Based on a Naaleh.com shiur by Rabbi Michael Taubes
In Parshat Bechukotai, the Torah tells of the disasters that will befall the Jewish people if they fail to observe the laws of the Torah properly. It says that people will panic and trip over each other. The Gemara in Sanhedrin comments on this phrase, one Jew will trip over the sins of his brother. “Melamed shekol yisrael areivim zeh lazeh.” This teaches us that each Jew is responsible for another.
In Parshat Nitzavim it says, “Hanistarot l’Hashem Elokeinu v’haniglot lanu u’levanenu.” The hidden things are in Hashem‘s domain, but that which is revealed is for us and our children.” The Torah tells us that if Jews won’t observe the mitzvot, the whole community will be punished. Rashi asks, how can one person be held responsible for what another thinks? He answers, that which is hidden is not our obligation. However, we have responsibility to stop that which we have the power to stop.
There is a dot on top of the words lanu u’levanenu to teach us that our obligation to another Jew didn’t go into effect immediately. It only began when the Jews entered Israel with the covenant that was made at Har Grizim and Har Avel.
The Mishna in Rosh Hashana takes the concept of arvut further. You can perform a mitzvah on behalf of someone else, provided you are also obligated in the mitzvah. Therefore, a cheiresh (deaf mute), a shota (a deranged person), and a katan (a minor) cannot perform a mitzvah for others.
The Gemara says, even if one has already discharged his obligation he can still perform the mitzvah for someone else. Rashi explains that this is because of the rule of “Kol yisrael areivim zeh ba’zeh.” However, this does not apply to birchat hanehenin (blessings on food and pleasant smells) because the concept of arvut is only for a mitzvah that one has a responsibility to fulfill. Eating is an optional activity.
Rava asks, can you be motzi someone (fulfill someone’s obligation) with a blessing on food, when there is an obligation to eat? For example, can one person recite a blessing for someone else when eating matzah at the seder? The Rambam answers that you can. The Shulchan Aruch rules that one can recite Kiddush for others, even if one will not be eating the meal together with them. However, to be motzi someone with Hamotzi, one must eat some of the bread too.
Does the concept of arvut apply to a biblical mitzvah or to a rabbinical mitzvah or to both? The Tzlach writes in his commentary on Gemara that it only applies to biblical mitzvot. He brings proof from the Gemara in Sota that the law of arvut only took affect at Har Grizim and Har Avel. Tosfot comments that that they took upon themselves the 613 biblical mitzvot. The Tzlach infers that since at the time that arvut was introduced they only took upon themselves the biblical mitzvoth it does not apply to rabbinic mitzvot.
He brings another proof from the Rambam, who rules that if an arev did not specify an amount the arevut is worthless. He points out that while there’s a fixed body of 613 mitzvoth in the Torah there is no set amount of Rabbinic laws. Therefore, arvut does not apply there.
The Chida, the Birkei Yosef, and the Ktav Sofer disagree and maintain that the principle of arvut does apply to rabbinic mitzvot. In fact the Shaagat Aryeh says that the rule of arvut only applies to mitzvot d’rabbanun and not to d’oraysa.
How does the halachic mechanism of arvut work? Although one has already discharged his obligation, since there is another Jew who needs help, it is as if one has not fulfilled his complete obligation yet. The Chikrei Lev explains that when you do a mitzvah for someone else you connect to the person on such a deep level that in a sense his obligation becomes your obligation. According to Rav Akiva Eiger, the maximum you can do is what you were originally obligated. According to the Chikrei Lev, one’s level of obligation is irrelevant, as arvut applies in whatever way the person needs that connection.