Between Representation and Application (Column 399)

With God’s help

Disclaimer: This post was translated from Hebrew using AI (ChatGPT 5 Thinking), so there may be inaccuracies or nuances lost. If something seems unclear, please refer to the Hebrew original or contact us for clarification.

In the series that begins in column 379 I discussed the conceptual representation of content. Thus, for example, I argued that the commandments represent a more abstract content, which is called Torah. I brought two examples for this. One was from Zen and its various representations in pursuits such as flower arranging, fencing, and archery. All of these are different forms through which the same abstract idea of Zen appears. They represent it within the real conceptual world. This is a relation between the abstract and its tangible expressions. The second example I brought dealt with logic and its applications. There I claimed that logic is the general theory, and every specific application is a representation of it. Consider the following schema:

Every X is Y.

a is X,

therefore a is Y.

This is a general logical schema. If we substitute specific contents for the variables, we obtain a valid logical argument: if every frog is green, and Yankele is a frog, then Yankele is green.

The transitions I dealt with there were meant to demonstrate a relation between the abstract and the concrete or tangible, and I called this “representation.” The claim was that the Torah in its origin is a collection of abstract ideas, and their expression in our world is the Torah we received. This expression is a concrete instantiation of the abstract ideas. In the comments (see the thread beginning here), the question arose whether this is the same as the relation between an example and a rule, what was called there “realization” or “application” (demonstration).

To the crux of the problem

To sharpen the difficulty, let us look at an example from logic. There, it would seem, we are dealing with a transition from a rule to a particular instance of it, that is, with a demonstration and not with a representation. True, above we saw that there is also a dimension there of a passage from the abstract (a schema with variables) to the concrete (specific contents), but this is not entirely similar to representational transitions like those I described regarding the Torah. It is, after all, merely substituting a concrete element—a particular example—for a general variable. It is hard to pinpoint the difference between these relations. Seemingly, the transition I described regarding the Torah is also from a rule to a particular example. There is an abstract rule, and under the circumstances in which we act its appearance is in this form. In a different reality it would appear differently. If so, the Torah in our hands is also a particular example of that abstract rule. Is there a real difference between representation and demonstration or application?

If we think of a specific application of a law of nature, such as an application of the law of gravitation (a book falling to the ground), apparently we again see a passage from the abstract to the concrete. But on second thought it seems to be a transition from a rule to an example, that is, a particularization. There does not seem to be an element of “illustration” here. The rule is: all massive bodies attract one another. The particular example is: the ball in my hand (which has mass) is attracted to the earth (which also has mass). Just like in the logic example.

In Tolginus’s post in that thread, several additional examples are brought that also reflect the similarity, and perhaps identity, between these two mechanisms:

What is the relation between a priest and a house stricken with leprosy (beit menuga) and the principle of chazakah demeiikara (presumption of prior status)? What is the relation between a one-dimensional theorem (the fundamental theorem of calculus) and its generalization to a two-dimensional theorem (Green’s)? What is the relation between a theorem (e.g., the fundamental theorem) and its application (to a concrete function)?

Explanation: The Gemara in Chullin (10b) derives the rule of chazakah demeiikara from a leprous house (after the priest sees the plague he exits the house and assumes the plague has not shrunk in the meantime). Is the case of the leprous house an example of the general rule of chazakah demeiikara or a representation of it? A mathematical theorem that deals with one dimension (and there it is intuitive) is generalized to a theorem in a higher dimension, and perhaps to a general theorem in as many dimensions as you like. Is the one-dimensional case merely an example or a representation? Although on the way to the general theorem there is a process of abstraction, it still seems that once we have arrived at the general and abstract formulation, the one-dimensional case is only an example. There is a difference between the way out and the way back, of course, since on the way out we performed a generalization, which is a synthetic inference. But on the way back we performed a particularization (application to a specific case), which is, apparently, a relation between rule and instance. Tolginus’s last example (by the way, think about the relation between these examples and his general question) is a general mathematical theorem being applied to a particular function. Here it quite clearly looks like a demonstration and not a representation, at least for someone familiar with the mathematical language. It is a transition from a rule to one of its examples.

We can already see here one aspect that will be important later. The transition from examples to a rule is always accompanied by a speculative inference, and certainly not by deduction. In contrast, once the rule has been formed, the relation between it and the example is a simple deductive relation, and then we are dealing with a relation between an example and a rule and not a relation of representation. So perhaps application and representation are nothing but inferences in opposite directions (from particulars to the general or from the general to particulars)?

Analogy and Deduction

It would seem that this difference is precisely the relation between deduction and analogy or induction. The passage from a rule to a particular example is a deductive inference: a principle that holds for an entire class of items holds in particular for one of them. This is a simple demonstration. By contrast, analogy is a passage based on similarity from one example to another. There is some creative/speculative dimension here, and this looks more like representation than realization or application. In induction, too, one passes from one example to many other examples (a general law that includes many instances), and as noted this process is, of course, non-deductive.

But this difference in itself does not seem essential. Analogy, induction, and deduction differ only with respect to the extensional relations between premise and conclusion. In deduction, the extension of the premise includes the extension of the conclusion; in analogy, these extensions are disjoint; and in induction, the extension of the conclusion is the broader one. In my books Shtei Agalot and Emet ve-lo Yatziv I argued that at the basis of analogy lie induction and deduction in a covert way. If I draw an analogy from frog A to frog B (if A is green then B is also green), I have in effect implicitly inferred that all frogs are green (induction) and then particularized that to the second frog (deduction). This is not a difference related to abstract versus concrete but to the sizes of sets: from the particular to the general and vice versa (generalization and particularization). So where on this map can we place an inference that expresses a passage from the concrete to the abstract or vice versa (abstraction and illustration)? The foundation lies, of course, in the justification for that inductive generalization. Why did I generalize the color to all frogs rather than to all dwellers of this particular pond, or to all quadrupeds, or to all croakers? There is some explanation behind this, and it already goes beyond the question of extensional relations. Here there is indeed a dimension of abstraction.

Abduction and Induction[1]

It seems to me that this passage is the subject of a newer logical distinction, that between induction and abduction. The American philosopher and logician Charles Peirce, who worked in the second half of the nineteenth century and the beginning of the twentieth, was the first to introduce the term “abduction,” contrasting it with analogy and induction. Analogy compares some object a to another similar object b. From the presence of some property in a one may infer by analogy that the same property is present in b. The condition is that there is a known and given similarity between them. Induction, by contrast, is a generalization, in which from the presence of some property in a (and perhaps in several other particulars) we infer a general law that states that this property is present in an entire class (which includes those particulars as well). Abduction, too, is an inference that proceeds from several situations we have observed, except that here we derive from those situations a general theory that may explain those situations as particular cases of it. Abduction differs from the other two non-deductive modes of inference (analogy and induction) in that it describes a passage from cases to a theory, whereas analogy and induction are inferences that carry us from one case or cases to other case(s). Induction deals with sets of different sizes, but abduction does not deal with relations between sets; rather, it relates a collection of particulars (or a set) to a theoretical explanation (a theory).

For example, analogy can teach us that if we released our grip on some book while it was in the air and it fell to the ground, the same will happen if we do so with another book. There is similarity between the two objects because both are books, and therefore there may be justification to compare them also with respect to falling to the ground. Induction will infer, by similar reasoning and on the basis of the same similarity, that all books will fall to the ground. A broader induction will infer this of all massive bodies. But here there is already some abstraction. It is not only a procedure of widening the extension of the set of objects under discussion. The claim regarding all bodies presupposes implicitly that having mass is the property responsible for that behavior. At this point there is already a theory operating at a meta-level. We have moved from the particular cases we are discussing (those we observed and those about which we wish to generalize) to a level that is one step more abstract, namely the theory responsible for these phenomena. Incidentally, even the generalization to all books has a theory at its base. Otherwise we could have generalized to the set of books in this library, or to the set of books of this thickness, or with a cover of this particular color, and so on. Every generalization (induction) or comparison (analogy) presupposes at its base some theory that provides it with justification. Uncovering that theory is abduction.

Induction is a generalization from certain cases to a broader set of cases, but all of it takes place at the same level of abstraction. Abduction, in contrast, examines the various cases and infers from them an abstract theoretical conclusion, that is, it constructs a theory that explains those cases (and predicts what will happen in other cases). Thus, for example, in the case of gravitation it infers a general law: there is a force that causes bodies with mass to fall to the ground. Now we can say that the law of gravity states that every massive body falls to the earth, and books are a particular case of it (because they are massive bodies). But this is a deduction that can be carried out only after we have created the theory by means of abduction. The passage from the general law to the particular cases is realization or application, since it is carried out deductively. But the creation of the general law itself out of the particulars is a creative, non-deductive process. It is a passage from the tangible level to a more abstract level: from cases to theory. A theory contains theoretical principles and also theoretical entities. These are entities that we in effect “invented.” They are not observed by us, but they offer a good explanation for what we observed, and therefore we posit their existence. This is a process of abstraction.

We thus learn that, in the passage from the general law to the particular example, two kinds of moves are possible:

1. The passage from the theory to the particular cases is in fact a deductive procedure, but this procedure includes not only particularization (a move from general to particular) but also illustration. It is a passage from an abstract formulation (abstract principles and theoretical entities) to a tangible formulation (an experiment, or a case).
2. The passage from a general law to a particular case—for example: all human beings are mortal, therefore Socrates is mortal—contains no element of illustration (a passage from abstract to concrete) but only a reduction in extension. Everything takes place at the same level of abstraction.

When in those columns I spoke about the representation of one idea by another idea (such as a commandment), I meant that the first is an abstraction of the second and the second is an illustration of the first. The Torah of the angels does not deal with father and mother but with an idea that belongs to their world. It constitutes an illustration of an even more abstract idea, and another illustration of it is the commandment of honoring parents in our Torah. These are two representations and illustrations of the abstract idea called “Torah.” Our Torah and that of the angels are particular examples of the abstract idea, but not only in the sense of move 2, rather chiefly in the sense of move 1. It is possible that our Torah is also an illustration of the angels’ Torah (as it descends into a more material world), but it is also possible that these are two different illustrations of the abstract idea within two different conceptual worlds.

In mathematical terminology one can say that the abstract Torah is the “theory,” and our tangible Torah and that of the angels are models of that theory. There is an analogy between the two models, and it is based on both of them fitting the theory (which is a process of abstraction).

I note that we can now understand that there is a connection between the demonstration–illustration distinction and the induction–deduction distinction. When we go from examples to another example, we are not merely drawing an analogy from particular to particular, and likewise in the passage to a general law we are not merely performing an induction. In the background of these processes there is abduction, that is, abstraction. After we have discovered the abstract theory, the application looks like a simple deduction (demonstration). But that is true when we consider the relation between the law of gravity and a particular case. Yet the theory of gravity contains additional elements that explain how that law operates, which particles carry it (gravitons), and so on. The passage from the theory to the particular case is not a simple deduction. In this there is certainly illustration and not merely particularization.

Resolution

We can speak of the difference between representation and realization from another angle. For example, when we enlarge a drawing or a photograph we see gaps between the data points. In reality itself—the reality that is demonstrated in the drawing or photograph—this is not the case. There are no gaps there (for the purposes of this discussion, let us set aside quantum theory and microworld physics). We thus learn that the drawing or photograph are sparse representations of reality. There is no full analogy between them, since some of the information is missing. But the resemblance certainly exists, and therefore this is similar to representation or illustration. It does not look like mere demonstration (realization or application). From here it follows that what is attributed to these representations does not necessarily hold of reality itself.

The same holds for the digitization of an image or any data. There, too, we are dealing with a representation and not with a realization (there are theorems in mathematics and engineering that state what conditions a representation must satisfy so that it contains the full information). These are of course only analogies to our topic, since the passages from reality to its representations are not accompanied by an illustration of something abstract. But this logic still helps reflect the distinction between representation and application.

Talmudic casuistry

In several places I have already noted that the Talmud has a casuistic character. It hardly deals with rules but with cases (= casus), and the assumption is that halakhic rulings will be made by analogy to these examples (and not by deduction from general rules). It seems the Talmud holds that rules are not a good tool for legal and halakhic work. A rule is too rigid a principle, and if we set rules, decisors will tend to apply them literally, that is, to see reality as an example of the rule. In truth, reality is an illustration of abstract rules, not an example of them, and therefore learning from rules to reality is not a simple deductive application, but rather complex and intricate analogies.

The passage from a case discussed in the Gemara or in some responsum to another case that comes before me is accompanied by an analysis of the new case, an understanding of the principles relevant to it, and only then an attempt to apply to it the principles of halakha. In the background of Talmudic analogies there are always abductions (theories). The commentators try to conceptualize those theories by performing abductions, that is, by formulating explicitly the theoretical rules whose application is the very operation of halakha on the cases before us—and this is what is called “analytical study” (limud iyyun). But the Talmud insists on not doing this. The reason is probably those infuriating and widespread phenomena of overly simplistic interpretation of precedents, that is, applying them as they are to the present-day situation before us. Such is the nature of rules: we tend to see them as rigid and to derive from them the ruling for the concrete case by means of simple (and simplistic) deduction.

This Talmudic approach has a source in the “middot by which the Torah is expounded.” The Nazir already noted that all the middot express an approach of “soft” logic (analogy rather than deduction), and the reason is that deduction is a coarse tool that is not suited to handling the complexity of life. As noted, at the foundation of every analogy a theoretical abduction lies hidden; hence, we are dealing with procedures of abstraction and illustration, not of generalization and particularization. Several of Rabbi Ishmael’s middot deal with procedures of demonstration, namely learning a principle by means of an example without its explicit formulation. All the versions of “a matter that was in a general category” belong to this category, and they well exemplify the Talmudic approach that believes in analogy and representation (illustration of abstract principles) more than in application and realization (an example of a rule).

Let us take for example the first middah of this type:

Every matter that was in a general category and left the general category to teach—its purpose was not to teach about itself but to teach about the entire general category.

This concerns a particular case that is written explicitly, even though the entire general category is also mentioned in the Torah. It “left the general category” in the sense that there is a certain law that is stated only with respect to it. One might have said that it was singled out to say that the law applies only to it and not to the general category as a whole. But this middah teaches us that this is not so. The example was singled out so that we learn from the law written about it and apply it to the entire general category (through abduction and induction).

In the “Baraita de-Dugma’ot” (the scholion) that appears at the beginning of the Sifra, immediately after Rabbi Ishmael’s baraita of middot, an example of this rule is brought:

“Every matter that was in a general category and left the general category to teach—its purpose was not to teach about itself but to teach about the entire general category.” How so? “And the soul that eats the flesh of the sacrifice of the peace offerings that are the Lord’s while its impurity is upon it, that soul shall be cut off.” Were not peace-offerings included among all the sacred things, as it is written: “This is the Torah of the burnt-offering, the meal-offering, the sin-offering, the guilt-offering, the consecration offerings, and the sacrifice of peace-offerings”? And when they left the general category to teach, it was not to teach about themselves but to teach about the entire general category—to tell you: just as peace-offerings are distinctive in that their sanctity is sanctity of the altar, so I have only anything whose sanctity is sanctity of the altar; this excludes sancta of bedek ha-bayit (Temple maintenance funds).

In this case, the example comes to tell us not to apply it to all sacred things but only to things sanctified to the altar. Seemingly the result is that the peace-offerings are an example of the general category of sancta of the altar. That is, this appears to be realization and demonstration (a particular example of a broad rule) and not representation (an illustration of an abstract rule). But now you can see that this is not so.

For we could just as well have generalized only to “lighter sancta,” or only to offerings eaten for two days, or only to offerings not brought for sin, and the like. The generalization here is not simple and not unequivocal. How did the Sages decide on the correct generalization? How did they choose the extension of the class to which this law applies? Clearly, they had to try to understand the essence of this law and, from that, to think where it is appropriate to apply it. This involves performing an abduction (formulating a theory), and only afterwards determining the scope of the induction (setting the scope of the rule to which the law applies).

In the background, of course, lies the question: why does the Torah not explicitly write this law regarding sancta of the altar? Why does it prefer to write an example and let us infer conclusions from it, thereby taking the risk that we will err in interpretation? It seems the Torah trusts us to make the correct interpretation, that is, to understand where it is relevant to apply this rule, and from there to derive the range of contexts in which it holds. It wants us to perform an abduction and from it derive the induction, and this is preferable in its eyes to an explicit and clear formulation of the rule that there is karet for eating sacred things in impurity in all sancta of the altar. A rule that is written explicitly and in rigid wording does not require understanding but only simple deductive application. Therefore, the Torah feared that we would apply this in an overly simplistic way and err. Transitions between set sizes (analogy and induction) without recourse to theoretical abstractions are apparently more dangerous than the risk of error that exists in performing those abstractions. Without moving to the abstract level one cannot correctly perform the passage between the sizes of the sets.

The fourth book of my quartet, Ruach ha-Mishpat, is devoted entirely to the distinction between differentiation and branching in interpretive and halakhic inferences. In the first section of the book I demonstrate this distinction with regard to rabbinic laws (in the Rambam’s First Root), and in the second section I show it with regard to laws derived from derashot (in the Rambam’s Second Root). Here I will confine myself to summarizing the main point relevant to us, that is, I will show the connection to the discussion of demonstration and illustration. There the matters are, of course, expanded and explained more fully.

Differentiation and branching: rabbinic laws

Regarding rabbinic laws, the Rambam in the First Root and at the beginning of Hilkhot Mamrim writes that their binding force stems from the command “Do not deviate” (lo tasur). The Ramban, in his glosses to the First Root, disputes him on this, and his main argument is that according to the Rambam, every rabbinic law should have the status of a biblical law, for one who transgresses it violates “Do not deviate.” Thus, for example, a doubt in a rabbinic law should be ruled stringently. Much ink has been spilled in answering this, but that is only a specific formulation of the difficulty (its demonstration). The more fundamental difficulty (more abstract and general) is whether, according to the Rambam, there is any difference at all between biblical and rabbinic laws. Seemingly according to him there are only biblical laws (except that for some of them the general rule is that their doubt is to be ruled leniently). This is obviously unreasonable, and that is the essence of the difficulty in his view.

On the other hand, the Ramban’s position also seems problematic, for according to him it is not clear why one should obey the Sages. If there is no verse in the Torah that obligates this, whence the binding force of their directives? I argued there that this is a “short blanket” (you cover one problem and another is exposed). If we answer the first difficulty (what is the difference between biblical and rabbinic laws), we get stuck on the second (why obey them), and vice versa. The only way to resolve both difficulties without entanglement (and therefore I argued that both the Rambam and the Ramban likely agree to it) is to say that a specific rabbinic law is not a differentiation of the rule “Do not deviate” but a branching from it. I will explain a bit more.

A clear example of a differentiation of a law is the laws of vows. The Torah states that a person must fulfill what issues from his mouth in a vow or an oath: “He shall not profane his word” (lo yachel devaro). This is a general law. When a person forbids to himself some loaf of bread, he must keep his word and not benefit from that loaf. If he does benefit from it, he transgresses “He shall not profane his word.” That is, this specific case is an example of the general law that appears in the Torah. This is a differentiation of the Torah’s law, namely a particular case of a general rule. In contrast, we saw that even according to the Rambam it is not reasonable that anyone who eats poultry with milk has thereby transgressed the biblical “Do not deviate,” for then it would be a biblical prohibition. We indeed learn the prohibition of eating poultry with milk (or the obligation to obey the Sages who forbade it) from the verse “Do not deviate,” but eating poultry with milk is not a differentiation of the general law. It is a branching from it. The particular case branches from the general rule, but it is not a particular example of it.

Several commentators proposed to resolve the Ramban’s difficulty as follows: according to the Rambam, only one who eats poultry with milk because he does not recognize, in principle, the authority of the Sages has violated the biblical “Do not deviate” (and the reason he is not flogged is only because this is a prohibition that serves as a warning for a capital offense in the case of the rebellious elder; see Rambam, Hilkhot Mamrim 1:2). But one who ate poultry with milk because he did not withstand his evil inclination has violated only a rabbinic prohibition. This is very plausible in my view, and I explained it in my book there. Yet this explanation seemingly does not do the full job, for now the difficulty returns: why obey the Sages’ command if it is not derived from “Do not deviate”? If one who violates it does not violate “Do not deviate,” whence is the obligation to obey learned? Why should I not eat poultry with milk if I feel like doing so (while fully acknowledging the Sages’ authority in principle)?

I explained there that although one who ate poultry with milk did not violate “Do not deviate,” there is nevertheless a prohibition here learned from “Do not deviate,” and this is what is called a “rabbinic prohibition.” It is not a differentiation of “Do not deviate” but a branching interpretive inference from it (unlike the case of the prohibition “He shall not profane his word” in vows). How does this work? In the verse “Do not deviate,” the Torah warns us to obey the Sages. But on the other hand, even one who does not heed their word (for example, when he ate poultry with milk) has not violated that prohibition. So what does “not obeying them” mean? When do you rebel against their command? When you eat poultry with milk out of a principled non-recognition of their authority. But if in eating poultry with milk there is no prohibition in itself, and only the principled rebellion is the prohibition, then why does such eating constitute non-recognition of their authority? I fully recognize their authority, and therefore when I eat poultry with milk it is only because of my evil inclination. It follows that the Sages’ authority is empty of any substantive content. There is an obligation to obey them, but their decrees have no force. I can acknowledge their authority in principle and nonetheless transgress whenever I please everything they forbade. This resembles the amusing situation in A. A. Milne’s Winnie-the-Pooh, where above Piglet’s cottage there hung a frightening sign: “Offenders will be punished,” without defining who or what an offender is—in fact, without defining what constitutes an offense. That is, of course, an empty prohibition. But, as I explained, “Do not deviate” is likewise seemingly an empty prohibition, for nothing is defined as an offense apart from defiance itself. One may do anything, so long as one does not do it out of principled defiance. We are forced to say there must be a prohibition on eating poultry with milk in itself. Now an offense is defined. If I do it out of a principled denial of the Sages’ authority, I also transgress the biblical prohibition of “Do not deviate,” and if I do it because of my evil inclination, I transgress only a rabbinic prohibition. But without a rabbinic prohibition on poultry with milk as such, one cannot define non-compliance with the Sages’ authority.

Thus the verse “Do not deviate” indeed forbids only principled non-compliance. But from the existence of such a prohibition we learn indirectly that there must also be a prohibition on the act itself (even if it is done because of the evil inclination). From here comes the conclusion that the Torah recognizes the existence of rabbinic prohibitions (though it does not itself forbid them. One must remember that without an explicit command and prohibition in the Torah there is no biblical prohibition, even if I can deduce from the Torah in some way that it “disapproves” of this or that act). These prohibitions are not differentiations of “Do not deviate” (for one who eats poultry with milk does not transgress that prohibition, unlike in vows), but branching inferences from the verse “Do not deviate.” There is interpretive proof of their existence, though there is no explicit command about them in the Torah (as noted, “Do not deviate” does not command them).

Differentiation and branching: laws derived from derashot

A similar phenomenon I show there, in the second section, with regard to laws learned from derashot. According to the Rambam in the Second Root, their status is like rabbinic laws (and there, too, the Ramban in his glosses attacks him sharply for this). On the one hand, these are not ordinances or decrees founded on the Sages’ reasoning and on specific real-world circumstances; rather, they are learned from a verse. On the other hand, one who violates them has not transgressed a biblical prohibition or neglected a biblical command. So are these laws learned from the verse or not?

There, too, I explained that they do not differentiate from the verse but branch from it. The Rambam himself senses this in the Second Root and devotes a paragraph to it. He describes it with the metaphor “like branches that emerge from roots.” That is, the laws learned from derashot are growth from the trunk (the command in the verse), or an expansion of it. These are not the fruits of the tree itself. The Rambam brings there the example of the amplification the Sages made from the word “et” (see, for example, Pesachim 25b):

“You shall fear the Lord your God”—this includes (also) Torah scholars.

He explains that fear of Torah scholars is not a biblical law, for it is not written in the verse. The simple meaning of the verse is fear of the Lord. The Sages expanded this to an obligation to fear Torah scholars. When a person does not fear a Torah scholar, he has not neglected the biblical positive commandment of “You shall fear the Lord your God.” And yet, from this verse there branches a duty, by rabbinic authority, to fear Torah scholars. I explained there that, according to the Rambam, this is an expansion of the idea of the verse, or the “spirit of the verse.” One who violates this expansion has not violated the command in the verse because this is not the verse’s content. One cannot extract by interpretive means the conclusion of fear of Torah scholars from the verse; however, the Sages made a derashah (which, according to the Rambam, is not an interpretive method), and thus they established that he violates the spirit of the verse; in other words, it is prohibited by rabbinic authority.

It is important to understand that a takkanah or gezeirah is founded on reasoning. The Sages feared that people would come to eat meat with milk and therefore forbade poultry with milk. There is a need to commemorate the miracle of Chanukah, so they instituted lighting candles. This is legislation enacted by the Sages by virtue of their reasoning. It has no connection to verses. In contrast, the obligation to fear Torah scholars is learned from a verse and is not based on reasoning alone. In principle it could exist even if the Sages had no compelling reason for it (see the dispute between Rabbi Akiva and Shimon ha-Amsuni in Pesachim 25b). They learn it from the spirit of the verse, and this could be prohibited even if the Sages had, in fact, no independent reasoning that forbids it. That is, it is not merely a law created by the Sages, like a rabbinic takkanah or gezeirah; rather, it is a law that branches from the verse, but does not constitute a differentiation of it.

The connection to our topic

The distinction between representation and realization resembles in its logic the distinction between branching and differentiation. Differentiation (as in vows) is drawing a conclusion about a particular example from a general principle, that is, a reduction in extension without any illustration or abstraction. In contrast, branching (as in “Do not deviate” or in derashot) is based on a generalizing interpretation and on a theoretical background that provides its foundation. Here an abduction lies in the background, and in this sense we are dealing with a process of abstraction, and the particular case is a representation of it. This holds at the general level: rabbinic laws branch indirectly from “Do not deviate,” and also at the particular level of each and every derashah: from the verse “You shall fear the Lord your God,” we understand that there is a broader principle of reverence for anything sacred or spiritual, and from this we infer the duty of fearing Torah scholars.

[1] See on this in my book The First Being, Fourth Conversation, Part One, Chapter 2.