The Logical Status of the Hermeneutical Methods

With God's help

Tzohar – 5763

Introduction

The Sages generally do not tend to make explicit reference to the methodology of Torah study and interpretation. Therefore, the systems of rules by which the Torah is expounded constitute an unusual rabbinic formulation, in that they deal directly with the methods of interpretation.[1] Rabbi HaNazir points out in several places the profound significance of the rules for understanding the essence of Torah study, and of Torah thought in general. Against this background, the fact that the methods of interpretation are usually not entirely intelligible to the contemporary learner takes on added significance. Changing this state of affairs requires in-depth study of the rules on several planes.

In this article I wish briefly to examine one general point within this deep topic, which is only an introduction to the subject: the logical status of the methods of interpretation. Within this framework I will also address the somewhat worn question whether the rules are 'creative' or 'supportive,' which is closely bound up with clarifying the matter before us.[2]

A. Are the Rules 'Creative' or 'Supportive'[3]

There is a basic question concerning the legal midrashim, and especially those in which the thirteen rules are employed: is the midrash 'creative' or 'supportive'? That is, is the law that emerges from the halakhic midrash created by that particular exposition, or is it rather an already known law (from a plain-sense interpretation of the Torah, from reason, or from tradition—a law given to Moses at Sinai), and we merely attach it to the verses?

As noted, there are quite a few discussions of this topic, mainly among scholars. Therefore I do not wish to enter into the details of the evidence in both directions, especially in light of the fact that it is very difficult not to see that among the Sages there are midrashim of both kinds: creative and supportive.[4] Beyond that, among the medieval authorities (and especially in Maimonides, see below) one can find explicit statements that establish the existence of creative midrashim. Here I wish briefly to examine the logic underlying these two approaches and to draw several conclusions.

At first glance, the claim that the rules are merely supportive is difficult to understand. Why would any sage trouble himself to attach to Scripture a law that is already known and clear, especially by means that are so unconvincing from a logical standpoint?[5]

It seems to me that the simple reason that leads one to adopt the view that the thirteen rules are supportive rather than creative lies precisely in the fact that they appear to rest on dubious reasoning. The use of the rules and methods of interpretation appears, at first glance, arbitrary, as though the interpreter uses them to derive from the verses whatever he wants. Therefore some tended to adopt the convenient approach that we do not derive laws from these rules, but merely support known laws by means of them. A clear example of such an approach is found in Gersonides' introduction to his Torah commentary, where he writes as follows:

…That is because they [=the sages of the Talmud] attached these true matters, which they had received concerning the commandments of the Torah, to those verses [=by means of the thirteen rules], insofar as they are like a hint and an asmachta for those matters, not because they thought that these laws were actually derived from those passages. For one can overturn all the laws of the Torah by means of such inferences, to the point that one could even declare a creeping creature pure…

As stated, such an understanding of the role of interpretation is highly problematic. The difficulty is sharpened if we note that Gersonides' words here imply that the method of exposition by the thirteen rules has no internal logic, and is also not univocal; that is, Scripture can be expounded in several different ways by means of it. If so, why attach known laws to verses (which are not the true source of those laws), and in such ways at that? It would seem that Gersonides' view requires considerable examination.

Another approach is that the midrash is not only 'supportive' but also 'creative.' Maimonides, in the Laws of Rebels 1:2 and 2:1, writes that the Great Court of every generation can expound the Torah by means of the thirteen rules.[6] It clearly follows from his words that these are new, creative expositions, since a court in one generation may dispute, by force of an exposition, with a court of the previous generation.[7]

The same also appears from Maimonides' words in the Second Root. There Maimonides deals explicitly with the status of the laws derived from methods of interpretation. He determines there that these are 'divrei sofrim' ('rabbinic law'). The commentators disagreed about his intent: whether he means Torah laws that have a different status from laws explicit in Scripture, or whether these are actually rabbinic laws (as the plain sense of his language there suggests). In any event, from the reasoning Maimonides gives there—that these expositions are like 'drawing branches from roots'—it clearly emerges that this is a creative interpretation of the verses.[8]

In addition, from the words of some of the medieval authorities regarding gezerah shavah (verbal analogy) (and according to some of them the same holds for other rules as well), it appears that under certain circumstances a person can derive various laws on his own by means of this rule.[9] The conclusion is that the rules are also 'creative,' and not merely 'supportive.'

According to the conclusion that the rules are 'creative,' it is clear that the rules must be univocal (contrary to Gersonides), for otherwise it would be impossible to create new laws by means of them (as Gersonides argued). Accordingly, the vagueness that accompanies the exposition of verses apparently stems from our lack of knowledge regarding the rules for using them. Admittedly, there is no necessity that the rules constitute a truly logical-mathematical system. The next chapter will deal with the question of the logical status of the rules.

B. The Relation Between the System of Rules and Logical Systems

The place and significance of the system of rules by which the Torah is expounded can be understood in three basic ways:

• The rules are a kind of axiomatic system, or an interpretive-exegetical code.
• The rules are an alternative logic in place of accepted logic.
• The rules are a foundation of principles with philosophical significance.

Let us explain these points briefly.

 

1. An axiomatic system, an interpretive-exegetical code

Sometimes a person sends his friend a text encrypted with a certain code. In order to decipher the message, the reader must possess a 'key.' A well-known example is the Atbash cipher, which is composed of a system of 22 decoding rules that tell us how to 'translate' each letter in the encrypted text into our language. The rules of the code are arbitrary, and therefore meaningless in themselves. The same text could have been encrypted by different means, and there is no importance to the particular method I chose.

If we understand the system of rules as a code that enables us to extract laws hidden in the Torah, then we will naturally treat this system as arbitrary. The Holy One, blessed be He, gave Moses at Sinai a key, so that we could 'decipher' the midrashic layer of the Torah. According to this, there is no point in seeking any meaning in the rules themselves.

Such an approach is implied (though not necessarily) in Maimonides' book Millot HaHigayon, at the end of Gate 7, where he writes:

For us there are other syllogisms, called legal syllogisms, and there is no occasion to mention them in the course we are following.

That is, the system of rules does not belong to the domain of the science of logic. These are arbitrary rules that are relevant only in the realm of Torah study, and there is no place to discuss the rules in the context of the laws of logic.

2. Alternative logic

There are those, mainly in our own time, who understand matters differently. In their eyes the system of rules is not arbitrary at all. According to them, the Torah operates on the basis of a deeper, prophetic logic, different from accepted logic.

Rabbi HaNazir's words, in which he expresses himself in several places as though the system of rules constitutes a special Hebrew logic ('auditory,' in Rabbi HaNazir's terminology) that stands in opposition to Greek ('visual') logic, seemingly express such positions and serve as an inspiration for them.[10]

Taken literally, this approach is problematic, if not impossible. It is implausible that we are required—or even able—to abandon the mode of thought of classical logic when we are engaged in Torah. Classical logic is forced upon us, like all mortals.

Imagine that you were commanded to abandon the law of non-contradiction (the law that determines that a proposition and its negation cannot both be true simultaneously).[11] In such a situation, when the Torah says that it is forbidden to marry the rival-wife of one's daughter, we would also be able to infer that it is permitted to marry her, for according to this approach the law of non-contradiction is not in force within the framework of halakhic discussion.

It is therefore clear that these statements of Rabbi HaNazir cannot be understood literally. Clearly, in practice we do not act this way, and cannot act this way, even in Torah study.

3. A foundation of principles with philosophical significance

In Rabbi HaNazir's writings there are, apparently, contradictions on this subject, and in several places a third, mediating approach is implied. It seems that this is his fundamental approach, as well as the approach of the commentators on the rules whom he himself cites.[12]

Greek logic relies on necessary inference (deduction). According to Rabbi HaNazir, Hebrew logic (= the rules by which the Torah is expounded) adds to it the modes of analogy. It does not come to replace scholastic logic, but to supplement it, and in practice to spell out, in certain ways, additional forms of thought (analogy and induction).[13]

These remarks require clarification. It is implausible that Rabbi HaNazir intends to reject deductive logic, for it is forced upon us. On the other hand, it is presumably true that no one would dispute that there are non-deductive forms of thought that can also be used. If so, it is not clear exactly what is meant by the statement about an alternative logic.[14]

It seems to me that the difference lies in the question whether one regards this addition as 'logic.' In the course of our thinking we employ many forms of thought, but not all of them are granted the status of 'logic.' Within the general science of logic, discussion ordinarily focuses mainly on deductive-mathematical forms of reasoning. Usually analogy and induction are not considered as belonging to that domain.[15]

This difference is expressed in the degree of trust accorded to the conclusions of non-deductive inferences. As noted, even the 'Greek' thinker uses these forms of inference, but he does not grant them full trust, and sometimes the attitude is as though these are only subjective conclusions (some would call this 'feeling').[16] Hebrew logic grants these forms of inference full trust, since we punish—and even execute—on the basis of laws derived from the rules by which the Torah is expounded (with the exception of a few particular cases).

If so, as Rabbi HaNazir also states at length in the fourth essay of his book, the rules by which the Torah is expounded spell out and define the rules of analogy, and turn these forms of inference into 'logic' in the full sense of the word. The essence of his novelty is that the absence of mathematical character in the system of rules does not necessarily indicate vagueness.

In light of what has been said here, one can see the difference between this position and that of Gersonides. Gersonides argued that these forms of inference can be used in different ways and are not unambiguous. Gersonides, like most sages of the Middle Ages, takes a 'Greek' approach on this point. He holds that non-deductive forms of inference cannot have a definite meaning. Rabbi HaNazir, by contrast, sees them as a kind of different logic, in addition to (and not instead of) deductive logic.[17]

Against this background, let us add that the vagueness that characterizes the rules in the eyes of the modern observer derives from the influence that 'Greek' thought exerts even within the study hall. One who uses auditory logic (which, in Rabbi HaNazir's eyes, is an aspect of prophecy) grants high credibility also to analogical and inductive argumentation. This, of course, requires an 'auditory' capacity, which today can develop only through Torah study.[18]

To conclude this chapter, let us emphasize that according to Rabbi HaNazir's approach—and only according to it—there is room to learn intellectual-philosophical principles from the rules themselves, since they are not arbitrary rules (a code), but principles that have significance in themselves. As far as I can understand, Rabbi HaNazir's book is entirely devoted to spelling out and clarifying this point: Torah-halakhic logic is 'logic,' and it also constitutes the philosophical basis on which the Torah understanding of the world—that is, Jewish philosophy—must be founded. Just as Aristotle placed at the head of his philosophy the Organon, his book of logic, so we must place at the head of our philosophy the logic of the rules (in addition to 'Greek' logic).

Rabbi HaNazir sees in auditory logic, as it appears in the rules by which the Torah is expounded, a prophetic logic that will constitute a focal point for the revival of prophecy in Israel. In a state in which prophecy dwells among us, we will be able to examine inductive and analogical inference with 'precise' tools, and we will have certainty in the conclusions of these inferences, as in the deductive case.[19] At that time the distinction between feeling and intuition (which is part of the intellect), which today appears vague and elusive, will be sharpened.[20] In this way as well, the fog that hovers over the rules will disperse.[21]

C. The Logic of the Rules – A General Picture

The previous two chapters dealt with the question whether the rules are 'creative' or 'supportive,' and with the question of their logical status (arbitrariness, or meaningfulness). There is a close connection between these two questions.

As we have seen, hidden at the root of the approach that the rules are supportive is the assumption that they are vague, as Gersonides held. We have already noted that according to this it is not clear why one should engage in the midrash of the rules at all. By contrast, according to the approach that they are creative, it is clear that they must be clear and not vague. Still, one must discuss whether they have logical standing, meaning, or whether they are arbitrary.

Maimonides apparently thought that they have the status of a kind of system of arbitrary code, and from this it follows that they must have a rigid mathematical structure. Perhaps this is a result of Maimonides' philosophical position (like those medieval sages mentioned above), that only rigid deductive logic is entitled to the title 'logic.'

Maimonides' (implicit) view—that the rules are an arbitrary code—is problematic also from a theological perspective: how can the Holy One, blessed be He, create something arbitrary in the world, something that has no role in and of itself? There seem to be superfluous degrees of freedom in creation here, and it is difficult to understand why the Holy One, from whom nothing is withheld, created a world in which there are arbitrary components that have no meaning or role in themselves.[22]

Rabbi HaNazir, by contrast, understood the rules as having an analogical character (and not a rigid one). Their use is accompanied by the intuitions of the sage who is expounding, and is not merely a technical application of formal rules. It is important to emphasize that Rabbi Shmuel Ariel (in his above-mentioned article) showed that it is impossible to understand the midrashim of the rules as a technical operation without the intervention of the learner's reasoning.

According to Rabbi HaNazir, the rules create new laws, and therefore such an approach requires the assumption that we place full trust in the results of analysis and study by means of the rules, despite its analogical (non-mathematical) structure. This trust is a result of the significance of the principles expressed in the logic of the rules.[23]

This conclusion leads us to ask: what internal logic lies at the foundation of each of the rules? And following that, what philosophical-intellectual lesson does each of the rules come to teach us? Concrete illustrations regarding the meaning of particular rules will, God willing, be presented in the future. In the next chapter we will discuss several theoretical foundations needed for developing such an understanding.

D. Deduction, Induction, and Analogy

At first glance, the ways of drawing logical conclusions are varied and different from one another. It is customary to divide the modes of rational inference into three main types: deduction (from the general to the particular), analogy (from one particular to another, and also from one general rule to another), and induction (from the particular to the general). Let us illustrate this briefly.

1. Deduction

A deductive argument infers from the general to the particular, for example:

Premise A (the major, inclusive premise): All frogs are green.

Premise B (the minor, particular premise): A is a frog.

Conclusion (particular): A is green.

One should note the fact that every argument with such a structure is valid regardless of the concepts that appear in it. Therefore one can formulate a form of argument of this type as follows:

Premise A: Every X is Y.

Premise B: Z is X.

Conclusion: Z is Y.

Any three concepts that we place in place of these 'variables' will produce a valid argument. The truth of such an argument depends not on the concepts that appear in it but only on its form. It is worth noting that in such an argument all of its components may be false, and yet the overall argument is still valid. For example:

Premise A: All human beings are perfect.

Premise B: The primordial serpent is a human being.

Conclusion: The primordial serpent is perfect.

The validity of a deductive argument means that its conclusion follows from its premises (not that its conclusion is correct). A deductive argument is, of course, necessarily valid.[24]

2. Analogy

An analogical argument infers conclusions from one particular to another, for example:

Premise A: Frog A is green.

Premise B: B is also a frog.

Conclusion: B is also green.

Such an argument is common, but it is obviously not necessary. Beyond that, it is also not formal: if we replace the concepts used in the argument, we will not necessarily obtain a reasonable analogical argument. Replacing the term 'green' with the term 'having a length of exactly three centimeters' will create an unreasonable analogical argument.

As we see, analogy is a more problematic form of inference than deduction. In order to use it, a formula does not suffice; we are required to assume assumptions regarding the contents involved in the argument. The property 'having green color' seems relevant, that is, essential, to a frog, and therefore it can be learned from one frog to another. By contrast, the property 'having a length of three centimeters' does not seem relevant to the species frog, and therefore it cannot be learned from one particular to another.

The concept of the relevance of properties is highly problematic. If indeed, even before the conclusion of the argument, we already know that green color is relevant to frogs, then there is nothing new in the conclusion of the argument. If we knew that green color is essential to the species of frogs, we implicitly knew that every frog would be green. If so, such an argument, to some extent, begs the question.

3. Induction

An inductive argument infers from the particular to the general, for example:

Premise A: Frog A is green.

Premise B: Frog B is green.

Conclusion: All frogs are green.

There is no necessity to use knowledge of the existence of the property in two particulars. One can certainly infer the conclusion from one particular, three, or more.

It goes without saying that this argument too is not formal. One cannot replace the concepts that appear in the argument and create, in every case, another reasonable argument. If we saw one person wearing a hat, that is not enough to infer that all human beings wear hats. As in analogy, here too we require the relevance of the similar properties between the particulars and the general. Having five fingers is relevant to the human species, and therefore one can infer the existence of this property inductively with respect to all human beings, unlike wearing a hat. Therefore begging the question characterizes induction as well.

It is important to note an essential difference between these three types of inference. Deduction is necessarily valid, but this property derives from the fact that its conclusion is in fact already hidden within the premises. That is, even before the inference, we already knew the conclusion of the argument. If I know that all frogs are green, it is clear that at that stage I already effectively know that A, which is a frog, is green. The argument serves only to clarify knowledge that we already possess. Only because of this fact are deductive inferences necessary.

In arguments that use analogy and induction, by contrast, it is clear that the conclusion is broader than the premises, and therefore it is self-evident that the conclusion is not hidden within them. For this reason these forms of inference are not necessary.

This is the weakness of analogy and induction, but precisely here lies their advantage as well. Induction and analogy, unlike deduction, teach us new things about the world.[25]

E. Back to the Methods of Interpretation

In light of these remarks, one can clearly see the nature of the thirteen rules of interpretation and the root of their vagueness. As we have seen, deduction is a logic common to all human beings. The logic of the rules is not intended to replace it, but to add to it. According to Rabbi HaNazir, the rules try to define, as precisely as possible, analogical and inductive forms of inference, and these are forms that are vague by their very nature (in an age of the concealment of prophecy). Hence the importance of the interpreter's reasoning in the interpretive process. The interpreter is the one who decides whether the resemblance between the derived case and the source case lies in properties relevant to the laws under discussion or not.

Precisely in light of this, it is important to sharpen another point. According to all the approaches of the medieval authorities, the thirteen rules are a law given to Moses at Sinai.[26] If the rules merely express simple, Greek logical rules, it is implausible that we would have needed to receive them from Sinai. We use deduction, and also induction and analogy, in every area of our inquiry and activity even without explicit permission from the Holy One, blessed be He. We do so in Torah study as well at every step. It is highly unlikely that the primary content of the rules is simply a formulation of permission (or command) to use ordinary human reasoning. These forms of thought are a condition for understanding what is written in the Torah.

If so, it is clear that the rules cannot be deductive.[27]  However, for the same reason it is also unlikely that they are merely a different formulation of analogy and induction. Clearly, each rule must express a principle more specific than a standard human mode of thought. There must be some reason why we need a law given to Moses at Sinai to present to us the use of these rules at all. The necessary conclusion is that regarding each and every rule we must ask ourselves what its philosophical significance is; that is, what point it introduces beyond the common logical rules.

F. The Relation Between the Three Forms of Inference

To conclude, I will try to point to the reason for the central status of the rules in Rabbi HaNazir's eyes. At first glance, the three forms of argument presented above—deduction, induction, and analogy—form a clear hierarchy of validity: deduction, which as noted is necessarily valid, stands at the top of the pyramid, whereas analogy and induction, which are not, come after it. Even between the latter two there is, apparently, a hierarchy. Analogy infers a conclusion only with respect to one particular, and therefore it 'dares' less, and is consequently more valid (safer). Induction is more 'bold,' since by virtue of the existence of a certain property (law) in a few subjects it infers the existence of that property in an entire group, and therefore it is apparently the less valid of the two.

However, the relation between the forms of inference is not so simple. If one reflects on deduction, the question immediately arises: from where did we learn the general premise on which it rests (all frogs are green)? Apparently this can be learned only by means of inductive inference (that is, an inference that generalizes from the color of specific frogs we have encountered to the color of all frogs). But if that is so, the validity of the conclusion of the deductive argument is subject to the same doubt as the conclusion of the inductive argument on which it rests.[28]

If we conduct a similar examination of the relation between induction and analogy, we will notice similar problems. Is the process of analogy not, in fact, disguised induction? When we inferred from the green color of frog A that the color of frog B is also green, we actually assumed implicitly that the color of all frogs is green. There is nothing special about frog B beyond the fact that it is a frog, and therefore this argument implicitly assumes that the color of all frogs is green. More generally, one may say: at the foundation of every analogy stands a disguised induction.

Let us now consider induction, and ask ourselves how we inferred from the color of frogs A and B to the color of all frogs. Is the generalization from the color of a particular frog to the color of all frogs not in fact built from a collection of analogies? Did we not make a comparison between frog A, whose color is green, and frogs B and C, etc., and express this as one general conclusion? We arrive at the exact opposite conclusion from the previous one: at the foundation of every induction stand analogies.

The situation appears awkward. Apparently it is not possible to arrange these three forms of inference in any hierarchy, and in fact it is not even possible to distinguish them sharply. At the foundation of deduction stands induction, and at the foundation of that stands analogy, and at the foundation of that again induction, and so on without end.

Yet one conclusion can nonetheless be drawn clearly. Deduction is always preceded by arguments of an analogical or inductive character that create its premises. If so, one may say that human thought—or perhaps the human accumulation of information—always begins from certain particulars about which some information is known to us. From there we advance by analogy or induction, and arrive at a generalization regarding the existence of the properties in some complete group. Finally, once the generalization is known to us, we can return and infer, by a deductive process, the existence of the property in another particular.

If so, one may say that human thought that adds knowledge about the world is not all that diverse. Almost always, this is an analogy between particulars, for the sake of which we use an inductive generalization (usually hidden, and perhaps itself based on analogies), and from the general law we return and derive, by deduction, a particular conclusion.

In the example above, frog A is green. We make an analogy to frog B and infer that it too is green. This analogical process is composed of two stages: 1. an inductive generalization (which may itself be based on a collection of analogies) that leads us to the conclusion that all frogs are green. 2. a deductive specification of the rule that leads us to the conclusion that frog B in particular is green.[29]

An additional conclusion is that accepted logic (deductive logic) describes only a certain part (the simpler part) of human thinking. The more important and more problematic parts are described by analogy and induction. Real human thought (including scientific thought), thought that adds knowledge about the world, is not described by logic.

From Rabbi HaNazir's words, according to the above analysis, it seems that the systems of rules constitute a more precise definition and classification of the modes of analogy (and induction). These processes would turn analogy into a more precise 'logic.'

Accordingly, deciphering the meaning of the rules and returning to their use have far-reaching significance beyond a merely halakhic interpretive tool. This is the only precise description of real thinking (as distinct from pure mathematical thinking), of the scientific mode of inference, and of human reasoning in general.

In this article we have described, in a general way, the logical status and significance of the methods of interpretation. In the future, God willing, we will try to offer several concrete illustrations of the philosophical significance of specific hermeneutical rules.

[1]  As is well known, there are several systems of rules: seven rules, thirteen rules, and thirty-two rules. There are also disputes regarding methods of interpretation, for example between Rabbi Akiva and Rabbi Ishmael, and this is not the place. Let us note that Maimonides, at the beginning of the Second Root, refers to fourteen methods of interpretation: Rabbi Ishmael's thirteen rules and ribbui.

 [2] This is the place to mention two articles adjacent to the subjects discussed here. One, by Rabbi Moshe Pintchuk, in Alon Shevut – Graduates 7, Elul 5755, and the second by Rabbi Shmuel Ariel, in Gulot 6, Cheshvan 5759. In his article, Rabbi Pintchuk addresses the question whether the rules are interpretive or creative. Anyone who studies it there will see that this is a different question from those discussed here. Rabbi Ariel addresses the question whether human reasoning takes part in the midrashic process, or whether this is an entirely technical formal procedure. Our remarks here also touch on this point, as will be explained below.

[3]  As noted, many have already discussed this question. See, for example, J. N. Epstein, Mevo'ot LeSifrut HaTannaim, Jerusalem, 1957, p. 501, and Rabbi Yitzhak Isaac Halevy, Dorot HaRishonim, Frankfurt am Main, 1906, part 1, vol. 3, p. 146, both of whom held that the rules are supportive. See also volume 4 of the responsa Seridei Esh, by Rabbi Weinberg. In Dov Schwartz's article (which will be noted below), in note 68, he brought additional relevant references.

According to Schwartz's interpretation, Rabbi HaNazir's view is that the exposition is supportive and not creative. In my humble opinion, his book Kol HaNevuah (at least the part that has been published) virtually cries out the opposite. It seems to me that Rabbi HaNazir's intent in the passage cited there is only to say that the laws were not newly created in the period of the formalization of the rules, but had existed beforehand. It was the formalization that was renewed in the Second Temple period (on this, see at the beginning of the Netziv's introduction to Ha'amek She'elah on Genesis, 'Kidmat Ha'Emek,' sec. 1, letter 2). However, even in his view, the essential relation between the laws and the rules that derive them from the verses is a relation of creation and not of support. The quotation brought there by Schwartz is truncated and, in my humble opinion, somewhat misleading, but this is not the place.

On this matter, as on the whole subject before us, see the illuminating article by E. E. Urbach, 'Derashah as the Foundation of Jewish Law and the Problem of the Scribes,' Tarbiz 27, 1958, p. 166.

[4]  It is true that in a large portion of the cases it is not clear from the midrash itself to which of the two categories it belongs.

[5] Encyclopedia Talmudit, in the entry 'Asmakhta,' brings several explanations for the practice of making various sorts of asmachtot. In our context, none of these explanations seems relevant, and therefore the difficulty we raised remains in place.

[6] And, simply speaking, not only the Great Court can expound; rather, with respect to the prohibition 'do not deviate,' one transgresses only when one disputes an exposition of the Great Court.

[7]  And for this, one does not need a court greater in wisdom or number. Only for enactments and decrees do we require that they be greater than their predecessors.

The editor pointed out to me that in Maimonides' introduction to the Mishnah (letter 4) he explicitly brought also a type of supportive exposition, such as the one that determines that the phrase 'the fruit of a beautiful tree' refers to an etrog (citron), see there.

[8]  To be sure, there are those who understood Maimonides' view to mean that these are rabbinic laws, and then the question does not arise at all. But then his position is exposed to the same difficulties that we saw in Gersonides' approach.

[9] See Encyclopedia Talmudit, entry 'Gezerah Shavah,' and Rabbi Shmuel Ariel's above-mentioned article.

[10] See passages from part 2 of Kol HaNevuah published by Dov Schwartz in Higayon, vol. 2, Aluma, Jerusalem, 1993 (especially sections 5–9), and in Da'at 27, 1991. See also his article in Sefer Higayon, Zomet Institute, 1995.

[11] This is sometimes called 'the unity of opposites.' In my humble opinion there is no such thing, for the reasons detailed above. See also my article in Tzohar 2.

[12] See Schwartz's above-mentioned article in Da'at, where he cites passages in which Rabbi HaNazir describes a logic that does not recognize the two fundamental laws of classical logic: the law of non-contradiction and the law of identity. Still, in my opinion, this must be on the interpretive plane and not the essential one, for as noted we are unable to forgo these rules. The alternative mentioned there, 'until the third verse comes,' is also an interpretive and not a logical alternative. See there as well at the end of Schwartz's introduction, where he brings Rabbi HaNazir's view that the method of Hebrew logic is a combination of visual-Greek logic and auditory-Hebrew logic. See a similar distinction in my above-mentioned book, Gate 12, chapter 1, in the footnotes (especially notes 62–63).

[13]  In chapter 4 we will elaborate somewhat on these modes.

The editor drew my attention to what is said in Kol HaNevuah, p. 18, sec. 11, where induction is included in Greek wisdom. The status of induction requires a discussion of its own, and see a little on this in my book Shtei Agalot VeKadur Pore'ah, in chapter 1 of the eighth gate. In fact, the relation between analogy and induction is probably subject to dispute among the medieval authorities, but this is not the place.

[14] Professor Rabbi Eliezer Berkovits, at the end of his book Torat HaHigayon BaHalakhah, in the section called 'On the Margins,' writes that the thirteen rules express, in a different form, classical logic itself. Below we will hint that this cannot be fully correct.

[15]  To be sure, in recent years there have been attempts to formulate an 'inductive logic,' but as far as I know these are attempts to give mathematical formulation to inductive thought processes. These attempts usually also strip induction of its essential non-formal characteristics (see below). There is no 'upgrading' here of the status of inductive thinking itself. See in Kol HaNevuah Essay 1, letter 2; Essay 2, letters 6–7 and 10; and Essay 4, letters 14 and 29 onward, where Francis Bacon (the proponent of the new, analogical logic) is alluded to.

 [16] Often these are only declarations, and in practice full trust is also given to inductive or analogical conclusions. Science proves as much. The distinction I proposed here is not entirely sharp, but it seems to me that it contains much truth. These matters are set out in detail in my above-mentioned book.

[17]  See explicitly Kol HaNevuah, opening remarks, sec. 3 and the notes there.

[18] In my above-mentioned book I discussed the differences and the struggle between deductive and analogical thought (there: 'analytic' and 'synthetic'). The reader interested in a broader treatment is referred there.

[19]  Here we can return once again to the question addressed by Rabbi Shmuel Ariel in his above-mentioned article. At least according to Rabbi HaNazir's conception, the question whether reasoning is involved in the interpretive process is answered here in the affirmative, since the rules are grounded in considerations of analogy and induction, which depend on the judgment of the sage who expounds (and see below). However, this is a qualified affirmative. For in the future, this reasoning of the sage who expounds, or the unification of all the true lines of reasoning advanced by all the sages, will become as clear as deductive logical inference. In such a state, halakhic exposition could specifically be perceived as a process that does not depend on the reasoning of the sage who expounds (or depends on it far less).

[20]  See in my book, Gate 11, chapter 1.

[21]  It should be noted that some of the rules do not express forms of thought but forms of interpretation (primarily linguistic). These are directed toward inference from a feature of the text, and not from the internal logic of the subjects under discussion. The existence of rules of this kind seemingly points toward the understanding that the rules are a kind of code and do not possess philosophical meaning in themselves.

However, if we understand that biblical language is not arbitrary like other human languages, then the way opens before us to say that even the interpretive rules have logical, philosophical significance.

Maimonides, as Rabbi HaNazir showed in his book (Essay 1, sections 26–29), understood that biblical language is no different from other human languages, and that it too is arbitrary and conventional like them. It is therefore reasonable that he would infer from the existence of linguistic rules within the system of the thirteen rules that the character of the rules is axiomatic-arbitrary. Above we saw that this is also implied by Maimonides' words in Millot HaHigayon. However, according to the approaches of most of the medieval authorities who disagree with him, the possibility remains open to hold, in line with Rabbi HaNazir's approach, that the rules have meaning.

[22]  To be sure, in Maimonides one sees such a theological approach in several contexts. For example, in understanding the holiness of the Holy Tongue, which Maimonides conceives as conventional-arbitrary (see the previous note). So too in his theory of providence (that there are groups that are watched over only at the collective level and not in every detail), and so too in his theory of the reasons for the commandments (in which, according to Maimonides, the details are arbitrary), and more. The mystics, almost without exception, disagree with him on this point, and they hold that every detail in creation has meaning in itself, and that in the acts of the Creator there is no arbitrary detail. It seems that Rabbi HaNazir follows them here.

In this context, see for example the book HaKelalim, by the author of Leshem, principle 15, branch 11, where he describes Maimonides' dispute with Maharam Gabai regarding the question whether every created thing has a purpose in itself, or whether there are created things that are only means. This is precisely the point discussed here regarding the rules of interpretation.

[23]  Trust in intuition is the foundation of the synthetic position, which is discussed at length in my above-mentioned book. As I showed there, without this trust there is no possibility of grounding even our trust in the rules of logic.

[24]  Let us note that the term 'deductive' is used to describe a necessary argument in general. There are necessary forms of argument that are not formulated as an inference from the general to the particular (although usually there is a 'translation' into such a form), for example:

Premise A: If A is true then B is true.

Premise B: A is true.

Conclusion: B is true.

[25]  In philosophy this property is called 'the emptiness of the analytic.' See in my above-mentioned book, Gate 1.

[26]  In the passages brought in Schwartz's article, Rabbi HaNazir cites the Shelah, who tried to proceed in a different way, see there.

[27]  The natural candidate to represent the deductive component in the thinking of the Sages is the rule of qal va-homer (a fortiori reasoning). In my article in Higayon 2, I showed that even the rule of qal va-homer is not deduction. In my above-mentioned article I noted that according to some of our masters of legal rules there is a kind of qal va-homer that is deductive ('included in two hundred is one hundred').

[28]  This is the challenge to deduction raised by the philosopher John Stuart Mill. See in my above-mentioned book, in the eighth gate.

[29]  This conclusion can be represented symbolically as follows: analogy = induction + deduction (the addition means the inclusion of a subsequent logical operation).

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To Rabbi Ariel, many greetings.

A. Attached is a shortened version of my article. I shortened mainly at the beginning (given the less comprehensive aim of the article, there was no point in expanding on the general significance of studying methods of learning and interpretation), but also later on. By my count I have reached the desired length, but clearly within this framework there was no room to add anything that is not truly necessary for understanding the article.

B. It is important to me to note that the goal of the article is to understand the significance of the rules of interpretation, and not to understand the relation between auditory logic and Greek logic (nor to understand Rabbi HaNazir's doctrine as such). Clearly the matters are related, but the second point is the subject of the book I wrote and not the subject of the article. Against this background, the omissions—especially in the attached version—will be understood.

C. As for your comments, I will address them one by one (the numbering here follows the numbering of the footnotes in the version you sent me):

4. The word 'reflexive' was omitted.
5. Indeed. I corrected it to Rabbi Moshe Pintchuk.
6. I referred (while mentioning you) to the supportive expositions in Maimonides' introduction. It should be noted that this poses no problem at all for my argument, since I explicitly write that even according to Maimonides' view and that of his school there are supportive expositions. The main claim is that there are also creative expositions (unlike Gersonides).
7. I changed the wording slightly, but the elaboration later clarifies what needed clarification. Here these are only headings.
8. 'Scholastic' logic was omitted. 'Greek' logic, in my humble opinion, is familiar to readers, since this is not a term unique to Rabbi HaNazir. Any educated person knows that the rules of logic accepted by us were first formulated in ancient Greece.
9. As for your valid comment on induction, it requires a broad discussion, and this is not the place (that was the purpose of the article that was planned to be the second). For the sake of simplicity, and since there is no room to expand, I omitted induction in most places and defined the rules as analogical (more closely following Rabbi HaNazir). I hinted that this depends on a dispute among medieval authorities regarding the relation between analogy and induction (the next article?!). Here too I mentioned your comment in your name.
10. 'Classical' logic seems to me a reasonable term.
11. I find it difficult to produce this 'miracle,' and therefore I made do with references in those places where this was truly required. Wherever it was not really needed for understanding, I gave it up.
12. It seems to me that I deal with this argument explicitly in the article. The paragraph dealing with the law of non-contradiction is intended precisely for that.

I cannot understand the type of argument that emerges from your remarks (and also from many others), for if we give up 'Greek' logic (more accurately: human logic), then we can both give it up and not give it up at the same time. Even if the Torah determines that the rival-wife of one's daughter is permitted, we can infer that she is also forbidden simultaneously. In such a situation words lose their meaning. See the beginning of Gate 12 in my book, and my article in Tzohar 2. All the operations of comparison and analysis in study are simple human operations, to which the auditory level is added (and not in their place). Ramchal, Maimonides, and many others prefaced the rules of logic (which they themselves learned from non-Jews) as necessary introductions to study.

The invention of 'the unity of opposites' is a new phenomenon in the world of Jewish thought (Christian in its root—Cusanus), and in my humble opinion it has no source, root, or branch. Things that I do not understand certainly exist, but things that contain contradictions cannot exist in the world of my human thought (nor even in my beliefs about God). Therefore, in my eyes, anything that appears to be a contradiction is either not a real contradiction (and then there is no need for a unity of opposites), or it is simply not correct (and again there is no need for a unity of opposites).

24. See the previous note. I do not understand such statements, and therefore I cannot address them. The only possibility is to understand that Rabbi Kook does not mean a genuine logical contradiction (see the beginning of the aforementioned Gate 12).
25. In my humble opinion, analogy is the tip of the iceberg of the power of faith. See at the end of Gate 11 in my book. Here there is no room to spell out the relation between the two (perhaps in the next article?!).
26. 'Syllogism' was deleted.
27. 'School' was deleted.
28. I have no room here to elaborate on this. It seems to me that the article can be read even without it.
29. I would not call this 'feeling' (see Gate 11 on this matter). As for the guiding word, and the very comparison to artistic reading, I tend to agree. It seems to me that I cannot address this here.
30. I corrected the wording slightly, and I hope that it is now clearer. Incidentally, in my eyes this is a point that deserves an important article in its own right.
31. Here I have no room for this. I referred the reader to the book. It seems to me that my remarks can be understood even without further detail on this point.
32. I do not see a good way to do so.
33. Accepted.
34. A 'valid' argument is a familiar expression, and I also explain it in the article in its logical context (formal truth, whose correctness depends not on content but on structure).
35. I addressed this indirectly when I spoke about the return of prophecy.
36. Accepted.
37. I am speaking about the vagueness of the thirteen rules of interpretation, and not of methods of interpretation in general, and therefore, in my humble opinion, there is no unsupported generalization here. As for your first comment, in my humble opinion yes. In a footnote I spoke about the interpretive rules, and there I explained (briefly, as best I could) that these too are founded on analogy (and perhaps also induction).

A note that is also worth an article: the principle that what serves as a partition for Sabbath serves as a partition for Sukkah (or that something can be a vessel for Sabbath and for ritual impurity, and many other cases), according to most interpretations, can be said only if there is an interpretive analogy (between words, and not between objects or phenomena). A similar (identical) word in the Holy Tongue points to a similar (identical) phenomenon, or law, and this is not the place.

As for the question itself whether all expositions are included in the thirteen rules (although I did not claim that here), this is certainly an interesting question. Maimonides, as I noted, refers to fourteen interpretive rules (thirteen and ribbui). It seems to me that all the other derivations are not really halakhic exposition, but rather a kind of peshat, perhaps more complex. This depends on the question what exposition is, and what its relation is to peshat (see, for example, in HaMa'ayan 1977–1978 an interesting exchange between Henshke, then a young student, and Rabbi Witman). Some of this is supposed to be included in my article that was planned to be the second. Incidentally, as is already beginning to emerge from these comments, there I anticipate an even more severe problem of space.

45. Such legal systems are quite common, and jurists call them 'casuistic.' I found no room to expand here on this matter. As for your comment itself, see Rabbi Zini's article in Sefer Higayon, and in my book in Gate 10.
46. This is certainly correct, and this is the essence of 'mah ha-tzad' (third article?!), but in my humble opinion it is not needed here. In the philosophy of science, much ink has been spilled on the question why (and whether) this is indeed so. Incidentally, I am occupied with this precisely now in the course of writing the second part of my book (which, God willing, will deal with the reciprocal relations between myth, religion, and science, against the background of some of the rules by which the Torah is expounded).
47. 'Synthetic' was omitted.

From me,
one bound in the cords of space-time,
woe to us, for the Torah was given only to those who ate the manna,
who entreats the Most High that 'and He appointed' be fulfilled in us speedily,
and that He say to the destroyer: enough, from plagues of killing, destruction, ruin, and loss.

Seeking your welfare always,
the humble, Mikhi Abraham,
of the holy community of Yeruham.

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