Marriage: A Math Problem

Literary critic Adam Kirsch is reading a page of Talmud a day, along with Jews around the world.

The Talmud is a famously pluralistic text. Though its subject is law, it doesn’t lay down the law; rather, it records a variety of traditions and interpretations about what the law is supposed to be. When different tannaim, the rabbis of the Mishna, have different understandings of the law, all the versions are recorded, since each is taken to represent a sacred tradition. Usually, the Gemara will decide to follow just one tanna—indeed, deciding which authority is most authoritative is one of the Talmud’s regular preoccupations. But the rival interpretations do not always exclude one another, and it regularly happens that legal disputes are raised but not resolved. That is one reason why Jewish law is a living organism, inspiring generation after generation of codes and commentaries.

In practice, however, it’s easy to imagine that this open-ended legal system could present some problems. If two sages followed different legal traditions, rival litigants could easily engage in “sage-shopping,” finding the one who would be most sympathetic to their claim. And if rabbis of equal sanctity made opposite rulings in a case, whose view would prevail? Exactly this problem came up in this week’s Daf Yomi reading, in Ketubot 94b. Chapter 10 of Ketubot deals with complex issues of inheritance and debt, one of which is how to cope with rival deeds to the same property that were issued on the same date. Say that Yaakov owns a house, and he signs a deed giving it to Reuven, but later the same day he signs another deed giving it to Shimon. Who gets the house?

This is a case where different sages offer different answers, with neither prevailing over the other. Rabbi Meir, one of the earliest and most revered tannaim, says that a deed becomes valid when it is signed. And since a legal document typically does not include the hour it was signed, only the date, both Reuven and Shimon’s deeds are equally valid, since they bear the same date. (To avoid this very problem, we learn in passing, courts in Jerusalem would include the exact hour of signing in a deed.) Rav, one of the first and greatest amoraim, reasons based on Meir’s view that since Reuven and Shimon have an equal claim to the property, it should be divided equally between them.

But Rabbi Meir’s view is not the only one to be considered here. For another great tanna, Rabbi Elazar, holds that it is not the signing of a deed that makes it effective, but actually giving it to the recipient. In accordance with this principle, Shmuel, the amora who is Rav’s great partner and rival, holds that it is up to the discretion of the judges whether to award the property to Reuven or Shimon; presumably, they would rule in favor of whichever party could produce witnesses to the fact that he received his deed first. In this case, Rav and Shmuel can each rely on an authoritative tradition, so neither can impose his view on the other. And in the absence of a unified system of appeals courts, this means that Reuven and Shimon might bring their case to two different judges and get two different verdicts, each equally valid.

That is exactly what happened, we learn, to the sons of Hama, Rami, and Mar Ukva. Their mother wrote a deed in the morning transferring ownership of her property to Rami, and then in the evening she wrote another deed giving the same property to Mar Ukva. Rami brought his case to one sage, Rav Sheshet, who ruled in his favor; while Mar Ukva went to another sage, Rav Nachman, who ruled in his favor. This set up a confrontation between Sheshet and Nachman, with Nachman pulling rank: “I am a judge, and the Master is not a judge,” he insisted. But the Talmud does not explain why he said this, and the commentaries disagree: Was there a dispute over local jurisdiction, or was Sheshet disqualified for some reason (for instance, because he was blind, which is a disqualification under Jewish law)? The case remains murky and leaves the reader wondering what would happen in a situation where neither judge agreed to give ground to the other.

Why, one might ask, does this dispute about the dating of legal documents find a place in Tractate Ketubot, which is supposed to be about marriage law? The reason is that, here as often before, the rabbis treat disputes over marriage contracts as special cases of more general rules regarding debt and inheritance. If a man dies and leaves a widow, their marriage contract or ketubah specifies that she can claim a certain amount of money from his estate. But what happens if, in this polygamous society, a man dies and leaves three widows, but his estate doesn’t have enough money (or, more likely, land) to pay all their contracts? Whose claim gets paid first?

The law holds, sensibly enough, that the first wife to be married has the first claim on the estate, and so on chronologically. But what if the man married all three wives on the same day? (This would surely be an unlikely event, but apparently it could happen.) If they each are owed the same amount under their marriage contract, then they divide the husband’s property equally. But what if each wife was owed a different sum? What happens, asks the mishna in Ketubot 93a, if “one who was married to three women died and the marriage contract of this wife was for one hundred dinars, and this wife for two hundred, and this wife for three hundred?”

There are, it would seem, two logical ways to deal with this situation. One would be for all the wives to divide the estate equally; then they would each get at least some of their contract paid. Another would be for the estate to be divided proportionally, so that, in this case, the wife owed 100 dinars would receive one-sixth of the estate, the wife owed 200 dinars would get one-third, and the wife owed 300 dinars would get one-half.

As it turns out, however, things are not so simple. As the Talmud approaches the problem, we have to imagine that each widow has a claim only up to the amount of the estate that she is owed. Each wife, then, has an equal claim to the first 100 dinars of the estate, and if the estate contains exactly 100 dinars, then each is paid an equal share, 33 and 1/3 dinars. If there are 200 dinars in the estate, then, it would seem to follow that the first 100 dinars is divided among all three wives, as in the previous example. But the second 100 dinars can be claimed only by the wife who is owed 200 dinars and the wife who is owed 300 dinars, and so they would divide it in half between them. The result would be that the first wife would get 33 and 1/3 dinars, while the other two would each get 83 and 1/3. However, what the mishna actually says is that the first wife gets 50 dinars, while the other two each get 75. Why?

This discrepancy puzzles the rabbis of the Gemara, but they manage to find an ingenious explanation. The mishna, they decide, is talking about a case where the second wife, the one owed 200 dinars, disclaimed her share of the estate owed to the first wife, the one owed 100 dinars. As a result, there were only two claimants to the first 100 dinars of the estate, and each takes 50. That explains why the first wife ended up with 50 dinars. But if this were so, then it would seem that the second wife should also end up with 50 dinars: This would be her half of the second hundred dinars, which she divides with the third wife. In that case, the third wife, the one owed 300 dinars, should get 100 dinars—half of the first hundred, split with the first wife, and half of the second hundred, split with the second wife.

Why, then, does the mishna say that the second and third wives each take 75 dinars, an equal sum? The reason, the Gemara explains, is that while the second wife disclaimed her share of the estate with regard to the first wife, she did not disclaim her share of the estate with regard to the third wife. After the first wife is paid her 50 dinars, then, the second wife has a claim against the third wife for half of her 50 dinars, as well as for half of the remaining estate of 100 dinars. For this reason, they divide the 150 dinars in half, leaving each with 75.

You can practically sense the intellectual excitement of the rabbis as they work through these hypotheticals. Things get even more complicated when they consider what to do if the estate is valued at 300 dinars; or if the estate is a creditor for amounts that are paid in installments; or if business partners invest in an asset that can’t be divided, such as an ox. And that’s not to mention the case, which arises near the end of the chapter, when a man dies leaving two wives, a creditor, and a piece of land, and the first wife disclaims her rights vis-a-vis the creditor, which results in a situation where the land passes from wife to wife to creditor and back again forever. This vicious “cycle,” as the mishna calls it, seems like the kind of thing a well-designed legal system would preclude. But it is conundrums like this that make the study of Talmud, even in seemingly dry subjects like inheritance law, such a stimulating mental exercise.

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Adam Kirsch is a poet and literary critic, whose books include The People and the Books: 18 Classics of Jewish Literature.