The Rule of Majority at Moments in Time (Column 509)

A few days ago, a question was asked here about the sugya of “an open opening (petach patuach)” in Ketubbot 9a. It sparked some interesting lines of thought for me about the rule of majority (rov) and about the time axis. I thought the holiday is a good opportunity to use for a bit of learning in the object (cheftza).

The Question

That Gemara discusses situations in which a husband claims that at the first act of intercourse he discovered his wife was not a virgin (“I found an open opening”). This has monetary ramifications (the amount of the ketubah), prohibitive ramifications (perhaps she is forbidden to him because she committed adultery; for a kohen she is forbidden even if it was rape, or if the one who had intercourse with her was someone who disqualifies her), and of course ramifications regarding the status of the child from that act, if there is one. Among other things, the Gemara raises, with respect to such a claim, the doubt whether she committed adultery “under him” (after the betrothal), in which case if it was willful she becomes forbidden to him and to the adulterer, or before that, in which case she does not become forbidden.

The questioner wonders why the Gemara does not resolve this doubt by means of the majority (rov). As is known, halakhah rules that we follow the majority, even in matters of prohibition (in monetary law this is disputed). Suppose she was betrothed to him at age twenty; then twenty years passed in which she was not “under him” and only a shorter period (in those days they practiced twelve months between betrothal and marriage) in which she was under him. If so, the majority of the time she was not under him, and therefore it is more likely that the intercourse occurred at a time prior to the betrothal, and the doubt should be resolved by the majority.

Statistical Logic

At first glance I thought of a statistical logic. Probability deals with random events. When some event occurs from among several possibilities, and the choice among them is random, the assumption is that the chance of each event is equal, and from this one can compute the probability of each outcome. For example, when rolling a fair die there are six equally likely outcomes, and therefore the chance of getting a 5 is 1/6 and the chance of getting an even number is 1/2. But what would you say about a person who places a die and chooses which face to place down? Here we can no longer assume all possibilities are equally likely. He decides the number according to his own considerations. Perhaps he does not care and just draws lots or does it arbitrarily, but if it is his choice, the application of probabilistic considerations is no longer automatic.

From here, if the intercourse were an event that happens naturally and “chooses” at random to occur at some point on the time axis, then there would be logic to follow the majority of time. The chance of each moment being chosen would be equal, and therefore the probability that the event occurred in the longer time segment is higher. But intercourse is not a random event; it is a deliberate action by the people who performed it. They decide, based on their own considerations, whether to do it and when. In such a case, there is no logic to hang the likelihood of the event on the length of the time segment in question. Of course they have various considerations (they prefer night; they prefer certain times of year or week, and so forth).

One could raise an additional argument: presumably they prefer to do this when it is permitted, rather than be transgressors and endanger themselves. But this consideration is also irrelevant for the same reason. If they had the option to perform the act at any time they wished and they themselves chose the moment, it is reasonable that they would choose a moment when she was not forbidden to him (i.e., before betrothal). But who says they knew each other then? Why assume they had the opportunity or desire to do the act before the betrothal? It could be they only met after it, or that desire only arose after the betrothal. Therefore, even here it is not reasonable to apply probabilistic tools that assign equal standing to every moment on the time axis.

A halakhic example of the distinction I just made can be seen in R. Shimon Shkop’s words about the sugya “we do not follow the majority in monetary law,” which I cited in Column 226. The Gemara brings a dispute in a case where someone bought an ox for plowing and the ox died; the seller claimed he sold it for slaughter (leredya), not for plowing, and then its short life expectancy is not a problem. Factually, most oxen sold in the market are for plowing and not for slaughter. The Amoraim dispute whether such a majority suffices to rule in favor of the buyer (we follow the majority in monetary cases) or not. The halakhah is that we do not. Some Rishonim and Acharonim argue that this is not true for every type of majority, but only for a specific type. Thus R. Shimon explains in Sha’arei Yosher, Gate 3, ch. 3 (sec. 47 in the Bar-Ilan Responsa Project edition):

“It can be said that the reason is per the Ramban in Milchamot (Kiddushin ch. 2), cited in Shev Shma’atsa IV ch. 6, who wrote regarding the majority of those who send gifts and then betroth, that it is difficult why we are concerned for the gifts and do not follow the majority. His words: ‘But the reason for this question is that this majority is not like the dispute of R. Meir and the Sages, for there the majority is a necessity of obligation and nature and cannot be otherwise; but here it is only a custom, and many times a person behaves like the minority’s custom, therefore in the place of the prohibition of a married woman they were stringent.’ End quote. It is evident from his words that from the Torah such a majority would be effective even regarding a married woman, only the Sages were stringent. And according to what we wrote, the matter is that such a majority is a Torah majority and not an intellectual majority, and is effective from the Torah, only the Sages were stringent. And therefore also the majority ‘they buy for plowing’ is not an intellectual majority, for if this man needed [it] for slaughter, this does not at all depart from the laws of nature and normalcy; rather it is a Torah majority, and it is not effective in monetary law and capital law for the reasons we wrote—regarding monetary law, certainly we require an intellectual majority, as we wrote, because it is a matter of logic; and regarding capital law, because it is written ‘the congregation shall judge,’ as we wrote.”

His argument is that in the debate about the ox, the discussion is not about the nature of the world but about human decisions (whether he wanted to buy/sell for plowing or slaughter). A person who buys an ox for slaughter is completely normal; it is the way of the world—just that generally there is more demand for plowing oxen than for slaughter. Therefore, if a person claims he belongs to the minority—that is, he wanted to buy an ox for slaughter—you cannot raise the claim of the majority against him. Even if most of the world buys oxen for plowing, does this in any way prove that this person did not want to buy for slaughter? There are people who buy oxen for slaughter, and it depends on their decision. That person is not making a strange or illogical claim. Here, belonging to the minority is entirely reasonable and plausible, and therefore the majority has no evidentiary standing. (The source is the Ramban regarding the sugya of gifts (sevalonot).) Similarly, if I claim my height is 1.95 m, you cannot argue against me that most people are shorter. Does that show I am wrong? I claim I belong to the minority, and since such a minority exists, there is nothing illogical here. The fact that I happened to be in a situation where I belong to a minority group proves nothing about my claim (that it is illogical).

Accordingly, when the dispute is about human decisions, we do not follow the majority. A person has the right to claim he belongs to the minority, and the fact that the majority acts otherwise tells us nothing about him.[1] This is exactly what I argued regarding a majority on the time axis for intercourse. Intercourse is not a natural random event but a human decision, and therefore the tools of random probabilities and uniform distribution of chances across the time axis should not be applied to it.

The Difficulty: Mikveh

However, this explanation will not heal another case in which we also do not follow the majority on the time axis. The Gemara in Kiddushin 79a discusses a mikveh that at one moment was measured and found valid, and after some time—say a week—was found lacking and invalid. Between those two moments, a person who was impure immersed in the mikveh, and the question is whether his immersion was effective or not. The discussion is whether we follow the prior presumption (chazakah de-me’ikara—that the mikveh remains valid until it is proven to have become invalid) or the present presumption (chazakah de-hashta—that now it is invalid and we should not assume it was valid until clarified), as well as the presumption of the one who immersed (he was impure before immersion). The prior presumption leads to the conclusion that his immersion was effective, for we presume that until the moment it was discovered to be lacking, the mikveh was valid. If we follow the present presumption, his immersion was not effective.

But seemingly here too we should consider the length of time that passed until the immersion. Suppose the mikveh was valid on the first day of Sukkot and found lacking on Shemini Atzeret. Someone immersed on the first day of Chol HaMoed. We must now decide at what moment the mikveh fell below forty se’ah. If it happened before the immersion, the immersion was not effective; if after, it was. But these two time segments are not equal. From the first day of the holiday until the first day of Chol HaMoed one day passed, and from the first day of Chol HaMoed until Shemini Atzeret seven days passed. If so, the majority rules that the mikveh became lacking after the immersion, and therefore the immersion was not effective—regardless of whether we follow the prior or the present presumption. Presumptions are meant to decide doubtful cases, but here the majority resolves the doubt.[2]

Note that here we are dealing with a natural, random event, not a human decision. If my explanation above were correct, then here we indeed should follow the majority of time and invalidate the immersion. And yet, as I mentioned, the discussions in the sugya completely ignore the question of time and suspend everything on presumptions (prior and present).

One might have said that indeed, when there is a time gap we follow the majority of time, and the Gemara is discussing the hypothetical case in which the two time segments are of equal length, for it seeks to clarify only the question of presumptions. But when in fact there is a gap between the time segments, we would follow the majority and attribute it to the longer one. But this is forced, and certainly the poskim do not adopt such an approach.

The conclusion is that resolving the difficulty about majority on the time axis in the sugya of petach patuach is not based on the fact that we are dealing with a non-natural event. Even for natural events we do not follow the majority on the time axis, and the question returns: why?

An Alternative Explanation: The Rule of “Kavuaʿ” (Fixed)

Ultimately I thought of another, more substantive explanation. The question of when the intercourse occurred is a question about some moment in time. The intercourse occurred at a specific moment on the time axis, and the question is which moment it was: before the betrothal or after. If so, we have a situation where we must decide whether the moment in which the intercourse happened belongs to the set of moments before the betrothal or to the set after it. Following the majority assumes a situation the halakhah calls “parish” (separated), i.e., that the element about which we are uncertain separated from the mixture, and now we must decide whether it belonged to the minority or to the majority.

For example, a piece of meat is found in the street, and it is clear it came from one of the city’s shops. Among the shops, most are kosher; therefore we assume it likely came from one of the majority shops. The piece “separated” from one of the shops and is now in a neutral state, and when asking from which it separated we follow the rule “whatever separates, separates from the majority (kol de-parish me’ruba parish).” By contrast, if we enter one of the shops and take a piece of meat, and later forget from which shop we took it—there we do not follow the majority, because at the time the doubt arose there was no “separation.” The piece was fixed in its place. This is the rule of kavuaʿ, and the halakhic maxim is: “anything fixed is treated as half-and-half (kol kavuaʿ ke’mechetzah al mechetzah dami).” (For a more detailed explanation, see Sha’arei Yosher at the beginning of Gate 3.)

In principle, the same should apply when a non-kosher piece of meat is cooking in a pot with five kosher pieces. If we were to take one out, we would be forbidden to eat it despite the majority of kosher, since this is a case of kavuaʿ. The piece did not separate; we took it from the pot itself. At the time the doubt arose, the piece was in its place, and in such a situation the rule is to treat it as an even doubt and not follow the majority. True, there is also the rule of nullification by majority in mixtures of kosher and non-kosher, and therefore, strictly speaking, it is permitted. The distinction between kavuaʿ and parish was stated only regarding following the majority (as in the shop case), not regarding nullification by majority in a mixture.

In our case of intercourse, the situation is very similar. The different moments are “laid out” along the time axis. The couple chose a particular moment and performed the act at that moment. The moment did not “separate” from the time axis at the time of the act but remains “in its place” (i.e., “in its time”),[3] and therefore the rule “whatever separates separates from the majority” does not apply; rather, “anything fixed is treated as half-and-half.”[4]

The Rashash’s Formulation

Someone pointed out to me that this difficulty appears in the Rashash (R. Shmuel Strashun) on the Ketubbot sugya there:

On “Ve-i ba’it ema”—And if you will say: If so, in a case of a double doubt she should also be forbidden… It is difficult in light of what we say in Chullin 72b that we rely on the minority of those resembling [males] to the half [that are] females, etc.; and likewise in Yevamot (119) we join the minority of miscarriages to the half of females, etc. And see also earlier (67) in Rashi s.v. ‘All of them male.’ Perhaps one could say that there the ‘half female’ is in birth and the nature of the world, and therefore it is a definite half—unlike the doubt of ‘under him,’ etc. But it is difficult: why do we not follow, for the wife of a kohen, the majority of time that passed over her before she was betrothed? Like [the rule of] coins found on the Temple Mount which are always [treated as] chullin (non-sacred), even at festival time (Shekalim 7:2), for we follow the majority of the year. Similarly, it is difficult in Niddah at the beginning of ‘The Woman’ (ch. 9) regarding three women who wore one garment—that we should follow the one who wore it for a longer time than the others. And likewise in many places. And although one can deflect the proof from Shekalim—that there one could say the reason is that if you aggregate all the chullin coins of the whole year, they will be more than the second-tithe coins of the festival and of the whole year—nevertheless, the logic itself is straight, that we follow the majority of time; and when the majority and the closer [factor] conflict, we follow the majority. See Pesachim 7b.

The Rashash raises this and leaves it as a difficulty. He offers no explanation. Moreover, in his words you will find two examples of situations in which the question of following the majority on the time axis arises. Incidentally, these are two examples of natural events (even though they happen to people, they are not by their conscious choice). Seemingly we must examine whether my explanation above is consistent with his two examples.

The first example is from Mishnah Shekalim 7:2:

Coins found in front of animal merchants are always [treated as] second tithe; on the Temple Mount they are [treated as] chullin; in Jerusalem, at festival time, [they are] second tithe, and on all other days of the year [they are] chullin.

This concerns coins found on the Temple Mount; the rule is that they are always treated as chullin even if found during the pilgrimage festival, when they might have been sacred (second-tithe money that fell from a buyer before purchase). The reason is explained in Pesachim 7a: there is a majority, across the time axis, of non-festival days, and we follow the majority. The loss occurred to a person, but it is not his conscious act; it is a natural event. Here, according to my first explanation above, we should indeed follow the majority.

But according to my suggestion that we do not follow the majority on the time axis because of the rule of kavuaʿ, why here do we follow the majority? Seemingly, we should have kavuaʿ here. The Rashash himself resolves the difficulty by saying that the chullin coins accumulated over the entire year are more numerous than the second-tithe coins; that is, it is a majority of chullin coins circulating on the Temple Mount, not a majority of moments. If so, this does not touch the question of the fixedness of moments of time. Moreover, the assumption that most of the coins are chullin is a majority of the “not-present-before-us” type (rov d’leita kaman)—for there is no set of lost coins to which these particular coins belong—and regarding such a majority the rule of kavuaʿ simply does not apply. By contrast, the majority of time moments we discussed in the petach patuach sugya is a “present” majority (rov d’aita kaman), and therefore one can apply the rule of kavuaʿ to it.

The second example is from Mishnah Niddah 59b:

Three women who wore one garment or sat on one bench, and blood was found on it—all are impure.

Blood was found on the garment, and the question is which of the three women who wore it is the one who is impure. The Rashash asks: why not follow the woman who wore the garment for the longest time and decide she is the impure one? He follows his view that logic dictates following the majority on the time axis. But according to my view this is actually evidence for what I say—that on the time axis we do not follow the majority because of the rule of kavuaʿ.

However, at first glance the discussion there does not relate to our topic at all, for there is no situation in which blood “chooses” a moment in time to come out. The question is not about a moment on the time axis among other moments, but about one woman among three women. If the question were about a drop of blood that fell from the heavens and the discussion were whether it fell on the garment at the time when woman A, B, or C was wearing it, then perhaps there would be room to compare this to the rule of kavuaʿ for moments in time. But here the question is from which woman the blood came. Therefore, here one might not follow the majority even if there were a rule of majority over the time axis, since these women did not separate from anywhere.

Is Time a Cheftza (Object)?

Perhaps one could tie my proposed logic to the question whether time is a “cheftza” (an entity) or not. Viewing the set of moments along the time axis as a kind of mixture, and asking to which part of it the relevant moment belongs, expresses a conception that moments of time are a kind of objects, and the discussion is to which category to assign each one.

As is known, philosophers disagree whether time exists in reality or not. Kant, for example, argues that it is only our form of perceiving reality—that time exists only within us (a mode of thought and data organization). Others see time as something that exists in reality itself. One can also wonder, even assuming time exists in reality, whether a moment of time “exists,” or whether it is an abstraction. Time intervals can exist, but not a point on the time axis (likewise in space).

I once thought one could adduce proof from the Talmud that, at least in the halakhic conception, time is an existent entity. I preface by noting that there are two ways to take a vow: nedirah (creating a new prohibition) and hatfasah (linking to an existing prohibition). The rule is that one can “link” only to something that is prohibited by a vow or sanctity (i.e., cheftza-based prohibitions), not to something prohibited for other reasons; for most interpreters, hatfasah transfers the existing prohibition from one object to another, since the difference from a regular vow is that here there must exist in reality a prohibition on the first object, whereas a regular vow creates a prohibition ex nihilo. That is, hatfasah is done in an object-prohibition that rests upon an actual object.

And behold, the Gemara in Shevuot 20a and Nedarim 12a brings the following law:

“What is the ‘issar’ mentioned in the Torah? [One who says:] ‘Behold, I undertake not to eat meat and not to drink wine—like the day on which his father died, like the day on which his teacher died, like the day on which Gedaliah son of Ahikam was killed, like the day on which I saw Jerusalem in its destruction…’”

Here there is hatfasah of an oath or vow onto the day on which Gedaliah son of Ahikam died. Seemingly this proves that the “day” is an existent entity and not merely our fictive designation, for we link to it; and, as noted, according to most views one can link only to objects and cheftza-type prohibitions that have come to rest upon them.

If so, this fits nicely with our conclusion that one can speak of majority and of kavuaʿ with respect to moments of time, since time is an existent entity. But this can be refuted by saying that the linkage is to the food that was prohibited on the Fast of Gedaliah, not to the “day,” and there is no proof that a day is an existent entity. Conversely, one can argue that even if time is not an existent entity but only our subjective designation, we can still speak about majority and kavuaʿ regarding moments in time, since, in our subjective picture, they do have standing, and in that subjective image the different moments are defined as lying in their “places.”

A Note Relevant to the Season: Time as Part of the Cheftza-Definition of Sukkah

Beyond the question whether time exists, there are halakhic situations in which time takes part in defining halakhic entities, and one example is in the laws of Sukkah.[5]

In Nedarim 28b–29a there is a dispute between Abaye and Bar Pada whether sanctity of the body (kedushat ha-guf) can lapse by itself (bikhdei—i.e., by mere speech, without an act) or not. Abaye holds that it can: he thinks one can consecrate an object with sanctity of the body for a set time, and when that time ends the sanctity lapses on its own; or one can stipulate a condition that will cause the sanctity to lapse on its own if unmet. Bar Pada holds there is no way for sanctity of the body to lapse without an act. The halakhah follows Bar Pada.

Yet we find in Beitzah 30b that the wood of the sukkah is prohibited in benefit because it is sanctified with sanctity of the body, like the festival sacrifice:

“But did not Rav Sheshet say in the name of R. Akiva: From where do we know that the wood of a sukkah is forbidden all seven days? For it is said (Leviticus 23): ‘The festival of Sukkot, seven days, to the Lord.’ And it was taught: R. Yehudah ben Beteira says: From where do we know that just as the name of Heaven rests upon the festival offering, so does the name of Heaven rest upon the sukkah? Scripture says: ‘The festival of Sukkot, seven days, to the Lord.’ Just as the festival is ‘to the Lord,’ so the sukkah is ‘to the Lord.’”

The Gemara discusses whether a stipulation about the sanctity of the sukkah’s wood is effective, and concludes it is not. The Rashba there raises a difficulty:

“Moreover, it appears that according to Abaye even with sanctity of the body a stipulation is effective and it lapses on its own, as we learn in Nedarim ch. ‘Four Types of Vows’ (28b)… If so, even if he holds that the sukkah is like sanctity of the body for all seven days, as Scripture compared it to the festival, how could Abaye say here that a stipulation is not effective? Would this be superior to an ox that is an olah for thirty days and afterwards a shelamim?”

He asks: according to Abaye in Nedarim, why can one not make a stipulation on the sukkah wood? Even if it has sanctity of the body, Abaye would allow a stipulation, for he holds sanctity of the body can lapse on its own.

The common understanding is that the “sanctity of the sukkah wood” is only a borrowed expression and not truly a cheftza-status like regular sanctities (see also a slightly different formulation in Kovetz Shiurim to Beitzah §69). But the Rashba assumes it is real sanctity, like a festival offering. He therefore offers a resolution that he himself calls forced:

“Under compulsion, one could say that Scripture compared it to the festival offering precisely: just as once sanctity comes upon the offering it cannot lapse, so too with the sukkah wood.”

But it seems we can resolve the matter differently. Consider what happens if a sacrifice were to evaporate at some point: does the fact that its sanctity has ‘lapsed’ contradict the rule that sanctity of the body does not lapse on its own? Certainly not. The reason is that here the sanctity is perpetual; only the object is temporary. Lapse of sanctity of the body is a situation in which the object remains while the sanctity flies off on its own. But here we describe a situation in which the object itself dissipates and disappears, not that the sanctity flew off. In such a case, the sanctity is perpetual, and indeed it did not lapse on its own; rather, the object upon which it rested vanished. In the cited chapter I brought more examples of this mechanism.

Now I continue and ask: why does the Rashba not himself struggle with the question of how, at the end of the festival, the sukkah wood becomes completely non-sacred and its prohibition of benefit lapses on its own? Why does this not appear to him to contradict the principle that sanctity of the body does not lapse on its own?[6] According to the Rashba, who assumes the sukkah wood has actual sanctity of the body, then according to Abaye its sanctity cannot be temporary and dissipate on its own at the end of the festival.

It seems that, in his view, after the eight days of the festival, this wooden structure is not a sukkah but just a pergola. Here too what has lapsed is not the sanctity but the structure itself. A “sukkah,” in its halakhic sense, is not a wooden structure with certain features, but such a structure during the eight days of the festival. Time is a necessary and essential component of the object’s definition. Therefore, once the time has passed, the object itself has passed and ceased to exist, similar to a sacrifice that evaporated. The sanctity of the sukkah wood is perpetual, but circumstances do not allow it to express itself in practice because the sukkah disappears at the end of the festival.

This may also resolve the well-known question of the author of Onoig Yom Tov (cited and discussed in Kovetz Shiurim to Beitzah 30b §70), who wonders why someone who remains sitting in the sukkah while it is raining is merely called a fool (hedyot). Seemingly he is actually transgressing the prohibition of using the sukkah wood (infringing upon its sanctity), since he is using it not for the sake of the mitzvah. The Kovetz Shiurim there answers:

“What is asked: since the sukkah is prohibited in benefit except for the mitzvah, then when rains fall it should be forbidden to sit in the sukkah, since there is no mitzvah. Perhaps, when the sukkah is not fit for its mitzvah, it has no sanctity—just as after the festival: its sanctity is at all times because it is designated for its mitzvah; yet if the sukkah is fit for the mitzvah, but the person does not fulfill the mitzvah (e.g., he intends not to discharge his obligation), in such a case perhaps benefit is forbidden.”

That is: when the sukkah is not serving for the mitzvah, it is not sanctified. Again one can ask: how does its sanctity lapse on its own? It seems better to say that when it is not serving for the mitzvah, this is not a “sukkah” (the sukkah dissipates, not the sanctity), similar to what we saw above regarding the time after the festival.

Can we conclude from here that time is an existent entity? I am not sure, for we are speaking of a definition of a halakhic cheftza, not of a factual object. When speaking of a cheftza-status, one is not necessarily speaking about an existent reality but about a legal definition of the status.

[1] Seemingly, according to this we should not follow such a majority even in prohibitions and not only in monetary matters, and the Gemara’s wording that ties this specifically to monetary law is difficult.

[2] In such cases, majority overrides presumption, as we see in Niddah 18b (the infant found near the dough). See Kovetz Shiurim, Bava Batra §78, and Sha’arei Yosher, Gate 4 ch. 24, and many more.

[3] For an example of abstract “separation,” see the Mordechai in Chullin (cited in Column 237) regarding majority in a court. He writes that we follow the majority because the judge’s voice separated from its place. Clearly he does not mean physical separation of the voice but conceptual separation: something not lying in its place within the mixture.

[4] There is room to deliberate here, since at the moment of intercourse there was no doubt: the couple knew whether she was betrothed or not. The doubt arises in the court after the husband comes and complains—that is, long after the act. At that stage one might view the moment as if it had already “separated” and is no longer in its place. But it is more plausible that this is still kavuaʿ, for the moment that generated the doubt is the moment of intercourse, even if the doubt itself arose much later. However, according to my proposed explanation of kavuaʿ in Column 237, it is doubtful whether one can apply it in such a situation on the time axis.

[5] On this example and others, see the fourth volume in the series Talmudic Logic, The Logic of Time in the Talmud, chapter 11.

[6] One might argue that here the sukkah’s mitzvah has been performed, and therefore it reverts to non-sacred status, as with an offering whose mitzvah has been performed. But this does not seem correct, for usually “its mitzvah has been performed” refers to an act that removes the sanctity; thus, even when the mitzvah is performed, the lapse of sanctity is not “on its own” but via an act. Here, however, the lapse occurs at the end of eight days, without any act.