A Proposed Explanation of the Rule of 'Kavua' (Column 237)

With God's help

Recently, questions were raised on the site as to how the rule of 'kavua' can be understood in the laws of majority. In response to those questions, I wrote that I would try to address the issue soon, because following Column 226 I had thought of an explanation of the rule of 'kavua' in light of the distinction I discussed there. This Sabbath we read the verse and lay in wait for him and rose up against him, from which the rule of 'kavua' is derived, and I thought this would be a good opportunity to discuss the matter.

The beginning of this discussion was in Column 79, where I presented an explanation of the distinction between two types of majority: de'itah kaman and de'leitah kaman. In light of that distinction, I also suggested there an explanation of the Talmud's determination in Hullin 11 that majority in a court is a de'itah kaman majority. In Column 226 (and also 228) I dealt with legal evidence, and to explain the puzzle that arises regarding it I used that distinction. Here I want to continue and, in its light, also offer an explanation of the rule of 'kavua'. To do so, I have to restate the main points and explain them a bit further. I should note that these matters are not sufficiently clear to me, and I am placing them here for the readers' consideration. I considered splitting this column into two parts because of its length, but decided not to. Those few who read it can do so at whatever pace seems right to them. Because of the breadth of the topic, in most places I have not elaborated or provided detailed sources.

The rule of 'kavua'[1]

The rule of kavua is a limitation on the laws of majority. Ordinarily, in Jewish law we follow the majority, both in judicial contexts and in matters of prohibition and permission. This rule is derived from the verse follow the majority ('follow the majority'). However, the Talmud in several places states that if the mixture, and the item under discussion, is fixed in its place, one does not follow the majority. The source for this rule is brought in the Talmudic passage in Ketubot 15a:

Returning to the text itself, Rabbi Zeira said: Anything fixed in place is treated as if it were half-and-half, whether for leniency or for stringency. From where did Rabbi Zeira derive this? Shall we say from the case of nine stores, all of which sell properly slaughtered meat, and one that sells carrion, where one bought from one of them and does not know from which of them he bought—the doubt is forbidden; but if it was found, one follows the majority?

We have already encountered the case of the majority of stores. This is a case of a person who found a piece of meat in a city street and does not know whether it is kosher or not. If most of the stores in the city are kosher, then as a matter of basic law he may eat the meat, since the assumption is that it came from the majority stores (the kosher ones). In halakhic formulation: Anything that separated is presumed to have separated from the majority, that is, whatever has separated is presumed to have separated from the majority. By contrast, if a person entered a store and took a piece of meat from there, and now does not remember from which store he took it, then even if most of the stores in the city are kosher he may not eat it. This is a case of 'kavua', since the doubt arose about a piece that was fixed in its place (in the store), and did not separate from it; therefore here we do not follow the majority. True, the piece in question is not regarded as certainly non-kosher, but it has the status of a doubt. Such a situation is treated as though the doubt were evenly balanced, and in a Torah-level doubt we rule stringently: Anything fixed in place is treated as if it were half-and-half. Why is there a difference between these two cases? In the second case, the piece of meat about which the doubt arose – or, more precisely, the store that sells non-kosher meat – is fixed in its place, and when something is fixed in its place, one does not follow the majority.

However, in the conclusion the Talmud rejects this:

There, it is for stringency.

It may be that the rule of 'kavua' was stated only to be stringent, and not to be lenient. That is, here the instruction not to follow the majority leads to a stringent result (forbidding the piece of meat), but perhaps in a case where the result would be lenient, Jewish law would indeed instruct us to follow the majority even if the item is fixed in its place.

In the next stage, the Talmud suggests another source for the rule of 'kavua':

Rather, from the case of nine frogs and one creeping creature among them, and he touched one of them and does not know which one he touched—his doubt is impure. There too, it is for stringency. Rather, from the case of nine creeping creatures and one frog among them, and he touched one of them and does not know which one he touched—in the private domain his doubt is impure; in the public domain his doubt is pure.

The source they bring is a situation in which there is a majority of impurity-conveying creatures and a minority that does not convey impurity (a frog). A person touched one of them and does not know which one. If we followed the majority, he would be impure (because most are impurity-conveying creatures), but the rule of 'kavua' says that this is a case of doubt. And in the laws of ritual impurity, the rule is that a doubtful impurity in the public domain is pure.

So here we have found a Talmudic source for the rule of 'kavua'. But this source is itself a law that requires a source from the Torah. From where did the Sages learn that in a case of a majority of impurity-conveying creatures one does not follow the majority? This is exactly what the Talmud now asks:

And from where do we know this on the Torah level? The verse says, "and lay in wait for him and rose up against him"—meaning, he must have intended him specifically. And the Rabbis of the school of Rabbi Yannai said: this excludes one who throws a stone into a group. What are the circumstances? If we say that there are nine Canaanites and one Jew among them, then it follows already that the majority are Canaanites. And if alternatively it is half-and-half, in cases of capital law we are lenient. No, it is necessary for a case where there are nine Jews and one Canaanite among them, so that the Canaanite is fixed in place, and anything fixed in place is treated as if it were half-and-half.

In the end, the Torah source for the rule of 'kavua' is the verse and lay in wait for him and rose up against him, which is said regarding a murderer. The verse in Deuteronomy 19:11 says:

But if a man hates his fellow and lies in wait for him and rises up against him and strikes him mortally so that he dies, and he flees to one of these cities:

A deliberate murderer is liable to death, and an inadvertent one is liable to exile. But that is only if he lay in wait for him and rose up against him. What does this exclude? When do we have a killing in which the murderer did not 'lie in wait for him and rise against him'? The Talmud explains that this refers to a case of a person who threw a stone into some group containing mostly Jews and one gentile (one is not liable to death for killing a gentile), and killed a Jew. Had we followed the majority, he would be liable to death, because from the outset this was an act of killing a Jew (since the majority were Jews). But the rule of 'kavua' teaches us that such a situation is treated as half and half, and therefore it is as though he threw a stone into a group containing half Jews and half gentiles. This is not an act of murder that incurs the death penalty.

The fundamental problem: can there be an explanation of the rule of 'kavua'?

So, in the ordinary case (when the object under discussion is not fixed in its place), the rule is Anything that separated is presumed to have separated from the majority, that is, we follow the majority. In the case of 'kavua', the rule is Anything fixed in place is treated as if it were half-and-half. At first glance, it is very difficult to understand the difference between the cases of 'separated' and 'kavua'. Even if the item is fixed, the probabilities are the same as in a case where it is not fixed in its place (= 'separated'). Indeed, many have already wrestled with this issue, and a number of suggestions have been made to explain the rule of 'kavua', most of them not especially convincing. It is therefore customary to think that this is a scriptural decree, that is, a law without rationale.

But this claim is very difficult. I have already pointed out several times that midrashic derivations always involve an element of reasoning. Were there no reasoning here, how would the interpreter know to derive from the verse and lay in wait for him and rose up against him that it comes specifically to exclude a case of 'kavua'? One could imagine many other cases in which there is reason to exempt (for example, where he acted indirectly, or alternatively according to Rabbi Shimon, who disagrees and derives from this verse that the murderer must have intent, and so on). The interpreter chose specifically to exclude the case of 'kavua', and did so on the basis of reasoning. We are forced to conclude that even before the interpreter learned this from the verse, there was some reasoning in the matter; that is, at the basis of this conclusion there must be some logic.

On the other hand, it seems that such an explanation cannot exist. To clarify this, I will mention here an anecdote from my own life. I have an old friend with whom I studied as a study-partner for many years, and from time to time he would come with yet another proposal to explain the rule of 'kavua' on the probabilistic plane. I would always say to him: before I address your proposal, just tell me whether you are also willing to drink poison on its basis. The rule of 'kavua' permits prohibitions (or at least turns them into a doubt). If it were based on chances and probabilities, we would have to act in accordance with it even in a case of poison and danger. For example, suppose before us there is a crate of ten cups, nine of which contain poison and one water. In another crate there are three cups of water and seven of poison. You are now offered a choice between two options: either take a cup from the first crate (a case of 'kavua', which is treated as half and half), or drink a cup that separated from the second crate (a 70% chance it is poisonous, because this is not a case of 'kavua'). Any sensible person understands that the second situation is preferable, even though halakhically the first situation is treated as 50% danger and the second as 70% danger. Therefore any sensible person will choose to drink the cup that separated from the second crate, even though halakhically this is the more 'dangerous' case. It follows that there is no probabilistic explanation for the rule of 'kavua'. Therefore, as I told him, there is no need even to examine an explanation that claims to be probabilistic. I am prepared to examine an explanation after you tell me that you rely on it for drinking poison as well, and not only for halakhic prohibitions, in line with Danger is treated more stringently than prohibition (danger is treated more stringently than prohibition).

So on the one hand there must be a rational explanation, and on the other hand it seems impossible that there be one. There are several suggestions for explaining this law (see below), and what they all have in common is that they are explanations of a legal rather than a probabilistic character (on this distinction, see Column 228). Probabilistically, the two cases are similar, and so apparently the only possibility left is to draw a legal distinction between the situations of 'separated' and 'kavua'.

Before proceeding, I need to present a distinction between two types of majority (and we already addressed it in Columns 79 and 226).

Rov de'itah kaman and rov de'leitah kaman

The Talmud in Hullin 11 distinguishes between two types of majority:

• Rov de'itah kaman – a piece of meat found in the city street when most of the stores in the city sell kosher meat. As a matter of basic law one may rely on the majority, that is, assume that the piece came from the majority stores, and eat the meat.
• Rov de'leitah kaman – most women are not infertile. When a particular woman comes before us and the question arises whether she is infertile or not, one may assume that she belongs to the majority group of women who are not infertile.

The literal expressions itah and leitah kaman (= before us) suggest the presence of the mixture before us (the whole mixture, not only the majority). At first glance, the difference between the two types of majority is that in the case of the stores the whole mixture is before us (we are speaking of a concrete, defined collection of specific stores known to us), whereas in the case of infertility the mixture is all the women in the world, who of course are not concretely before us and are not all known to us. In other words, rov de'itah kaman is a case of a mixture about which we have complete information, and the individual about whom the question arises is one of that group. The question is to which part of it she or it belongs. By contrast, in rov de'leitah kaman we do not have complete information about the whole group. Even if we have information about some of the women, the woman before us is one about whom we have no information, and we are trying to infer something about her from the information we have about the other women (or some of the other women).

But as I explained in Column 79, this is not the root of the difference between the two types of majority. My claim there was as follows:

• Rov de'leitah kaman is a kind of law of nature, that is, a claim about the nature of the world and not about a specific state of affairs. We are making a claim about a typical group not concretely known to us (all the women in the world). We know only a sample (presumably representative), and as I explained, such a majority-rule is obtained by generalization on the basis of a representative sample. Most of the women we have encountered are not infertile, and assuming this is a random and therefore representative sample, one can infer a conclusion about the nature of the world: that most women in the world are not infertile. All of this is true of rov de'leitah kaman, which deals with a mixture that is not before us and is not concretely known to us.
• By contrast, in the case of the stores we are not dealing with the nature of the world. There is no rule or law of nature that, in the world, stores are usually kosher (in fact, the opposite is true). This is a specific case in a specific place about which we have specific information. We simply know the group of stores in the city and know that most of them are kosher. This is not a generalization on the basis of a sample but based on concrete knowledge. Beyond that, this is an accidental majority (it just happens to be a place where most stores are kosher) and not something essential in the nature of the world.

It is important to understand that the notion of 'separated' is essential to the law of rov de'itah kaman. In these cases we are always dealing with a defined group about which we have complete information and that is divided into majority and minority. The doubt arises because at some stage one of the particulars separated from the group, and the question arises as to its status. Here the assumption is that the separation was from the majority subgroup, and that is the rule of rov de'itah kaman. By contrast, in rov de'leitah kaman there is no 'separation'. The woman about whom the discussion arises was at no stage found within some concrete group of women and then separated from it. True, she belongs to the general group of the women of the world, but there is no separation here (see further below).

There is no rule of 'kavua' in rov de'leitah kaman

I should note that according to most commentators, the rule of 'kavua' does not exist in rov de'leitah kaman (nor in the law of nullification by majority. Almost every case of nullification by majority is a case of a fixed mixture, and if the rule of 'kavua' applied there, there would be no law of nullification by majority in Jewish law). In rov de'leitah kaman one follows the majority even if the minority is fixed in its place. Only in rov de'itah kaman was the distinction stated between 'separated', where one follows the majority, and 'kavua', where one does not follow the majority (rather, it is treated as half and half). At first glance, this only further supports the idea that the rule of 'kavua' is a scriptural decree. If there were logic here, why should we not say the same regarding rov de'leitah kaman? In the verse and lay in wait for him and rose up against him there is no hint of such a distinction, and as I already noted, even if there were such a hint, reasoning would still be required in order to derive a halakhic conclusion from that hint. Therefore the conclusion is that since the rule of 'kavua' is a scriptural decree, part of it is the distinction between the two types of majority. The scriptural decree of 'kavua' was stated only regarding rov de'itah kaman.

But as we saw earlier, the rule of 'kavua' cannot be a scriptural decree without reason,[2] and therefore, beyond explaining the rule of 'kavua' itself, we must also look for an explanation of why it does not apply in a case of rov de'leitah kaman.

Majority in a court

The law of majority is derived from the verse follow the majority. When a dispute breaks out among judges, Jewish law is ruled in accordance with the majority opinion. Simply speaking, this is a case of rov de'itah kaman, since the panel of judges is a specific group of people present before us. And indeed, the Talmud there in Hullin derives from this verse the law of rov de'itah kaman, and not that of rov de'leitah kaman, which is different.

However, the Mordechai in the first chapter of Hullin asks why one follows the majority here, for the judges and the court are fixed in their place, and in a case of 'kavua' one does not follow the majority. He gives two answers there that require explanation, and I will not enter into them here. But it is worth noting that there is another difficulty here: the concept of separation does not belong to this case. No judge separated from the panel, and the question here is not what the source of the separated object is, or what this or that judge thinks. The judges' opinions are fully known, and they are all before us. The question that arises is on an abstract plane: what is the law ruled by the court. Therefore, apparently, this is not at all a question of following the majority.[3]

I can now present two explanations that I found for the rule of 'kavua'.

First explanation of the rule of 'kavua'

Rabbi Gordin, in his article, opens by presenting the difficulty we have just seen: the majority in a court differs from the case of the majority of stores, because in the case of the majority of stores we are looking for the identity of the piece under discussion (which separated), whereas in a court the opinions of the judges are known and the question is what the law is. He therefore explains that in both cases this is a majority that comes to clarify the identity of some collective, the city's stores or the court, and from that to derive the conclusion about the object before us. We are not discussing the piece, but the collective to which it belongs. Its status is derived from the very fact of its belonging to that collective. If this is a city of kosher stores, then the city's stores as a whole are kosher, and the piece of meat is therefore also kosher. If this is a court (the collective combination of the three judges) that rules to obligate, then the law issuing from it is that the litigant is liable. This is unlike rov de'leitah kaman, where the discussion is directly about the object before us and not about the whole (because the whole is already known, since it belongs to the nature of the world). Thus, in his view, in rov de'itah kaman I am discussing the identity of the collective, whereas in rov de'leitah kaman I am discussing the identity of the specific object.

From this he also explains the rule of 'kavua'. He says that if the piece separated from the store and is found in the street, then the discussion is about the stores and, through them, about the piece, and therefore this is rov de'itah kaman and one follows the majority. But if I took a piece from the store itself and do not remember from which store, then there is no discussion here at all about the character of all the stores in the city, but about this particular store. In such a case the law of majority was not stated. This is the explanation he offers for the rule of 'kavua'.

From this he derives a conclusion about the character of rov de'itah kaman:

In light of the explanation we are now proposing for rov de'itah kaman, we will say that the statistical survey is not a factual clarification but an instrument meant to determine the character of the place. If most voters in a certain city voted for the red party, then the city is a 'red city', and therefore the residents who live in the city are 'red'.

According to what we have said, reliance on the majority in a case of itah kaman is directive rather than clarificatory – the Torah determined that follow the majority, and therefore in every case of determining the character of a body, we determine it on the basis of the majority.

According to him, this is not a clarifying majority because it is not dealing with statistics but with determining the identity of some collective.

From here it is also clear why the distinction between 'kavua' and 'separated' was stated only in the context of rov de'itah kaman. In rov de'leitah kaman, in any event, the question is not about the collective, and so it does not matter whether we are dealing with 'kavua' or not.

But in my humble opinion, his remarks are difficult in several respects. First, what he describes is a question of determining the character of a collective from observation of the distribution of its particulars. But this is not the law of following the majority; it is nullification by majority, or perhaps the principle that the majority counts as the whole. Second, from the very distinction that I described here in contrast to rov de'leitah kaman it emerges that even when the discussion is about the piece itself, one uses the law of majority (that is the situation in every rov de'leitah kaman). So why should one not use it in a case of 'kavua' within rov de'itah kaman? Admittedly, according to Rabbi Gordin, in such a situation one cannot determine the status of the collective because the question does not concern it. But one can still use the law of majority to determine directly the status of the piece itself. Third, even if I took the piece from the store and the discussion is about the piece itself and not about all the stores, why should I not treat that store as something that separated from the totality of the stores in the city and ask about the store, instead of about the piece, the same question: I would derive the store's status from its belonging to the totality of the city's stores.

One could perhaps, with some effort, argue that in such a case there is no question about the store but only about the piece, since I do not know which store it is and the entire question is only whether the piece is permitted or forbidden. In such a situation, the discussion is conducted only for the sake of determining the status of the piece in my hand, and in such a case one does not need to determine the character of the store but only of the piece. But this is a formalistic distinction, and it is hard to see in it an explanation. At most, it is a proposal for defining the concept of 'kavua', but I do not think there is an explanation here. Why, in situations defined this way, should we not follow the majority?

Second explanation of the rule of 'kavua'

A similar but different explanation (and in a certain sense the opposite one) for the rule of 'kavua' can be found in Moshe Koppel's lecture. He presents a container with ten balls in it, nine white and one black. Now think of two scenarios: 1. I put my hand in and remove a ball. The question posed before we see the ball is: what is the color of this ball? 2. A hypothetical question: if we were to put in a hand and remove a ball, what would its color be? The first question can be answered either black or white, and either answer might be correct. Probabilistically, the color is probably white. But the second question cannot really be answered at all. There is no well-defined way to answer the hypothetical question. All that can be said is that the container contains nine white balls and one black one. So long as no ball has been removed, the question is not well-defined. This can be understood if we think about the fact that the question is how the removal of the ball would be carried out. Different modes of removal would yield different answers. For the time being, as long as this has not happened, there has been no removal and there is no ball. Therefore the question of its color is meaningless. In such a situation one can discuss the group as a whole and not a specific individual within it. This is exactly the situation called 'kavua' in Jewish law.

Why can one not ask the hypothetical question: if a person puts his hand into the container and randomly removes a ball, what will its color be? Seemingly, I am dealing here with a defined event and trying to describe it. Because the answer to such a question cannot be anything other than: sometimes black and sometimes white. Notice that at this stage, neither the answer black nor the answer white is correct. For the time being there is no specific ball whose color can be asked about, and therefore the question is not well-defined. In such a situation one can ask questions only about the group and not about any specific ball.

Now, Koppel continues and explains, the case of someone who throws a stone into a group is exactly like the example of the hypothetical question. For there is no question who that person is who is killed. We know he was a Jew. The question concerns the state before the throw, and it is a question about the future: if a stone is thrown, who will be the person killed – a Jew or a gentile? Therefore here too the question about a specific person is not well-defined, because such a person does not yet exist. At most one can speak about the character of the group as a whole. According to him, this is also the meaning of separation. When the object separates from the group it has independent standing, and then one can ask questions about it. But so long as it is fixed in its place, it has no standing apart from the group and one can therefore ask only questions about the group as a whole.

In summary, his claim is that a state of 'kavua' is a state in which the question about the piece or the individual under discussion is not well-defined, as in the two cases we saw here. This is a state in which one can deal only with the group as a whole and not with an individual from within it. On that basis he also explains that the statement Anything fixed in place is treated as if it were half-and-half does not mean that the probability is one-half (an evenly balanced doubt), but that we cannot have a position regarding this question. The two answers here stand on the same footing not because we have reasons to equate them, but simply because the question is not well-defined and therefore no answer can be offered. There one can see several halakhic proofs for his claim that the status of 'kavua' is not an evenly balanced doubt but lack of knowledge.

He himself points to difficulties in his proposal. There are several Talmudic passages that make the rule of 'kavua' depend on the question whether the object changed or changes place, or whether it is found in its place. They also distinguish between situations in which the whole is moving or stationary. But on his approach there is no room for such a distinction, because what matters is the status of the doubtful object relative to the whole to which it belongs, and it does not matter whether that whole is stationary or mobile. Various extensions of the rule of 'kavua', in the Talmud or in the medieval authorities, really do not fit all the explanations proposed for this law, and it seems that there is no escaping the conclusion that the extensions no longer preserve the logic from which the law arose. Once it was created, it was already understood linguistically: whatever is fixed in its place has the law of 'kavua', and whatever is mobile does not. The explanation offered here is only for the original source of the distinction between 'kavua' and 'separated', but it does not fit all the cases in which the Talmud or the medieval authorities make use of it. That is probably true of all the explanations I know.

Why did I write that in a certain sense this is the opposite explanation from Rabbi Gordin's? Because Rabbi Gordin argues that specifically in the law of 'separated' we ask a question about the group, whereas in the law of 'kavua' the question is about the object before us. But on a second look it may be that these are two aspects of the same matter. After the separation, the object under discussion has independent standing, and then one can ask questions about it. This is what Koppel explained. But how are those questions answered? How is its status determined? In light of the character of the group from which it separated. And so here a discussion of the group is indeed required, and this is what Rabbi Gordin is talking about. The question is asked about the object, but the answer is determined by the character of the group. Still, it is clear that these are two different explanations of the rule of 'kavua'.[4]

Still, even according to Koppel it is not clear why one should distinguish between rov de'itah and de'leitah kaman. Even in the case of infertile women one could say that we are asking a question about the whole and not about a particular woman. And if she separated and stands before us, then the question is about her.[5] Moreover, when I take a piece of meat from the store, why can one not say there that the question is about the piece and not about the store or about all the stores? This is a piece that I took, and I ask whether it is kosher or non-kosher. Why should it matter whether it separated or not? It is important to understand that the case of the stores is the essence of the rule of 'kavua', and it is very hard to accept that even there the law of 'kavua' is applied when the original logic of the law does not exist in such a situation (as I suggested above regarding other passages). This is the primary case brought in that very sugya in Ketubot that brings the source from the case of one who throws a stone into a group.[6]

I will now offer an explanation of my own that will also answer the distinction between de'leitah and de'itah kaman, and at the end I will return to explain why it too is related to those two explanations.

The Chinukh's explanation of majority in a court

Before I offer my explanation, I will preface it with another difficulty. The Chinukh, in commandment 78 (see Column 69), explains that following the majority in a court is based on the reasoning that usually the majority of judges is more correct than the minority (when they are roughly equal in wisdom). At first glance, this is rov de'itah kaman, since it deals with a certain court panel that is present before us and not with the nature of the world, and this is also what the arguments brought above regarding majority in a court assumed. But at least according to the Chinukh, this is not correct. Notice that the Chinukh changes the rules of the game. The majority under discussion is not the majority of the judges, but the majority of judicial panels in which disputes arose in different courts in different periods. He is not discussing the mixture of judges in the specific court before us, where there is a majority that obligates and a minority that exempts and one is to follow the majority. That is what Rabbi Gordin, for example, assumed, and what many others assume. The Chinukh, by contrast, claims that the mixture under discussion is the totality of the cases in which disagreements have arisen in courts since the dawn of history.

But in light of this, R. Shimon Shkop's objection to the Chinukh is called for. R. Shimon argues that such a majority is rov de'leitah kaman and not de'itah kaman. Here we are not dealing with a claim about a certain concrete court wholly before us, but about the nature of the world: what happens in all cases in which there are disputes in courts. The claim is not about this particular panel, but about the collection of judicial panels in which disagreements arise. The assumption underlying follow the majority is that in most such cases the majority is the one that was correct, and from this it follows that this is what we should assume in the case before us as well. As stated, this is a general claim about the world and not something about the panel before us. If so, it is true that the panel before us is physically present here (= itah kaman), but that is irrelevant. This is not the mixture in question, nor the majority in question. The judgment regarding this case is derived from a majority in the nature of the world. This is a mixture of cases and courts that is certainly not before us, and we have no concrete information about it. Therefore, R. Shimon Shkop argues – and rightly – that this is rov de'leitah kaman. If so, this explanation of the Chinukh does not accord with the Talmud's determination in Hullin 11 that majority in a court is rov de'itah kaman.

Resolving the difficulty: another explanation of the difference between rov de'itah and de'leitah kaman

I remind the reader that above I explained that in rov de'leitah kaman we do not have information about the whole group. We arrive at the majority rule by way of generalization on the basis of a sample (from several women we met we infer regarding women in general that most are not infertile). By contrast, in rov de'itah kaman we have direct acquaintance, and we are dealing with a specific group to which the object under discussion belongs. In a case of rov de'itah kaman there is no way to create a sample and generalize from it. For example, in the case of the stores (which is rov de'itah kaman), there is no way to separate pieces of meat from a collection of stores in a random and uncontrolled way and examine their source. Even if we gather lost pieces, we have no way of knowing to which store each one belongs (whether it is kosher or not). Therefore in such a case one cannot do statistics, that is, generalize from the findings of an experiment and establish a general rule according to which most pieces in such a situation come from the kosher stores. The loss of a piece of meat is a process that happens accidentally and not in an intentional way.[7]

The conclusion is that in the case of the stores we are dealing with a priori reasoning and not with generalization from a sample. Our logic tells us that if most of the stores in the city are kosher, then the piece under discussion probably came from one of them. Thus, what characterizes rov de'itah kaman is that it is a product of our reasoning and not of generalization from a sample. Rov de'leitah kaman, by contrast, is a law of nature produced scientifically: one takes a random and representative sample and infers from it conclusions about the nature of the world (about all such objects or all such phenomena in the world).

We can now also understand the words of the Chinukh. Even in the case of disagreement in a court, we have no possibility whatsoever of making a generalization from a representative sample. To do so, we would have to examine a sample of cases in which there was a dispute in court and see whether the majority was indeed right or not. If we discovered that in most cases the majority was right, we could infer the general conclusion that the majority is usually right. But no such experiment can be performed. We have no way of testing whether in a given case the majority was right, because we have no way of knowing the truth beyond the evidence presented before the court. We have no way to test the claim on a sample, and therefore the general conclusion (the majority rule) is not the result of generalization from a sample. So on what basis do we determine that the majority is usually right? On the basis of a priori reasoning. That is what seems reasonable to us (one can even build models for this, and I did so in Column 145). Therefore, majority in a court is rov de'itah kaman, since its basis is a priori reasoning and not generalization from a sample.

From here we learn that what chiefly defines rov de'itah kaman is not that it is a local and accidental claim (rather than a claim about the nature of the world), but that it is a priori reasoning and not generalization from a sample. Therefore majority in a court, although it is based on a claim about the nature of the world, is rightly classified by the Talmud as rov de'itah kaman. The majority among butcher shops obviously has nothing to do with the nature of the world, but with the specific and accidental reality before us. Rov de'leitah kaman, by contrast, is a law of nature arrived at by generalization from a sample, as we know with all laws of nature. One examines certain observations and generalizes them into a general law that describes the nature of the world.

An explanation of the difference between two types of statistical evidence

In Column 226 I explained in this way also the difference between two types of statistical evidence in law. There we dealt with the example of a mass assault by prisoners on a guard, where out of the hundred prisoners who were in the yard only one did not participate in the events. In such a situation one cannot convict a prisoner who is standing trial merely because 99% of the prisoners participated in the incident. By contrast, if there were an eyewitness who incriminated him, that evidence would be accepted even though the reliability of an eyewitness also does not exceed 99%. The explanation I proposed there was that the reliability of a witness is something that can be empirically tested and is obtained by generalization from a sample (one can test the reliability of the sight of a random group of witnesses), and this parallels rov de'leitah kaman. By contrast, the conclusion based on the fact that most of the prisoners participated in the incident is not obtained through generalization from a sample. There is no way to conduct an experiment that would test it empirically. This is a priori reasoning that parallels rov de'itah kaman. What is the advantage of rov de'leitah kaman? Why should only it be accepted as admissible legal evidence? I explained that such a majority is the result of empirical research and not of mere reasoning, and in law we want a basis in facts and not in conjectures.[8] Below we will see an additional explanation for the superiority of rov de'leitah kaman.

Is rov de'itah kaman based on information?

The explanations I have presented up to this point raise a more fundamental question: is a consideration of rov de'itah kaman really a statistical consideration at all? In what sense is the decision that the piece of meat separated from the majority group of stores statistical? The statistics here are not the result of examining a representative sample but the result of reasoning. After we adopt the reasoning, one can speak of probabilities and statistics. By contrast, in rov de'leitah kaman the statistics are the result of empirical observation and not of assumption. In rov de'itah kaman the use of the term 'statistics' is misleading. We are dealing with reasoning, and only after adopting it can one, by its force, speak of probabilistic calculations. The probability here is the outcome of the reasoning and not the result of observations and calculations, and therefore this is not really statistics. The same is true regarding majority in a court and the majority of the prisoners in the violent prison incident. In both those cases, too, we are not really dealing with statistics. The statistical calculations are only an expression of a priori reasoning. This is unlike rov de'leitah kaman, or eyewitness testimony in the legal context, where the statistics are the basis for our trust in the general rule. That is not an a priori law but an a posteriori one (a product of experience).

Just to illustrate the point, think of a person who claims that in his opinion an overwhelming majority of Ashkenazim are criminals. He now considers whether so-and-so, who is Ashkenazi, is a criminal or not, and convicts him on the basis of that assumption. Even if he is completely convinced of this assumption, it does not seem reasonable to convict someone on its basis. This is his a priori assumption and not the product of statistics. Moreover, even if that person speaks of a statistical consideration, since in his opinion most Ashkenazim are criminals and the defendant is Ashkenazi, this is taking the name of statistics in vain. The statistics in this case are the result of his reasoning (a priori) and not the result of observation and calculation (a posteriori). By contrast, if a person were to conduct research and discover that empirically most Ashkenazim are criminals, then his use of a statistical consideration in order to convict a defendant would be more reasonable (though even that would still be inadmissible, for other reasons). Notice that this description is true even from that person's point of view, if he is fully convinced of his assumption. That is, my criticism does not stem from the fact that his assumption is false, but from the fact that he convicts a defendant on the basis of an a priori assumption and not on the basis of facts and observation.

We saw that the assumption that a piece that separated did so from the majority of the stores is an a priori assumption and not a statistical consideration, and therefore one cannot convict on its basis in criminal law or make halakhic determinations on its basis alone. Not because it is incorrect, and not because it is not agreed upon. In this case the assumption is probably correct and is also accepted by an overwhelming majority of people. And yet, this is a priori reasoning, and reasoning alone is not enough to convict. A statistical consideration has force because it has an objective factual basis and is not mere reasoning. Perhaps that is the reason that rov de'itah kaman requires a source from the verse follow the majority. Without the source, perhaps we could not make use of it.

In light of this, one can understand why R. Shimon Shkop, at the beginning of Gate 3 of his book Sha'arei Yosher, rules that rov de'itah kaman is not a matter of reasoning but a novelty of the Torah (learned from the verse follow the majority):

And in truth, if we come to judge in the case of the nine stores and decide that the separated meat is from the nine stores that sell properly slaughtered meat because the majority makes it more likely that this occurrence happened with them, this clarification is not true. For with respect to each and every one of these ten stores we can determine that it did not separate from it, since there are nine others opposed to it, yet in any case it separated from only one of them. And in the reality of the separation there is no distinction between properly slaughtered meat and carrion, and therefore the whole notion of clarification and decision is nullified here. And since there is no clarification of the reality regarding the very separation of the meat, there is consequently no clarification at all regarding the kashrut of the meat.

Further on there, he rules that this is not a clarification at all but only a legal-halakhic mode of conduct:

Likewise, the rule generated by the majority of stores against the minority is a rule that we are to act in accordance with, even though in reality there is no clarification here at all; and based on this principle the Talmud says that a majority that is before us is derived from the verse, "follow the majority"…

At first glance, his remarks are puzzling, and I never understood them. Every reasonable person would say, even without a verse, that if a piece of meat is found in the street it probably came from the majority stores. This is accepted reasoning, and it is hard to understand the claim that this is a scriptural decree and not clarification. Do systems that do not rely on verses of the Torah and Talmudic derivations not adopt this kind of reasoning? Every reasonable person accepts the logic of this reasoning. In light of my remarks above, one can perhaps suggest that what he means is that although there is reasoning here, this is not a majority on which one can rely as a clarification (that is, as a statistical consideration). It is reasoning, but it is not the result of empirical research, and therefore it is hard to treat it as 'clarification' (= legal evidence by way of majority as a statistical consideration).[9]

Another formulation: rov de'leitah kaman describes a mechanism rooted in the nature of things

In another formulation, one can explain the difference between the two types of majority as follows. Rov de'leitah kaman uses a sample to uncover a property of the world. The conclusion that most women are not infertile testifies to something about the nature of the world. Through observation of the women in the sample, we discovered that there is something in the physiology of the ordinary woman that gives her the ability to bear children. The claim regarding some woman that she is infertile is a claim that the law of nature does not apply in her case. This is a problematic claim that requires grounding and justification. Without that, the assumption is that there is some physiological factor in every woman by virtue of which she can bear children. Therefore, regarding every woman who comes before us, our assumption is that she has the ability to bear children. This is a result of her nature. The majority that we examined merely points to that trait and that female nature. The conclusion regarding the woman before us is not derived from the women we examined in the sample, but from the law of nature that we discovered through them. Once we have discovered it, the assumption is that it exists in every woman, and by virtue of it we conclude that she has the ability to bear children.

By contrast, in rov de'itah kaman there is no law of nature. There is no reason in reality because of which we assume that the piece of meat before us is kosher. Here we really do infer a conclusion from the properties of the group as a whole about this particular member of it. There is no natural mechanism that causes this result (that the piece of meat be kosher). This is an external indication and not an internal mechanism (a law of nature).

At the beginning of Gate 3, R. Shimon Shkop notes that Maimonides' view is that rov de'leitah kaman is stronger than rov de'itah kaman. He is puzzled by this, for rov de'itah kaman is a majority based on concrete information lying before us, whereas rov de'leitah kaman is only a conjecture or a mere generalization. But in light of the picture I have presented here, this can be explained as follows. In rov de'leitah kaman, regarding every woman who comes before us, we have a positive reason to claim that she is not infertile. Therefore the conclusion that she is not infertile is well grounded and is considered relatively solid. By contrast, in rov de'itah kaman we have no specific reason within the object to assume that this is its nature (that the piece of meat is kosher), and we do this only because of a reasonable assumption or because of the character of the group to which it belongs. I gave an example of this from what I called the 'David Levy effect'. David Levy was a Knesset member in Likud, and he argued before the party center that members of his faction were not receiving proper representation in the institutions and executive positions. The members answered him that all appointments were determined democratically by vote, and the majority decides. David Levy answered them that this is exactly the problem. Every position that comes up for a vote is decided by the majority faction, and so 100% of the positions are filled by members of the majority faction. This is exactly what happens in rov de'leitah kaman. Every woman is considered not infertile because regarding each and every one of them there is a positive reason to assume this (even though we know that infertile women exist, the nature of the world is that a woman has the ability to bear children). In rov de'itah kaman there is no such reason with respect to each particular object; there is only an evidentiary directive to assume that most cases are of that kind. In the absence of another reason, we will not assume otherwise with respect to any particular object, but there is still no positive reason for such a conclusion with respect to each and every individual. Therefore rov de'leitah kaman can be considered stronger.

Implication: does rov de'itah kaman describe a probability?

At first glance, this is only a legal claim. From a probabilistic point of view, in the two cases there is a similar likelihood (assuming the majority is similar). Why should it matter that in rov de'itah kaman the basis is not a mechanism rooted in the nature of things, but rather some external, accidental evidentiary matter? At the end of the day there is a certain chance that the claim is true, and that is what counts.

But that is not correct. This distinction also has a probabilistic dimension. In the case of the pieces of meat, there is in fact no probabilistic basis for the conclusion that the piece is kosher. This is an assumption that stems from lack of information. In reality, it may be that the chance of losing a piece of meat from store A or B is higher or lower. The matter can vary from place to place and from one situation to another. In the absence of information, we assume that the chance that the piece is kosher is equal to the proportion of kosher stores, but this is an assumption without basis, made only because we have no logical way to assume anything else. Therefore even probabilistically it is not correct here to say that the chance that the piece is kosher is 90%. All we can say is that if we are forced to adopt some position, we will adopt the position that the piece is kosher. Thus, this is a difference that belongs also to the probabilistic plane. Someone who would want to gamble on the chance that the piece is kosher in a case of nine against one is a rash person. In any case, he is not relying on information but on an assumption called for by lack of information. The determination regarding a woman that she is not infertile is the result of positive information that we have about the nature of women in the world generally. By contrast, the result regarding the piece of meat is specifically a product of lack of knowledge. In the absence of any other information, we have no choice but to assume that this piece is kosher.

This is similar to rolling a die. If we know that the die is fair (for example, on the basis of a sample of many throws that were distributed uniformly among the six possible outcomes, or because we know the structure of the die and know it is symmetrical), then the conclusion that the throws will be uniformly distributed is the result of positive information. If I am asked what the chance is that the result will be 5, I can answer, on the basis of information, that the chance is 1/6. This is an answer on a probabilistic basis. By contrast, if I have before me a die about which I have no information at all, and I am now asked what the chance is that it will land on 5, then apparently I cannot answer. When the distribution is unknown, there is no way to give a probabilistic answer. But if I nevertheless have to guess, it is reasonable that my answer will be 1/6. Because I have no concrete information, there is no reason to prefer one outcome over the others, and therefore the least bad answer would be that the chance is 1/6. But this is not really a chance, because it is not the result of a probabilistic calculation.

I think this is the Torah's novelty in the fact that we follow rov de'itah kaman. In rov de'leitah kaman we follow information, and there is no novelty in that (except for the legal-halakhic novelty that one may rely on probabilistic information as evidence). But in rov de'itah kaman there is a novelty in the very 'probabilistic' determination, for here I am not relying on information at all but on a principle of equal weight among possibilities in the absence of information. In the absence of information all possibilities have equal weight, and from that point on I treat this as though I had information. The answer here is not the result of a probabilistic calculation, nor of positive information, but of reasonable reasoning (what it is reasonable to answer in the absence of information).

A further look at rov de'itah kaman

In light of these remarks, one can perhaps offer another explanation of the rule of 'kavua'. First, if indeed rov de'itah kaman is not a probabilistic majority, then the identity between the case of 'kavua' and the case of 'separated' is no longer necessary. That distinction required explanation mainly because we assumed that in both cases there was the same probability, and therefore an explanation was needed as to why in 'kavua' one nevertheless does not follow the majority, whereas in 'separated' one does. But once we have seen that following rov de'itah kaman is founded on a priori reasoning and not on a probabilistic majority based on information, and that the Torah innovated that even this may be treated as a majority, then there is more room to distinguish between the situations. Perhaps this novelty exists only in 'separated' and not in 'kavua'. But that distinction still requires explanation. Even if this is not probability, it is still not clear why we should assume that the Torah's novelty regarding rov de'itah kaman was stated only about 'separated' and not about 'kavua'. What is the difference between these two situations?

To understand this better, we must understand what exactly the novelty is in rov de'itah kaman. As stated, this majority, even in the case of 'separated' (where a piece separated and is found in the street), is not probabilistic. So on what basis is the majority determined? R. Shimon Shkop, at the beginning of Gate 3 (chapter 1), after determining that rov de'itah kaman is not probabilistic (see above), explains this rule as follows:

Rather, it appears that the matter of the nine stores is like the matter of the law of majority rule among judges. Since the meat necessarily separated from one of the ten stores, each and every store generates a legal consideration regarding the meat, casting doubt on its status. Thus, with respect to the meat there are nine factors generating a basis for permission and one factor generating a basis for prohibition, and the Torah said, "follow the majority"—for that is likewise the rule with judges, that the Torah said that we must act in accordance with the ruling that emerges from the majority. Likewise, the rule generated by the majority of stores against the minority is a rule that we are to act in accordance with, even though in reality there is no clarification here at all. And based on this principle the Talmud says that a majority that is before us is derived from the verse "follow the majority." And on this Rabbi Meir does not disagree by saying that we are concerned for the minority, just as he does not disagree in the case of judges. But a majority that is not before us—such as the idea that most animals are kosher and the like—which is not comparable to a majority that is before us, so as to make it analogous to judges: in a majority that is not before us, there is no concrete reality before us generating permission or prohibition, only an evaluation of reality based on the more common and usual occurrences. This kind of majority is not derived from that verse concerning judges, for there it is not based on clarification, whereas a majority that is not before us is based on clarification. Therefore we must say that this matter—that we follow a majority that is not before us—we received as a law given to Moses at Sinai; or that the Sages received that the Torah included this too in the verse "follow the majority." And regarding this Rabbi Meir disagrees and says that we are concerned for the minority. And where there is no alternative, it is different—meaning that there we are compelled to say that in just such a case the Torah imposed liability or declared valid, since the Torah said, "One who strikes his father shall be put to death," it imposed liability in just such a case, and so too with everything else brought there in the Talmud in the first chapter of Hullin.

What he means is that when a piece of meat separates from the collection of stores, each store presents one possible side or explanation for where that piece came from. There are nine sides according to which it came from a kosher store, and one side according to which it came from a non-kosher store. Since this is not a matter of probability and chance, the Torah tells us to count sides and possible explanations or answers, and to go after the majority of sides. He explains there that this is also how following the majority in a court works (each judge contributes a side that the law is such-and-such, and therefore to determine the law one follows the majority of sides).[10]

This may explain the view of several halakhic decisors[11] who maintain that the law regarding a found piece of meat does not depend on the number of pieces in each store (that is, the size of the store). Even if the non-kosher store has many more pieces of meat than all the other stores together, one still follows the majority of stores. Why? Because one counts sides and possibilities, not numbers of pieces. The question is from which store the piece separated, not what kind of piece it is.[12] To that question there are ten possible answers, and when one counts possibilities one goes after the majority of possibilities. As stated, this is not a probabilistic claim but a halakhic mode of conduct.

Third explanation of the rule of 'kavua'

The picture I described exists only when there is separation of the piece from the stores. In such a case, the question concerns the origin of the piece, and each of the stores offers a possible answer. In such a case there are ten answers, and nine of them lead to the conclusion that the piece is kosher. The rule of rov de'itah kaman instructs us to treat such a situation as though there were a 90% probability here. By contrast, when the piece is taken from the store itself and the question arises whether the piece (and the store) is kosher or not, there is no separation of something out of a mixture. The piece and the store are fixed in their place, and the question is not where the piece came from, but what the status is of this piece (and this store). In such a situation there are before us only two possibilities: either the piece (that is, the store from which I took it) is kosher or it is not. When there are two possibilities, the conclusion is that this is an evenly balanced doubt (half and half). As stated, this is not a probabilistic claim that the chance is 50%, but that I do not have a majority of sides (possibilities) here, and therefore the halakhic directive cannot prefer one option over the other. If this is not a matter of probability but of counting sides and possibilities, then what determines things is the number of possible explanations for each side. This is strengthened by Koppel's claim, cited above, according to which the law in 'kavua' is not that of an evenly balanced doubt but of the absence of an answer. This is exactly what I explained here: rov de'itah kaman is a state of lack of information.

If we again use the example of rolling a die, above I compared rov de'itah kaman to a die whose nature is unknown to us (whether it is fair or not). In such a case, following the majority is a default in the absence of information and not the result of a probabilistic calculation based on information. Rov de'leitah kaman resembles a die known to be fair (whether because we carried out repeated throws and discovered that it is fair – generalization from a sample – or because we know its structure). In both types of case, the answer is a result of the character of the die, and the difference is only whether we know it (rov de'leitah kaman) or conjecture something about it in the absence of information (rov de'itah kaman). But the case of 'kavua' is somewhat similar to a situation in which a person is required somehow to choose a certain face of the die, and we ask which face he will choose. Here there is no distribution, and one cannot answer on the basis of a probabilistic calculation. It depends on how he touches it and how he chooses one face rather than another. In such a case, the answer does not depend on the properties of the die but on the nature of the person's action, and we have no idea about that.[13] Therefore, in the absence of information, when asked whether he will touch the 5 or another face, in principle we cannot answer. The question is not well-defined until they define for us the manner of the person's action (with a die whose character is unknown, the question itself is perfectly well-defined; only the answer is hidden). The answer that the chance of getting 5 is 1/6 is not reasonable, because one cannot speak of chances in such a state. If nevertheless, for some reason, we were forced to adopt a position (for example, for some halakhic purpose), Jewish law tells us that we must treat it as though the chance were 1/2 (there are two possibilities: either he will touch 5 or he will not).

The same applies to the case of one who throws a stone into a group, or one who touched either an impurity-conveying creature or a frog. When the mixture is fixed in its place and there is no separation of one object from it, the question that arises is a question about the object itself and not about the character of the whole mixture. Therefore there are not many sides and possible explanations here, and all that remains are two possible answers: an impurity-conveying creature or a frog, a Jew or a gentile. Therefore in these cases too the halakhic rule is that one should relate to it as half and half.

Several remarks on the proposed explanation

The starting point for the discussion was a dilemma. On the one hand, there must be an explanation for the rule of 'kavua', for otherwise the Talmud would not have derived it from the verse. On the other hand, it seems that on the probabilistic plane it is difficult to point to a distinction between 'kavua' and 'separated', and therefore the explanation here will not be probabilistic but legal-halakhic (see Columns 226 and 228).

At first glance, my explanation too of the difference between 'kavua' and 'separated' is legal-halakhic and not probabilistic (I would not drink poison on its basis), but one should note that it nevertheless differs in character from the earlier explanations. First, my point of departure is that rov de'itah kaman in itself, even in the cases in which it is used (= 'separated'), is not probabilistic. Within it there are two situations, 'kavua' and 'separated', and the difference between them is a difference in the question being asked. But in both cases, on the probabilistic level, there really is no clarification here.

From here a surprising conclusion emerges. I already mentioned that it is customary to think that the rule of 'kavua' is the novelty, since its probability is identical to that of 'separated'. But according to my approach, neither involves a probabilistic consideration. Therefore the novelty is specifically the halakhic determination that in 'separated' one does follow rov de'itah kaman (even though there is no probabilistic clarification here), and not the limitation that in 'kavua' one does not follow it. At the same time, it is important to understand that this still is not a 'scriptural decree', that is, a law without reason. As I showed, our logic tells us that in the absence of information one should give equal weight to all the possibilities (the explanations). This is admittedly not a probabilistic determination, but one still cannot say that it is not logical. Every reasonable person behaves this way.[14]

According to my approach it is also self-evident why the distinction between 'separated' and 'kavua' was stated only with respect to rov de'itah kaman, for the whole point is rooted in the fact that in rov de'itah kaman we are not dealing with probability but with counting possibilities. From this it is also clear that the law of nullification by majority applies even in a situation of 'kavua', for in situations of nullification by majority the question under discussion concerns the character of the entire mixture and not the status of a particular piece within it.[15] One must understand that in both types of majority, both itah and leitah kaman, the question is about the piece under discussion and not about the whole mixture, and therefore both these cases are classified under the heading of following the majority and not of nullification by majority.

In conclusion, I will note that even according to my explanation it is difficult to understand the distinction drawn in several Talmudic passages between a mixture fixed in place and a moving mixture. At first glance there is no difference between the two situations, and what matters is only whether or not there was separation of the piece from the mixture. As I quoted above from Koppel, it may be that this is a later extension that does not fit the original logic of the rule of 'kavua'. The matter still requires further study.

[1] See an overview here and here.

[2] Almost all (and perhaps literally all) scriptural decrees have a rationale. See on this in my article on scriptural decrees.

[3] Several later authorities have already noted that the situation in a court fits the rule Its majority is like its entirety ('the majority is as the whole') – and perhaps the law of nullification by majority – better than the law of following the majority.

[4] Gordin does not claim that the question in a case of 'kavua' is meaningless. But perhaps one can nevertheless identify the two explanations, though this is not the place to elaborate.

[5] Regarding nullification by majority of a fixed minority, he explains that the nullification operates before the law of 'kavua', and after the nullification there is no longer any minority piece here. See there in greater detail.

[6] And indeed, Koppel himself senses some shade of this difficulty and feels the need to propose a solution. He argues that in such a case the doubt is defined a moment before touching the piece, and therefore this is still a hypothetical question, so the law of 'kavua' applies there. But I do not understand why one should assume this. In practice, the question arises after my choice of this piece of meat, and there is no difference between such a case and a case of 'separated'.

[7] In theory, perhaps one could mark all the pieces in all the stores in some city as kosher or non-kosher, then gather all the pieces that were lost and found in the streets of that city, and then examine how many of them are kosher and how many are not. This could count as one case that would serve as a sample, from which one could infer conclusions about all losses in all cities. If so, then even in the case of rov de'itah kaman one could carry out an experiment and generalize to a general rule. But it nevertheless seems that this is not enough to make it similar to rov de'leitah kaman, as I will now explain:

• Theoretically one could say that since this is not the operation of laws of nature but an accidental situation that varies from place to place, such an experiment cannot serve as a basis for establishing a general law. Perhaps there are no general laws regarding the condition of a specific city chosen at random. Research is done on the nature of the world and not on a particular case. More radically, one could say that one cannot conduct such research on a specific city. Because here we are not dealing with a law of nature, we have no confidence that the findings we obtained are general and characterize also all situations that will occur in the future. It may be merely an accidental state of affairs. When we deal with the nature of the world, the problem of induction still exists (how one can infer from the past to the future), but there the assumption is that there are laws that persist over time. In a situation that is not governed by laws of nature, such an assumption is not at all simple.
• But beyond that, even if we were prepared to accept the validity of such a study, in practice it is not carried out and is not likely to be carried out, certainly not for each and every city separately. Therefore, at least so long as no such study has been carried out, we are in a situation of rov de'itah kaman. According to this suggestion, if such a study were indeed carried out in a certain city, the rule regarding a piece of meat found in that city would indeed be a rule of rov de'leitah kaman.

[8] In another formulation, I explained that in the case of the prisoners we are dealing with an act that is the product of the decision of the person under discussion. A person can always claim that he acted properly, and one cannot force on him membership in a criminal group. But if there is eyewitness testimony about him, then we have direct evidence about him that he is a criminal. In such a case a person cannot argue against the witness that he has a personal interest. In other words, the witness's error is random (I am ignoring for the moment the possibility that he is deliberately lying), and therefore statistical tools can be applied to it. By contrast, the prisoner who separated from the majority group among the prisoners (those who participated in the event) – that separation is not a random mechanism but his own decision (whether to participate or not). Therefore it is not correct to apply statistical tools to it.

[9] On the plain meaning of his language, this does not seem to be his intention. It sounds somewhat as though he thinks there is no clarification here at all, but that is really extreme. The reasoning seems very logical and hard to deny. True, if someone were to deny it and claim otherwise, it would be impossible to prove to him in any way that he is mistaken. This raises the possibility that we are dealing with a cognitive bias of ours, that is, reasoning with no basis in reality. Therefore such reasoning is not clarification in the legal sense.

[10] This explanation does not fit the explanation we offered above of the Chinukh's view (that one relies on the majority because the majority is usually right). He rejects the Chinukh's explanation because, in his opinion, the Chinukh's explanation turns majority in a court into rov de'leitah kaman, as we saw. The Chinukh's explanation is admittedly not probabilistic (as I explained, there is no way to test it), but there is logic and a priori reasoning in it. R. Shimon Shkop's explanation (counting sides) is completely formal.

[11] Pitchei Teshuvah, Yoreh De'ah 110:2; Binat Adam, Sha'ar HaKavua, sec. 16; Rashba, Hullin 94.

[12] If there were only one store in which most of the pieces were kosher, then with regard to a piece that separated from it, we would indeed follow the majority.

[13] This explanation resembles Koppel's claim regarding questions about the future.

[14] In this context it is interesting to note the dispute surrounding the physico-theological proof. My claim is that a complex world requires a factor that assembled it. Special laws that govern it lead to the conclusion that there is a lawgiver who established them. Against that claim, a counterclaim common among various atheists is that we have no distribution regarding the formation of systems of laws or worlds, and therefore one cannot speak of the chance that a special world or a special system of laws would come into being. There is no probabilistic calculation that could give us such a chance. In response, I argue that although it is true that we have no information about the mode of formation of worlds and systems of natural law, in the absence of information it is still reasonable to give equal weight to all possibilities. If every world or every system of laws has equal weight, then the 'chance' of getting a special system is very small. Alternatively, when there is a special system, the 'chance' that it arose blindly and arbitrarily, without a guiding hand, is tiny. This is an example of a reasonable, quasi-probabilistic consideration based on lack of information. It is admittedly not probability (because there is no given distribution), but it does have a kind of probabilistic logic. In the absence of information one should assume a uniform distribution over all possibilities – not because this is true, but because there is no reason to assume anything else.

[15] However, the Rosh and the Rashba disagreed over whether nullification of dry in dry is nothing but the law of following the majority (see briefly here and in the Tur and Shulchan Arukh, Yoreh De'ah 109:1, and the commentaries there). Suppose a pot contains pieces of meat, one non-kosher and all the rest kosher. The Rashba argues that the mechanism of nullification is essentially a mechanism based on the rule Anything that separated is presumed to have separated from the majority. That is, each time one takes a single piece from the pot, the assumption is that it separated from the majority and one may therefore assume that it is kosher.

According to this explanation, we would expect that in such a case there would be no nullification, for when the doubtful piece is taken from its place the doubt arises already at the moment of taking, and therefore this is a case of 'kavua'. So why should such a case be seen as one in which one follows the majority (Anything that separated is presumed to have separated from the majority)? In light of my remarks here, one can explain that even according to the Rashba, who holds that this is a law of following the majority, since the question is about all the pieces in the mixture and not only about the one I took, the ruling regarding all of them is that the mixture is kosher. Here too there is an element of nullification and not only of following the majority. Therefore, according to his view, one may eat each and every piece taken from the pot (though one must consider the dispute, cited in the Tur and Shulchan Arukh there, whether according to his view one may eat the last two pieces, when there is no longer necessarily a majority of kosher pieces in the pot; but this is not the place).