Positivism in Halakha and in General, Lecture 5
This transcript was produced automatically using artificial intelligence. There may be inaccuracies in the transcribed content and in speaker identification.
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Table of Contents
- The paradox of matzah from the new crop and stepping outside the system
- The human being versus a computer, weighing rules and authority
- Qualifying the rule in the new-crop paradox: a prohibition that is overridden is not an “offense”
- Studying the rules themselves: a historical innovation in Jewish law
- Analogies: Aristotle, logic, hermeneutic rules, and the study of language
- The process of abstraction from the Mishnah to the Talmud, from medieval authorities (Rishonim) to later authorities (Acharonim)
- Loops, rule-based thinking, and going back to the case itself
- Philosophy of science: a final theory, a “theory of everything,” and a methodological distinction
- Erdős’s “Book” and the question of a book of the rules of Jewish law
- Wittgenstein and follow-the-rule: doubt at the foundation of the very concept of rules
- Didactics: learning from examples to the rule, not the other way around
- The structure of the Talmud against automatic application of rules
Summary
General overview
The text presents a halakhic conflict created by the intersection of several rules, and concludes that when a system of rules produces a loop with no decision, there is no solution from within the rules themselves; instead one must step outside the system in order to weigh, qualify, or establish a hierarchy among the rules. It describes a historical process of abstraction and conceptualization in Jewish law, in which the transition from casuistic thinking about cases to formal thinking through rules also creates the possibility of noticing such loops, and it parallels this with developments in logic, linguistics, and the philosophy of science. It also adds a philosophical critique of the very idea of “working by rules” through Wittgenstein’s claim about follow-the-rule, and shows that the Talmud itself often emphasizes the limits of generalizations and the danger of automatic application of rules.
The paradox of matzah from the new crop and stepping outside the system
The speaker presents a case on the eve of Passover in which matzah from old grain costs half of all one’s wealth, while matzah from the new crop is free but forbidden until the day of the Omer offering, and sets this against the rules that a positive commandment overrides a prohibition, that for a positive commandment one spends up to a fifth and no more, and that for a prohibition one spends all one’s wealth. The speaker argues that these three rules together create a non-transitive loop in which every choice seems to be displaced by a preferable choice, until one reaches a dead end. He defines this as a conflict with no solution from within the system rather than an internal contradiction between the rules, and proposes that the solution requires “stepping outside the system” and judging the rules themselves rather than merely applying them.
The human being versus a computer, weighing rules and authority
The speaker draws a distinction between a computer, which applies a given set of rules without the ability to decide when there is no rule of decision, and a human being, who can weigh rules, qualify them, or determine priorities among them. He argues that deciding such a conflict, by definition, requires stepping outside the system, because now the rules themselves become the object of thought rather than merely tools of operation. He explains that even without a Sanhedrin, a person still has to decide in practice in a situation of conflict, whereas the question of authority arises mainly when one tries to obligate others to accept a particular ruling.
Qualifying the rule in the new-crop paradox: a prohibition that is overridden is not an “offense”
The speaker describes a solution in which he qualifies the rule requiring one to spend all one’s wealth in order not to violate a prohibition, arguing that it applies only when we are dealing with a prohibition as an offense in its own right. He claims that if one violates the prohibition in order to fulfill a positive commandment in a place where a positive commandment overrides a prohibition, then this is not a sin in the sense that requires avoidance at any cost, and even the question of repentance becomes unintelligible because Jewish law itself requires the act. He presents the possibility that a different line of reasoning would have led to stringency and to not eating when it is possible to buy old grain with all one’s wealth, but argues that the qualifying interpretation resolves the conflict and is therefore preferable as long as no decisive proof has been brought against it.
Studying the rules themselves: a historical innovation in Jewish law
The speaker attributes to Rabbi Yehuda Brandes the claim that the phenomenon of systematic books such as Shev Shema’tata and Sha’arei Yosher, along with works dealing with mechanisms of monetary decision-making, is a relatively late phenomenon that developed mainly in the last two hundred years. He argues that in the past people used rules to decide cases, but did not make the rules themselves into an abstract subject of study standing on its own, whereas in recent generations people use the laws and the cases in order to clarify the meaning of the rule itself. He describes the difference between clarifying “when do we say ‘whoever is stronger prevails’ and when ‘the burden of proof rests on the claimant’” for purposes of halakhic ruling, and an analysis that clarifies “what is the idea and logic of ‘the burden of proof rests on the claimant’” and how that affects applications.
Analogies: Aristotle, logic, hermeneutic rules, and the study of language
The speaker compares the move to study rules to Aristotle’s innovation in writing about logic in the Organon, where the rule itself becomes the subject of inquiry instead of the intuitive use of patterns of inference. He argues that a similar process took place with the hermeneutic rules: at first people used similarities between verses without calling that a rule, and once concepts such as verbal analogy were created, rules appeared that could themselves be discussed. He adds an analogy to linguistics, where a native speaker uses rules without knowing how to formulate them, and only a scholar notices the pattern and formulates it as a rule that becomes an object of inquiry.
The process of abstraction from the Mishnah to the Talmud, from medieval authorities (Rishonim) to later authorities (Acharonim)
The speaker cites a scholarly view of a process of abstraction between the Mishnah and the Talmud, and argues that the Mishnah tends toward concrete description of cases whereas the Talmud turns them into abstract definitions. He gives the example of the four primary categories of damages, in which “horn” in the Talmud is not the animal’s physical horn but a type of damage “whose intent is to harm and which is atypical,” and therefore biting, goring, crouching, and kicking become derivatives. He describes the continuation of the process in which the Talmud creates rules to explain the cases, the medieval authorities (Rishonim) clarify the boundaries of application of the rules, and the later authorities (Acharonim) turn the rules themselves into an independent field of analysis.
Loops, rule-based thinking, and going back to the case itself
The speaker argues that loops and conflicts of the type under discussion usually arise from the use of a rule that dictates a decision instead of direct thinking about the case, because several rules can apply to the same case and send one back and forth in a loop. He notes early signs of loops in Tosafot, and connects this to the fact that Tosafot already operates in a world rich in rules. He argues that the development of formal thinking in Jewish law increases the ability to generate loops, and therefore solving them requires a methodological regression: stepping out of the rules, returning to the mode of thinking about the case, and reconsidering the validity and scope of the rules.
Philosophy of science: a final theory, a “theory of everything,” and a methodological distinction
The speaker presents a parallel question in physics: if two physical rules create a contradiction, is a third rule necessarily required to decide between them, and he ties this to the philosophy of science and to the distinction between assumptions that are methodologically fruitful and claims of truth about reality. He mentions Steven Weinberg and the aspiration to a universal theory, and Einstein, who thought there was one law behind everything, connecting this to a reductionist outlook according to which a fundamental physical law would also explain chemistry, biology, and the human sciences. He warns against a “theory that explains everything” in an uncritical sense, and argues that a valuable theory must have conditions that allow it to be falsified, bringing examples of an “everything theory” and of Marxist propaganda that fits every event into the doctrine.
Erdős’s “Book” and the question of a book of the rules of Jewish law
The speaker tells about Paul Erdős and the concept of “a proof from the Book,” meaning mathematical elegance for which there is no formal criterion, though a mathematician recognizes it as the aesthetic quality of a work of art. He proposes a parallel question in Jewish law: is there a finite and sufficient set of rules from which all answers to every halakhic situation can be derived in a way that a halakhic scholar would recognize as “from the Book,” or is the structure of Jewish law “Gödelian,” such that stepping outside the system of rules is essential and not merely a technical problem of lacking knowledge? He links this to the discussion of Gödel’s theorems and to the idea that perhaps a non-finite axiomatic system is needed in order to achieve completeness, and concludes that at least in practical terms it is clear that one cannot suffice with merely operating rules.
Wittgenstein and follow-the-rule: doubt at the foundation of the very concept of rules
The speaker presents the claim of the later Wittgenstein in Philosophical Investigations, according to which “following a rule” is not something that can be fully grounded, because every instruction requires learning through examples and generalization, and generalization can always be otherwise. He uses the example of teaching counting in order to show that a student can continue the series in an unexpected way and still claim that he is continuing “according to the same rule,” stressing that every series has infinitely many possible continuations. He presents the conclusion that “rules” are to a large extent a function of structural similarity among human beings and of practical agreements, rather than something for which there is necessary indication, and adds that the psychometric exam tests fit with an agreed-upon way of thinking more than abstract “intelligence.”
Didactics: learning from examples to the rule, not the other way around
The speaker argues that pedagogically it is correct to teach mathematics from examples to the idea, and only afterward to formulate a rule and prove a theorem, because a top-down proof may remain parrot-like imitation without grasping the logic behind it. He explains that the ability to work from a rule to examples exists only after fundamental concepts have already been learned, but the acquisition of the concepts themselves rests on an exemplary process, and the rule is always exposed to the possibility of a different generalization. He stresses that the use of rules is very helpful, but does not prove that there are “real rules” in a metaphysical sense.
The structure of the Talmud against automatic application of rules
The speaker argues that the Talmud, in its associative structure, prefers examples over the presentation of formal principles, because rules can get lost through over-application or incorrect application. He brings the rule in tractate Kiddushin, “we do not derive from general rules, even where it says ‘except,’” and presents this as guidance not to rely on rules even when they appear to be formulated with exceptions. He cites the Talmud’s question in tractate Bava Kamma, “what does the common denominator come to include?” regarding the rule “they are under your responsibility, and when they cause damage, the damager is liable to pay compensation for the damage from the best of the land,” and interprets the question as a preference for examples over a summary rule. He concludes with an example highlighting the limits of generalization, such as “your property” as against the liability of a custodian, and presents this as an illustration that rules are an approximation requiring caution rather than mechanical operation.
Full Transcript
[Rabbi Michael Abraham] Three aspects of the obligation of restoration. Again, the fact that this is also a lost object joins in here. First of all, it was lost before me. Meaning—
[Speaker B] There’s no full-fledged robbery here.
[Rabbi Michael Abraham] It’s a combination of three things, and only all three together produce the result. Meaning: first, that it was lost from you, even though that seemingly says nothing because there is an obligation upon you to return it. Second, that you picked it up in order to rob, not in order to return it. And third, that the despair happened after you picked it up to rob it, but before you intended to return it.
[Speaker C] Why does the fact that it was lost from you contribute anything? Because it’s not strong robbery. As long as he hasn’t despaired, then it’s like saying—what’s the obligation to return?
[Rabbi Michael Abraham] The obligation to return is to restore it to the state it was in before I robbed it. Return it to the street. Again. And then what? Now I take it. Now it’s already after despair. The obligation to return is to restore the previous state of affairs. If I robbed you, I have to return it to you. I’m just raising a possibility now; this needs thought. But here I’m obligated to restore it to the state it was in before I robbed it. Fine, I’ll return it there. Think of it, basically, as if when I picked it up nothing happened; it’s still lying in the street. Meaning, the obligation of robbery only forces me to restore the previous situation. So think of it as if it had been lying there the whole time. Now a person despairs, now it’s in my hand. So now I picked it up in order to return it. And therefore I’m not obligated to return it.
[Speaker B] So how does this fit with the dispute whether despair alone acquires or doesn’t acquire? So is this according to the view that despair alone acquires?
[Rabbi Michael Abraham] This is despair plus change of possession.
[Speaker B] Here there was despair and change of possession because you picked it up, because I picked it up.
[Rabbi Michael Abraham] Even though the order was reversed. There was robbery and then despair. Robbery and then despair. Again, the lost object probably nevertheless does do something.
[Speaker B] How does this fit with “if one robbed and the owners had not despaired, neither of them can consecrate it, this one because it is not his and that one because it is not in his possession”? That implies that if the owners did despair, then now he can consecrate it because it became his?
[Rabbi Michael Abraham] That’s only according to the view that despair alone acquires.
[Speaker B] Only according to that view? Think about it.
[Speaker E] The robbery itself effects a change of ownership.
[Rabbi Michael Abraham] Yes, but despair alone, according to most opinions, does not acquire; it’s a dispute. But according to most opinions it does not acquire. Although again, it’s still not fully his. There’s a Talmudic passage in Bava Kamma at the beginning of the chapter HaKones. The Talmud there discusses: if bandits took it out, the bandits are liable. And they discuss a case where they took it out with the intention of robbing it. The Talmud asks: that’s obvious—bandits are liable because they acquired it. So what does it mean that they acquired it? It’s only despair; there wasn’t anything else there. They took it out and pulled it in order to acquire it. And nevertheless the Talmud says it’s obvious that it is their property, and if it caused damage they are liable for its damages. Meaning, they are considered owners even after despair alone. Now Tosafot there asks exactly this question. Meaning, he says because this is only despair alone, it comes out from… I don’t remember exactly anymore, but what comes out there from Tosafot is that this is not full ownership; it’s partial ownership.
[Speaker D] And according to all—
[Rabbi Michael Abraham] According to all opinions, even in Jewish law there is ownership after despair alone. But it depends for what matter. For example, with regard to being liable for its damages, I’m considered the owner according to Tosafot.
[Speaker D] The Rosh says not so.
[Rabbi Michael Abraham] According to Tosafot I’m considered the owner. But clearly I still have to return the object itself, unlike despair plus change of possession, in which case the object is mine and I have to return the value but not the… But if, say, he robbed the—
[Speaker F] The object, and the owners had already despaired, then… was there before the robbery?
[Rabbi Michael Abraham] What? Before the robbery?
[Speaker F] No, after the robbery.
[Rabbi Michael Abraham] After the robbery that changes nothing.
[Speaker F] He still has to return the stolen item itself and not its monetary value.
[Rabbi Michael Abraham] Despair after you already became obligated to return it changes nothing. But here something strange happens, because here it was a lost object beforehand. It was a lost object beforehand, so it turns out that that probably does make a difference. Yes, really interesting.
[Speaker G] What do you mean it was a lost object? What? What do you mean it was a lost object?
[Rabbi Michael Abraham] No, he’s talking about a passage in Bava Metzia. Someone lost an object, I picked it up in order to rob it, and then the owner despaired.
[Speaker G] Robbery in broad daylight? Was it in front of the owner?
[Rabbi Michael Abraham] No, I picked it up in order to… In the language of the Talmud, robbery isn’t necessarily specifically that, even though it says, like “and he stole the spear,” you really need a forceful act of robbery. But they call it robbery for anyone who takes property that isn’t his.
[Speaker H] What is it then— theft or robbery?
[Rabbi Michael Abraham] They call everything robbery.
[Speaker H] If he stole a sheep secretly he pays double payment; if he robbed it openly he pays the principal, or four or five.
[Rabbi Michael Abraham] Obviously, but they say the sheep is “robbed” in the broader sense. In the language of the Sages, any money that isn’t yours—they say it is robbed property in your hands, even though actually it came to you through theft and not robbery. Last time we talked about paradoxes and stepping outside the system. Meaning, in the end I concluded there with this paradox of matzah from the new crop. The claim was: I’m on the eve of Passover, and matzah from old grain costs me half of all my wealth, for the positive commandment of destroying leaven and maybe even I’m not allowed to spend more than a fifth. And matzah from the new crop, which is forbidden at this stage until the day of the Omer offering, which is the day after Passover, costs the regular price. Then the question is, of course, here every action you choose has another action that is preferable to it. There is no transitivity here. Meaning, if you decide to eat matzah from the new crop because a positive commandment overrides a prohibition—what do you mean? Spend half your wealth and buy matzah from the old grain, because in order not to violate the prohibition of the new crop you have to spend up to all your wealth, even. So I’ll spend all my wealth, or half my wealth, and I’ll buy matzah from the old grain. What do you mean? Don’t eat at all, because in order to fulfill the positive commandment of matzah you don’t have to spend more than a fifth of your wealth. Don’t eat at all. Why not eat at all? Because of the prohibition of the new crop. A positive commandment overrides a prohibition, so take matzah from the new crop and eat matzah from the new crop—and so on and so forth. I said that in order to solve this loop, what you really need is to step outside the general system. Meaning, there are basically three rules here that get us into this tangle. One rule is that a positive commandment overrides a prohibition. A second rule is that for a positive commandment you have to spend up to a fifth of your wealth and no more. And for a prohibition you have to spend all your wealth. These three rules together create the conflict for us. I said this is not a paradox, meaning not a contradiction, because there is no contradiction among the rules. But the rules create, in a certain situation, a state of conflict with no solution. Not really a contradiction between the rules. The rules do not contradict one another in principle in terms of their content, but the three rules together, regarding this specific situation, create a problem of how to decide what the law is in such a case. I said that if I look at myself, say, as a kind of computer, taking the rules and carrying out the calculation in order to know what the Jewish law is, then there is no answer. Within the rules there is no answer. But that, one might say, is the advantage of the human being over the computer: a person can also step outside the rules. A computer receives some set of rules from the programmer and works within them. It’s a golem. Meaning, whatever you put into it is what is there.
[Speaker I] But the rules are there in the first place.
[Rabbi Michael Abraham] What do you mean, they’re there in the first place?
[Speaker I] It finds once, the rules that are there in his head or something.
[Rabbi Michael Abraham] So that too is a rule, it doesn’t matter. Assuming that a person—well, not assuming, you can see it here—a person can step outside the system of rules within which he operates, even though many times we aren’t aware of it. And that is exactly my goal here, meaning to show that in fact we have to step outside the algorithmic box. Meaning, to say: there is a set of rules, okay, what do we do? Then we automatically place ourselves into the situation of a computer. And a person is not a computer. You have a set of rules—that does not give you a solution. Go outside, beyond the rules, and look at the rules. True, you didn’t determine them; the Holy One, blessed be He, determined them. So it’s not in your hands—you can’t say that you don’t accept one rule or another. That you can’t do. These are all rules of Jewish law. But if I’m in a conflict, I do still have to make a decision, and in order to make a decision I have no choice but to weigh the rules or decide which of them is more important than which. Now, when I decide how to weigh the rules, by definition I have stepped outside the system of rules, because I am judging the rules themselves. An action within the rules is an action that uses the rules; it is never an action in which the rules are the object of the thought, meaning that they themselves are what I’m dealing with. By the way, this is a very interesting point, because I think it relates to us. I once saw an article by Rabbi Yehuda Brandes, which also goes back somewhat to his dissertation, where he talked about the fact that the phenomenon of these books that deal with systems—systems like Shev Shema’tata or Sha’arei Yosher—books of that kind, is a new phenomenon. It didn’t exist until… And what was introduced there: Takfo Kohen, Kuntras HaSefeikot, all kinds of things like that. Takfo Kohen is somewhat earlier; it’s not exactly the same type. All these works take the rules that Jewish law establishes for deciding monetary dilemmas—“the burden of proof rests on the claimant,” “whoever is stronger prevails,” “I can maintain my position,” all kinds of rules for deciding monetary dilemmas—and basically, almost for the first time in the history of Jewish law, and this began around two hundred years ago, they turned the rules themselves into an object of study. Until the time of the Shev Shema’tata, say—maybe there was a bit before that; the Shev Shema’tata is the clearest—but before that, perhaps the Shakh and Takfo Kohen, maybe one can also see that as this kind of work. Until then they used these rules in order to decide problems that stood before them. Even Tosafot at the beginning of Bava Metzia, say—right now Bava Metzia—the first Tosafot on page 2a there, whose parallels are in Bava Batra in the third chapter, on all these rules: when do we say “whoever is stronger prevails,” when do we say “they divide,” when do we say “the burden of proof rests on the claimant”—he does deal with the rules a little and with the relations between them and when each rule is said. But it’s not a discussion whose subject is the rule itself; rather, it is the relations between rules in order to know what to do with them. He doesn’t say, wait, let’s look at what “the burden of proof rests on the claimant” is. What is the idea behind it? Let’s see what the implications of that idea are, and where we apply it, and why—meaning, the subject of the discussion is the rule “the burden of proof rests on the claimant,” not using the rule “the burden of proof rests on the claimant” to decide a halakhic question that he needs to decide. Most halakhic decisors and commentators, the medieval authorities (Rishonim) and also the later authorities (Acharonim), who dealt with such passages used the rules; they did not study the rules. And in the process they can say this rule applies here and not there, of course; the medieval authorities (Rishonim) do that. But again, that’s while dealing with some problem they had and things didn’t work out for them and they had a difficulty from somewhere else, so they said: here “the burden of proof rests on the claimant” is not relevant; here it’s “whoever is stronger prevails.” Fine, okay, that’s clear, it’s called for. But nowhere was there a book written on the rule “whoever is stronger prevails.” It wasn’t perceived as a subject that is itself a topic for analysis. It’s an instrument. It’s an instrument that I use. And that is somewhat like the innovation of Aristotle, in a certain sense, in that Aristotle wrote a book on logic, the Organon. Even before Aristotle they knew that if every X is Y and A is X, then A is Y. They didn’t call it A and X and Y, but they said: if every goat has four legs, and I see a goat in front of me, then obviously it has four legs. Everyone understood that. That wasn’t Aristotle’s innovation. Aristotle noticed that there is some rule here behind all these forms of thought, a rule that can itself be discussed—not only to use that rule in order to draw conclusions about goats and legs, but on the contrary, to leave the goats aside and leave the legs aside and try to think about that rule itself: if every X is Y and A is X, the conclusion is that A is Y. It doesn’t matter what A is, what X is, and what Y is. The rule itself. No one noticed that there was a rule here; they simply used it, because it was obvious to them that that is how one infers the conclusion. And Aristotle was the first to notice this point, that there is some pattern here that repeats itself in many places, and this is in fact a pattern that can be discussed in its own right. Let’s study logic. That is how this field called logic was created. And essentially we study a system, a system of rules, which is really a toolbox that helps thought. And suddenly that toolbox itself became the subject of research, meaning people investigate it. That’s an innovation. Okay? Now in Jewish law as well it’s the same thing. There was a system of rules before too, of course, but only in roughly the last two hundred years—even later in many places; before two hundred years ago it’s rare—did people start dealing with the rules themselves as a subject for analysis.
[Speaker J] Are those rules, or are they stepping outside the box?
[Rabbi Michael Abraham] No, no, those are rules. “The burden of proof rests on the claimant” is a rule.
[Speaker J] But not everyone agrees. One says it’s “the burden of proof rests on the claimant,” one says “whoever is stronger prevails.”
[Rabbi Michael Abraham] No, no, that’s not a dispute. Meaning, regarding “the burden of proof rests on the claimant,” there is a dispute between Sumchus and the Sages—whether “they divide” or “the burden of proof rests on the claimant”—and it depends exactly when, but in principle these are accepted rules, and one has to examine when one applies “whoever is stronger prevails,” and when “they divide,” and when “the burden of proof rests on the claimant.” It’s not that there is a dispute over which rule to use; rather, in every kind of doubt there are different types of doubt. If both are in possession, if one is certainly a liar, not certainly a liar, or things of that kind—you classify the situation. And there are also disputes among the medieval authorities (Rishonim) about exactly how to classify it, but in principle these are different situations, and in each type of situation one applies a different rule. And the Tosafot I mentioned, and the medieval authorities (Rishonim) who discuss it there, really do discuss the rules. It’s simply a rare case in which the rules themselves are the subject of the discussion. That’s rare. And even there, it’s not really that the rules are the subject of the discussion; rather, you have to understand: in the Talmud it says “whoever is stronger prevails,” and it says “the burden of proof rests on the claimant,” so Tosafot asks himself: okay, when do we apply this and when do we apply that? That is still a halakhic question. It is not a discussion of the rules themselves. And now, suddenly, whole systems open up around what “the burden of proof rests on the claimant” is, where it comes from, what its meaning is, what its logic is. And from that, of course, there are also implications for where to apply it and where not to. And they also use cases in which the Talmud says that we do say this rule or do not say this rule, and from that one can understand how the Talmud understood this rule. But the subject of the discussion is not to use the rule in order to issue a halakhic ruling; it is to use the laws in order to clarify what the rule says. And that is something new. Now, in a certain sense, that is the stepping outside the box that I’m talking about, because until the period in which people looked at the rules themselves as a subject of discussion, it was much harder to make a move like the one I’m making now. Here you are inside a situation where you have five rules, and now they trap you. What do you do? There’s nothing you can do until you are prepared to step outside and say: wait, wait, wait, let’s discuss the rules themselves—their force, their strength, where they exist and where they do not exist, where they come from, what their logic is. Let’s try to weigh which rule overrides the other, who is more important, who comes before whom. When you weigh rules you have to decide what is more important and what is less important. For example, right now I remember another one—majority and proximity, say. That too is a Talmudic passage already trying to weigh rules in Bava Batra: is majority preferable or is proximity preferable? Things like that are also in the Talmud and in the medieval authorities (Rishonim), but it’s still not the discussion we find in Shev Shema’tata and Sha’arei Yosher; it’s not the same discussion. There is something there, some type of conceptualization, that really came only in the later generations. By the way, this is a known tendency among scholars: that even between the Mishnah and the Talmud there is a process of abstraction. The Mishnah generally speaks about cases. The Talmud sometimes—again, not all that much; in the medieval authorities (Rishonim) and later authorities (Acharonim) it keeps happening more and more—but the Talmud already turns things into something more abstract. And we usually learn the Mishnah through the lens of the Talmud and don’t notice this, but scholars have a certain method: they read the Mishnah simply on its own terms, without caring what the Talmud says. After that they learn how the Talmud understood the Mishnah, and then they ask whether it is the same thing. And the assumption is that it is not the same thing. One who reads the Mishnah simply often does not see what the Talmud understood in the Mishnah, and then they can notice more clearly the process that happened here. And in very many cases the process is a process of abstraction. Ben Shel Vestrich—Avishalom—wrote about this in his dissertation. He wrote on the four primary categories of damages, and he shows that the conception in the Mishnah is a concrete conception of the primary categories of damages. There is horn, there is pit, there is fire, foot—you see concrete things in front of you. In the Talmud, horn is not that thing on the animal’s head. Horn is a type of damage whose intent is to harm and which is atypical. That’s it—it has become an abstract definition. And then, of course, biting, goring, crouching, and kicking are derivatives of horn, because those too are forms of damage that are atypical and intended to harm, even though they have no connection whatsoever to those growths the animal has on its head. That is a kind of abstraction that typically happens between the Mishnah and the Talmud. Now the process of abstraction continues. The Talmud creates rules in order to explain the cases of the Mishnah. The medieval authorities (Rishonim) already discuss the rules: where do we apply this rule and where do we apply that rule? The later authorities (Acharonim) already turn the rules themselves into a subject of discussion. And there is an analytical topic that talks about migo—what is migo?—or about “the burden of proof rests on the claimant,” or about “whoever is stronger prevails,” it doesn’t matter. One can see books now being written on that rule from that toolbox. Who would have thought that the toolbox itself is a subject of discussion? The toolbox is what one uses in order to discuss halakhic issues, and suddenly the toolbox itself becomes the subject of discussion. That is exactly the stepping outside the box that I’m talking about. And historically this is something that took a long time; it is a very long and very subtle process. Of course, again, this does not happen in a very crude, stage-by-stage way. There are certainly certain beginnings in earlier generations, but it is definitely a process that develops very clearly over time—a process of abstraction, of conceptualization. Once you conceptualize something, it becomes a subject; you can discuss it. Before you conceptualized it, you didn’t even feel that you were using some kind of rule here; you just used it, that’s all. I once talked about the hermeneutic rules and said that basically something similar happened there too. At first, people simply used the hermeneutic rules, but no one thought that there were hermeneutic rules there—just like Aristotle’s logic. You use them because that is how you learned to interpret the Torah. You see two similar words, so apparently the laws are similar, the laws should be similar in the two contexts—but no one called it a verbal analogy. What difference does it make that they didn’t call it that? It makes a big difference. When you call it a verbal analogy, you are saying that there is some rule here that is being applied in many places, and it is the same rule. No one ever noticed that it was the same rule, because they didn’t understand that there was a rule here. They simply use it and that’s that. It’s like—we talked about this—a speaker of a language, who uses rules, speaks correctly. In his life he has never known that at the beginning of a word certain letters take a dagesh. He never heard of it, but he speaks correctly, and at the beginning of every word he pronounces them with the dagesh. Why? Because he never thought there was a rule here; he’s just accustomed—this is how one speaks. Until someone comes from the outside and says: wait a second, in all the occurrences of this letter at the beginning of a word you pronounce it one way, and not at the beginning of a word you pronounce it another way. So what is this? Suddenly he can say, ah, there is a rule here: at the beginning of a word these letters take a dagesh. Ah—and now we begin to ask, wait, this is a rule, that’s interesting. Is it this way in other languages too? And then a field begins called linguistics, or whatever, the study of language. But that requires abstraction, because before that no one would have imagined that language is something one can study. Language is simply the opposite: within language we speak. How can it make sense to think about language itself? Language is the framework within which we work. To think about the framework itself is something that requires a non-trivial abstraction—that the framework itself is a subject of discussion, something we can investigate or think about. So if I return to us, then the claim is basically that in order to solve loops, paradoxes like these within Jewish law, you basically have to—these loops usually arise, as I said last time, usually from the use of rules. Because otherwise, a loop always arises when you use one rule and it leads to one conclusion, and then that rule takes you here and this rule takes you there. If there is no rule, no loop will arise. You think about the case and say: what is the law there? Either the law is this way or the law is that way. In order to produce a loop, you need some rule that dictates to you what the law is not through thinking about the case, but through the application of a rule that also applies to this case. Then you say: yes, yes, but this case is also governed by that rule and this rule, and then you enter a loop. Therefore I think—I don’t know, maybe there can be something else—but usually loops and paradoxes of this kind, conflicts of this kind, are created by using rules. And therefore the solution to these loops, if there is a solution, should also be by stepping outside the system of rules and trying to weigh or judge, to discuss, the rules themselves. Or to qualify them, or to weigh them differently. What I did in this paradox, the conflict of matzah from the new crop, was to qualify one of the rules. What I claimed was that the obligation to spend all your wealth in order not to violate a prohibition applies only when you are simply violating the prohibition. But if you violate the prohibition in order to fulfill a positive commandment, then here there is a prohibition such that a positive commandment stands opposite it and overrides it. To avoid violating a prohibition of that kind—am I supposed to spend all my wealth? That is a weak offense, if it is even an offense at all. On the contrary, maybe it isn’t even an offense, because I am supposed to do it. I did it—do I need to repent for that afterward? What repentance? במסגרת repentance I am supposed to accept upon myself that I will never return to this sin. But Jewish law says that in such a situation I am supposed to eat the matzah. So what does it mean, “I will never return to this sin”? This is what Jewish law says—it isn’t a sin at all. So for such a thing I have to spend all my wealth in order not to do something that isn’t even a sin? Why? When there is a prohibition standing on its own, you have to spend all your wealth in order not to violate the offense. Fine. Now, what I’m saying here is not something trivial. Meaning, you need to think about the rule that a positive commandment overrides a prohibition, discuss it, weigh it, or qualify it. In this case I qualified it; I didn’t weigh it. I didn’t say that it is less important than another rule. Sometimes the solution will be that rule A is less important than rule B, so if there is a clash between them, rule B will prevail over it. That is one possible solution, and for that too you have to step outside the system. You have to decide which rule is important and which rule is less important. When you are inside the rules, you don’t have important and less important. A computer doesn’t know how to decide which rule is more important, unless the programmer told it: if there is a clash, this rule overrides that rule. If he didn’t tell it, then the computer will enter an infinite loop; it won’t know what to do with such a thing. Okay? So the assumption is that in order to weigh rules or establish a priority scale among rules, a value hierarchy, you have to step outside the system of rules, outside the box. Also in order to qualify a rule you have to step outside the box, because you have to think about what this rule says and where it makes sense to apply it and not apply it. If the rule is just simply imposed on you, you are not even authorized to think about it and discuss it. There is a prohibition—you have to spend all your wealth. That’s it. I don’t know which prohibition, when yes—who are you to even look at it? Jewish law says that’s it. You have to set this rule up as a subject for discussion, to think about a positive commandment overriding a prohibition and understand that there is a problem here: avoiding an offense to the point of spending all my wealth. But if a positive commandment overrides a prohibition, then when I violated the prohibition, that wasn’t even an offense at all. So why spend the money? Who said I have to spend all my wealth? There was room to say yes. There was room to say that still—meaning, if you can spend all your wealth and not violate the prohibition, then maybe it is an offense after all. A positive commandment overrides a prohibition when there is no choice, when I cannot fulfill the positive commandment without violating the prohibition. But if you have an option—spend all your wealth and get rid of the prohibition—then it could indeed be that you must spend all your wealth, because in such a case, if you do not do that, then the prohibition really would be an offense. There was room for such reasoning. But someone can come and say: no, I don’t accept that reasoning, and in my view, when a positive commandment overrides a prohibition, there is simply no proof that I have to spend all my wealth for that prohibition. And if I am here in a conflict, then my assumption is that the burden of proof rests on whoever wants to put me into the conflict. And if this interpretation gets me out of the conflict, then I prefer this interpretation of the rule. Maybe I don’t have proof for it, but it sounds reasonable to me. It gets me out of the conflict, so I go with it. Okay? So basically the conclusion is that, first, paradoxes are usually created by the operation of rules. I don’t know if it’s always so, but it’s very typical. Maybe it’s always, maybe almost always. Fine—they are created by the operation of rules that in a certain situation produce a conflict. And accordingly, the solution of this conflict must be some kind of stepping outside the system of rules, turning the rules themselves into the subject of discussion, not the situation. Not to ask myself what to eat—matzah from the new crop—that is what an experienced halakhic decisor from the medieval authorities (Rishonim), from the Talmud, would do. They would ask: what am I supposed to do in such a case? The question is a halakhic question. Here the question is no longer a halakhic question. I am now going to deal with the topic of a positive commandment overriding a prohibition. That’s all—that is the topic I’m dealing with, not the topic of matzah from the new crop. A methodological topic. And from that I may perhaps also solve my halakhic question. So I have to perform the abstraction I spoke about earlier, by which I turn the rules into the subject of the discussion. I place them before the test of critical thought, critical thinking, and I ask myself when this applies and where it applies and how far it applies.
[Speaker K] And then when I arrive at a decision, there has to be someone with authority in that, who…
[Rabbi Michael Abraham] All right. The question of authority—who is authorized to do this—that’s a separate discussion. I don’t think there needs to be authority here. Say today there is no Sanhedrin.
[Speaker K] When you’re in a conflict,
[Rabbi Michael Abraham] Today there is no Sanhedrin. You’re in a conflict and you need to decide what to do? You have to make the decision. You can consult a rabbi, a halakhic decisor, no problem. In the end, you’re on your own. What will you do? You have no choice—you have to decide. It’s not that the question of authority arises in a case where you claim that this is the right decision and that all of us must obey you. Let’s say you have no authority. A Sanhedrin can force everyone to accept what it decided.
[Speaker B] That’s the question of authority, but to solve a problem, each person has to solve the problem if he’s in it. If he can consult, he can consult. Is that also true of physical laws? Meaning, if I have two physical laws that lead to contradictory predictions, then there has to be a third law that decides between them?
[Rabbi Michael Abraham] That depends on your philosophy of science. If you think that in the end the correct, complete science is not just a collection of rules—that’s not a simple question. Philosophers of science cast doubt on that. Scientists usually assume it is. But philosophers say yes, that’s a productive assumption, because otherwise science wouldn’t have advanced. If you didn’t believe that behind the cases there are rules, then you wouldn’t look for the general law, and science wouldn’t have progressed. That doesn’t mean it’s actually true. It only means it’s a very fruitful assumption in the methodological sense. I wrote about this in one of the columns: you have to be careful with assumptions that are methodologically fruitful not to turn them into claims about reality. And that’s exactly what philosophers of science are saying here. You scientists are convinced that there is some set of rules—even though we don’t yet have them, we still don’t understand everything, we’re getting closer to them. And in the final analysis, if we succeed—there’s no guarantee we will—but the assumption is that even if we don’t succeed, in the end there is some set of rules. And Einstein was especially optimistic—he thought there was one rule behind everything. But even if he wasn’t right, then there is some set of rules. Right now I’m reading a book by Steven Weinberg called Toward the Final Theory or something like that, singularity or something like that—no, The Final Theory, something like that… Toward the Final Theory or something like that, reflections or thoughts on the final theory. Fantastic formulation in physics, particle physics and high energies. So he talks there exactly about this assumption—that we are getting closer and closer to some complete theory that will explain everything, a theory of everything. And many times “theory of everything” is said critically: a theory that explains everything and in fact explains nothing. Because a theory that explains everything… Kaveh was president of Bar-Ilan, he was a great mathematician in Torah… he was an artist at theories of everything. You could do insane work, sweat blood, do crazy calculations, think of solutions, and finally arrive at a solution. You’d come show him the solution, he’d look at it and say: “Obviously. Why did you need to do the calculation? I could tell you straight away that that’s what would happen.” And then… no, no, intuitively. Obviously in the end you still need to do the calculation, but why get tangled up, I would’ve told you in advance to look in that direction, because obviously the solution has to be exponential, has to be like this. He could show me that it had to be something like that, and then there’s the point that the solution is exponential, so I assume an exponential solution, plug it in there, and I find the parameters, I solve the problem.
[Speaker L] What? That’s already in the category of “that actually happened to me.” No, they always say this at work—people come and say, what, why, I knew that already, and so on.
[Rabbi Michael Abraham] No, he explains it to me, he convinces me, he shows me that that really is what the logic says, that I just wasn’t looking well enough at the equation. Except that—I no longer remember whether this is an urban legend or whether it really happened to me personally. I think it didn’t happen to me personally, but the memory sits very strongly because maybe that’s how people tell stories about him, but I don’t know. What? No, so he really did go off course—why? Because if you’d come with the opposite result, he could explain that too. Just a real artist, you know—whatever it was, he’d show you why that was really the natural solution to the problem.
[Speaker L] To declare the creeping creature pure with 159 arguments.
[Rabbi Michael Abraham] Exactly—to declare the creeping creature pure with 159 arguments. Now that’s often said in a mocking tone, “theory of”
[Speaker N] everything, and the theory of everything—what?
[Rabbi Michael Abraham] Was he at the institute? A physicist, of course, Einstein, he was here and later president of the university. So the point is that once a theory explains everything, it’s worth nothing. I mean, for a theory to be worth something, you have to be able to point out what would have to happen for me to throw it away. If nothing that happens would make us discard the theory, then it’s worth nothing, it says nothing. It’s like Marxist theory, which explains everything—Marxist theory explains everything. Whatever happens fits. The literature around the thought of Lenin and Stalin is astonishingly similar to religious apologetic literature. That is, the principles of religion are never refuted, the Holy One, blessed be He, is always right, always just, our predictions—the redemption is on the way. No matter what happens—yes disengagement, no disengagement, yes peace agreement and war—whatever you want to happen fits the theory.
[Speaker O] Everything was written in heaps upon heaps of literature.
[Rabbi Michael Abraham] Exactly. So there too, the same kind of literature was written in the communist context, explaining that Lenin and Stalin foresaw everything with divine inspiration, and no matter what happened, they foresaw quantum theory in advance. I have a book that came out in Hebrew too, translated into Hebrew by Stalin’s followers back in the 1950s.
[Speaker M] The maestro—what? That’s Marx’s theory.
[Rabbi Michael Abraham] Marx and Lenin and Stalin—each had his own body of thought. If you read Solzhenitsyn, you could see his scientific works, The Gulag Archipelago—I mean Stalin’s scientific works. He has books on linguistics, books on various scientific fields. I have no idea who wrote them for him; it’s possible he wrote them himself, I’m not sure. And they studied this as the pinnacle of science in the Soviet Union. By the way, they also had good scientists, incidentally. But because of the indoctrination, because they had to fit things to the doctrine, it clipped their wings—they couldn’t say things that didn’t fit the doctrine. But some of them, incidentally, believed the doctrine; they didn’t want to say things because they thought it wasn’t true if it didn’t fit the doctrine. Meaning, not that they were afraid like Galileo, afraid they’d burn him, but some—some of them, of course, were, I don’t know—but the whole thing is fascinating. I have a book called Lenin and Modern Physics, Omelyanitsky or something like that, some guy from Sifriyat HaPoalim in the struggle. Tell him—what a bizarre bunch, yes—the Stalinists, the shmutsniks of the 1940s and 1950s, who explain that everything appears in Lenin and Stalin and they foresaw everything, and what they didn’t foresee is of course not true, so by definition they foresaw everything, because whatever they didn’t foresee simply isn’t true, so that’s that. And that’s what’s called “theory of everything” in the negative sense. But here it’s “theory of everything” in the positive sense. That is, Einstein wants to claim that this is a theory that will really yield predictions such that all of them fit reality and all reality fits them—not that whatever happens in reality, a thing and its opposite, can both be squared with the theory. No, the opposite won’t happen.
[Speaker H] The theory will yield—the theory always,
[Rabbi Michael Abraham] Yes, that was his aspiration and he believed it exists. And Weinberg writes in his book, which is meant to support the claim that it really does exist, that the progress of physics over the last hundred or two hundred years—roughly since Newton, but especially in the last hundred or two hundred years—leads us to think, and to ground more solidly, Einstein’s assumption that behind all this sits one theory. Now, in reductionist thinking, you have to understand that if there is one law that explains all of physics, then it also explains chemistry and biology and physiology and psychology and sociology and anthropology and whatever else you want. Because in reductionist thinking, in the end it’s all physics. Everything else is just greater degrees of complexity, and that’s all. Basically there is one law responsible for everything, and that gets you to the Holy One, blessed be He—that’s the end of the story. Meanwhile, until we know the theory, we won’t know, but the hope is that one will be able to calculate everything from it.
[Speaker I] No, I mean the side that says there is no theory, in the sense that there is a reality that each time has the form of a theory, but it’s simply too complex for us to grasp.
[Rabbi Michael Abraham] Yes, but what does “too complex” mean? If you don’t arrive at…
[Speaker I] Not its applications—the law itself.
[Rabbi Michael Abraham] You can decide on a theory. The theory says birds fly in the air and fish swim in the sea. That’s my theory; it describes all animals. That’s not a theory. It’s hard to define exactly the point at which you understand that you’re standing before some theory, but that’s what Steven Weinberg tried to describe there: you can’t give a criterion, but every scientist standing before it knows whether it is or isn’t. You feel there’s something here. Something that isn’t just a collection of facts.
[Speaker I] A collection of facts is not a theory. There’s no criterion. What do you mean there isn’t?
[Rabbi Michael Abraham] They say there is no indication that there is. No indication that there is.
[Speaker I] Meaning there is a series of facts that are not separate.
[Rabbi Michael Abraham] You won’t succeed in making some formulation from which all the facts come out. An economical formulation, again—a formulation whose number of parameters is equal to the number of facts it explains—that’s maybe about as close as you can get to a definition. If the number of parameters in it equals the number of facts it defines, that’s not a theory. Fine. So the claim is that to solve loops of this kind, you need to step outside the rules. Now here I’m really getting to the heart of our discussion. Because what does it mean to step outside the rules? And that’s really connected, incidentally, to what we discussed earlier in the philosophical debate about scientific rules, scientific theories. In Jewish law it’s the same thing. The question is whether in the end, the true Jewish law—after we know and uncover, if that ever happens, after we know and uncover everything—the Holy One, blessed be He, all right, wants to write the book of the ultimate rules of Jewish law. He Himself—can He write such a book? Is there such a book? Do you know Erdős’s expression, “a proof from the Book”? Do you know it? Paul Erdős. A Hungarian mathematician, a Hungarian Jew. A crazy character. He has a book—the book from heaven. What? Erdős, yes. My father used to tell me stories
[Speaker D] about his meetings with him at the Technion.
[Rabbi Michael Abraham] A very amusing book. A fascinating man. He was a homeless person, a citizen of the world, and whenever he came to a country—just this mathematical genius—he’d come by invitation to various countries. In Israel he came a lot because he was Jewish, and he was very often at the Technion and the Hebrew University.
[Speaker C] There’s a chair here
[Speaker M] in the State of Israel.
[Rabbi Michael Abraham] Yes, yes. He died thirty years ago.
[Speaker C] I remember there’s Erdős one and Erdős two—whoever wrote with him.
[Rabbi Michael Abraham] Right. So each time he’d be invited to a country and he’d arrive with only the clothes on his back. He had nothing in his world. No property, no clothes, certainly no house. And when he arrived, they had to support him. Whoever wanted him would buy him the relevant clothes, give him a place to live, food, and until he found someone else—after a month, two months, a year, I don’t know how long—he’d move on to the next country, the next university. A character straight out of the movies. And he did lots of collaborations, lots of joint work. Because whenever they invited him, what did they invite him for? To work with him. He was apparently a very stimulating person, had lots of ideas. And there were lots of ideas. And that Erdős number we heard about earlier—that’s right, whoever co-authored a paper with Erdős has Erdős number one. Whoever co-authored with that person—not with Erdős, with him—has Erdős number two, Erdős number three. In other words, your pedigree in mathematics is what your Erdős number is. So: a proof from the Book. Ah yes, a proof from the Book. In mathematics there’s an expression—I think it comes from Erdős—that when you stand before a proof and see just a proof, something amazingly elegant, that’s “a proof from the Book.” A proof from the Book. And someone can come and tell you, wait, there’s an amazing elegant route here, in five steps I’ll show you the proof. Even in geometry you can encounter this from time to time. So these are proofs from the Book. Now incidentally there is such a book called Proofs from THE BOOK; I have it. You can find it online: Proofs from THE BOOK. It collects all the elegant proofs of theorems in mathematics, all the proofs of which it is justified to say that they are proofs from the Book. Now ask: what is a proof from the Book? There will be no criterion—just as you asked earlier about theory. Every mathematician who stands before it understands that this is a proof from the Book.
[Speaker C] What is elegance? Yes, exactly.
[Rabbi Michael Abraham] It’s something where you understand that there is some amazing aesthetic here. It’s something that when you stand before it you understand that it’s a work of art. It’s not—just as there are no criteria for works of art.
[Speaker B] It also seems to me that he himself was an atheist, and all the time he was an atheist and said “proofs from the Book” like that, so he contradicted himself.
[Rabbi Michael Abraham] Yes, all right, you know, the image of God. Fine. Fine. Lots of atheists use the jargon, yes, “the image of God.” “Where’s your image of God?” Image, not image. No, granted, the image of God. God without a body, but still. In any case, so the question—I wanted to ask this—is: in the book of halakhic proofs, not the… is there a finite set of rules, finite, a set of rules from which one can derive all the answers to every halakhic problem? At the principled level, again—without getting into questions of elegance. You can always define some ad hoc rules; at worst, make one rule for each case. And who knows what counts as a rule—how many cases it takes to count as a rule. For every case you can define a rule for every case, yes. But a system of rules such that a scholar of Jewish law would stand before it and understand that this is from the Book, meaning that it’s a rule, not just ad hoc for the cases—is there such a set of rules? Because if there is, then stepping outside the framework of the rules, which I talked about earlier, is only a technical problem. Because we just don’t yet have the perfect system of rules, and our rules are only an approximation. So there’s no choice: sometimes we get stuck with them and need to step outside. But in principle there ought to be some larger system, or more fundamental one—sometimes actually smaller, but more fundamental—outside of which there would be no need to step. The final system, yes. Like Gödel’s theorems, which I mentioned last time: in order to prove Gödel’s theorem, you need to step outside the axiomatic system it’s talking about. But there are axiomatic systems to which Gödel’s theorem does not apply. And it may be that in the end, in mathematics, if I understand correctly—I may be missing something here, you’d have to ask mathematicians—but if I understand correctly, it may be that in the end all of mathematics can indeed be one axiomatic system, despite Gödel’s theorems. Such an axiomatic system that is itself not subject to Gödel’s theorem, meaning that within it, it is complete and everything can be proven.
[Speaker B] But last class you said that it’s a number of axioms that is not countable, right? So that means it’s not finite.
[Rabbi Michael Abraham] What did I say? Not finite, a set of axioms, yes—not finite. If it’s finite, Gödel’s theorem always applies, I think, if I remember correctly. Any finite axiomatic system—I think Gödel’s theorem applies to it, I think. In any case, the claim is that if there really is some sort of Book, then stepping outside the axiomatic system is only a technical matter. We just haven’t yet reached the most fundamental and most correct system, and then the approximations don’t work and you have to step outside. But in principle there is some complete set like that. Or maybe not. Maybe Jewish law really is something Gödelian, meaning there is no set of rules outside of which one need not step, and rather stepping outside the rules is essential to Jewish law. It’s not a technical problem because I don’t know the true rules; it’s essential to Jewish law, because you can’t write a book. Even the Holy One, blessed be He, cannot write such a book of rules from which you can derive all the halakhic answers for all situations. In any case, for us this is only a hypothetical question, because for us it’s clear that one must step outside the rules. Whether this is a technical question or not is a question in the philosophy of Jewish law, because in the practice of Jewish law there’s no doubt that we cannot suffice with merely applying rules. Whoever thinks so—and many delude themselves. And that’s the halakhic positivists. But that’s an illusion. Come on, no, you can’t do such a thing. And here I want to talk a little about the meaning of rules in Jewish law and in general. There’s a work by Wittgenstein, the later Wittgenstein, Philosophical Investigations, where he talks about the problem of following a rule, which I already mentioned once, I don’t remember in what context. And his claim there is that rules are a fiction altogether. And here this is really already getting close to the philosophical statement, though it may be that only because of our limitations, and that’s why I’m not… but he has an important claim. His claim is that people think, for example, that mathematics works with rules. In life we can’t work with rules—or either it’s too complicated or there are no rules, that’s another question. In mathematics we work with rules. He says: even in mathematics there are no rules. There’s no such thing as working according to a rule. And that’s his famous argument called “following a rule.” That we cannot really follow a rule. And why? Because when I want to teach someone a certain rule so that he’ll succeed in following it, that act of teaching itself will not use rules, because otherwise I also need to teach those rules. I need to begin in some other way that does not use rules. How do I do that? With examples. And with those examples I expect him to understand the rationale behind them and infer the rule from them. But then who says he inferred the correct rule? I don’t know. Any set of examples can be generalized in many ways. Who says he… He gives an example there: suppose you teach students to count. I think that’s his example. You teach students to count, okay? You teach them one, two, three, four, five, six, seven, eight, you teach them the decimal system, yes? Ten, eleven, twelve, thirteen, twenty, one hundred, two hundred, one thousand, okay, you get to ten thousand. How far are you going to count? From here on you understand it yourself, continue on your own. Good, so you finished teaching up to ten thousand. Now you, student, start counting. Fine, he starts counting: one, two, three, four, one thousand, two thousand, ten thousand, minus seventeen. Ten thousand and then minus seventeen. So you say to him: I don’t understand, why? We learned how to count. True, we didn’t get past ten thousand, but continue the same idea I taught you up to ten thousand. Yes, I continued, same exact idea. Ten thousand and minus seventeen. How can that be? He says: he understood that the rule is that the decimal system goes until ten thousand, and from there you go back to minus seventeen, and from there you start counting by ten thousands too. Can you rule that out? No, that also fits what was said before. Like what?
[Speaker C] Like those question formulas they ask—there’s a whole column of them—what’s the next number?
[Rabbi Michael Abraham] One, three, five, seven.
[Speaker C] Whatever you
[Speaker I] want.
[Rabbi Michael Abraham] Eleven. Those are primes. Fine, say one doesn’t count, okay. Those are primes, and you think it’s the odd numbers, so you continue to nine—maybe it’s primes. That’s a famous example of two series that have a natural continuation. But in fact, as Wittgenstein said, every series has infinitely many continuations. Obviously. Whatever you want to put at the end of the series, I can build a series for which that will be its continuation.
[Speaker C] Like with any collection of points you put on…
[Rabbi Michael Abraham] Right, that you can fit infinitely many functions through them. Right. Meaning, I can say: you want me to give you one, two, three, four, five, six—tell me what the next number is. Whatever you want, order it up. You want the next number to be minus seventeen? No problem, I’ll organize a rule for you in which in the first place there is… a defined rule, really a rule—not “a rule” in the sense that once you see it it’s a rule, but a formula. All right? Where n equals one gives one, n equals two gives two, n equals three gives three, and n equals seven gives minus seventeen. No problem; that’s seven coefficients, I can arrange such a rule for you. It’s not even terribly complicated. Okay? And if you want complex numbers or minus eight and a third or whatever you want, put it there, I’ll arrange a rule for you. So how is it that when they test someone on the psychometric exam, they tell him one, two, three, four, five, six, seven, complete it. If he writes minus seventeen, he won’t get into university. But if he’s too smart, then he’ll show them: what do you mean, I’m just as right as you are. Why do you think I’m stupid because I wrote minus seventeen? I just think differently than you. What, is it forbidden to think differently from you? On the contrary, I’m creative. You have to accept me into the university.
[Speaker P] Obviously it’s not practical to first teach a child the concept of number and then he’ll know on his own what to do. You no longer need to tell him how much… you don’t need to teach him multiplication tables once he understands the concept of number. You can’t.
[Speaker H] But you can’t.
[Rabbi Michael Abraham] That’s exactly the point. The illusion is that you can really do it through rules, and then everything is clear because he’ll apply them. But how do you explain the rule itself to him? The rule itself you will always have to explain through examples and say “and so on.” So that “and so on” means he’ll have to decide. You can’t avoid it.
[Speaker I] Is there someone who says, for example, that formally you defined this rule. Obviously there are many things that rest on examples, but formally you defined it. If you used other concepts—say n plus one—to explain how to do always plus one. Right, you can build a computer.
[Rabbi Michael Abraham] You can maybe teach a child—no, you can program a child, not teach a child. Because teaching him is always teaching him through examples, and generally
[Speaker I] through examples, and that’s always how we learn. But why is that necessary? Why can’t I tell him…
[Rabbi Michael Abraham] Always. There is no learning not through examples.
[Speaker I] But why is that necessary? What can’t I tell him? I can tell him every time you see the n, look, if
[Speaker Q] the number is written in base ten, with the rightmost digit…
[Speaker I] if the digit is zero, one, two, three, four, five, six, seven, eight… look at the rightmost digit.
[Rabbi Michael Abraham] But you need to explain to him what the rightmost digit is. You need to give him examples of what “right” means. You need to explain to him what it means to add.
[Speaker I] I’m assuming other concepts.
[Rabbi Michael Abraham] No, no, fine, but the concepts… after you assume a concept that was learned by examples, it may be that you’ll succeed in explaining to him using the concepts themselves. Obviously—after I explained to you what n plus one is, now you can put into n whatever you want, n plus one will always give the correct result. But in order to get there, you’ll have to pass through explanations and examples.
[Speaker R] Always. You can’t do without the concept of something that always…
[Rabbi Michael Abraham] Fine, so never mind—but you’ll rely on learning something else through examples. Never mind; in the end there’s always the possibility that he’ll generalize incorrectly and won’t understand you. So he’ll generalize the foundational concepts incorrectly, not what you’re teaching him now. In the end, we learn only through examples. And then Wittgenstein basically says that the claim that there are rules is just an illusion—there are no rules really. There are no real rules in some sense. There are conventional rules. And thank God we are all built similarly, so when I give you the examples and count on you to generalize, you’ll probably generalize more or less like I do. Sometimes not, but I can get you to a point where you’ll generally generalize like I do. And the psychometric exam simply doesn’t test whether you’re talented; the psychometric exam tests whether you think like me. Because if you don’t think like me, I don’t know how to teach you, so rightly I won’t accept you to university—not because you’re stupid. Because you don’t think like me, so what can I do? I can’t teach you. Meaning, in the… it may be that you’re just stupid. But if you put seventeen there and I can show you that you made a mistake—or if you put seventeen there because you built the sequence so that it would come out seventeen—then you’re smarter than those who built the psychometric exam. But if you didn’t build a sequence and you’re just putting… just putting seventeen, then you’re stupid.
[Speaker N] So that means it’s justified to have, say, a psychometric exam when Ethiopians, for example, don’t…
[Rabbi Michael Abraham] It’s justified because you can’t teach them at the university, not because they deserve less or because they’re more stupid. You can’t teach a group that the… they’re not suited to it, so what?
[Speaker E] Someone who doesn’t
[Rabbi Michael Abraham] know Hebrew—he’s a new immigrant, a genius like Einstein, but a new immigrant. Will you test whether he knows Hebrew before accepting him to university? I don’t know. Won’t you admit him? Won’t you test him? Then he won’t enter university because he won’t understand a word. People who don’t know Hebrew don’t study at the university? Only if they teach not in Hebrew. But if they teach in Hebrew, he can’t study at the university. Let them study on their own. Let them study on their own, but at my university they teach in Hebrew. In Hebrew. So you… and it’s not because you’re stupid, it’s because you won’t understand me. If you won’t understand me, there’s no point entering my classroom. And here too, it’s not a language, but it’s basically a kind of language. If you don’t think like me, I’ll have no way to explain things to you. If you’re an alien, then I have no way to explain to you—what can I do? You may be a genius, that’s unrelated, but I have no way to explain it to you, so what will you do in my class? Right? That’s the claim. And Wittgenstein’s claim is a fundamental claim against the existence of rules in general. Meaning, his claim—which of course is also not absurd—is that there is no indication… he cannot say there are no rules. He says there is no indication that there are rules at all. This whole notion of thinking according to rules is a fiction we created. And perhaps it’s just that we’re built similarly, and therefore we generalize similarly, and that’s why rules arise. But who says there are any rules at all, really? This is an attack on the concept of rules itself, not only on the technical problem. Now of course this too itself could just be our limitation, that we don’t understand what rules really are. But maybe there will be some being with a different kind of thought, and there he’ll understand that it’s possible somehow to get directly to rules without going through examples. And he could tell us, “Guys, in my experience there really are rules, only you are limited; you don’t know how to get to them except through examples. But there are rules.” Wittgenstein’s claim doesn’t prove that there are no rules; he proves that there is no proof that there are rules. Meaning, he proves that there is no necessary indication that there are rules.
[Speaker B] What is even the meaning of the question whether there are or are not rules? It’s not—I mean, it’s an abstract concept.
[Rabbi Michael Abraham] The question is whether you work top-down. The question is whether you work from the rules to the examples, or whether you work from the examples to the rules. That’s a very important question; pedagogically too it’s an important question. How to teach, how to understand. When you teach, say, a topic in mathematics, for example, there are lecturers who begin with the theorem and afterward—and many lecturers do this, because that’s how mathematics is structured logically—and then from it solve various examples. In my opinion that’s bad teaching, pedagogically wrong. Mathematics is built that way, but pedagogically it’s a mistake to teach that way. You need to begin with examples. Take an example through which you can understand the idea, and then show the person how I take that idea and create a rule from it, and with that rule I apply it to many places, and there, look—in fact this idea is the rule, and now prove the theorem to him. When you now prove the theorem to him, he’ll understand the logic of the theorem and he’ll be able to follow you. If you prove the theorem to him like a parrot, then he understands the proof like a parrot, but he doesn’t understand what the theorem says, what the logic behind it is. And then what? When he comes to examples, he won’t know how to solve them. And therefore didactically—it’s not a logical question; maybe there is someone who isn’t built that way, and for him it would indeed be right to teach top-down. But generally ordinary human beings need to go from the examples to the rule and not from the rule to the examples. I think it’s a didactic mistake, in my view, to teach that way.
[Speaker I] But that pedagogical question is not Wittgenstein’s question.
[Rabbi Michael Abraham] No, no, it’s a different question. No, but Wittgenstein’s own claim may be that everything he says is only a pedagogical claim. Because he says: we are built in such a defective way that we have no choice; we must go through examples to the rule. But maybe there is some creature built differently, and from its point of view it can grasp the rule directly, not through the example.
[Speaker I] No, but I’m saying that even the fact that we can grasp the rule through examples doesn’t mean it doesn’t exist in many cases. It could still be that in many cases we can build from the rule to the examples.
[Rabbi Michael Abraham] After we’ve grasped the rule, obviously. Once the rule is formed, we learn from it to other examples. But in order to grasp it…
[Speaker I] Not after we grasped that rule—after we grasped some other rules by means of which we learned the rule.
[Rabbi Michael Abraham] Same thing we talked about earlier, doesn’t matter. Bottom line: once you’re already at the stage after generalizations, it doesn’t matter whether of the foundational concepts or of the derived concepts—once you’re after the generalizations, obviously that’s why you create rules, to apply them to further cases. I’m not claiming that a rule is not useful; it’s very useful. But one has to understand that it’s useful—again—in didactics or in these methodological assumptions, not as claims about the world. The fact that we use rules doesn’t mean there are rules. Those are two different things. We use rules because that’s how we’re built. Okay? So the assumption that if we learn
[Speaker I] something in, say, an inductive way or from examples, does that mean it’s something objective? No, I didn’t say it’s not objective, but there’s no indication
[Rabbi Michael Abraham] that it is really true, because some creature built differently could come along and wouldn’t make the rule that way; it would make a different rule here. A rule is a function of how you are built—that’s his claim. Because examples are examples; they can be generalized in many ways. You like straight lines, so you’ll draw a straight line through all the points on the graph, because it seems to you the simplest, the most natural. But if someone comes along with a sinusoidal mind, he’ll draw a sine wave through those points, and to him that will seem the simplest and most natural. So who’s right? Nobody is right. It’s a question of how you’re built, what seems simple and natural to you. Fine.
[Speaker B] That’s a Fourier series. What? A Fourier series, which can represent any function.
[Rabbi Michael Abraham] Very true. Here it’s a sum of many sine waves, but yes. As a result of this, I’m now moving to the character of Jewish law or of the Talmud. In Jewish law itself—and I think I already discussed this too—I mentioned earlier that there is a process of abstraction and generalization in the transition from the Mishnah to the Talmud, from the Talmud to the medieval authorities (Rishonim), from the medieval authorities (Rishonim) to the later authorities (Acharonim), and of course we are getting closer and closer to formal work over the history of Jewish law. Once, the responsum was intuitive, case by case. They would say about a certain case: the law is such-and-such. Today, maybe because we have less intuition—that’s what I discussed—when a case is brought to me, I have to analyze it: which rules does it belong to, apply some set of rules to it. And this is a process happening over history, that more and more we move from thinking about cases, from casuistic thinking, to positivistic thinking, thinking through the application of rules. And then of course it’s no wonder that only in recent generations people understood that there are paradoxes, and how you can get caught in loops. You won’t find these loops in early literature. There’s a Tosafot about a loop involving someone who divorced his wife—I think I mentioned this—there is a case of someone who divorced his wife on condition that she not marry so-and-so. So she married someone else, all right? Then that man divorced her, and then she married the original so-and-so. She violated the condition of the first husband who divorced her. She had three husbands, yes? The first husband divorced her on condition that she not marry so-and-so. She went and married someone else—that was all fine. But after she divorced that someone else, she married so-and-so, the one specified in the condition from the beginning. The moment she married him, then the divorce was not valid. And if the divorce was not valid, then she was not married to the someone else, because she was a married woman; betrothal does not take effect with a married woman. If she was not married to the someone else and she is married to the first one, then she also was not married to so-and-so, because the betrothal does not take effect for her—she is a married woman of the first one. But if she did not marry so-and-so, then she did not violate the condition. If she did not violate the condition, then she is indeed divorced from the first one. So if she is indeed divorced from the first one, then she did marry the someone else and is also married to so-and-so. Why do you need the someone else?
[Speaker I] So that there will be an interruption.
[Rabbi Michael Abraham] Maybe you don’t need the someone else. Then it creates problems with the mamzerim—that is, she has children from him and then the question is whether the children are mamzerim. But yes, I don’t think you need the someone else here. There are various paradoxes where you also need the someone else. In any case, that’s an example. Tosafot there puts a finger on it—Tosafot in tractate Gittin. But again, that’s—or there’s Tosafot talking about, I also mentioned, one’s lost object, his father’s lost object, and his rabbi’s lost object.
[Speaker K] His rabbi’s lost object and his
[Rabbi Michael Abraham] father’s lost object, his own lost object and whose takes precedence, and the honor of his rabbi and the honor of his father. The honor of his father. Yes. Tosafot also makes some kind of loop there. I’m saying these are the first buds where people start to see loops. And why? Because Tosafot is already late enough to begin thinking in terms of rules. Once you think in terms of rules, you begin to see that those rules can, in certain situations, enter into loops. And in the later generations, of course, Asaf—we collected, in one of the books on logic, many such loops. There are rules, but rule A is primary; in the Mishnah there are few, in the Talmud there are more—it’s an initial stage, and the rules themselves are still not formulated enough. Once you conceptualize the rules, suddenly you see that loops begin to form. And the process I described earlier is also a process of the formation of loops, not only a process of moving to rules, because these are two sides of the same coin.
[Speaker O] And the principle of conflicts between rules is
[Rabbi Michael Abraham] to step outside the rules and, in effect, go back—make a regression of this process backward. We are constantly working, constantly moving toward more and more rule-based thinking, but then we also get tangled up in more and more cases. And when things get tangled up, you have to understand that working through rules is really a kind of approximation. And we need to go back, step outside the rules, ask how the medieval authorities (Rishonim) or the Amoraim would have thought about this, and basically try to apply that to the situation. Step outside the rules, discipline them, qualify them, exactly like the examples I gave about “the finder from the new” or various things of that kind. And actually I think I spoke about this not so long ago regarding the question why the Talmudic text is built in such an associative way. Why, why doesn’t the Talmudic text give the principles and instead bring examples? Give the principles and I’ll apply them myself. Because the Talmudic text understood what Wittgenstein understood much later: that rules—if you give me the rules, you bind me. Give me the examples; that’s much better. Once there are rules, you’ll apply them everywhere, and you’ll probably apply them incorrectly. I think I mentioned a few examples; maybe I’ll bring two or three more and we’ll finish with those. The Talmudic text in Kiddushin says: “We do not derive from general rules, even in a case where ‘except’ is stated.” Every positive commandment dependent on time, women are exempt from, except for three or four examples. So the Talmudic text says: but what about Hakhel? There is another example. “We do not derive from general rules, even in a case where ‘except’ is stated.” Don’t make too much of it. What does that mean? After all, if they tell me every positive commandment dependent on time, women are exempt from, then you say, fine, except for a few exceptions—they didn’t go into all the details, that’s the general principle, there are a few exceptions, I get it. Now the Talmudic text says even more than that: even in a case where ‘except’ is stated. They tell you every positive commandment dependent on time, women are exempt from, except for A, B, C, and D. Then they say yes, but there’s also E, there’s also E—don’t make a big deal out of everything. What? You’re already stating the exceptions too? So if you’re stating the exceptions, then say the fifth exception also—why only the first four? That’s really strange. If you only state the rule and there are a few exceptions, fine, I understand—you didn’t go into the exceptions, you gave the rule. But “even in a case where ‘except’ is stated”—and notice, the Talmudic text understands that when ‘except’ is stated, that’s even worse, and still the Talmudic text says: “We do not derive from general rules, even in a case where ‘except’ is stated.” To me it’s laugh-out-loud funny what’s going on here. They’re basically telling you: guys, what we’re trying to teach you is—don’t make too much of rules. And therefore we will deliberately confuse you, so that you learn not to treat rules too seriously—not too seriously. Obviously we need rules, but always know that rules also need to be thought about. Rules are not—for automatic application. We’re not computers. The Talmudic text—let’s maybe put another example—in Bava Kamma: “There are four primary categories of damages: the ox, the pit, the grazer, and the fire. This one is not like that one, and that one is not like this one,” and it gives characteristics for each of the primary categories of damages. On page 6 the Talmudic text says—sorry, the Mishnah concludes, the first Mishnah in Bava Kamma concludes: “What is common to them is that it is their way to cause damage, and they are your property, and their safeguarding is upon you; and when they cause damage, the one who caused the damage is liable to pay compensation from the best of his land.” “They are your property” is the Rif’s version. “Their safeguarding is upon you; and when they cause damage, the one who caused the damage is liable to pay compensation from the best of his land.” And the Talmudic text on page 6 asks: “What does the common denominator come to include?” What is that coming to include? Who needs this? Because it’s absurd. Instead of giving me the four primary categories of damages and all kinds of examples and explaining why this is like that and not like that, just tell me the principle! What’s the principle? That anything that is your property, or whose safeguarding is upon you, when it causes damage the one who caused the damage is liable to pay compensation from the best of his land. Just tell me the principle and leave me alone with all the examples and all the… I’ll derive the examples from the principle. Now for once the Mishnah does us a favor and also gives us the principle, not just the examples—so what does the Talmudic text ask? Who needs the principle? There are examples. The opposite! For once they did you a favor and told you the principle, so say: why did you bring the examples? You already did me the favor of the principle; why didn’t you do that everywhere? But here you already did it, so why do you need the examples? The Talmudic text says no, of course not—“What does the common denominator come to include?” Who needs the rule? I have examples. Because the Talmudic text wants to tell me: guys, leave the rules aside. The rules are an approximation; you have to be very careful with them. Don’t take them too seriously. Even when I say rules—okay, “your property and its safeguarding is upon you”—well then a bailee should also have to pay when the animal deposited with him causes damage. Why? “Your property”? So it’s not his property? Only “your property and its safeguarding is upon you” means he has to pay. What about a robber? Even though I already mentioned this in Kuntras Kohen, what about a bailee? Fine, because a bailee is also like an owner—that’s what Tosafot say, no matter, several medieval authorities (Rishonim) say that. What does that mean? So do you need ownership or not? You need ownership in general, except in cases where you don’t need ownership. In short, don’t make too much of everything. Okay? Moving on.