Tag: Shmuel Lubin - The Seforim Blog

Will the Real Shas Kattan Please Stand Up[1]
Shmuel Lubin

Shmuel Lubin is a doctoral candidate in biology and creator of “The Rishonim” podcast.

There is an old tradition commonly referenced in the yeshiva community that Masekhet Ketubot is the “Shas Kattan” of Talmud Bavli, that is, it contains ideas that connect to just about every other area of Shas (short for “Shisha Sidrei,” all six orders of the Mishnah). The source and importance of this idea is the subject of a nice article by R. Tovia Preschel, found here.[2]

Personally, I have long thought that this doesn’t really seem to be the case. While it is true that Ketubot includes lots of discussions of civil law (which connects it to many topics covered in tractates Bava Metzia, Bava Batra, and Shevu’ot), and one does encounter the laws of Shabbat and Yom Tov in the first 10 pages, it doesn’t contain much from Zera’im, Kodshim or Taharot (or Mo’ed really, after the beginning). It seems to me that if one truly considers “Shas,” that is, all six orders of the Mishnah, there are much better candidates for the title of “Shas Kattan,” such as Pesachim, which contains a good deal of material from Kodshim and Taharot.

Some time ago I realized that this question can be answered empirically, depending on how it is defined. Can one computationally determine which tractate is the real “Shas Kattan”; that is, which tractate of the Talmud Bavli is the best representative for the rest of Shas (all six orders)?

A map demonstrating the connections between each tractate of Shas. “Kol ha-Torah kulah ‘inyan ehad” (Tosefta Sanhedrin 7:6)

Approach 1: Unique Tractate Scoring

One simple approach is to count unique citations. For every tractate in Talmud Bavli, we can simply tally up how many unique tractates (whether it is a citation to the Mishnah, Bavli/Yerushalmi, or Tosefta) are cited within that tractate of Talmud, with the highest possible score of 62. Before you scroll down, here’s a challenge: there is only a single tractate of Talmud Bavli that contains at least one reference to every single tractate in Shas. Can you guess which one it is?

The obvious limitation to this approach is that as long as any tractate is cited at all, there is no difference between a single citation and one hundred citations to that same tractate, which is perhaps unfair (After all, should the “Shas Kattan” determination really hinge upon whether the tractate includes a single citation each to Parah, Yadayim, and Uktzin, instead of a hundred citations to Bava Metzia?). On the other hand, we could count up the total number of citations to other tractates, but this approach also suffers from the opposite problem (namely, that the presence of many citations to a single tractate does not demonstrate a representation for all of Shas).

A slightly more complicated way of scoring citations beyond simple counting methods would be to use a points system, whereby additional citations to the same tractate improves the score incrementally but by decreasing amounts. For example, if the first page of a tractate quotes from Shabbat, Eruvin, and Pesachim, that’s three points, and then the second page quotes Shabbat and Gittin, then it will get one more point for Gittin but only another fraction of a point for the additional Shabbat reference, since Shabbat was already cited on the previous page. My thinking is that scoring in such a matter should decrease geometrically: for the second time that tractate is referenced, add 0.5 points, then for the third time, allot 0.25, etc. (So, for example, if a tractate quotes Berakhot once and Shabbat thrice, it will have a score of 1 + (1 + 0.5 + 0.25) = 2.75). In the end, however, none of these alternative counting methods turned out to change the ranking very much.

Below, I used Sefaria’s list of its library connections to collect the number of times any tractate of Shas was quoted by each tractate of Talmud Bavli. Below is a table of how many unique other tractates are cited by each tractate of the Talmud Bavli. In this case, a ‘citation’ counts whether it is a reference to the Mishnah, Tosefta, Talmud Yerushalmi, or Talmud Bavli to any one of the 63 tractates in Shas. With both the highest “geometric decrease score,” the most citations overall, and the only tractate to cite all 62 tractates of Shas, the clear winner is…. Chullin! In all likelihood, this is simply due to the fact that Chullin is one of the largest tractates of Talmud Bavli.[3]

Tractate	Unique Tractates Referenced	Geometric-Decrease-Score	Total References to Elsewhere in Shas
Chullin	62	116.90	1373
Menachot	58	104.11	1335
Eruvin	58	104.12	1104
Berakhot	56	101.77	881
Gittin	55	99.06	1124
Avodah Zarah	55	93.15	720
Bekhorot	55	95.36	711
Bava Metzia	54	96.76	1184
Pesachim	53	98.13	1192
Niddah	52	91.60	494
Chagigah	51	87.71	322
Shabbat	51	93.73	1351
Bava Kamma	51	91.51	1133
Bava Batra	51	93.48	1225
Kiddushin	50	90.78	1174
Ketubot	48	86.27	1086
Beitzah	47	79.65	537
Sukkah	47	84.70	956
Sotah	45	76.47	468
Megillah	45	77.96	382
Arakhin	45	76.91	408
Sanhedrin	44	83.25	1088
Makkot	44	75.13	400
Nazir	44	78.29	350
Keritot	44	71.54	356
Nedarim	43	75.32	372
Temurah	41	70.45	407
Shevuot	41	72.19	591
Rosh Hashanah	40	68.45	312
Moed Katan	37	63.70	204
Horayot	37	56.53	171
Yoma	36	71.15	712
Yevamot	36	69.95	999
Zevachim	36	70.46	991
Meilah	35	54.75	207
Taanit	33	57.52	235
Tamid	20	26.12	61

As an aside, we can use this database to ask of Masekhet Ketubot (or any tractate): does it have the most references to Nashim and Nezikin, compared to any other tractate? If not Shas Kattan, is it at least “Bas Kattan” (for ב סדרים)? The answer to that question is also no; all three “Bava”s beat Ketubot if you sum up citations to both Nashim and Nezikin. Here are some of the heavy-hitters in terms of “Bas Kattan”:

Tractate	Citations to Nashim	Citations to Nezikin
Ketubot	689	385
Gittin	627	311
Kiddushin	502	284
Bava Kamma	279	854
Bava Metzia	334	775
Bava Batra	401	706

Approach 2: Balance Between “Six Orders” References

There is another possible way of interpreting “shas kattan”-ness, which would refer to how well ‘balanced’ all of the citations are relative to each other in terms of being a fairer representation of the six orders of the Mishnah. A perfectly ‘balanced’ tractate will have 1/6 of its references to tractates in Seder Zera’im, 1/6 of its citations would be to Mo’ed, and so on.[4] If we categorize each citation according to the six orders of the Mishnah, which tractate is closest to this idealized representation of Shas?

Here too I used the cross-references (“link”) count from Sefaria’s github, and categorized the results based on Seder, which are color-coded differently in the bar graph below (click here for a colorblind friendly version). Although there are ways to put numbers on this dataset to calculate a “balance score,” from the figure below it seems like, once again, Chullin is in the running for the tractate of Talmud Bavli with the most evenly balanced set of references![5] In this case, we cannot simply blame it on the fact that Chullin is one of the longest tractates, since this is normalized to how many citations appear in total. (Numbers in parentheses reflect the fraction of citations to that Seder, if the number fits in the bar).

This dataset might indicate something interesting about Ketubot, which is that once you discount the self-references (that is, citations to other places in Masekhet Ketubot, or to its own Tosefta and Talmud Yerushalmi), Ketubot has more citations to Seder Nezikin than to Nashim. However, Ketubot is not at all unique in having more citations to tractates that are “out of order [seder]” than to its own. Berakhot, Avodah Zarah, Horayot, Arakhin, Keritot and Niddah all have more citations to Mo’ed than to their own order, Pesachim and Yoma both have more citations to Kodshim, and so on. On the other hand, it is worth noting that both Nedarim and Nazir, which might not seem like natural fits for Seder Nashim,[6] do both have more citations to Nashim than any other Seder.

Approach 3: Diversity of Topics

Another legitimate approach would be to understand the term “shas kattan” as a non-literal reference to “all the topics in the Torah,” and ask the question: which tractate of Talmud Bavli covers the most unique topics? In the past, this question would have been much more difficult to answer simply because there were no tools which identified “topics” as they appear in the Talmud in the same way that people have been identifying talmudic cross-references since R. Nissim Gaon in the 11th century.

But today, we have Sefaria! Included in the Sefaria database and API docs is a way to identify which topics come up in any source which the Sefaria team (and users) culled from few sources to make something rather impressive. Of course, the reality is that the topic ontology is still kind of messy. For one thing, some topics are much broader than others, to the point where smaller topics might even be included in larger ones. (For example “Moses/Moshe” is a topic, but so is “Moshe’s Anger,” and most of the sources belonging to the latter also belong to the former). Additionally, because of how the topics list was built, there is an over-representation of topics belonging to Aggadah and the halakhot that appear in the Shulhan Arukh, as opposed to halakhot dealing with sacrifices and ritual impurity. With all its faults, the topics count still seems like it could be interesting, so I also used Sefaria’s API to count up all the unique topics that show up throughout each tractate of Talmud Bavli.

And the winner of the most unique Sefaria-topics referenced is… Shabbat! This is not so surprising, considering that Shabbat is the largest tractate by word count (Chullin, which won the last two rounds, is third-longest), and its central topic is one that takes up nearly 10% of the Shulhan Arukh, which is responsible for many of these “topic” identifications in Sefaria’s database. Likewise, the second-to-longest tractate by word count (Sanhedrin) takes second place in Sefaria’s topics count.

Tractate	Topics Count	Unique Tractates Referenced
Shabbat	1133	51
Sanhedrin	1038	44
Berakhot	954	56
Pesachim	864	53
Bava Batra	781	51
Sotah	708	45
Bava Metzia	680	54
Ketubot	678	48
Eruvin	662	59
Yevamot	634	36
Kiddushin	630	50
Chullin	623	63
Gittin	616	55
Bava Kamma	611	51
Yoma	592	36
Avodah Zarah	577	55
Nedarim	541	43
Megillah	537	45
Taanit	488	33
Menachot	462	59
Chagigah	394	51
Rosh Hashanah	393	40
Niddah	384	52
Sukkah	351	47
Zevachim	313	36
Bekhorot	310	56
Moed Katan	293	37
Arakhin	289	45
Makkot	272	44
Nazir	251	44
Shevuot	242	41
Beitzah	217	47
Keritot	193	44
Horayot	183	37
Temurah	177	41
Meilah	104	35
Tamid	101	20

As mentioned, this Sefaria-based topic count comes with many caveats as to how much it truly represents the number of topics discussed. Therefore, one more attempt in this vein is worth trying, in order to salvage the idea that Ketubot is “Shas Kattan.” After all, what people truly intend when using this term is probably not that Ketubot has quantitatively the most citations to elsewhere in Shas, or even that it has the most topics as would be defined by aggadic encyclopedias such as Aspaklaria or topics found in Tanakh. What they mean, surely, is that Ketubot is the most central location for the most topics frequently encountered in “real” Gemara learning, the study of halakha and its conceptual foundations.[7] Instead of using Sefaria’s topics, then, I tried to use the citations in the popular book Kovets Yesodot ve-Hakirot by R. Ahikam Keshet, which the author has conveniently made available online through a few websites. The version I used, from the “Wikishiva” website hosted on yeshiva.org.il, had 419 unique entries.[8]

Unfortunately, no edition of Kovets Yesodot ve-Hakirot has a clear way to identify the citation to a particular tractate, and so as a shorthand I simply counted up the number of entries containing the name of a tractate (e.g., ‘ברכות’, ‘שבת’, etc.). This is certainly not perfect,[9] but I believe it serves our purposes well enough. Using this tally, we come to the rather surprising conclusion that the tractate cited by the most entries in Kovets Yesodot ve-Hakirot is, once again, Shabbat! In this case, Ketubot at least does well for itself, ranking in fourth place after Shabbat, Kiddushin, and Bava Batra.

Tractate	Kovetz Topics	Sefaria Topics
Shabbat	201	1133
Kiddushin	177	630
Bava Batra	167	781
Ketubot	163	678
Bava Metzia	152	680
Bava Kamma	119	611
Gittin	117	616
Pesachim	114	864
Yevamot	102	634
Nedarim	92	541
Sanhedrin	91	1038
Chullin	85	623
Berakhot	84	954
Sukkah	67	351
Eruvin	58	662
Avodah Zarah	58	577
Shevuot	49	242
Makkot	48	272
Yoma	48	592
Beitzah	47	217
Nazir	43	251
Bekhorot	40	310
Temurah	39	177
Megillah	34	537
Chagigah	33	394
Sotah	33	708
Niddah	32	384
Zevachim	29	313
Rosh Hashanah	29	393
Meilah	28	104
Taanit	25	488
Menachot	23	462
Keritot	19	193
Arakhin	17	289
Moed Katan	16	293
Horayot	9	183

As a final note, I’d like to mention an article I saw a few years ago by Daniel Boyarin about Rabbi Haim Zalman Dimitrovsky. Boyarin records how Rabbi Dimitrovsky helped prepare him for his doctoral exam in talmud:

…he also wanted me to learn several whole mesechtas or sections of the Talmud. Kesubos was one of the mesechtas that he insisted I learn, because as the proverb goes: “Kesubos holds the shlisslokh,” the keys to the entire Talmud. It is sometimes called “Shas Katan” (“the little Talmud”) because it includes virtually all of the halakhic themes that the Talmud explores. He used to say, “In order to be a Talmid hakham, you have to know three massekhtas really well”—Kesubos was one of them, along with Baba Metzia, but now, after nearly 60 years, I can’t remember the third. He said, “If you know those three massekhtas”—and when he said know, he meant know, which included Rashi, the tosafot, all the rishonim, and selected aharonim—“then you will be a talmid hakham.” I never learned the third massekhet.[10]

When I originally read this, I was intrigued by the thought that there was a mysterious ‘third tractate’ that held the keys to becoming a talmid hakham, alongside Ketubot and Bava Metzia. After thinking about it for a little while, I speculated that the third tractate Boyarin couldn’t recall was Shabbat. Considering Rabbi Dimitrovsky’s own publications of Rashba’s commentary to tractates of Mo’ed, he was certainly not one to underestimate the importance of learning a large tractate from that seder, even if many yeshiva curricula today emphasize Nashim and Nezikin over the rest. Whether or not my guess is correct, it seems as though Shabbat and Hullin, in addition to being among the largest tractates, also have good claims to holding the keys to the rest of Shas.

[1] This article was expanded from a post on the website MiYodea, the Judaism StackExchange: https://judaism.stackexchange.com/q/141647/5083
[2] According to the website, the original article was printed in Ha-Tzofeh 21, Tishrei 5729 (1970).
[3] In theory, this can be corrected for by normalization, but because tractates of Talmud Bavli vary so widely in word count, simply using a tractate’s length as a denominator will provide a skewed picture; I believe that the approach taken in the next section is a better method of normalizing to ‘total citation count’.
[4] In reality, each Seder is a different size, and so an “ideal balance” would cite each Seder proportional to its size. I believe that this is not worth correcting for, because we would also need to correct for the fact that some tractates have two Talmuds, while some tractates only have a Talmud Bavli and others only a Talmud Yerushalmi or neither, and so a true correction would have to account for all the possible citation material of each tractate.
[5] Actually, to be precise, Chullin may come in second place to Bekhorot in terms of most balanced tractate. To calculate a “balance score”, I used a chi-square test to determine the extent to which the citation counts to each Seder deviates from an ideal ⅙ of the total citations. According to this calculation, Chullin is narrowly beaten by Bekhorot. However, because the six orders of the Mishnah are not equally large in ways that are not so easily accounted for (see previous footnote), this balance test (of expecting ⅙ of citations to refer to each Seder) is imprecise.
[6] See the discussion in Talmud Bavli Sotah 2a and Rambam’s observation in his Introduction to the Mishnah that the Torah’s presentation of vows is in the context of marriage.
[7] This statement is reflective of an attitude that is not necessarily shared by this author, but this is not the place to discuss the question of what constitutes the “true” or “primary” learning of Shas.
[8] Although there are many more unique titles, nearly a third of these are merely redirect pages to other entries.
[9] Importantly, it is possible that an entry might reference the concept of “Shabbat” without citing Tractate Shabbat. I mostly assume that citations to either the concept or the tractate of the same name will overlap, with one major exception: my guess is that the word תמיד likely appears in more contexts as a concept and not as a citation to a particular tractate. Since the tractate of Tamid is obviously not in the running for “Shas Kattan,” however, I believe it is safe to ignore.
[10] Walking and Learning on Shabbos with Prof. Haim Zalman Dimitrovsky – Tablet Magazine