Rabbi Dr. Michael Abraham – Different Types of Doubts in Logic and Law_13-11-16 – Nitzotzot Forum
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 Zadorov case and reasonable doubt
- A halakhic example: capital cases and a unanimous ruling
- Epistemic vagueness and probability
- Ontic vagueness: vague reality, betrothal, and quantum theory
- The role of the judge versus the legislator, and regarding Judge Tal
- Vagueness in physics: chaos versus quantum theory
- The heap paradox and conceptual vagueness
- Additional applications: atypical performance on the Sabbath and dilemmas about exams
- Summary of three kinds of vagueness
Summary
General overview
The text argues that not every case in which a judge has difficulty deciding stems from an ordinary factual doubt, and it draws a distinction between several kinds of vagueness that judges and Jewish law are required to decide under. It uses the disagreement among the judges in the Zadorov case to distinguish between a minority that believes the defendant did not commit the murder and a minority that believes he probably did commit it, but that the level of certainty does not meet the legal threshold. It brings an analogy from capital law in Jewish law regarding a unanimous ruling that acquits, in order to show that a judge is obligated to say what he thinks and not to make outcome-based calculations. It then defines epistemic vagueness as a state of missing information handled probabilistically, ontic vagueness as a state in which reality itself is not unequivocal, and conceptual vagueness as arising from the fact that everyday concepts are continuous rather than binary, and concludes that a judge also has a role in deciding vague reality and not only in clarifying facts.
The Zadorov case and reasonable doubt
The text describes a dispute in the Zadorov case among judges over whether to convict or acquit, and argues that if there is one reasonable and skilled judge who believes the defendant did not commit the murder, it is hard to say that a conviction meets the certainty standard of beyond a reasonable doubt. It distinguishes between a situation in which the minority opinion is a determination that the defendant did not commit the murder, and a situation in which the minority thinks he probably did commit it but the level of certainty does not reach the threshold required for conviction. It states that when everyone in practice thinks he committed the murder and the argument is only over whether the doubt is reasonable, one can follow the majority regarding the assessment of whether the doubt is reasonable, and it tends to think that in such a situation it makes sense to convict. It adds that there is a gray area when the minority’s degree of doubt is higher, but the principle it proposes is to distinguish between a disagreement about reality and a disagreement about the level of doubt.
A halakhic example: capital cases and a unanimous ruling
The text brings a halakhic rule according to which in capital cases, in a religious court of twenty-three, if all of them unanimously impose the death penalty, the defendant goes free, and only a majority ruling of at least two can convict. It explains that the accepted rationale is that unanimity points to bias and that there are no “clear cases,” so absolute uniformity arouses suspicion. It presents the dilemma of the last judge: if he says “liable,” he will cause acquittal, and if he says “not liable,” he will cause conviction, and it states that in Jewish law the judge must say what he truly thinks and not choose a statement that will produce a desired result. It argues that if the judge calculates outcomes and conceals his opinion, he “empties this Jewish law of its content,” because the Jewish law itself wants to expose the bias and lead to acquittal in a case of unanimity.
Epistemic vagueness and probability
The text defines the first case as epistemic vagueness, that is, doubt arising from lack of information about reality. It argues that in such situations the natural tool for decision-making is probability or statistics, because probability “covers the gap” created by partial information. It illustrates this by means of rolling a die and shows that probability changes according to the information one has about the outcome, and concludes that probability is a tool that replaces missing information and is not needed when there is full knowledge. It adds that in law judges do not carry out formal numerical calculations, but the actual mode of decision-making is similar to probabilistic thinking.
Ontic vagueness: vague reality, betrothal, and quantum theory
The text defines the second case as ontic vagueness, in which reality itself is not unequivocal and it is not merely a matter of human lack of knowledge, and it formulates this by saying that even the Holy One, blessed be He, “does not know more,” because there is no sharp fact in reality. It rejects the suggestion that statements about the future are an example of ontic vagueness, arguing that a future statement is either true or false even if there is no way to check it right now, and therefore this is merely epistemic doubt. It presents the Talmudic topic of “betrothals that were not given over for intercourse” and explains the distinction drawn by the Talmud between a situation of “and he does not know,” where there was a defined reality and they forgot it, and a situation in which the identity of the betrothed woman was never defined in the first place, so that in reality there is no “one woman who is really my wife,” but rather vagueness in the very state of affairs. It states that in ontic doubt there is a dispute among the Amoraim whether the betrothal has legal validity, and emphasizes that most laws of doubt in Jewish law are epistemic doubts, whereas here we are dealing with a different structure of vagueness. It adds that the mathematical tool appropriate to ontic vagueness is fuzzy logic or multi-valued logic, not probability, whose purpose is to complete missing information.
The role of the judge versus the legislator, and regarding Judge Tal
The text presents the position that kinds of vagueness that are not merely lack of information still “fall at the judge’s doorstep,” because the norms have already been set and the problem is how to apply them to a situation that is not sharply determined. It argues that the legislator can set rules that will bind judges both in epistemic doubt and in ontic doubt, but that this does not change the fact that the initial case is revealed in adjudication and not in the language of the statute. It presents an objection to the position attributed to Zvi Tal, according to which the judge deals only with doubts about a clear reality, and states that the judge is also required to decide vague reality and cases in which there is no normative lacuna but rather unclarity as to which norm applies. It emphasizes that a lacuna in the law is a situation in which a norm is missing, whereas in his examples the norms exist and the difficulty is classifying the case under them.
Vagueness in physics: chaos versus quantum theory
The text distinguishes between unpredictability in chaos theory and real vagueness in quantum theory. It describes an example of a marble that may fall to the right or to the left and argues that the development is dictated by the initial conditions but cannot be predicted in practice, and therefore this is epistemic doubt. It describes the double-slit experiment and argues that the resulting pattern indicates that the particle passes “in some sense” through both slits together in superposition, and therefore the doubt there is ontic and not epistemic. It explains that this is a case where it is not a matter of not knowing which possibility occurred, but rather that in some sense “both happened.”
The heap paradox and conceptual vagueness
The text presents the heap paradox and the bald-man paradox by means of three assumptions, each of which sounds reasonable on its own but together create a contradiction, and expands that this challenge applies to almost every everyday concept, such as “afternoon” or the boundaries between images such as in Escher drawings. It describes a solution by analytic philosophers who define an arbitrary formal threshold, and rejects it as a solution that formulates a new language instead of solving the problem of vagueness in natural language. It states that the solution is to give up the assumption that adding one unit changes nothing, and to replace binary logic with multi-valued logic in which there are continuous degrees of “heap-ness” or of a similar property. It concludes that when a law uses vague terms, the judge is required to set a legal line on a continuum of degrees in order to decide whether the case falls under a category like “heap,” even though the factual reality itself is clear and the vagueness lies in the language.
Additional applications: atypical performance on the Sabbath and dilemmas about exams
The text brings the halakhic concept of “performing a transgression in an unusual manner” and argues that there is a continuum of degrees of unusualness, so that a mild deviation may be prohibited on a rabbinic level, while an extreme deviation may be entirely permitted because it no longer resembles the original act. It presents a dilemma-style argument against exams according to which diligent students will study even without an exam and lazy students will not study even with an exam, and rejects it by arguing that the world is not binary but continuous in levels of diligence, and therefore an exam affects those in the middle. It ties this to the general claim that trying to impose yes-or-no logic on continuous concepts and properties generates paradoxes, and that judicial decisions require working with continua.
Summary of three kinds of vagueness
The text summarizes three kinds of vagueness: epistemic vagueness, which is doubt arising from missing information; ontic vagueness, in which reality itself is not unequivocal; and conceptual vagueness, in which the concepts themselves are continuous rather than binary. It states that the judge is required to deal not only with clarifying missing facts but also with situations of vague reality and with cutting lines within a conceptual continuum in order to decide whether a legal category exists from which a norm of prohibition, permission, or obligation follows. It stops after this conclusion and presents it as an answer to the claim that the judge has no role in questions that are not binary beyond ordinary doubt.
Full Transcript
[Rabbi Michael Abraham] So I’ll just say what I said before we started talking here about the air conditioner. Let me remind you of what I said a little earlier, and now we’ll wake up with the Zadorov case, where there was an argument among the judges whether to convict him or not convict him, and the minority opinion wanted to acquit him, while the majority decided to convict him, in the final instance I think. And the argument there was: if there’s one judge who thinks he didn’t commit the murder, then you can’t say that those who determine that he did commit the murder are determining it with certainty beyond any reasonable doubt. After all, the third judge is also a reasonable person, and if he himself thinks that Zadorov didn’t commit the murder, then you can’t say that the certainty here is absolute. A reasonable person, skilled in law, a Supreme Court justice, decided that Zadorov didn’t commit the murder. So you can’t say there’s no reasonable doubt at all. You can say, in my opinion he did commit the murder, but you can’t say the certainty is such that every reasonable person has to decide that he committed the murder. Right next to you there is a very reasonable person who thinks otherwise, and therefore that creates reasonable doubt. Now here I think one has to distinguish between cases. I won’t get into it because this is a legal issue and a different topic. I’ll just make a comment about it, something I really think there’s room to distinguish, and again, I’m not sufficiently familiar with the legal literature on this issue. I know this was said there. The question is: what is the minority opinion based on? If the minority thinks Zadorov didn’t commit the murder, and that’s his opinion, that’s the bottom line, then it’s very hard to say there’s no reasonable doubt here. After all, there’s a very reasonable person who thinks he didn’t commit the murder. But if the minority thinks there is reasonable doubt that he committed the murder, while he himself would say that he did commit it—if you told him, come on, let’s bet, he’d say: I think he committed the murder, but this doesn’t meet the legal standards that say my certainty has to be beyond a reasonable doubt. Let’s say that beyond a reasonable doubt means ninety-five percent, just for the sake of the game. Some people mention numbers like that. I don’t know how compelling they are. Of course it has no real meaning, but let’s say ninety-five percent. So I can say: the third judge says that as far as I’m concerned there’s twenty percent that he committed the murder—he didn’t commit it at all, nothing. If I had to decide privately by myself whether he committed the murder or not, I would say he didn’t commit it. That’s one situation. In such a situation, it seems to me hard to accept that this is not reasonable doubt, even from the perspective of those who think he did commit it. There’s a reasonable person, skilled in law, who says he didn’t commit it, so you can’t say every reasonable person has to reach the conclusion that he did commit it. But if the third judge, the one who says he doesn’t convict, claims: my doubt is ten percent, meaning ninety percent that he committed the murder—then if he had to decide privately to himself yes murder or no murder, he would say: he committed the murder. But there is a rule in criminal law that in order to convict for murder, you need a high level of certainty, beyond a reasonable doubt. So he says: we haven’t reached that. This is ninety percent; beyond a reasonable doubt is only ninety-five percent. So because of that, I can’t convict him of murder. Okay? In such a situation, I tend to think like what people in the legal world think today, that this really is not considered reasonable doubt. Because here the argument is over whether the doubt is reasonable. It’s not an argument about the case—what really happened. It’s not an argument about reality, whether he committed the murder or not, because everyone says he committed the murder. The only question is what the level of doubt is. And there are two judges who say this doubt is unreasonable; the certainty is good enough. One judge says this doubt is indeed reasonable doubt; the certainty is not good enough. When there is a dispute over whether the doubt is reasonable or not, you follow the majority. The majority say this doubt is not reasonable doubt and the certainty is sufficient, so here the majority determines it. And I think my own logic says that here one should decide to convict him. Even if for the third one the doubt is serious?
[Speaker B] That’s what I’m saying.
[Rabbi Michael Abraham] If the third one is doubtful at fifty percent, not twenty percent, it could be that even then it’s reasonable doubt—you can discuss that; that’s already the gray area. But in principle I only think one has to distinguish between an argument over whether he committed the murder and an argument over whether the doubt that he committed the murder is reasonable or not. If there’s one who says he didn’t commit the murder, then there is still at least reasonable doubt, even from the standpoint of the others.
[Speaker C] Don’t you think that if he were deliberating with them within the ruling itself—don’t you think that if he were aware that the other two were going to say he was guilty, maybe he would change his mind? Maybe he would decide that he is guilty just so as not to—after all, when the third judge decides to say not guilty, he knows the other two are going to convict him, so his word doesn’t determine anything.
[Rabbi Michael Abraham] I’ll answer you with a halakhic example. There are several halakhic decisors who ask the following. There is a rule in capital law in Jewish law that such cases are judged in a religious court of twenty-three. And there’s a very interesting rule there: if all twenty-three say that the person is liable—liable to death—then he goes free. Only by a majority ruling, a majority of at least two, does he come out liable. If it’s unanimous, he goes free. The accepted explanation is that if he comes out liable unanimously, that means the perspective there is biased. There are no clear cases. I think that’s true—I went a little into the field—there are no clear cases. And if twenty-three judges all say the same thing, then something here is biased, something is biased. It’s as if they’re probably following someone wiser than they are, or I don’t know what—someone who is swaying their opinion. Now think about a case—and this is my answer to you. They express their views according to the order in which they are seated. Twenty-two judges have announced that in their opinion the man is liable. Now what will the twenty-third judge say? If he thinks the man is liable and he says so, then the man goes free, right? Because then it turns out they all said he was liable. And if he thinks he is innocent and he says so, then the man comes out liable—he sentences him to death, right? So basically, on the principled level, the twenty-third judge is in your dilemma. He is really facing the dilemma of whether to say what I really think or to say what will bring about the result that I think ought to happen, the legal result that ought to happen. And it’s quite clear that in Jewish law you have to say what you think. That’s so in my opinion by simple reasoning, and halakhic decisors also say this, and to my mind the reasoning is completely straightforward. Completely straightforward. I’ll tell you why. Again, maybe there are those who disagree, but to my mind this is simple reasoning. Because if you make that calculation, you empty this Jewish law of all content. Because the Jewish law says that if you think he is liable, that means that even the fact that the others say he is liable is questionable, because something here has tilted the opinion. Now, if you don’t say what you really think, then we won’t know that the twenty-two on whose basis we are killing him are actually an incorrect or biased opinion. And therefore you should say what you think. The Jewish law already says that if everyone says he is liable, then we tell you: apparently something here was biased, and don’t kill him. If you conceal it and go by the result, you empty out what the Jewish law itself wants to achieve. Okay? The Jewish law itself wants to acquit him if all of you think he is liable. The Jewish law said he has to be acquitted. Say what you really think. Because if indeed all of you think he is liable, then in fact he really should be acquitted. Don’t play games. You’re not bringing the truth to light; you’re bringing falsehood to light. Right? Fine. So that’s… okay, so I’m closing the parenthesis regarding his comment about the legal issue. I’ll come back to it later, because there’s an interesting halakhic example there that we’ll discuss as well. In any case, the first case is a case of epistemic vagueness. In the first case I’m saying that we are on the spectrum between yes and no answers, binary answers. The first case is the simple one: epistemic vagueness—what in the usual jargon is called doubt. Doubt is a situation where I don’t have full information and I don’t know; I’m in doubt. Usually in, say, scientific or even everyday contexts, when I’m in a state of doubt, when my certainty is incomplete, what are the tools—what do you call the tools—that I use to make decisions in such a situation? Probability or statistics, right? Meaning, I use probabilistic tools to assess what the correct decision is under conditions of uncertainty. For example, let me give you an example. Suppose I roll a die and ask you: what is the chance it lands on five? If I don’t know anything about what happened there, then I’m supposed to say the chance is one sixth, right? Assuming it’s a fair die, of course. The chance is one sixth. If I’m told in advance that the die landed on an odd face, what is the chance it landed on five? One third. Meaning, the answer depends on how much information I have about the situation, right? In other words, probability covers the gap in my information. If I had full information, if I knew the die landed on five, then what is the probability that it landed on five? One, right? Meaning, there is no need to resort to probability. Probability is a mathematical tool that helps me deal with situations of missing information. When I lack information, I use probability to cover for that and make a decision. But it’s a function of how much information I have about reality. Therefore probability is a tool for completing missing information, or for making decisions in the absence of information. It supplements the information, but I know how to make decisions when I have partial information. That’s what happens in a situation of epistemic vagueness. Epistemic vagueness means that when I look at reality, I want to know what the reality was, and I don’t know—I don’t have all the facts. I hear evidence from here, evidence from there, and I have to decide what happened here. So many times we don’t use formal probabilistic tools. A judge doesn’t make probability calculations and say this is sixty percent, seventy percent, or ninety percent. But basically, if we could, we would be doing a probabilistic calculation here. The correct mathematical tool for such a situation is a probabilistic tool. It’s just a bit too complicated and impossible to do it probabilistically, but the form of the process is probabilistic. Probability is a tool for dealing with situations of partial information. So that’s the simple case. Maybe an example—well, we’ll come back to this example in a moment. The second case, or the second type of case, is ontic vagueness. Ontology as opposed to epistemology. Epistemology is the theory of knowledge. Epistemic doubt is doubt in my knowledge of reality. I have partial information; I do not fully know reality. Ontology is the theory of being, let’s put it in plain words. It’s one of the areas within metaphysics. Ontology is part of metaphysics, philosophy—the theory of being, what exists and what doesn’t exist, what happens in the world. When I speak about ontic doubt—and this is what Judge Tal did not address—he assumed that such a thing does not exist, at least in one sense, but it does exist. There are situations in which reality itself is vague, not that I have partial information about reality. There is something vague in reality itself. I have full information; I am missing no information at all. Even the Holy One, blessed be He, doesn’t know more than I do about this reality. He knows everything—that’s the assumption—but He doesn’t know more than I do about this reality, because in it itself there is something that is not unequivocal. Let me give you an example.
[Speaker D] What? Free choice?
[Rabbi Michael Abraham] Well, free choice is not that, although there are those who compare the things. Something future? Something future is also only lack of information. I don’t know what will happen in the future. But in the future either X will happen or Y will happen. Still. No—if the question is what he intends now, that’s another question. If the question is what he will do in the future, then let’s wait for the future and see. That’s only a lack of information. What? Lack of information about reality?
[Speaker D] Right, right.
[Rabbi Michael Abraham] That’s just a lack of information. I’ll give you an example; let’s do an interesting topic in philosophy, one that appears in Aristotle’s writings. Aristotle asked: what can I say about the statement, “Tomorrow there will be a naval battle”? Can I say that it’s true, that it’s false, or neither? So he argued that basically it’s neither. I can’t say that it’s true, and as you said, I also can’t say that it’s false. I don’t know. Tomorrow either there will be a naval battle or there won’t be a naval battle. His claim was that, basically, about future statements I need to say: I don’t know. Then along came the Pole Łukasiewicz in the twentieth century—the one who established the logical powerhouse, Polish logic, the Polish school, that Polish intellectual force. Łukasiewicz built a three-valued logic, which says that statements dealing with the future are statements to which the relevant logic is not a logic of truth or falsity alone—not just two possibilities—but three possibilities: either true, or false, or unknown. And basically, with regard to the future, it’s simply unknown. There’s no truth or falsehood, unless, let’s say, I know something about the future in some way. Fine, I don’t want to get into Łukasiewicz’s ideas; I’ll explain why I think that’s incorrect, and it connects to other philosophical topics. If I say, for example, “The sun is shining outside now,” then in order to know whether that statement is true or false, I have to make a comparison, right? Take the content of my claim, take the state of affairs in the world, look, and compare. If the state of affairs in the world matches the content of my claim, then it’s a true claim. If it doesn’t match, it’s false. Okay? Now what happens if I say, “Tomorrow the sun will rise”? So I can’t make that comparison right now, correct? Now suppose I wait until tomorrow and then make the comparison—tomorrow I make the comparison, and I see that the sun did rise. Doesn’t that mean that the statement I made today was correct? Of course it does, right? That statement said then—today is Sunday—so I say that on Monday at such-and-such an hour there will be sun in the sky. At noon there will be sun in the sky. So right now I can’t make the comparison because the time hasn’t arrived yet. But if I wait until tomorrow and I see that there is sun in the sky, no problem. I can make the comparison between the claim made yesterday and the state of affairs in the world that it described, namely the state of affairs tomorrow at noon, and see whether it matches. If it matches, it’s true; if it doesn’t, it’s false. Future statements are subject to exactly the same logic as present statements. They’re either true or false. The only issue is that I don’t know which. What does that mean in the language I used earlier? It means that this is an epistemic doubt, not an ontic doubt. It’s a doubt that stems from lack of information. It’s not that reality itself contains something not fully sharp, neither yes nor no. Reality itself is yes or no. I don’t know it because I don’t know how to know the future. I don’t know what will happen in the future. When I get to the future, I’ll know. Therefore I need to wait until I know whether that statement is true or false, but it’s clear that it’s either true or false; there is no third state. And therefore I disagree with the Rabbi. So there’s a lot of philosophy packed into your barrage there, but I don’t agree with that claim. I think statements about the future need to be evaluated in binary logic: yes or no, true or false. Let me give you another example. This is the topic in the Talmud in Kiddushin and Yevamot that deals with betrothal not fit for consummation. Betrothal not fit for consummation means the following: a man betroths a woman by giving her a perutah and saying to her, “Behold, you are betrothed to me with this ring according to the law of Moses and Israel.” It can be a ring. I can also do this through the woman’s father. I give the father the ring when she is a minor, and I say to him, “Your daughter is betrothed to me with this ring according to the law of Moses and Israel.” Now suppose a father has two daughters, and I give him a ring and say, “One of your two daughters is betrothed to me with this ring according to the law of Moses and Israel.” I don’t define which daughter, and I’m also not saying that it’s one of the two daughters you’ll decide to put the ring on. No—I’m determining right now: one of the two, and I don’t care which. If both are good in my eyes, that’s fine; I don’t want two, one is enough for me. Okay? One of your two daughters is betrothed to me. So the Talmud itself—and this is an interesting point—the Talmud itself makes the distinction here between ontic doubt and epistemic doubt. And the Talmud itself says that a case like this is ontic doubt, not epistemic doubt. In the Talmud—I’ll maybe read you a passage from Yevamot, page 37. The Mishnah says: “One who betrothed one of two sisters and does not know which one he betrothed must give a bill of divorce to this one and a bill of divorce to that one.” I betrothed one of two sisters and I don’t know which one, so in order to release both of them I have to give a bill of divorce to this one and to that one, just to be safe, because I don’t know which of them is betrothed to me. So in order to solve the problem, I have to give a bill of divorce to both of them out of doubt. So the Talmud asks: “Infer from this that betrothal not fit for consummation is valid betrothal.” Why? What’s going on here? When I betroth one of two sisters in such a case—say there are Rachel and Leah—if I betrothed Rachel, then Rachel is now my wife. What about Leah? Leah is my wife’s sister. A wife’s sister is one of the forbidden relations. There are forbidden relations with whom betrothal does not take effect and with whom sexual relations are forbidden. A wife’s sister is one of them as long as my wife is alive. So now, if Rachel is betrothed to me—say Rachel is the one of the two who is betrothed to me—then Leah is, for me, a forbidden relation, right? I can’t betroth her; she is my wife’s sister. If Leah is my actual wife, then Rachel is my wife’s sister. So as a result, this is essentially betrothal that cannot be realized. When I want to have sexual relations with one of them, I won’t be able to—with either of them—because each one might be my wife’s sister, and then it would be forbidden for me to have sexual relations with her. Therefore this is, in essence, betrothal that cannot be realized, betrothal not fit for consummation. And there is a dispute in the Talmud whether this is valid betrothal or not. So the Talmud says: after all, in the Mishnah it says that one who betrothed one of two sisters and doesn’t know which must give a bill of divorce to both out of doubt. What does that mean? It means that we see this situation as one in which there really is doubtful betrothal regarding each one, right? Why do I need to give a bill of divorce? If such a thing isn’t called betrothal at all, because betrothal not fit for consummation is not betrothal at all, then we wouldn’t have had to give a bill of divorce to either of them; there simply is no betrothal, and neither one is betrothed to me. To release them, I wouldn’t need to give them a bill of divorce. If the Talmud says I need to give a bill of divorce to both out of doubt, the Talmud assumes that in such a case there is betrothal, or at least doubtful betrothal. Okay? And then the Talmud asks: wait, but isn’t there a dispute about this? There is an amoraic opinion that says that betrothal not fit for consummation is not betrothal. Right, there’s no mistake here. So how does that fit with the Mishnah here? Look at what the Talmud answers; it is exactly this distinction. “What are we dealing with here? A case where they were identified and later became mixed up.” What does that mean? The Talmud—maybe I’ll read one more sentence—“This too is precise from the wording, for it teaches: ‘and he does not know,’ and it does not teach: ‘and it is not known’; infer from this.” So the Talmud says like this: we need to distinguish between two situations. There is a situation in which… I betrothed one of them and forgot—I forgot which one. That’s one case, right? That is epistemic doubt. Why? Because one of them really is my wife in reality. I just don’t know which one. So that doubt is epistemic doubt. Right? I lack information about reality; I forgot. Okay? In such a case, it really is doubtful betrothal. But that’s not what the topic of betrothal not fit for consummation is talking about. That’s a case where they were identified and afterward got mixed up. What does that mean? Earlier there was some woman, and it was clear who she was, and afterward things got mixed up and I no longer remember. Suddenly there’s a gap in my information. I don’t know reality as it truly is; I’m missing information. So that’s epistemic doubt. In epistemic doubt, this really is doubtful betrothal, because one of them is betrothed to me and I simply don’t know which. Betrothal not fit for consummation is not that, says the Talmud. Betrothal not fit for consummation is a situation where in reality there is no one clear woman who is betrothed to me. The problem is not in my knowledge of reality; the problem is in reality itself. Even the Holy One, blessed be He, in His very glory, would not be able to tell me who my wife is. Is it Rachel or Leah? Why? Because neither of them is actually my wife. It’s not that I don’t know. The Holy One, blessed be He, has complete information about reality. Everything I don’t know, He does know. He also doesn’t forget; He knows everything. Any lack of information, in principle I could ask Him about, and if He were kind enough to answer me, He would tell me and give me that information. But here it’s ontic doubt, not epistemic doubt. I’m not… there is no woman who is my wife. It’s not that I don’t know which of the two is my wife—there isn’t one. I decided that I want one of them, and I didn’t define which. The moment I didn’t define which, there isn’t one woman who is really my wife and I just don’t know. Neither of them is really my wife. There is here something—you can call it doubt; people sometimes use the term doubt here, but it’s a completely different use of the term. And this is ontic doubt. And with ontic doubt there is a dispute among the amoraim whether betrothal in a case of ontic doubt counts as betrothal or not. In epistemic doubt, according to all opinions, it is doubtful betrothal. Here it is explicit in the Talmud itself that it makes a distinction between ontic doubt and epistemic doubt. Wait, so ontic doubt is not doubtful betrothal? So there is a dispute. One opinion in the Talmud says that this too is doubtful betrothal, like epistemic doubt, and another opinion says that it is not. It seems to me that this is what “not fit for consummation” means. If a person takes two gentile women who are not related and says, “One of them is betrothed to me,” both are doubtfully betrothed. Here the Talmud disputes whether such betrothal is Torah-level. In ordinary cases, if I take a woman who is forbidden to me by a prohibition… there are many examples. I won’t get into all the details so as not to complicate things. Clearly there is a yes here. What is doubt due to lack of knowledge, which the halakhic decisors in Yoreh De’ah discussed? That’s epistemic doubt. Every ordinary doubt is epistemic doubt. When we speak about doubt, we mean epistemic doubt. I have a piece of meat and I don’t know whether it is kosher meat or non-kosher meat. In reality it is either kosher meat or non-kosher meat. I just don’t know. Okay? So that is epistemic doubt. All the rules of doubt in Jewish law, all the situations of doubt that Jewish law deals with, are epistemic doubt. Here, and maybe in only a very few other places, the doubt is—it’s not even really doubt, if we were precise in our language—it’s ontic doubt. But it’s not doubt in the sense that I lack information about reality; rather, you can call it a vague reality. The mathematical tool, by the way, that is used in epistemology, that is used to handle vague reality—in what I’m calling ontic doubt, ontic vagueness, not doubt, because doubt is always epistemic—there is epistemic vagueness, which is doubt, and there is ontic vagueness. The tool that deals with ontic vagueness is called fuzzy logic. Or multi-valued logic, which is a different mathematical tool, not statistics and probability. There are those who want to argue that statistics and probability are an example of that logic, so you can debate it, but it’s something else. And the difference is that statistics or probability come to compensate for missing information. When I lack information, I use probability to make decisions in the absence of information. Fuzzy logic deals not with missing information but with reality that is not unequivocally defined. It’s not that my information about reality is lacking; I’m not missing any information. No one can add more information to me beyond what I already have. My information is complete. But it is information about a reality that is itself undefined. So that is ontic doubt. Think about this. Think about Judge Tal—think about a judge before whom this case is brought. Abaye and Rava, who disputed betrothal not fit for consummation—treat them right now as judges. A case like this comes before them and they have to decide what to do. Of course, you can say that this is a question for the legislator and not for the judge. But I think naturally this is a question for the judge and not the legislator. Because the legislator already said his piece. The legislator said there is betrothal and this is how it is carried out. The legislator said what happens when a woman is betrothed to a man, what the laws are that apply in the matter. He said everything. So what now? There is some situation in reality and I don’t know how to apply the rules the legislator established. I have some vague reality. This is a decision that at its root is a judicial decision. It’s true that if it becomes interesting enough and comes up more than once, then maybe the legislator will also address it and establish a legal rule that applies to the case. But on the principled level, this is a case that the judge encounters first, not the legislator. The legislator gave all the norms relevant to this reality. He determined what betrothal is and what it is not. He determined the laws that apply to a betrothed couple. Everything was established. I just don’t know whether this woman is betrothed to me or not. But I don’t not know because I lack information—which is certainly the judge’s domain—but because in reality itself there is no one woman who is clearly my wife or clearly not. In that sense it functions exactly like epistemic doubt. There is no difference. Just as epistemic doubt is a matter for a judge’s decision, so too ontic doubt is a matter for a judge’s decision. Because the norms have already been established. The legislator has spoken, said everything. I now just don’t know how to apply that to the reality before me. Obviously at stage two, obviously at stage two, the legislator can come and establish a legal rule that binds all judges. But he can do that in epistemic doubt too. The legislator can say that even in epistemic doubt you must do such-and-such. It’s not necessarily the judge’s decision. The legislator may tell him that in epistemic doubt he must do this. By the same token, he can tell him that in ontic doubt he must do that. But that’s not essential. Essentially, the one who makes the decision in these cases is the judge, not the legislator. And that’s why I said I disagree with what Zvi Tal said. I think the judge deals also with vague reality, not only with doubts about clear reality. There are situations in which we work with fuzzy logic, or vague logic, and not with probability. According to that, when does a lacuna in the law arise? Because if in the end I can say that it’s ontic doubt all the time, then every gap I have is a lacuna. No—a lacuna is not ontic doubt. Why not? Because if the law did not say what the status of a betrothed woman is—suppose it didn’t say what the law is—that is a norm, not a doubt in reality. That is a pure norm. That is what the legislator has to say. To say that if a woman is betrothed to me then she is forbidden to marry someone else. But law is always with respect to some reality. In other words, in the end you can see the law as an obligation in relation to reality—what the law is in that reality. True. So if the woman is my wife, the law determines one thing; if she isn’t my wife, the law determines something else. But in a situation where there is no ontic doubt in reality itself—reality itself is vague, as you say—then here I don’t understand how that works. It is vague, meaning I don’t know whether the woman is my wife or not. But I don’t not know because I lack information; rather, because the situation itself is vague. I don’t see why that differs from epistemic doubt. In both cases, the judge confronts a question regarding which there is no normative lacuna. There is no lacuna. The law says with certainty what to do if there is a married woman and what not to do if there is not a married woman. Everything is clear. The problem here is that I don’t know which norm to apply. Not that a norm is missing from the law books. I’ll say again: it is always possible that the legislator will come and add a norm to the law books to deal with these situations in order to spare judges the dilemmas. But he can do that in epistemic doubt too, not only in ontic doubt. That is always true. But here the norm is: you are permitted to do this or forbidden to do this; you may betroth a woman or you may not betroth a forbidden relation—that’s all. Now decide what this case is, what the nature of this case is: is he betrothing a woman, or is he violating his wife’s sister? It doesn’t matter. Right. But maybe not. In other words, the legislator’s norms are clear. You can betroth a woman; you cannot betroth a forbidden relation. Someone who is a forbidden relation, you cannot betroth. That’s it; it’s closed, there is no lacuna here. Now a case comes before me where I don’t know. Just as you cannot cross a double line and sell an apartment to two people, right? Same thing, the legislator… No, the legislator did not determine that. The legislator determined what to do with a married woman and that one may betroth a woman and may not betroth a forbidden relation. That’s what he determined, and it covers all the possibilities. What else is there besides a single woman or a forbidden relation? A permitted woman or a forbidden relation? There are no other options. But a case arises in which I don’t know which norm to apply. That is not a lacuna on the normative plane. Again, it can be solved by a normative addition. The legislator can say… you must act in such-and-such a way, just as the judge, just as the legislator establishes rules of evidence. When he establishes rules of evidence, he is basically telling me how to determine reality. Rules of evidence are not a norm in the pure sense. Rules of evidence are about how to determine reality correctly. So he can, if he chooses. But fundamentally this is not a question that must be handled in the house of the legislator; this is a question first encountered by the judge. Let’s continue for a moment, and maybe afterward I’ll come back to this. The example in criminal law would be if someone had sexual relations with one of these two women. Do you punish him or not? That’s criminal punishment. Now you are in doubt. You need to decide which of the women has a husband and which does not, what her status is. If the law has already solved the problem, then fine; but if the law has not solved the problem, then this is still in your domain as a question that has to do not with whether there is doubt, but whether the woman with whom he slept is a married woman or not. And here I am in ontic doubt, because I don’t know which of them is a married woman. Okay, so that is a second example—the difference between ontic doubt and epistemic doubt. I’ll just say in passing, and I won’t expand on it, that in the physical world too we distinguish between these two kinds of vagueness. There are two kinds of cases where we can’t say something clearly about reality. In one of them we use probability—actually in both we use probability in a strange way, but for different reasons. One of them is, for example, what is called chaos, chaos theory. What does that mean? Suppose there is some ball, and on the upper part of the ball I place a marble. Now it has to fall either to the right or to the left, and it is standing here, okay? And I need to know whether it will fall right or left. I have no way to predict that in advance, right? It depends on whether some slight wind comes from here, or maybe there is some asymmetry in the ball carrying this marble. I have no way to predict it. But you understand that my inability to predict it does not mean that the future result is not determined on the basis of the present circumstances. It is entirely determined; it’s just so delicate that I don’t know. That is epistemic doubt, even though there are physicists who somewhat confuse this with ontic doubt, but that is a mistake. It is epistemic doubt. In quantum theory, that is the only context we know in physics in which there is ontic doubt. Ontic doubt means, in the double-slit experiment, for those who know it: I have two slits here, there is a screen like this with two slits, there is another screen behind it, and we send particles. We send particles toward this screen, okay? So some pass through here, some pass through here; classically they would either make holes or not pass at all. In quantum theory it turns out that if this were classical theory, some would pass here and then we would see an accumulation here of particles that hit opposite this slit, and they were sent along this path and hit here. Okay? We would see two accumulations of particle impacts. In quantum theory we see particles hitting like this, some kind of graph: here they hit a bit, here less, here more, less, and so on. There is some pattern of particle impacts all along the screen. More than that—and this is a very interesting point—even if you send a single particle, one, so that it passes like this, what would happen classically? You would either see it here or see it here, right? Depending on which slit it passed through. In quantum theory you see something like this. You see something like this. What does that mean? That this single particle passed through both slits. Or in other words, there is ontic doubt here as to which slit it passed through. Not that I don’t know—because if I simply didn’t know, I wouldn’t see a picture like this. What I would see is either a picture like this or a picture like this; I just wouldn’t know which of the two. But if I see a picture like this, that means it can hit here and here. There is ontic doubt; the particle itself somehow passed half through here and half through here. Not that it passed through one of them and I don’t know through which slit it passed, but in some sense it passed through both, or half of it passed through here and half through here. It’s not literally half a little ball; that’s just a way of speaking. What it really means is that there are two possibilities here: one possibility is that it passed through here, one possibility is that it passed through here, and both happened. What happened was some combination—a superposition, as it’s called—of these two possibilities. That’s what is confusing in quantum theory. In quantum theory, the main thing that confuses us, or one of the main things that confuses us, is that the doubt there is not epistemic doubt but ontic doubt. Reality itself is vague. Because a situation where I don’t know something about reality—that they already knew before. With a die, I don’t know how to predict what number will come up. Okay? They already knew that before. That is a situation where physics does not give me sufficiently good tools to predict what will happen. In quantum theory, the point is not that I don’t know what to predict, but that both possibilities really occur. Not that I don’t know which of the two possibilities occurs. That is exactly the difference between epistemic doubt and ontic doubt. Fine. Now, that was the second type. The third type… fine, I’ll go to the fourth and then come back to the third. In philosophy there is a whole series of paradoxes that can be called the sorites paradoxes, the heap paradoxes. The heap paradox is basically built like this: first premise, one grain of gravel is not a heap—which is reasonable. Second premise… what was the first premise? If I have one grain of gravel, it is not a heap. It’s not a heap of stones. One stone. Two isn’t either, three isn’t either; many is a heap. So the first premise is that one grain of gravel is not a heap. Okay? Premise B: if I have a collection that is not a heap and I add one grain of gravel, that does not change its status. If I have a collection… if I have a collection of gravel stones that is not a heap, and I add one more grain of gravel, I have not changed its status. It remains not a heap. One stone doesn’t make a difference one way or the other. Premise C: a million grains of gravel are a heap. Okay? Each of these three premises on its own sounds reasonable. But together they are a contradiction, right? They don’t fit together. What? Remove one more, remove one more. Remove one more… it will still be a heap, because removing one stone does not change the status, right? Until you get to one, and it will still be a heap. Exactly. And therefore, if you adopt these three premises, each of which sounds reasonable, if we adopt all three of them together we run into a contradiction. An internal contradiction. Another example: the bald man paradox. If there is a person who has one hair on his head, he is bald, right? If you add one more hair to a bald person, that doesn’t change his status. But a million hairs—then he is not bald. Right? Exactly the same thing. I’ll tell you more than that: there is not one everyday concept that is not vulnerable to this attack. Not only concepts like heap or baldness or things like that. There is not one everyday concept that is not vulnerable to this attack. From when is it afternoon? My children asked me that several times when they wanted to go out so they wouldn’t make noise between two and four. From when is it already afternoon? Twelve o’clock is not afternoon, right? If you add one second, that doesn’t really change the situation. But four o’clock is already afternoon. So when does it switch? How can it be that it switches? That is true of every concept. Think about Escher’s metamorphosis, right? Between the birds and the fish. You know Escher’s drawings? So from when does it stop being a bird and start being a fish? And vice versa. Not the birds—they move between them. So from when does it change from a collection of fish to a collection of birds? There too you can’t know. A shift of one millimeter to the left doesn’t really change the situation from a collection of fish to a collection of birds, but clearly if we moved sufficiently to the left, we are in the bird section and not in the fish section. And every everyday concept can be attacked this way. So what do you say? What’s the solution? Yes. To make some kind of arbitrary decision, but to give it a rule that can’t… Okay, you think like a lawyer. Meaning lawyers, or certain analytic philosophers—that’s what they’re called. He has… not only lawyers, but in Jewish law it works that way. Right. Analytic philosophers solve this paradox this way: they define formally that seventeen stones and up is a heap, and then there is no problem at all. What fell away here? The rule that if you add one grain of gravel the status doesn’t change, right? Because if we’re at 16 and we add one, we get to 17, and that is a heap. So they gave up the second premise, but they gave it up in the manner of analytic philosophers, like a bull in a china shop. In other words, they did not really solve the problem. What did they do? They formulated a language in which the problem does not appear. But when I ask a question about the everyday language we use, we do not mean a heap of 17 stones and up, right? For us the concept of heap really is a fuzzy concept, not fully sharp, not fully clear. So you can’t solve the paradox the way the analytic philosophers do. So what can you do? Where does our everyday thinking actually escape this paradox? Not by defining some other language in which the paradox doesn’t appear. That’s a Stalinist solution to problems: forbid expressing them. Okay, but I don’t want to solve the problem that way; I’m asking what the real solution is. The answer is—and I’ll keep it short because we need to finish soon—you really do have to give up the second premise. The premise that says that adding one grain of gravel does not change the status—it does change it, slightly. And here you have to give up binary logic. In other words, the concept heap / not a heap is not something that should be judged by binary logic, either yes a heap or not a heap. So how should it be judged? It should be judged by multi-valued logic, a continuum. That means you can say that the degree of heap-ness of this collection is 0, 0.1, 0.32, 0.45, 0.9. And there is a continuum of levels of heap-ness. And that is the correct logic for dealing with concepts like heap, and in fact with every everyday concept. Then the first premise is true—one grain of gravel is not a heap. The third is also true—a million grains of gravel are a heap. The second premise is the incorrect one. The second premise, which says that adding one grain of gravel does not change the status, is incorrect—but not because we decided that seventeen and up is a heap, like the analytic solution. It is incorrect because we determined that the concept of heap is not judged by binary logic. We do not discuss every collection as either yes a heap or not a heap; we discuss the degree of heap-ness of the collection. Then I say: if I add one grain of gravel, I have increased slightly the degree of heap-ness of the collection. That is what changed. Okay? What does that actually mean? It means that when we think about everyday concepts, it is incorrect to judge them by binary logic. When a judge has to decide whether—for example, if the law says that a heap of stones belongs to someone if it is a heap and not scattered—yes, in a state where justice matters—if it isn’t scattered then it belongs to someone. What is a heap? So the judge can’t say, “What is a heap? Figure it out yourselves. Whatever people call a heap.” The legislator can’t say that. So now the judge has to decide what is before him in a case of 10 stones, 100 stones, or 1,000 stones, and he has to decide whether that falls into the category stated in the law, whether it is a heap or not a heap. How will he decide? There is a continuum of answers here between yes a heap and not a heap, and he will have to draw some legal line. Again, I’m saying the legislator can also draw the line in his place; the legislator can intervene and establish things that bind the judges. But on the principled level, this is the work of the judge or the legislator: he has to decide whether this thing is a heap, in which case norm A applies, or whether it is not a heap, in which case norm B applies. But what can you do, when heap / not a heap are only the two extreme endpoints? There is a continuum of levels of heap-ness, and the judge has to decide where on this continuum I place the cutoff, the threshold—when is it considered a heap? Notice that this is different by one second from the example I gave earlier, of betrothal not fit for consummation or from quantum theory. That’s why I called it a third type. How is it different? In those cases there is doubt in reality itself, or in quantum theory there is vagueness in reality itself; something in reality itself is not unequivocal. Here, in reality itself there is nothing at all that is not unequivocal. I know there are 10 stones here. What I don’t know is what, in human language, is called a heap. The human language is what is continuous here, not reality itself. The vagueness is in the language and not in reality, and therefore this is a third type. But on the other hand, it also is not epistemic doubt. It is not a case where I lack information about reality. I am uncertain. So it is not epistemic doubt and not ontic doubt. It is conceptual doubt. What would be a real-life example? Let’s say when it comes to interpretation? A real-life example? From when is it afternoon? Isn’t that a real-life example? When are you allowed to go outside and make noise? No, because there the legislator set the threshold like you did with the heap. But if the legislator had not set it—when in the afternoon is it forbidden to make noise? Sometimes the legislator can intervene. He can also intervene in betrothal not fit for consummation and decide yes or no. But fundamentally this is a decision that falls to the judge. Sometimes the legislator can say, okay, I don’t want judges deciding whatever they want, so I’ll decide. But fundamentally it is the judge’s decision. So you’re saying that more or less every judge has to calculate every matter and arrive at some threshold of certainty. But Judge Atza actually rejected that on purpose; he showed something more heuristic. Meaning he came to show all kinds of things where you could say what his heart tells him. I’m not asking—fine, I have no problem with that. He doesn’t need to do something formal and say from what number of stones it is a heap. He needs to sense what is called a heap in this context. What it is reasonable to call a heap. But you still need to distinguish between ontology and ontological and epistemological doubts. I distinguish them in legal theory, not in practice. In legal theory I ask whether there are non-binary questions that fall to the judge beyond a lacuna in recognizing reality. That’s what Schart asked. And he argued that there aren’t. And here I’ve shown you two types of examples—two types of examples where there are. Legal theory is different; in practice he makes similar decisions, fine. But isn’t there a field where they don’t do this intentionally—where a judge will not do it intentionally? That’s not theory; in practice every judge decides this way. What can you do? And if the legislator decided he doesn’t want that, then what counts as afternoon is four o’clock, and so the municipalities determine that afternoon is four o’clock, because they don’t want everyone deciding for himself. No problem. But fundamentally, as long as it has not been determined, that is the judge’s decision in the face of vague reality. I’ll give you an example. There is a halakhic concept called performing a prohibited act in an unusual manner. In the laws of the Sabbath, we perform prohibited labor on the Sabbath, and when it is done in an unusual manner—say with the left hand or in some strange way—then it is forbidden only rabbinically and not on the Torah level. Now there are situations in which one performs a certain prohibited labor on the Sabbath in an unusual way, and we see that it is completely permitted. And the commentators ask: wait, but doing it in an unusual manner is something that is rabbinically forbidden, so why is it completely permitted? There is a rabbinic prohibition, a lighter prohibition that the sages forbade and not the Torah. And the answer is of course that there is a continuum of degrees of unusualness. When the unusualness is very significant, far from the normal manner of doing it, it will be completely permitted. No one will say that when I dance the hora, that is trapping in an unusual manner. Because it is not similar to trapping deer, even though there too people run. There are minor similarities, right? Something is there. It’s a continuum of levels of similarity. And therefore, once again, we have to beware of this binary fallacy that says either yes or no. Moderate departures from the normal way are rabbinically forbidden; what is not similar at all, a very significant departure, is completely permitted. People often ask questions involving dilemma paradoxes. Let’s move to the fourth type. Dilemma paradoxes. People say there is no point in giving exams. Because those who study will study even without an exam, and those who don’t study won’t study even with an exam, so there’s no point in exams. What is the flaw in that argument? The pathologically diligent—true, they will study even without an exam. The pathologically lazy—true, they won’t study even with an exam. But the world is not divided into pathologically diligent people and pathologically lazy people. There is a continuum of levels of diligence in between. The concept of laziness or diligence is not a binary concept. There is a continuum of levels of diligence, and for many people who are somewhere in the middle, the exam is precisely what will make them study. Therefore there is a point. So again, the attempt to deal with things by binary yes-or-no logic produces all sorts of paradoxes, and you have to notice that there is actually a continuum of levels between the two poles. If I summarize—I didn’t manage to go over everything, but if I summarize—then basically we have three types of vagueness. The first type, which Judge Tal spoke about, is epistemic vagueness, what is called doubt in halakhic jargon. The second type is ontic vagueness, where there is vagueness in reality itself, as in betrothal not fit for consummation or the example from quantum theory. The third type is conceptual doubt, conceptual vagueness, where our everyday concepts are not judged by black-and-white logic, yes/no, by some binary logic, but rather by a continuum of levels. And here too the judge will have to decide whether we are above or below the forbidden, permitted, or obligatory level. Fine, let’s stop here.