israel, and the other with regard to the gentiles.

The midrash then summarizes the first stage by saying that, in light of what has been said so far, it is unclear why the prohibition of kadesh is written: “what then does Scripture teach by saying kadesh?” It is not clear why the midrash does not address the difficulty concerning the permission of kedeshah among the nations as well.

The midrash explains that the statement regarding kadesh is nevertheless needed, because if there had been only the statement about kedeshah, then although we would know that kadesh too is forbidden in Israel, we would think that a severe prohibition such as kadesh would apply also to gentiles, while the permission among the nations would apply only to kedeshah. Therefore the Torah added the prohibition of kadesh among the children of Israel, to teach us that even the prohibition of kadesh, though more severe, applies only among the children of Israel and is permitted among the nations.

An asymmetry between prohibition and permission

At this point a difficulty arises in understanding the midrash. The midrash explains why it would not have been enough to write only the prohibition of kedeshah. That is, the wording under discussion would then have been: “There shall not be a kedeshah among the daughters of Israel.” The solution proposed by the author of the midrash is that if the Torah had written only this, then we would infer that the more severe prohibition of kadesh — which in Israel is learned by kal va-homer from kedeshah — would apply even to Noahides. But how can one learn a prohibition in such a way? This is not an ordinary kal va-homer at all. Among the nations there is permission with respect to kedeshah, but there is no explicit permission with respect to kadesh. The Sages are telling us that we would have innovated a prohibition of kadesh among the nations on our own, and that the additional clause in the verse is therefore needed in order to teach us that there is no such prohibition. But how could we have innovated such a prohibition on our own?

It seems that the derivation would rely on the principle of “from the positive you infer the negative” — see the page on Parashat Eikev, where we discussed this principle as a hermeneutical rule. Precisely the permission stated regarding kedeshah would have served as the basis for innovating a prohibition regarding kadesh. Since the Torah permits, among the nations, what is forbidden under the heading of kedeshah, we would infer from this that specifically that prohibition was removed, whereas the prohibition of kadesh would still apply to them.

It should be noted that in the opposite direction this difficulty does not arise. If only the prohibition of kadesh had been written, then we could have thought that kedeshah is permitted even in Israel. Here there is no difficulty at all in innovating a prohibition or a permission on our own. Anything that the Torah did not forbid is by default permitted. It is clear that if the Torah had forbidden kadesh, and kadesh is more severe than kedeshah, we would permit kedeshah even in Israel.

This is an asymmetry between permission and prohibition. Prohibition is the Torah’s innovation, and if we wish to generate it on our own, that must rest on a legitimate tool — a hermeneutical rule, a rational argument, or some other mode of interpretation. But to establish permission, no interpretive or midrashic anchor is needed. Whatever was not forbidden remains permitted.

Still, this asymmetry may not be absolute. In the case of acts that plain reason tells us are forbidden, the default may actually be to forbid, and explicit permission would be required in order to permit. Only in prohibitions that are innovations of the Torah do we refrain from forbidding unless the matter is explicit. If so, with the prohibitions of kadesh and kedeshah there may indeed be a rational basis, for these are moral prohibitions, and therefore even without explicit prohibition we would not permit them. For the same reason, we would forbid kadesh to a gentile even without a verse that explicitly permits it.

If so, the asymmetry is not between prohibition and permission, but between a law that accords with reason and a law that runs against reason. Of course, on this way of understanding, there is no need to appeal to the rule “from the positive you infer the negative” in order to understand the midrashic reasoning here.

We should note that this distinction is not necessary, because it may be that creating a halakhic prohibition requires an explicit command, and that bare reason is not sufficient for this purpose.¹³ Therefore, even where there is reason to forbid, we still would not create a formal prohibition without a command.

The end of the midrash

The end of the midrash is also unclear. First, we saw that the midrash treats the prohibition of kadesh specifically as the redundant element. It explains that the prohibition is indeed redundant, but that it is written in order to teach the permission of this prohibition among the nations. If so, why does the alternative interpretation brought at the end of the midrash refer specifically to the prohibition of kedeshah? The redundancy that needs explanation is the prohibition of kadesh. Beyond that, the meaning of the words “a warning concerning the available one” is unclear. Nor is it clear what role is played by the verse in Genesis about Tamar and Judah.

A possible explanation

It seems likely that, as we saw above, the difficulty for the author of the midrash concerned the pair of prohibitions and not specifically the prohibition of kedeshah. In the author’s view, either one could have been omitted, and therefore both require a statement of mutual necessity. According to this explanation, the prohibition of kadesh is needed in order to teach its permission among the nations, whereas the prohibition of kedeshah is needed in order to teach us about the “available woman.”

What does “a warning concerning the available one” mean? On its plain meaning, it means that this warning is indeed free, that is, redundant, and therefore serves as a warning for something else, though the midrash does not specify what that something else is. But it is possible that there is a textual problem here, and that the wording should read: “a warning concerning the unmarried woman,” instead of “the available one.” The proof brought for this is from Tamar, who is called in the Torah a kedeshah even though she was unmarried. If so, the meaning of the word kedeshah is an unmarried woman ready for promiscuity, and after the giving of the Torah such a state was forbidden in Israel.

According to this, however, it is not clear what we were supposed to think before this explanation. The prohibition of kedeshah had already been interpreted at the beginning of the midrash as a prohibition concerning an unmarried woman, so it is not clear what is being added now.

The Malbim’s version

The version of the midrash as it appears in the Malbim is different. There the picture is completely symmetrical, and the midrash asks why both kadesh and kedeshah are needed. The considerations are the same as in our midrash, namely that one can derive one from the other by kal va-homer or by homer va-kal. The conclusion of the midrash in the Malbim’s wording is likewise symmetrical: the prohibition of kadesh is needed so that we do not come to forbid kadesh among the nations, and the prohibition of kedeshah is needed so that we do not come to permit kedeshah in Israel, on grounds symmetrical to those found in our midrash.¹⁴

According to this, it is clear why the prohibition of kedeshah is indeed needed, since it too is redundant and requires explanation, as we noted above. It is also clear that the prohibition concerns an unmarried woman, and not “the available one,” as in the wording of our midrash, and it teaches that there is a prohibition of kedeshah — an unmarried woman, or an unmarried woman designated for promiscuity — in Israel. The two opinions in our midrash are not really two different opinions, but rather a statement of the mutual necessity of the two prohibitions. The Malbim’s version seems more precise, and it is apparently the version that also underlies the midrash with which we are dealing here.

B. Two Kinds of Redundancy: Content Redundancy and Verbal Redundancy

Introduction

In the previous chapter we dealt with clarifying the text of the midrash and its meaning, and with explaining the course of the discussion in it. But if we look at the argument of the midrash more carefully, we will see that it contains a fundamental logical difficulty, and that is what we will discuss in this chapter.

A difficulty in the basic logic of the midrash: what exactly is redundant here?

At the outset, the midrash assumes that one of the prohibitions is redundant. The prohibition of kadesh in Israel can be learned by kal va-homer from kedeshah, and the permission of kedeshah among gentiles can be learned by homer va-kal from the permission of kadesh among gentiles.

At first glance, then, the midrash is raising a question of redundancy. Because these laws can be learned from one another, there is some redundant component here. For that reason, the midrash concludes that the purpose of the redundant part is to teach us some new law, or to prevent the emergence of an incorrect law. We saw the same thing above in the example of digging and opening a pit in the public domain.

But in the end it is not clear which of the two prohibitions is redundant. Which of them could have been deleted, were it not for the final answer?

Let us make this clearer. Even according to the objector, it was necessary to write the prohibition of kedeshah in Israel and the permission of kadesh among the nations. How could this have been written more economically than the Torah actually writes it? Put differently: suppose we would never have thought to generate a prohibition of kadesh for a gentile or a permission of kedeshah in Israel, even if the Torah had not explicitly blocked those conclusions. Even then, it is still not clear how the verse could have been written more economically.

Take, for example, the wording: “There shall not be a kedeshah among the Israelites, but there may be a kadesh among the nations.” This wording is sufficient, because it contains the two laws that must be written explicitly. But it is in no sense more economical than the wording that appears in the verse before us.

Apparently, the only possibility is that the wording with which the author of the midrash is dealing is: “There shall not be a kedeshah, and there shall not be a kadesh among the Israelites” — and perhaps one could also write, “There shall not be kadesh or kedeshah among the Israelites.” That is, were it not for the final answer, we would have had to omit the first limitation, “among the daughters of Israel,” because it can be learned by homer va-kal. But if that really was the difficulty, then the answer does not resolve it. After all, what is proposed is to omit only the permission of kedeshah among the nations, and that can certainly be learned by kal va-homer from the permission of kadesh among the nations. Everything else is not redundant, and therefore its being written would seemingly require no further justification.¹⁵

Two kinds of redundancy

In light of the force of this difficulty, it seems that we must explain the midrash in a new way. In truth, there is no question here of ordinary redundancy. There is no superfluous word in this verse. Yet it is still clear that it contains superfluous laws.

It seems evident that the author of the midrash is dealing with the alternative wording we proposed above: “There shall not be a kedeshah among the Israelites, but there may be a kadesh among the nations.” Here the two necessary laws are written, and the other two are learned from them by kal va-homer and homer va-kal. We noted above that this wording is not more economical, because it does not use fewer words than the wording before us. But it seems that the author of the midrash nevertheless prefers it, because it does not contain superfluous laws.

Thus we discover here a new kind of redundancy: not a text with superfluous words — verbal redundancy — but a formulation part of whose content is superfluous — content redundancy. Such a formulation too does not seem reasonable to the author of the midrash, and therefore, in his view, it is there in order to teach something additional.

Let us now try to clarify what problem the Sages saw in content redundancy.

First possibility: the optimality of content

We are familiar with the principle that underlies verbal redundancy: the wording of the Torah is optimal. There are no superfluous words in the Torah, and therefore anything that appears to us redundant must presumably be meant to teach something else. But what principle underlies the problematic character of content redundancy?

By analogy to ordinary redundancy, we may say that the relevant principle is that the content of the Torah is also optimal. That is, there is nothing in the content of the Torah that is superfluous. Anything that can be learned from the Torah is also taken into account, and is not written there for no reason.

Second possibility: the existence of degrees of freedom

The problem of content redundancy can be formulated somewhat differently. If there were content redundancy in the Torah, then several different formulations could be used to express the same idea. For example, in our case, instead of the wording in the Torah one could have written: “There shall not be a kedeshah in Israel, but there may be a kadesh among the nations.” Here we are not suggesting this as a better alternative because it lacks content redundancy, but as an alternative that is no worse than the existing one.

According to this proposal, if two formulations express the same content, then that is content redundancy. The formulation is not unique, and another formulation could have been used to express the same content. The problem is the lack of uniqueness of the biblical formulation. According to this suggestion, a similar problem also exists in verbal redundancy, because the same content could be expressed even if the superfluous words were omitted.

When the author of the midrash explains why the wording before us was necessary, he is showing that the intended content could not have been achieved by a different formulation, because that would have led us into error. Answers of this type are not meant to explain the formulation that was chosen, but to rule out the other formulations.

We will now bring several additional examples of approaches involving superfluous degrees of freedom, and of the problem they raise. We will do so through a brief consideration of Maimonides’ view in several different contexts, in all of which the question of superfluous degrees of freedom arises.¹⁶

C. Superfluous Degrees of Freedom

The hermeneutical principles

We saw on the page for Parashat Bereshit that Maimonides understood the thirteen hermeneutical principles as an arbitrary code. That is, the principles are arbitrary rules of inference that have no independent meaning or role of their own. The midrashic information could have been encoded in the Torah by other means as well, with no difference. By contrast, as we cited there, Rabbi David Cohen, the Nazir, strongly argued that the principles themselves possess intrinsic significance, and are not merely tools for deciphering information hidden within the biblical verses.

It seems that the root of the dispute is that the Nazir was unwilling to accept that God created His world, or the Torah, in a way that contains something arbitrary. Everything in the world and in the Torah must have significance in itself, and not merely serve as an arbitrary instrument designed to achieve some other goal. Maimonides, by contrast, is not disturbed by the fact that the Torah or the world contains arbitrary elements. Some code had to be chosen, so God chose one code out of many possible ones.

In our example, we saw that the midrashic information could have been encoded in several different ways. These are superfluous degrees of freedom in the Torah.

The holy tongue

On the page for Parashat Balak we noted that Maimonides holds that the holy tongue is conventional, and has no significance in itself. On his view it is not essentially different from any other language, and God chose it arbitrarily and not because of any special qualities. Nahmanides and Rabbi Abraham ben David, by contrast, hold that the holy tongue has several unique qualities not found in the other languages. On their view, the holy tongue is a unique mode of expression, and only through it can the precise content of the Torah be expressed.

Thus, according to Maimonides, there are superfluous degrees of freedom in the choice of language, because God chose a language that had other substitutes no less good. Here too it seems that Nahmanides and Rabbi Abraham ben David disagree with him precisely on this point, for they see the existence of degrees of freedom in the language of Scripture as a theological problem.

The purpose of creation

In Guide of the Perplexed, part III, chapter 13, Maimonides states that every detail in creation is an end in itself, and that not all creation was intended solely for the sake of man. Maharam Gabbai, in his book Avodat HaKodesh, in the opening chapters of the section on purpose — see also Sefer HaKelalim, from Leshem Shevo Ve-Ahlamah, rule 15, branch 11 — disagrees with him and holds that everything was intended for the sake of man.

Over the course of that chapter, Maimonides explains his view by saying that there were many possible options in creation, and God chose among them purely by will and arbitrarily. He could have done it in infinitely many other ways, equally well. Here too we encounter a conception of superfluous degrees of freedom, this time in creation itself.¹⁷

Reasons for the commandments

Maimonides’ position regarding the reasons for the commandments is well known; see Guide of the Perplexed, part III, at the end of chapter 26. Maimonides is among those who hold that the commandments have a rationale only in a general sense, but that the rationale does not fit the details. He explains that this is so in principle. God had to determine the details somehow, because one cannot leave gaps and ambiguities in the halakhah, and therefore He determined the details arbitrarily and without any reason.

This claim of Maimonides is also problematic, for what could prevent God from creating His world and the Torah in such a way that there would be a perfect correspondence between them? That every detail of the halakhah would correspond to some purpose in creation? Here too Maimonides is not troubled by the question of arbitrary and superfluous degrees of freedom in creation.

Maimonides’ theory of providence

Maimonides’ claim, in Guide of the Perplexed, part III, chapter 17, that God exercises providence only over species as wholes and not over every individual within them, provoked very broad controversy. Some even called it outright heresy. Here too we are dealing with superfluous degrees of freedom in creation. If there is no providence over each individual but only over the species as a whole, then replacing one ox with another changes nothing at all. A particular ox has no role; only the species of oxen as a whole does. This is once again a conception of superfluous degrees of freedom in creation. The distinction among individuals is not significant, and they can be exchanged without any essential change.¹⁸

This context provoked the harshest reactions, because here it is clear that a very problematic conception of divinity is involved. In our opinion, however, in principle there is no difference between this claim and the others presented here. In all of them the same problematic element is involved.

In fact, it is from here that we borrowed the term “degrees of freedom,” because in mathematics and physics a situation in which elements can be exchanged without affecting the state of the system as a whole is commonly called a degree of freedom in the system. Put differently, if the details can be exchanged, then two different states will appear exactly the same. This is again an arbitrary choice, without any reason, of one state from among several other states of equal standing.

Returning to the problem of content redundancy

All these examples point to the problem in the notion that God fashioned the Torah or created the world in a way equivalent to other possible ways — that is, that this particular way was chosen arbitrarily. Since God is the creator of the world and the Torah, nothing can prevent Him from doing so in such a way that every detail has essential significance, with no arbitrariness at all. Otherwise there would be some lack in the perfection and omnipotence of the Creator.

This same problem exists in content redundancy. If the content of the Torah is not necessary, then several formulations can contain the same content. That is a reality of degrees of freedom in the Torah and in language, that is, in the holy tongue. Therefore, the author of our midrash seeks to explain why the formulation that was chosen is essential and not merely one among many possible alternatives.

Footnotes