Q&A: Rabbi Yirmiyah’s Question, His Removal from the Study Hall, and the Mathematical Approach in the Talmud
Rabbi Yirmiyah’s Question, His Removal from the Study Hall, and the Mathematical Approach in the Talmud
Question
Hello Rabbi,
Since you deal with topics of logical thinking in the Talmud, I wanted to ask you about Rabbi Yirmiyah’s removal from the study hall in the context of the mathematical approach that I find to be common in the Talmud.
In Bava Batra 23b there is a discussion around the Mishnah:
A fledgling found within fifty cubits belongs to the owner of the dovecote. If found beyond fifty cubits, it belongs to the finder. If it is found between two dovecotes: if it is closer to this one, it belongs to that owner; if it is closer to that one, it belongs to that owner. If it is exactly halfway between them, they divide it.
Later, Rabbi Yirmiyah asks a question that causes him to be removed from the study hall:
If one of its legs is within fifty cubits and one of its legs is beyond fifty cubits, what is the law?
I found two answers to this:
- According to Rashi, they removed him because he asked a tiresome question.
- In Tosafot and online I saw more complex answers which, as I understand them, say that Rabbi Yirmiyah was trying to systematically undermine the Sages’ attempt to determine Jewish law by means of an exact number like fifty cubits in this case.
Regarding 1, it seems pretty clear to me that the question itself is not tiresome compared to many other questions in the Talmud. As for 2, that surprises me מאוד because my impression is that the Talmudic approach is very mathematical, and many times questions arise precisely from dealing with infinitesimal quantities. For example, a few weeks ago I read the passage about “a wafer does not reduce the opening” in Bava Batra 19b, and as I understand it the discussion there is based on the assumption that an opening of a handbreadth allows impurity to pass through it, but anything smaller does not; so there they challenge the ruling that a wafer does not reduce the opening.
In addition, even aside from mathematics, I didn’t see any reference in the answers I found to the fact that the Mishnah itself explicitly brings the case where the fledgling is found exactly in the middle, and in that case they divide it. So it is even more surprising to me that Rabbi Yirmiyah’s question would be considered tiresome at all.
I would be glad to hear your opinion on why Rabbi Yirmiyah was removed from the study hall.
Of course, it may be that I did not understand the assumptions behind the discussion correctly, and I’d be happy if you would correct me.
Thank you
Answer
The term “mathematical approach” is not a very good one. What you mean is a formalistic-quantitative approach. I think that usually the approach in the Talmud is not like that. Sometimes it is, yes. But passages are divided on other matters as well.
The wafer in the opening is not necessarily such a case. The question there is whether we regard the wafer as part of the opening, in which case it reduces the opening, or whether it is considered something else that is merely placed there, in which case the opening is still a handbreadth. You could also formulate it the other way around: if it is part of the opening, then it is nullified; and if not, then it reduces it. In any event, this is a conceptual question, not a quantitative one. Think about a table in a sukkah whose height is ten handbreadths. Does the table reduce the height of the sukkah? No, because it is a separate object placed there. But raising the floor does reduce the sukkah. You can see later in the passage that this is written almost explicitly (the question is whether he nullifies it to the opening or not).
I don’t think there is necessarily any difference between Rashi and Tosafot regarding Rabbi Yirmiyah’s removal. It now occurs to me that they removed him from the study hall דווקא because he challenged the Sages’ quantitative determinations and claimed they made no sense. They removed him because he assumed that such a determination was quantitative, and therefore his question constituted a refutation of it—but that is not so. Their claim is that this is only a principled measure, and it is not correct to take it as an exact quantitative determination. Think about measures like a cubit or a handbreadth, which today we translate into centimeters, but in their time they simply took the cubit or handbreadth of an ordinary person. That is very far from being quantitative.
Discussion on Answer
You are not correct. Look there later in the passage and you will see the discussion about a thick wafer and a thin one, and you’ll see that this is not the issue.
Right, that is what I meant. That he is asking about measures in general. The question may perhaps be interesting, but the Sages saw it as a nuisance because he revealed a lack of understanding regarding the nature of such measures. He took them as exact quantitative cutoffs, whereas they merely provide a rough practical tool.
As for the wafer, I explained it. It is not the same question at all. A. Because there it is clear that the measure is a handbreadth (incidentally, a handbreadth itself is not an exact measure). B. Because the question discussed there is whether the wafer is nullified to the opening or not. It is not a question of whether reducing a millimeter changes the law. Otherwise they should have asked: what about an opening of a handbreadth minus a millimeter?
I find Rashi’s explanation difficult—the claim that the Sages’ complaint against Rabbi Yirmiyah was that he was tiresome in the simple sense. I have not seen that the “common” case of someone falling from the roof and becoming lodged in his yevamah was also defined as tiresome, and there are many more such examples. That is, the rarity of a case is not a reason not to clarify it.
Maybe it is worth noting that Rabbi Yirmiyah’s questions are proverbial in the Talmud; there are many interesting examples, such as in “These Found Articles” regarding the measure of a kav within four cubits, where Rabbi Yirmiyah asked: what about half a kav in two cubits? That is a case of this corresponding to that—the ratio is equal, the quantity is smaller, but the bother is also less, and perhaps the owners did not despair. And so on—he could have gone on to ask: what about a quarter-kav in one cubit, all the way down to one grain in a millimeter. I do not think this is a tiresome question at all. As was his way, Rabbi Yirmiyah was showing his colleagues that measures built on probability can never really be universal. They did not like that, until one day they needed his wisdom and brought him back to the study hall.
Becoming lodged in his yevamah is a completely different matter. A hypothetical case that comes to clarify and work through an interesting theoretical conceptual question (what exactly is the nature of levirate marriage and intercourse in that context). That has not the slightest connection to Rabbi Yirmiyah’s question, which just nags about a hypothetical case without having any theoretical value.
I don’t see a difference. In both examples a hypothetical case is being used to clarify a point—there, with the yevamah as you wrote, and here with the fledgling, to challenge the fixing of measures and the laws of doubt regarding measures.
It would seem that they removed him from the study hall not because of the question itself, but apparently because of the way he presented it, which sounded provocative (insolent). And when they turned to him and he answered them, “I am not worthy, etc.,” they brought him back because they understood that he had abandoned his “bad” way.
More power to you
Thank you for the answer.
Regarding the wafer: as I understand it, the question is interesting only when the width of the opening (or its height) is exactly one handbreadth, and then placing any object on it (that has no use and no owner who will come claim it) reduces it—that is, makes the opening smaller than the minimum size needed for impurity to pass through. In other words, if the size of the opening were a handbreadth + x, where x is the thickness of the wafer, then there would be no question at all about the nature of the wafer, because in any case the opening would still be larger than a handbreadth.
In any event, I brought that passage only because there too there is engagement with numerical precision, except that there it is around the size 0, whereas in the case of the fledgling we are talking about a distance of 50 cubits.
Regarding the second part, I’m not sure I understood. Are you saying that he was challenging specifically the determination of the size 50 cubits, or that he objected to any specification of a number? To me it sounds like he would ask exactly the same question about any distance they were discussing, and therefore his question can be seen as a principled one and an interesting one.
If when the Sages mention measures like handbreadths they do not mean exact measurements, then I again come back to the passage of the wafer in the opening, where the precision of the measure of a handbreadth seems to be very important (that is, there is a discontinuity point for the passage of impurity at that size), and that is the basis for the whole discussion.