1) THE NAME OF YEHUDAH
QUESTIONS: The Gemara relates that Yehudah performed an act of public Kidush Hash-m when the members of his tribe walked into the Yam Suf first, before anyone else, with the trust in Hash-m that He would split the Sea for them. As a result of this act, the four letters of Hash-m's name were incorporated into Yehudah's name.
(a) Why should Yehudah receive the reward of having the letters of Hash-m's name incorporated into his name because of what his great-grandson, Nachshon ben Aminadav, would do many years later at the Yam Suf? Nachshon himself should have received the reward.
(b) What does the Gemara mean that Yehudah was rewarded by having Hash-m's name incorporated into his own name? His name was given to him at birth by his mother, Leah, (Bereishis 29:35), as an expression of her gratitude to Hash-m ("Odeh Es Hash-m") -- long before his descendant performed the act of Kidush Hash-m. How is it possible for a person to receive reward for a deed before that deed is performed? Since a person has free choice, he might not perform the deed for which he was rewarded.
ANSWERS:
(a) The Gemara earlier (10b) also cites the statement that Yehudah's name incorporated the name of Hash-m because he was Mekadesh Shem Shamayim, but with reference to another act of public Kidush Shem Shamayim which Yehudah performed. The Gemara there discusses Yehudah's public admission that Tamar was justified and that he had acted improperly. The MAHARSHA there points out the contradiction between the Gemara here and the Gemara earlier and answers that both Gemaras are correct: he was called Yehudah because of both reasons, the incident with Tamar and the act of his descendant, Nachshon.
This may be explained as follows. Yehudah set the precedent for public repentance for one's sins when he confessed in the incident with Tamar. The Gemara earlier (7b) teaches that Reuven learned how to repent for his sin from Yehudah, who confessed his sin and taught the concept of repentance.
Yehudah's momentous act instilled in future generations the ability to lead the way and be Mekadesh Shem Shamayim when necessary. Yehudah's precedent gave Nachshon the ability to jump into the Sea when everyone else hesitated. Therefore, it is Yehudah's name which incorporates the name of Hash-m.
(b) The RIF in the Ein Yakov (10b; see also MAHARSHA there) explains that Yehudah was named based on the future. The Gemara in Berachos (7b) teaches that sometimes a person's name hints to major events in his life. Ruth's name alluded to David ha'Melech who would eventually come from her, who "satisfied (she'Rivahu) Hash-m with songs and praises."
However, this concept is difficult to apply to the Gemara here. Ruth's name hinted only to the concept of "Rivahu," which does not have an inherently positive connotation; it could have meant that he satiated Hash-m with Mitzvos, or the opposite, and thus its connotation allowed for free choice. In contrast, the fact that Yehudah's name incorporates the name of Hash-m is inherently positive, as the Gemara implies.
The comparison to the Gemara in Berachos is particularly problematic according to the Gemara earlier (10b) which says that because of Yehudah's Kidush Hash-m he "merited" to have the entire name of Hash-m incorporated into his entire name, which clearly implies that his name was given as a reward for his future act.
Perhaps the Gemara means as follows. Yehudah was not the first person to teach the concept of Kidush Shem Shamayim. His mother, Leah, already taught that concept when she chose the name for Yehudah, as the Gemara says in Berachos (7b) that Leah was the first to express gratitude to Hash-m for the gifts He gave. Since she was Mekadesh Shem Shamayim by publicly thanking Hash-m, Hash-m put into her mind the idea to call her son "Yehudah" (rather than "Odeh"; see MAHARSHA) and to incorporate the name of Hash-m into his name. This naming instilled in Yehudah, and in his descendant Nachshon, the strength and courage to lead the Jewish people with Kidush Shem Shamayim (in the incident with Tamar, and in jumping into the Yam Suf), and his descendants eventually earned the kingship of the Jewish people.
The Gemara may mean that because Leah attained this trait of Kidush Shem Shamayim when she gave birth to Yehudah and she prayed that Yehudah should embody this trait, she instilled in Yehudah the merit to have the name of Hash-m in his name and to always find the strength to be Mekadesh Shem Shamayim publicly.
This may also be the intent of the Gemara in Berachos which says that a person's name can influence his future. It means that if the mother embodies a certain trait and she gives her child a name in the hope that the child will also embody that trait, it can influence the child. When Ruth called herself "Ruth" in the hope that she would have a descendant who would sing praises to Hash-m, she merited that David eventually came from her. When Leah gave birth to Reuven, she prayed that he should not be envious of his brothers as Esav was (see Berachos 7b), and her prayers bore fruit. For this reason, the Gemara describes the names of Reuven and Ruth immediately after it discusses how Leah thanked Hash-m when Yehudah was born.

37b----------------------------------------37b

2) RESPONSIBILITY FOR OTHERS
QUESTION: The Gemara records a dispute between Rebbi and Rebbi Shimon ben Yehudah about whether Rebbi Shimon maintains that each Jew is an Arev for every other person, or whether each Jew is also an Arev for the Arvus of every other person. What practical difference is there between the two opinions? According to both opinions, every person is responsible for what every other Jew does.
ANSWER: The TOSFOS HA'ROSH answers that a practical difference exists in a case in which a person dies after another person sinned. The punishment of Arvus apparently affects all of the Arevim at the same time. If one dies before the punishment for the Arvus was administered, he obviously will not suffer the punishment for that Arvus. According to Rebbi Shimon ben Yehudah, who says that each person is an Arev only for every other person's Mitzvah-observance (but not for every other person's obligation of Arvus), the death of the first person will not affect the punishment that the others are destined to suffer. However, according to Rebbi, who says that each person bears responsibility for the responsibility of the others, the punishment that the deceased person was supposed to receive will now be divided up among all of his survivors, since they have to bear his punishment for the Arvus that he took upon himself.
3) THE OBLIGATION OF "ARVUS"
OPINIONS: Rebbi Shimon says that for every one of the 613 Mitzvos in the Torah, 48 covenants were made, for every man who left Mitzrayim and received the Torah (603,550), for a total of 17,758,855,200 covenants. The number 603,550 represents the count of the Jewish men capable of going to war ("Anshei Tzava"), men between the ages of 20 and 60 who left Mitzrayim (Shemos 38:26, Bamidbar 1:45).
Does Rebbi Shimon mean that the obligation of Arvus is limited to the Mitzvah-observance of men between the ages of 20 and 60? Does the obligation of Arvus not extent to Gerim and Nashim, who were not included in the count of 603,550?
(a) GERIM. RASHI in Nidah (13b) cites a view which explains that the Gemara's statement that Gerim cause suffering to the Jews means that some Gerim are not sincere and the Jews must bear the burden for their sins. Rashi rejects this explanation and asserts that the obligation of Arvus does not apply to Gerim. The Jews are not responsible for the sins of Gerim, and therefore the Jews do not suffer for the sins of Gerim. Rashi proves this from the number mentioned by the Gemara here, 603,550. If Arvus includes Gerim, the number should be much higher because it should reflect the people of the "Erev Rav" as well.
TOSFOS there questions Rashi's statement. Perhaps the Gemara chooses this number simply because it is the only census number specified by the Torah. It is not meant to exclude any people who were not included in that particular count. It is obvious that men under 20 and over 60 are also included in Arvus, even though they are not included in the count of 603,550. Hence, the "Erev Rav" should be included in the obligation of Arvus as well.
Tosfos answers that the Gemara knows the number of people included in the "Erev Rav" (the Mechilta says that they were double the number of people who left Mitzrayim). Therefore, the fact that the Gemara does not include their number in the obligation of Arvus, even though their number is known, shows that Gerim are not included in Arvus.
Alternatively, the women, and the men below the age of 20 and above the age of 60, are considered ancillary to those who were counted, and therefore the number 603,550 alludes to them as well. The Gemara means that there are covenants for each individual of the group from which 603,550 were counted. The number of covenants, however, indeed include the other people as well. The "Erev Rav," in contrast, have no reason to be subsidiary to the men of the Jewish people who were counted, since the "Erev Rav" were just as capable as "Anshei Tzava" as those who were counted. Therefore, if the Gemara does not allude to their number, it means that they were not included in the obligation of Arvus.
(b) NASHIM. The ROSH in Berachos (3:13) writes that the reason why a man who ate only a k'Zayis of bread may recite Birkas ha'Mazon on behalf of a man who ate his full is because of the concept of Arvus: every Jew is responsible to ensure that every other Jew fulfills the Mitzvos (see Rashi to Rosh Hashanah 29a, DH Af Al Pi she'Yatza). The Torah thus allows one man to exempt another even if the first one ate nothing. The Rabanan, however, instituted that in order to exempt another man, he must have eaten at least enough to obligate himself to recite the blessing mid'Rabanan.
Nashim, on the other hand, do not bear group "responsibility." They have no obligation to ensure that every other Jew fulfills his obligation of Birkas ha'Mazon. Therefore, unless a woman's obligation to recite Birkas ha'Mazon is on the same level as a man's (i.e. mid'Oraisa), she cannot exempt him from his obligation.
The DAGUL MEREVAVAH (OC 271:2) refers to the MAGEN AVRAHAM (271:1) who rules that if a person recites the Shemoneh Esreh of Ma'ariv on Shabbos night, he fulfills his Torah obligation to recite Kidush (although he must still fulfill the d'Rabanan obligation to recite Kidush over a cup of wine). The Dagul Merevavah writes that according to this ruling, although a woman normally has the same obligation of Kidush that a man has, if a woman recited Ma'ariv on Shabbos night she cannot recite Kidush for a man who has not recited Ma'ariv. Since her obligation is now only mid'Rabanan (because she already fulfilled her d'Oraisa obligation), she cannot discharge a man's d'Oraisa obligation, because women are not in the category of "responsibility" which would enable her to exempt another person even when she is not obligated herself.
The Dagul Merevavah questions whether a man who already recited Ma'ariv may exempt a woman who has not recited Ma'ariv. Perhaps just as a woman does not have responsibility of Arvus for a man, a man does not have responsibility of Arvus for a woman (and thus he cannot exempt her if he is obligated to recite Kidush only mid'Rabanan).
The Rosh and the Dagul Merevavah seem to infer from the Gemara here that only men accepted the responsibility of Arvus, since the number 603,550 included only men.
REBBI AKIVA EIGER (Teshuvos 1:7) responds that when the Rosh writes that women are not bound by group "responsibility," he does not mean that they are never responsible for another Jew's fulfillment of the Mitzvos. Rather, a woman is not "responsible" only in the case of a Mitzvah which she is not obligated to perform herself. In the case of a Mitzvah which she is also obligated mid'Oraisa to perform, she does have "responsibility" for other Jews and other Jews have responsibility for her. Therefore, she may exempt a man from his d'Oraisa obligation to recite Kidush.
Rebbi Akiva Eiger's understanding is consistent with what Tosfos writes in Nidah, that the only reason why the number of women who left Mitzrayim was omitted from the count was because their numbers were unknown. They were, nonetheless, included in the obligation of Arvus.
However, according to the Rosh in Berachos and Rashi in Rosh Hashanah, who write that one Jew may exempt another Jew in his obligation of Birkas ha'Mitzvos because of Arvus even though the one who recites the blessing does not perform the Mitzvah himself, there is a problem. How can a Ger recite a blessing on behalf of a Jew, or vice versa? Rashi in Nidah (13b) writes that Gerim are not included in Arvus. Accordingly, a Ger should not be able to recite a blessing on behalf of a Jew, and a Jew should not be able to recite a blessing on behalf of a Ger!
The Rosh himself may follow his opinion in the TOSFOS HA'ROSH in Nidah (13b), where he rejects Rashi's suggestion that Gerim are not included in Arvus. According to Rashi, however, how can a Ger recite a blessing on behalf of another Jew, and vice versa?
The answer is that Rashi in Nidah refers to Gerim who did not convert wholeheartedly and who returned to their earlier ways. These Gerim are comparable to the "Erev Rav" who joined the Jews in order to leave Mitzrayim but later returned to their earlier ways of idolatry. Such Gerim are not included in the obligation of Arvus, and Jews bear no responsibility for their acts (since their eventual defection shows that they never converted wholeheartedly in the first place; see Rambam, Hilchos Isurei Bi'ah 13:16). However, a Ger who converts wholeheartedly certainly is included in the obligation of Arvus, and therefore he may recite a blessing on behalf of a Jew and a Jew may recite a blessing on his behalf. (If he later sins, the Jews do bear responsibility for his actions. This is evident from Shevuos 39a.)
(c) KOHANIM. As mentioned above, women are not included in the obligation of Arvus, at least not for Mitzvos which they are not obligated themselves to perform. Nevertheless, the Gemara says that every one of the 603,550 Jews was responsible for every other Jew's fulfillment of the 613 Mitzvos, which implies that a Yisrael is responsible for the Aveiros which a Kohen performs, even though the Yisrael has no Mitzvah to refrain from those acts. What is the difference between women, who are exempt from the Arvus of Mitzvos which they are not obligated to perform, and Yisraelim, who are not exempt from the Arvus of Mitzvos which only Kohanim are obligated to perform?
The answer is that the Torah exempts women from certain Mitzvos because of their obligations to their families and children which take precedence. This reason exempts them from the responsibility to ensure that others observe those Mitzvos, since they cannot be available at the time that others are supposed to fulfill the Mitzvos. However, Yisraelim were not exempted from the Mitzvos of Kohanim; rather, the Torah simple did not give those Mitzvos to Yisraelim. It gave them only to Kohanim because of their extra Kedushah. Hence, there is no reason to exempt the Yisraelim from the Arvus of those Mitzvos. (See AVNEI NEZER YD 352, cited by YOSEF DA'AS.)