Quantity and Quality – Lesson 3

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[Rabbi Michael Abraham] That the Holy One, blessed be He, should repent for the fact that He put me in a situation where I was forced to override the Sabbath in order to save a life. And as part of that repentance, I also need to take upon myself never to repeat this sin again, as is well known, right? So as part of the repentance, should I take upon myself that next time something like this happens, I’ll leave the person there to die? It’s like Eli Yishai’s apology in the hospital. What? Yes, exactly the same thing. He shouldn’t say he’s sorry, and he shouldn’t talk nonsense. It’s exactly the same here. There’s no such thing; it makes no practical difference.

So where do people say there is a practical difference? The practical difference is in the scope of the permission. Can you do things that aren’t really necessary for saving a life, but only make things easier for the patient? Or, for example, in cases where—do you have to minimize the prohibition, or can you do whatever you want, with no need to try to do the least severe option first, and all sorts of things like that? But even that isn’t a practical difference; I don’t agree that it is. Because obviously the Sabbath isn’t ownerless when there’s a patient. If there’s a patient, am I now allowed to watch a soccer game? No. A soccer game isn’t even a prohibition. To buy a ticket… what’s the practical difference? The practical difference is only when the thing is needed for the patient. Needed for what? To heal him.

Now, if I have carrion or Sabbath violation, and let’s say carrion is lighter than Sabbath, and therefore if I need to minimize, better carrion. If I don’t need to minimize, then do whatever you want, like Arik suggested earlier. That’s not true. Because what they permitted me is what is needed to save the patient. But it wasn’t necessary to slaughter on the Sabbath in order to save the patient; I could have saved him with carrion. So even according to the side that says it is entirely permitted, it still isn’t true that you’re allowed to slaughter. Why? Because if it’s entirely permitted, what was permitted? What was permitted is what’s necessary—not just anything whatsoever. But this isn’t necessary. So the contrast between lighter and more severe only reflects the question whether this prohibition is needed at all. If it’s needed, then of course it’s permitted. But if it’s not needed, then just because it’s entirely permitted doesn’t suddenly mean everything is totally allowed. What difference does it make whether it’s “entirely permitted” or “pushed aside”? In my opinion there’s no practical difference at all; it’s some invented conceptual distinction.

But that still isn’t the full formulation of the “pushed aside” position. Meaning, in the “entirely permitted” view, it doesn’t mean that on the Sabbath I’m allowed to fly to Copenhagen for fun. No. It means that in that action where you are saving the patient—the action you need to do—you don’t need to violate something… you don’t need to commit a transgression. But can you do it through whatever transgression…? Why? What suddenly justifies that? There’s no logic in it. No logic at all. Meaning, if you need to do the severe transgression, then it’s permitted, no problem. But if you don’t need to do it, because you have the option of saving him without that transgression or with a lesser one, then why assume that it’s permitted? Because the assumption is that when you commit a transgression in order to save the patient, you’re not really committing a transgression. But he isn’t doing it in order to save the patient. Why not? Because I wanted to save him with carrion. But that too… fine, that too is a transgression, it’s not that it changes the fact that I’m saving the patient. No, it does change it. If I can save him by means of carrion, then to say that he just feels like eating pork for pleasure. I don’t need this in order to save the patient, so I’m not doing it for the sake of saving the patient. There is no logic in saying “entirely permitted.” If I can save in some other way, then that means I’m not doing this for that purpose. Yes, obviously.

Why are you doing it for that? This is a topic—now I’m remembering—a topic in tractate Pesachim. You know the case of “it’s unavoidable and he doesn’t intend it,” in Pesachim 25. The Talmud discusses a case where I have two roads to get to my destination. I need to get somewhere, and on one of the roads there’s an idol shop, and if I pass there I smell the scent of idolatry. It’s a topic in tractate Avodah Zarah, I think, but the medieval authorities also bring it in Pesachim. And I have a route that passes by that idol shop. The Talmud says—and by the way, that’s how Jewish law is ruled—that if I want to go there, “it’s unavoidable and he doesn’t intend it.” What does that mean? I want to reach that place—not to save a life, just because I feel like being there, I’m going there for a stroll. Fine? And the route with the idol shop is a little shorter, two meters shorter. Fine? Then it’s permitted for me. I’m allowed to go that way even though I’m violating the prohibition of deriving benefit from idolatry, a Torah-level prohibition. It’s permitted. Why? Because that’s called “unavoidable.” What do you mean unavoidable? Go that way—it’s two meters longer—take the other road.

The point is that… wait, one second… no, the other way around: if it’s two meters longer with the idolatry, then I’m forbidden to go there. If it’s two meters shorter, then it’s permitted, because I don’t intend it. So why, if it’s two meters longer, is it forbidden? After all, I still don’t intend it. I want to get to my destination, not to the idolatry. The simple answer—at least that’s how I understand the topic—is that if I go by that road and it isn’t shorter, then why did I choose it? I chose it in order to smell the idolatry. Don’t tell me I don’t intend it—I do intend it. In other words, if I have a more convenient option and I choose the less convenient one, then don’t tell me I’m occupied with saving a patient; I’m occupied with violating the Sabbath. Because if you wanted to save the patient, you could also save him with carrion.

That’s not an option—pork isn’t an option. What? One time I would use carrion. It’s like if I need to take a tabernacle… What difference does it make, pork or carrion? Carrion isn’t an option. You have to violate a prohibition in order to save him—fine. Anything where there’s an option to save him without a prohibition, or whether to slaughter or use carrion—you have to violate some prohibition. So why slaughter? You could have saved him with carrion. You choose to slaughter—why are you choosing to slaughter? In order to save him? But this is exactly like “it’s unavoidable and he doesn’t intend it.” To save him, carrion would have been enough. So why did you choose slaughter? Because you want to slaughter, not because you want to save him. You’re violating the Sabbath. Why? Maybe that’s the normal way to do it on the Sabbath? No, actually pork is the normal way. If doing that would make you suffer, walk a much longer distance, or exert yourself a lot—I don’t know. A very long distance, to my mind, here is equivalent to a more serious prohibition. Once you’re doing a more serious prohibition when you could have made do with a lighter one, then the act… you’re not really doing it in order to save him, because you could have saved him with the lighter prohibition. So why are you doing it? You’re doing it because you’re a transgressor; you want to commit the prohibition. No, that’s forbidden. It’s not for the patient’s sake; it’s for the sake of the prohibition. You just have some evil urge to slaughter. Yes, an evil urge to slaughter—you want to violate the Sabbath, and you’re using the patient as an excuse to violate the Sabbath. Why would you do that? Why are you doing it? Because he’s disgusted by carrion? That’s something else; then it could really be permitted. Who says not? That’s a halakhic consideration. Right now I’m talking about a case with two options—a severe prohibition and a lighter prohibition—with no additional considerations. If there are additional considerations, we’ll discuss it differently. But if there aren’t, then why are you doing it? You’re doing it because you’re a transgressor, using the patient as an excuse.

Fine, but this discussion is less important for our purposes. So the Rosh says—yes, this is only… I’m just noting all this in parentheses. It has practical implications for the questions of the Achiezer, a responsum he brings there, Mishnat Chachamim, where he says… and there too there’s some story involving surgery—who should violate the prohibition? Let’s say I need to do something to myself that could kill me, the patient, or the doctor. So he says maybe one should have a non-Jewish doctor do it or something like that so that he won’t transgress. The Achiezer rejects that entirely, but there too… I don’t remember, I need to look there again. There too the claim came up: no, we do not introduce considerations of who will commit the transgression. That isn’t a consideration at all; once there is life-saving, it makes no difference. And then he brings various possibilities here, quite a few positions of medieval authorities. This is a topic a lot of medieval authorities discuss.

What matters to me is the well-known Ran on this topic. Wait—what is the logic of eating carrion as opposed to slaughtering and not eating carrion? What? Now he brings the Ran. The Ran writes—there are other reasons too—but the Ran writes the reasoning that… I think the Shulchan Arukh says to give the carrion. He rules, I think, that one should give carrion in practice. But the Ran writes to slaughter, and a great many intricate analyses were written about his reasoning; it’s very beloved in the yeshivot.

And the Raavad, of blessed memory, was asked in these words: If there was a dangerously ill patient and one needed to slaughter a chicken for him, why should we not tell a non-Jew to stab it and feed him carrion, which involves only a prohibition of a negative commandment, rather than slaughter and override the Sabbath, which involves a prohibition punishable by stoning? And he answered: What prohibition is standing in this patient’s way and preventing him? Surely the prohibition of the Sabbath, not the prohibition of carrion. That’s on someone who slaughtered while an adult stood over him—I don’t remember, does that not help? I don’t know, really not.

Fine, so he says: “And he answered: What prohibition is standing in this patient’s way and preventing him? Surely the prohibition of the Sabbath, not the prohibition of carrion.” Fine, these are problematic things; the Rosh also brings this reasoning. It’s a difficult argument. And I am astonished, he rejects it, but it seems to me that with respect to a patient, the prohibition of carrion is no lighter than the prohibition of the Sabbath. For even though carrion is only a prohibition of a negative commandment and the Sabbath is punishable by stoning, there is another stringency in carrion, because the eater violates a negative commandment for every olive-sized amount he eats. As we say regarding a Nazirite who was drinking wine: if they said to him, “Don’t drink, don’t drink,” and he drank, he is liable for each and every one. But with regard to the Sabbath, he violated only at the moment of slaughtering, and there is only one prohibition, since the products of Sabbath labor are permitted. Afterward, the product of Sabbath labor—you can take it; it’s only the product of Sabbath labor. For we hold: “It is holy, but its products are not holy.” Therefore the many prohibitions involved in carrion are not considered lighter than the single Sabbath prohibition, even though it is punishable by stoning.

What is he saying? He is basically saying—and this is the example brought also by the Avnei Milu’im, and from there he goes back and forth—that when you violate the prohibition of carrion, you violate a prohibition for every olive-sized amount, in fact for every half-olive-sized amount, because even less than the formal measure is forbidden by Torah law. So for every olive-sized amount you violate a prohibition, whereas in slaughtering you violate one prohibition when you slaughter, and after that the eating is permitted—assuming he doesn’t also cook it and do a few other things, that he eats it raw, I don’t know exactly, and somehow the blood was removed, or there are many other things there that I’m not exactly clear how one gets rid of. But right now we’re talking on the conceptual level. So he says that the quality of the prohibition—the Sabbath prohibition is qualitatively more severe because it is a more severe prohibition—is overridden by the quantity of carrion prohibitions, which apply to each and every olive-sized amount, even though each is lighter. So quantity outweighs quality. That’s basically what he says.

What? If this patient needs only half an olive-sized amount? Then according to the Ran it may really be preferable to give him the carrion, yes. And he could do like on Yom Kippur, where we give less than the required amount at long intervals, and then the… Less than an olive-sized amount is also a Torah prohibition; less than the formal measure is forbidden by Torah law. Yes, and still on Yom Kippur they tell you to eat less than the required amount. Yom Kippur is another question. First of all, because it’s lighter than a prohibition that carries a punishment, but it’s still a Torah prohibition. Rabbi Yohanan and Reish Lakish about less than the formal measure. Secondly, Yom Kippur is not at all a prohibition in the object itself; it may be that there there is no prohibition of less than the formal measure at all. But here we’re talking about eating something prohibited, a prohibition in the object itself.

In any event, the Ran is basically deciding here that a larger quantity outweighs a higher quality. And that is the basis—this is where the Avnei Milu’im begins. He brings many more sources and discusses them in various directions. But as I said earlier, the different sources lead to opposite conclusions. There are sources where quantity comes out superior, and sources where quality comes out superior. Here, for example, everybody brings this Ran and analyzes it. I’ll bring you just one example from the Sha’agat Aryeh in particular. You know the well-known intricate analysis? We just passed Purim, but never mind—it’s important for next Purim.

Abraham our forefather, yes, or Isaac, where they came and said: “There is no God in this place, and they will kill me. Please say you are my sister, so that it may go well with me because of you, and my soul shall live because of you.” Meaning, that they would kill Abraham so as not to violate the prohibition of a married woman. And in the yeshivot, of course, they ask: what is preferable, the prohibition of murder or the prohibition of a married woman? If they kill Abraham so as not to violate the prohibition of a married woman, what have they gained? Let them violate the prohibition of a married woman and not the prohibition of murder. And then they explain it according to this Ran. Why? Because if you violate the prohibition involving a married woman, then every act of intercourse is a prohibition; but if you kill Abraham our forefather, that’s one prohibition, and after that you can sleep with her as many times as you like. So according to the Ran, that has major practical consequences. I assume there are even people who said this seriously. You know, with these intricate analyses, sometimes people actually say them seriously, because the claim is that when the Torah wrote it this way—like Vashti and Ahasuerus participating in a dispute between Rabbi Akiva Eiger and the Noda B’Yehuda, all these Purim analyses—there are people who want to make such a claim seriously, because the claim is that the Torah, by writing in this way, is coming to teach us some halakhic idea, sort of. Maybe it’s the Ran—but of course that’s nonsense.

In any event, one more side note—someone once spoke about this with me, maybe in Ra’anana—that people bring proof here from an opinion that was not accepted in practice, because the Shulchan Arukh ruled not like the Ran. He ruled that one feeds carrion and does not slaughter. In practice, the Ran’s reasoning was rejected in Jewish law. Maybe it was because of what Maimonides said, that one must also salt the meat? Did you ask him? Right—here you can say that the question is why the Shulchan Arukh ruled not like the Ran. Did he accept the Ran’s reasoning, but for some other reason still rule against him? Very often people bring proofs from an opinion not accepted in practice, when the claim is that the one who ruled against that opinion did not disagree at this point, but at some other point—or at least the burden is on the person who claims that the dispute is specifically on this point. Because here there is an opinion that certainly says quantity outweighs quality. That is definitely what the Ran wrote. Now if the Shulchan Arukh disagrees with that specifically, or with something else, you don’t know. So uncertainty does not override certainty, and the assumption is that the Shulchan Arukh also says this, and disagreed on another issue. Fine, one can also argue with the reasoning.

I didn’t understand the Ran’s answer, though—how does he know how much an olive-sized amount is worth? He doesn’t make distinctions. His assumption is that once the quality is lesser, then once the quantity is larger, it doesn’t matter what the gap in quality is—the Torah wanted to establish a line. There’s no way to measure it. There’s no way to measure, so the bare number says: you need to establish a line. So when something has higher quality than something whose quantity is larger, quantity decides. No matter what the quality gap is. The question is also how much the patient needs to eat: if he needs to eat two olive-sized amounts, one and a half, three olive-sized amounts… no, this is years… I mean, I don’t know, the reward for commandments is seven, seven and a half… I’m just adding. Same thing—you’re asking how you determine the qualitative gap; I’m asking how you determine the quantitative gap. That too—how much does the patient need to eat? One olive-sized amount, one and a half, two, three—from when is he speaking? Why would three olive-sized amounts no longer be little for a patient? I don’t know how much meat he can eat. Depends how sick he is. We moved from Purim to Passover now.

In any event, in short, I think the Ran wants to say that there is some line according to which quantity outweighs quality, and we’re not getting into… Obviously there’s room here to take that into account, but we have no tools to determine it, and you need to establish some halakhic line, and he claims that this is the halakhic line. So in any event this Ran is a very well-known source for the idea that quantity outweighs quality. As I said earlier, this is a source that was rejected from practical Jewish law. And all those who bring a source from the Ran apparently understand that those who disagree with him did not disagree with this reasoning, but because of other considerations. Fine. Or that the practical halakhic ruling binds us on the specific point, but does not bind us regarding the reasoning behind it.

Fine, but still, when you need to bring proofs, you can’t bring proofs from an opinion that was not accepted in practice. Really not. If it’s only proof that such a possibility exists—fine, even I know such a possibility exists—but the question is what Jewish law says. When you… So that’s the question whether the Avnei Nezer, on Torah-level matters—that’s a big question—when the Avnei Nezer investigates whether quality outweighs quantity, is he claiming that there is one question here, and all the sources are proofs in one direction or the other, but in the end you need to decide, and the decision must be consistent? If I decide that quantity outweighs quality, then in all the topics I need to be consistent, and if not, then not. He gathers all the sources into one bundle, for whoever wants to analyze this topic, but he doesn’t claim that it really is the same question, because he doesn’t even bother to reconcile them. So apparently he isn’t claiming it is the same question.

There’s a similar question—I’m remembering now—where it comes up very strongly. There is a dispute in the methods of interpretation: Rabbi Ishmael and his school interpret by general and specific terms, while Rabbi Akiva and his camp interpret by inclusion and exclusion. Fine, that’s a different interpretive method; it doesn’t matter, I’m not going into what exactly it means. But these methods lead to different halakhic results. And these methods are disputed in many places. Every place where Rabbi Ishmael interprets by general and specific, or general-specific-general, or specific-general, in every such case Rabbi Akiva reaches a different result because he interprets by inclusion and exclusion, or inclusion-exclusion-inclusion, or exclusion-inclusion—he interprets differently, and the result is different, and this appears in the Talmud in many places. Okay?

Now, in Maimonides, if you check, there is no consistency. There are places where he rules—and it’s not always Rabbi Akiva and Rabbi Ishmael themselves; sometimes it’s the school of Rabbi Ishmael and the school of Rabbi Akiva, meaning students, like Rabbi Yosei HaGelili for example, or their disciples who follow their methods of interpretation. And if you check Maimonides, there is no consistency at all; there are outright contradictions. There are places where Maimonides rules like the interpretive method of inclusion and exclusion, and places where he rules like general and specific. That really is a big question, because there it’s clear that this is one thing. Meaning, if you accept that Rabbi Ishmael is right, that one should interpret by general and specific, then what does it mean that there you rule like the one who interprets by inclusion and exclusion? There it really is one thing, because that is exactly what they disagreed about. The Talmud says that they disagreed over whether to apply the tools of general and specific here, or the tools of inclusion and exclusion. So if you think like Rabbi Akiva here, then here Rabbi Akiva, and there Rabbi Ishmael? There you definitely need some sort of alignment.

I think that there one has no choice but to reconcile it. And H. L. Strack writes this in his book about the school of Rabbi Ishmael and the school of Rabbi Akiva—two volumes, his most well-known book. He writes there that apparently in later generations there were already combinations, meaning schools arose that sometimes interpreted by general and specific and sometimes by inclusion and exclusion, and certain rules developed for when to apply this and when to apply that. The history of the methods of interpretation is a fairly complex history. And therefore it may be that there is a consistent method that sometimes uses this and sometimes that, with rules for when to use each.

There is another question—I’m now reminded of it—in connection with the Shulchan Arukh. There are contradictions in the Shulchan Arukh, and there are later authorities who claim that one does not need to reconcile contradictions in the Shulchan Arukh. After all, the Shulchan Arukh is a summary of the Beit Yosef. It was not intended to be consistent; it was not intended to establish one uniform halakhic method such that if there is a contradiction you need explanations. It summarizes what emerges from the Beit Yosef. He didn’t mean necessarily to be systematic. After all, it’s a book built on the Tur, right? It is a commentary on the Tur. There he brings all the positions of the medieval authorities, fine. And in the Shulchan Arukh he gives a digest: there is this view, there is that view, it seems like this, it seems like that. But he does not mean to decide Jewish law according to those methods. He is simply trying to summarize a bottom line. So he brings what is common; sometimes he also brings “some say.” Fine? When he brings “some say,” that is not a final halakhic ruling, because he brings “some say” and the medieval authorities go this way. And then that basically means that you do not need at all to reconcile contradictions in the Shulchan Arukh, because that was never his goal. I don’t think that’s correct, by the way. I once saw such an approach. There was an article about this once in a journal published by the son of Rabbi Nissim’s grandson, Professor Nesiyahu or something like that, who once wrote in some article that he argues this claim. I think that’s where I saw it.

And that’s a bit difficult, because the Shulchan Arukh itself writes that it decides Jewish law according to the majority among the three—Rif, Maimonides, and the Rosh. I think he does mean here to decide Jewish law. Fine, it doesn’t matter. I’m speaking on the conceptual level. But if it really is one question, then when there are contradictions they need reconciliation. Meaning, here too, with quantity versus quality: if I claim there is one question here, and there are sources suggesting quantity decides and places suggesting quality decides, then I need to explain when yes and when no.

But here there is no reason to assume it is one question, unlike general-and-specific versus inclusion-and-exclusion. Why? Because it may be determined by the subject matter. For example, in the realm of wisdom we are searching for truth. So if we are searching for truth, then quality may determine, because quality aims at truth better than quantity does. In the matter of prohibitions, then it’s just a question of the weight of prohibitions—which matters more, quantity or quality? That may be something entirely different. So the fact that in all these places it looks like a clash between quality and quantity doesn’t mean it’s the same question.

But I want to claim more than that: the concepts themselves—here philosophy comes in—the concepts of quality and quantity themselves actually do not have one single meaning. Not only is the question not one single question. What is even the definition of quality versus quantity? What is quality and what is quantity? What is the difference between quality and quantity? That is not a simple question. And there are places where things we would call quality are called quantity, and vice versa.

Seemingly we are really talking about—let’s say the religious court, fine, that’s where I started. Do we follow the majority in wisdom or the majority in people? The tendency among later authorities is to present this as if it were a quantitative majority versus a qualitative majority—which is decisive. But why is wisdom quality and feet quantity? Seemingly this is quantity and that is quantity. It is quantity of an abstract thing and quantity of a concrete thing. Quantity of wisdom or quantity of people. But an abstract thing has no quantity—you can’t quantify wisdom. Why not? Why not? Listen, there’s an IQ test. If I can’t quantify it, how do I rank who is smarter than whom? Look—I can. It’s not something you can say you measure one against two—what is the majority? It’s not… Why? But clearly you can. Meaning, the one who says qualitative majority decides is also saying it can be measured. The halakhic question is only whether that is in fact the majority one should follow. There is no question whether I can measure it. Even the one who disagrees does not say it’s because it can’t be measured, but because it will lead to quarrels, since it is not always clear. In places where it is clear, it can be measured. And still Jewish law may say we do not follow that—not because there is a problem measuring it.

And I am asking what the definition of quantity versus quality is at all. Why does wisdom look to us like quality and number of people look like quantity? Is it because one is abstract and one is not? What would you say about time? Is that quantity or quality? If I say how much time has passed. That’s quantity, no? I think so. So if that’s quantity, then an abstract thing can also be quantity, not only something tangible, not only something concrete. So what is the difference between quantity and quality? Quality has a quantitative aspect, while quantity has no qualitative aspect. What does that mean? You said one can quantify quality, but one cannot “qualify” quantity. What does “cannot” mean? It’s the same thing. What do you mean “quantify quality”? I don’t quantify quality; I quantify quantity. I think there is no such thing as quality. What is it to quantify quality? There is no quality. Wisdom is quantity—a quantity of an abstract thing. I claim there is no such thing as quality at all, so don’t look for symmetry. Rather, it’s a quantity of an abstract thing. Why is that different? What’s the difference between wisdom and time? Both are quantities of abstract things. What, does quantity not apply to an abstract thing? Fine, so that’s already a more conceptual question.

This is brought by Rabbi Kasher there in his book in the name of Shlomo Maimon in Givat HaMoreh. Shlomo Maimon was a very interesting Jew, a well-known philosopher who in his youth studied in yeshivot and later left, but he called himself Shlomo Maimon after Maimonides. He was one of Maimonides’ admirers. He wrote a work called Givat HaMoreh on Guide for the Perplexed. A very interesting Jew. He lived at the beginning of the nineteenth century, or something like that, a relatively early period.

In any event, Shlomo Maimon’s claim—which in one form or another I think is already found in Aristotle—is that by increasing quantity, the quality does not change. That is the definition. If there is a magnitude such that adding more and more quantity does not change it, then that magnitude is called quality. Now think about, say, the temperature of water. Add more and more water at the same temperature, and the temperature does not change. So temperature is the quality of the water. Add more and more people with the same level of wisdom, and the wisdom does not change. It doesn’t matter whether I have ten people at that same level of wisdom or two people at that same level of wisdom. In other words, the quantity of wisdom here doesn’t change. So those things are called quality and not quantity, because they are things that do not change when quantity is increased.

This basically parallels what is called in physics extensive and intensive quantities. I brought here from Wikipedia: an extensive quantity is a physical quantity proportional to the amount of matter in the system it describes. By contrast, an intensive quantity is a physical quantity whose value is independent of the amount of matter in the system. If two identical systems are combined, the extensive quantities will double in value for the new system, while the intensive quantities will remain equal to their value in the systems that composed the new system. These are concepts from thermodynamics. Examples of extensive quantities are volume, number of particles, mass, electric charge, energy, heat capacity, entropy, and so on. For example, yes? Number of particles. If there are a thousand particles in each of two systems, then in the combined system there will be two thousand particles, right? So when quantity is added, that quantity also increases, and therefore it is extensive. By contrast, temperature: if you take two systems with the same temperature, the temperature of the combined system remains the same as that of the two parts, so it is intensive. Okay? So perhaps also heat capacity, or all sorts of divided quantities. For example, if I want something per unit volume, that turns it from extensive into intensive. Because if it is per unit volume, then it does not change when quantity is increased; you simply divide by the doubled quantity. That is in fact why specific quantities are always defined in physics. Specific quantities are simply a means of turning extensive quantities into intensive ones.

In any event, Shlomo Maimon’s distinction is seemingly equivalent to that distinction. An extensive quantity is basically quantity, and an intensive quantity is quality, because it does not change with increase in quantity. But it seems to me that this is not correct. Before that, let me bring a halakhic example.

There is, for example, the law of less than the formal measure. And in the Talmud, in tractate Yoma, two sources or bases are brought for the law of less than the formal measure. One basis is “all fat, all blood”—“all fat” means all fat; the Talmud expounds “all” to mean any amount. In other words, even a tiny amount, even less than the required measure, is a Torah prohibition. And in Jewish law we rule that less than the formal measure is a Torah prohibition. Another source brought there in the Talmud is the logic that it is fit to combine. Rabbi Shimon Shkop explains this logic as follows: take half an olive-sized amount of pork, add another half-olive-sized amount of pork, and the result is an olive-sized amount of pork. Now in an olive-sized amount of pork there is the full prohibition, right? It is prohibited fully, and one could receive lashes for it and so on. Now since the difference between the half and the whole is simply that you took the half twice, that means that the half contains the same quality of prohibition that the whole has; the difference is only quantity. Therefore Rabbi Yohanan forbids it by Torah law, this less-than-the-formal-measure case. Because he is basically saying that the quality of the prohibition exists even in the half. If you take the same thing twice, nothing new is created; the intensive quantity did not change at all, only the extensive. Right? The quantity increased, but it is the same pork as before—there is just more of it. So if in the larger amount there is prohibition, then the half too has the quality of the prohibition. Therefore, says Rabbi Yohanan, it is a Torah prohibition. The requirement of quantity is only for lashes, but the prohibition is determined by the quality of the prohibition. And therefore less than the formal measure is forbidden by Torah law. That is really the same reasoning as Shlomo Maimon.

But as I said earlier, I do not accept that. “The law of a perutah is like that of a hundred” is exactly because of this point: when you sit in judgment, what matters is the quality of the thing you are judging, not its quantity. And if you are judging money, then it makes no difference whether it is a perutah or a hundred, because a perutah is money and a hundred is money, because clearly a hundred perutot make money. So what difference does it make whether it is one perutah or a hundred? It is the same reasoning as less than the formal measure.

Though there is a Rashi in Sanhedrin that speaks about theft of half a perutah, where the question is whether that is less than the formal measure or not. There is the Maggid Mishneh and Rashi—whether there is a law of less than the formal measure in money. I no longer remember who says what; there is a Rashi in Sanhedrin against the Maggid Mishneh. And the claim of one of them is that half a perutah is not money at all. And that is a bit difficult for Rabbi Shimon Shkop’s reasoning, because if you take that half-perutah and add another half-perutah, that will produce money. But perhaps this is related to the fact that money is entirely conventional. Money is purely a matter of agreement. Therefore the decision is obviously conventional: if we decided that a perutah is money, then less than that is not money. There is no special quality here; in money there is no quality, nothing at all in the money itself, only convention. Yes? “A coin is form, and form is liable to be annulled,” as the Talmud in Bava Kamma says, right? A coin is form. We spoke about this in one of the previous lectures.

But why don’t I think this distinction between quality and quantity is correct? Because what are you saying? Let’s go back to the court. You say to me: add another five judges, each with an IQ of 100, fine? You’ll still have wisdom at a quality level of IQ 100. So what difference does it make how many judges you added? First of all, since the level of wisdom is the same, Sefer HaChinukh tells us that the majority is more likely to hit the truth than the minority, right? So three sages of the same strength are more likely to reach the truth than two sages of the same strength. So adding quantity does in fact change the overall wisdom, right? That’s one point.

Second, I could phrase the same thing the other way: if you add IQ to one person, the number of human beings has not changed, but the amount of IQ has changed. A sign that IQ is the quantity and the person is the quality; the number of people is the quality. It’s simply begging the question. You assume that the human beings are quantity, and then you say that what does not change when I add quantity is quality. But who said the human beings are the quantity? Maybe wisdom is the quantity, and then number of people would be quality. Because plainly, if I add more wisdom to the same person, the number of people does not change. You’re assuming what needs to be proved. In other words, we go back to the original question: why did you assume that this is quantity and that is quality?

Fine, this question bothered me quite a lot, until I heard some lecture in Yeruham, and luckily I didn’t fall asleep. There was a lecture there by the rabbi on Friday evening, on the Mishnah Berurah, a halakhic-type lecture—the kind where you know people always fall asleep, that classic sort of lecture where everyone sleeps. But for some reason I was awake in that lecture, unusually. And what? “And on that night the king’s sleep fled.” It was probably about a human king that time, not the King of the Universe.

And there he said the following. He brought, I think, Moshe Feinstein, who argued that it is permitted to measure temperature on the Sabbath. That one may measure temperature on the Sabbath—that’s what Moshe Feinstein claims. And he was puzzled by this, because after all measuring is prohibited, a rabbinic prohibition. There is a prohibition of measurement on the Sabbath, that one may not measure things on the Sabbath. And if you would say that temperature is an abstract thing and there is no prohibition of measuring it—measuring means kilograms, measuring the length of something, tangible things, not abstract things—then he says: what about measuring time? That too is prohibited. It is forbidden to measure time. I don’t remember exactly the source for this, but he took it as obvious that measuring time is also forbidden. What does it mean to measure time? It was obvious to him—not from the Talmud, perhaps later authorities write this. It is forbidden to measure how long it takes you to do something. Okay, so that’s what I’m saying: I don’t remember the source; he assumed it there as obvious. In other words, I’d have to check; I don’t remember the source at the moment. And that’s what he argued: measuring time is also forbidden, so we see that abstract things too are forbidden to measure. So what difference does it make if temperature is abstract?

Afterward the matter bothered me, because I felt there is a difference between measuring temperature and measuring time. And then I think I understood the point. And this is the point you said earlier, Avi, I think—or at least what you meant to say. There are two forms, two kinds of using numbers. In mathematics they distinguish between two types of number use. There are cardinal numbers and ordinal numbers.

Now among mathematicians it is common to say that this distinction really exists only with infinite numbers: infinite cardinals and infinite ordinals. Ordinals are ordering numbers—order, from the word order—and cardinals are counting numbers, they count quantities. So infinite cardinal numbers measure infinite quantities. There is a hierarchy among infinities—this is Georg Cantor—the hierarchy of infinities. For example, the number of points on the line between zero and one is larger than the number of natural numbers. He even denotes it with Hebrew letters, aleph, aleph-one, yes. So that is a bigger infinity, even though both are infinite. Those are what are called infinite cardinals.

There are infinite ordinals. Infinite ordinals mean some ordering of levels or intensities, okay? It does not measure quantities. I’ll demonstrate this דווקא with finite numbers because there it is easier to understand; with infinite numbers I myself don’t fully understand what the mathematicians are doing there with cardinals and ordinals. But with finite numbers it is very easy to understand, even though mathematically there is no difference between them; still, the meaning is different.

When you measure quantities, you say this: the number three contains three objects, yes? A set of three objects has a certain quantity of objects; a set of two objects has… What is its relation to the number two, and what is its relation to the number ten? Okay? The relation is simply whether you can include this in that, whether by adding one more unit you go from two to three. Here you have a common unit: here there are two units, here there are three units, here there are ten units. You are measuring a quantity of units. Fine? In that sense, time is a measurement of quantity. It is a cardinal number, not an ordinal number. It counts how much I have. How many seconds have passed. It doesn’t matter that it is abstract. One second, two, three. I count seconds the same way I count oranges, kilograms, logs of wood, whatever I am selling—and that is what is forbidden on the Sabbath because of commerce, and that is the concept of commerce. So since counting things is forbidden on the Sabbath, counting seconds is also forbidden. It doesn’t matter that it is abstract.

Measuring temperature is not counting. Not at all. What is the connection? Measuring temperature—the degrees of temperature—are measures of the various levels of heat. It’s not how many degrees I have. I’m not counting whether I have thirty-seven degrees in my pocket or thirty-eight. Not because it is abstract, but because there aren’t thirty-eight units here. There aren’t thirty-seven objects, each one a unit, such that in total I have a set of thirty-eight of them. What is thirty-eight degrees of heat? It is simply the heat level that comes after thirty-seven and before thirty-nine. You won’t be able to point for me to where the thirty-eighth unit is that you added in order to go from thirty-seven to thirty-eight. The numbers thirty-seven and thirty-eight are completely arbitrary. They simply determine what heat level is here. The first heat level is called one, the second is called two, the third is called three. It doesn’t matter that there is a continuum too—there is also thirty-seven point three. But on the conceptual level, let’s talk in whole numbers for simplicity. It doesn’t matter, because even on a continuum it’s the same.

So I am simply ordering heat levels, which is why it is an ordinal number. I am arranging heat levels one above the other. The number thirty-seven does not count how many units of something I have. The number thirty-seven orders this heat level before thirty-eight and after thirty-six. It merely says where in the series you stand. Therefore it is a designating number, not a counting number at all. It is a number that indicates at which level you are: you are at level thirty-seven, he is at level thirty-five. Okay? That does not mean I am larger than him by one unit.

Someone scored 110 on an IQ test, and someone else scored 109. And suppose the distinction is sharp, really sharp. Can anyone point to where his surplus ability is over the other person’s? What does he need to improve to get to that ability? It is not one particular thing that you improve. He is simply at a level of intelligence one level above you. That’s all. It relates to the totality. His entire level of intelligence is not a collection of one IQ plus one IQ plus one IQ, totaling 110. When my level of wisdom is measured, I am at level 110 and he is at level 109. That’s how we are ordered. It is an ordering of global levels. In counting there is nothing global. In counting, the collection of units is the group I have—that is how many units I have. The global measure is simply the collection of units. You see the connection to extensive and intensive.

Yes, although with temperature it is a bit different from IQ. Why? Because with temperature I can say, I don’t know, the number of collisions of particles within the volume—I know that’s not really how it works, I’m just saying—I can… You can’t. With heat you can, not with temperature. Those are two different things. Temperature serves to indicate—it’s just an external index—that says if there is such-and-such amount of collisions, this is how it will appear from the outside. No, no. That is exactly the point of thermodynamics—that it is not. You cannot translate heat into temperature. If you could, excellent—but you can’t. That is exactly the point. Since heat is a quantity—or energy, yes? Heat really is energy—an extensive quantity. And temperature is an intensive measure. It depends on heat, but it also depends on pressure, and on many other things. It is a combination of many things. You won’t be able to translate it into an extensive quantity—that is exactly the point. Otherwise temperature would be extensive. There is a sharp divide between extensive and intensive. It is not that one is just the translation of the other. That is precisely thermodynamics. You will not succeed in expressing temperature as a sum over microscopic quantities in statistical mechanics. You won’t. It is a derivative of all sorts of sums—it is the potential… No, I don’t remember it, but it is not a sum. Energy begins with two particles and afterward you take an integral. Extensive quantities are quantities you sum over all the units—that is exactly what extensive means. Intensive is something defined over the whole. So there are temperatures of eight and nine and ten. And velocity is like that too. What? I said, yes, velocity too is a derivative of length or… right. That also is not a count. Obviously. And all the same, velocity is certainly intensive.

Let’s go back… What? The report? Could that make a difference? Yes, if they sent it on the Sabbath maybe yes. On the Sabbath they measured, so that’s fine—it is permitted to measure speed on the Sabbath. What? I claim that according to this distinction it is permitted to measure speed on the Sabbath. Even though that’s measuring distance divided by time? What? No, if you measure in order to determine velocity, and you measure the distance and you measure the time and divide, I said that dividing extensive quantities—like specific heat—creates an intensive quantity. But if you measure the intensive quantity via division of two extensive quantities, that is forbidden. If, however, you can measure the velocity directly, then it is permitted—for example by the Doppler effect. In a Doppler detector it measures velocity not by directly dividing distance by time, but by measuring a frequency shift. So there it would be permitted according to my claim, fine?

In any event, the point is that you can see the connection between extensive and intensive. When I build the whole out of units additively, summing one plus one plus one, and in the end ask how much I have in total—that is extensive magnitude, that is quantity. It has nothing to do with abstract or non-abstract. It is not related to abstract or non-abstract, but rather to the question of how you use numbers. When you arrange levels of… I return to the court. When you arrange levels of wisdom, you are not collecting, you are not counting how many units you have. And therefore it is a qualitative magnitude and not a quantitative magnitude. It is a quality of the whole.

And therefore, for example, a court of three people, even with the same wisdom—if we really accept Sefer HaChinukh that it reaches better results than two people, or that two reach better results than one, if there is a conflict between majority and minority—then it means that something in the quality of the two overcomes the quality of the one. But it is not the sum of their wisdoms. In other words, it is not an extensive magnitude; it is an intensive magnitude. They simply reach a higher level of wisdom than the one does. Therefore in a two-against-one situation, the two decide even according to the view that quality outweighs quantity, because two is also a higher quality—not because it is a greater quantity, but because it is a higher quality.

And therefore Sefer HaChinukh will indeed say—this is what he says—that if the one has a higher quality and will reach better results than the two, whose level of wisdom is lower, then true, they will reach a better quality than each of them individually, but he is still on a higher quality level than they are. So even on the scale of quality, one should go with the one against the two, and therefore the one prevails. According to Sefer HaChinukh, the question here is quality versus quality, not quality versus quantity. The two constitute a higher quality than one, provided they have the same level of wisdom. So what prevails here is not quantity but quality, because wisdom is by definition quality. Determining a person’s wisdom is like IQ. Even if you manage to attach a quantitative index to it, like IQ—saying he has 110 IQ—this is a quantitative index for wisdom in the same way that thirty-seven degrees Celsius is a quantitative index for temperature. That changes nothing, because this quantitative index uses ordinal numbers, not cardinal numbers. We are using numbers, but only in an extended sense. It has nothing to do with counting numbers; it’s a mere homonym, two entirely different things.

By the way, this is connected to a lot of things. Maybe we’ll really talk about this—about counting in general. That might actually be a good idea; I hadn’t thought of it. Maybe I’ll talk about it next time. Counting in Jewish law: counting the Omer, counting the seven clean days, all sorts of countings—what are we counting? Are we counting qualities? Are we counting ordinal numbers or cardinal numbers? What is that thing?

So what I want to claim is that ordinal numbers are quality. Whatever is measured by ordinal numbers is quality. Whatever is measured by cardinal numbers is quantity. Fine? Now, true, that isn’t a definition, because it is only an indication. How do I know whether something is quantity or quality? If it is measured by counting numbers. Fine—but how do I know that the numbers measuring it are counting and not ordering? Because it is quantity and not quality. Right, exactly. I assume we all understand intuitively when counting applies and when ordering applies. I am only trying to give an indication that there really is such a difference between quantity and quality. I do not know how to define it.

And here perhaps I’ll end with an interesting link to a book—maybe I mentioned it—Zen and the Art of Motorcycle Maintenance, by Phaedrus, by Pirsig. He basically talks about a kind of meta-rhetoric, where that Phaedrus struggles with how to define the quality of essays submitted to him. Why does he think this one is better than that one? A bit like the postmodernism I mentioned at the beginning. Who says this is better than that? He writes essays this way—so what? He thinks it’s better; who are you to tell him it isn’t? Right? So how do you evaluate an essay? You give a grade, 70, 80, 100—how do you determine it? Just arbitrary. You understand that the grade on an essay is an ordinal number, not a cardinal one. A grade on a math exam—is it an ordinal number? It is a cardinal number. It simply counts how many correct answers he has. Okay? So that is the difference. There is a substantive difference here, not just that one is harder to evaluate. The evaluation itself is something else. Here you are evaluating my place in the class, not how many units I have. There you evaluate how much I am actually worth, not only my place in the class.

Could it be that four-unit and five-unit study tracks are also ordinal? No. Four units and five units—that is more—exactly. The level of difficulty is ordinal, yes, that is ordinal, not cardinal. Because level of difficulty—but within the four-unit track, the difference between me and you is cardinal, because I solved 10 questions and you solved 12, so you are better than I am. That is cardinal. No, but even there it could also be ordinal, because when you solve problems—if you solved problems 1, 5, and 7, and I solved 2, 6, and 9, and you didn’t solve mine, and overall you solved more problems than I did, that does not necessarily mean that… But if I solved your problems plus some more, then clearly that is better. Obviously there is complexity here.

I am just saying that I really think this is the correct definition of the difference between quality and quantity. And I claimed that wisdom in a religious court is always quality. There is no question here of quantity versus quality. The question is quality versus quality. And therefore Sefer HaChinukh says that where there are two against one at the same level of wisdom, quality prevails, not quantity—just that the quality of the two is better than the quality of the one, despite their having the same wisdom level. But if the quality of the one is much higher than that of each of the two, then perhaps it can overcome even the two. One who says not may be saying that nevertheless we want peace or something like that, or that one cannot measure it, or there are technical considerations of one sort or another—or he may really be saying like the Ran.

Since you need to establish a line—you can’t, as we said with the Ran, carrion versus slaughter on the Sabbath—we asked: fine, maybe three olive-sized amounts yes, but two not? Maybe slaughter on the Sabbath is only a little more severe and not much more severe? So the Ran established a line. He says, what can you do—once it is a bit more severe, that is enough for me. I am not entering into measurements now, because we do not know how to do that. If we knew, we would do it; we don’t know. So I determine that quantity outweighs quality, regardless of the qualitative gap.

Perhaps the same is held by those who disagree with Sefer HaChinukh regarding majority in a court. The theory is that there is a qualitative majority—let’s say the wiser one is wiser than both of them, but not by all that much. How will you measure how much wiser he has to be in order to outweigh their advantage of being two? You can’t. So establish an arbitrary line: quantity defines the quality. But it’s not quantity versus quality. Rather, the quality that results from your being two outweighs the quality of the one. So it is only quality versus quality; there are no quantities here.