The previous Mishnah ended by saying that one who is passing behind the synagogue and happens to hear the shofar can thereby fulfill one's obligation iff one has the kavanah (intention). This Mishnah riffs on that theme (the way the Gemara breaks up the mishnayot doesn't make so much sense) and in the process puts a respectable spin on two seemingly idolatrous passages in the Torah. (I mean, idolatry is already a positive commandment, as it is written, va'avadtem elohim acheirim v'hishtachavitem lahem, but stamping it out is still worth the effort.) When Israel is battling
The Gemara has zero to say about this part of the Mishnah.
The Mishnah continues: deaf-mutes, insane people, and children (all categories of people who were thought not to have full mental faculties, who are thus not obligated in the commandments) may not motzi (fulfill the obligation of) others. This is the general rule: anyone who is not obligated in something may not motzi others in that obligation.
This, of course, comes up all the time in communal discussions about pluralism and egalitarianism and all that. Because of this principle in the Mishnah, the starting point for the halachic discussions about egalitarian prayer involves proving that women are obligated in prayer (so that they can motzi others). (For me, egalitarianism is an axiom, but if other people are proving it from other principles, that's great too.) I am using MR's copy of the Gemara while he is in Israel, and the pencil markings are like a clipping service for sources related to gender egalitarianism; often there will be an underlined passage, deep into some endless Tosafot, that mentions something offhand about how women are or aren't obligated in this or that. So we were shocked to see that nothing was underlined on this page, but maybe it's just taken for granted.
A baraita in the Gemara: Everyone is obligated in shofar - country and western! Kohanim, Levites, Israelites, converts, freed slaves, but they're implicitly only talking about men. But two liminal gender categories are obligated, just to be on the safe side: the tumtum (who is of indeterminable sex) and the androgynos (who has both male and female genitals). The tumtum can't motzi anyone (even another tumtum), but the androgynos can motzi another androgynos. To apply the framework of quantum mechanics to these rules (based on Rashi's reading): As far as we can tell, the Talmud recognizes no "Copenhagen gender", i.e. someone whose sex is fundamentally indeterminate. Everyone has a definite sex, but sometimes (viz. for the tumtum and androgynos) it is a hidden variable, as in Einstein's understanding of quantum mechanics (before being smacked down by Bell's inequality). The difference between the tumtum and the androgynos: the tumtum's sex is a hidden variable that potentially has a different value for each individual tumtum, whereas the androgynos's sex has a single (hidden) value for the entire androgynos gender. Thus tumtum A can't motzi tumtum B, on the off-chance that A is male and B is female, but androgynos A can motzi androgynos B, because either they're both male (in which case all is well) or both female (in which case they're not obligated anyway. Mitzvot are hard, let's go shopping!). We also have a cameo appearance from the person who is half a slave and half free. This happens when a slave has two owners, and one of the owners frees him. At that point the other owner is also required to free him, but until that happens, he is in this weird linear combination of eigenstates like Schrodinger's cat. The Talmud found him at the same casting agency where they found the five brothers married to five sisters.
If you've already said a blessing for yourself, you can still say it for others, except the blessings for bread (hamotzi lechem min ha'aretz) and for wine (borei p'ri hagafen). However, if we can trust that Rav Papi was doing the right thing, this doesn't apply to the borei p'ri hagafen blessing kiddush, since in that case it's an obligation.
The final baraita: Don't pass out food and say hamotzi for your guests unless you're eating with them! But it's ok to do it for your children, for the educational value. As for hallel and megillah, even though you've already done it for yourself, you can still do it for others, so it's ok for that midnight megillah reading to be done by someone who was at the regular one.
Hadran alach "ra'uhu beit din"! (Or as my Vilna printing says, Har'ran alach!)
END OF CHAPTER 3
They also didn't do the greatest job breaking up the chapters. Just as chapter 3 began with stuff about witnessing and sanctifying the new moon (a continuation of chapter 2) before moving on to the shofar, chapter 4 now begins with more material about the shofar.
What happens when Rosh Hashanah falls on Shabbat?
When the Temple was still standing, they would blow the shofar on Shabbat, but only in the Temple. After it was destroyed, we had to get past that. Rabban Yochanan ben Zakkai is the one Jew whom everyone can agree on as a hero. For some, he represents the possibility (yea, requirement) for Judaism to evolve in order to adapt to changing times; for others, he represents the establishment of Normative Rabbinic Judaism. He decreed that the shofar would be blown (on Shabbat, but the "on Shabbat" part is taken for granted for the rest of the sugya, or so we think) in any place where there is a beit din (rabbinical court). (Whoa, maybe there's method to the madness? Chapters 3 and 4 both begin in nonintuitive places, and both begin with a beit din. Is there a deeper meaning here?) Well, we're arguing over what he actually said. Rabbi Elazar thinks the decree applied only to Yavneh. And the stam sees a dispute between two anonymous voices in the Mishnah over whether this applied to any beit din (including an ad hoc one) or only a fixed beit din.
Jerusalem is still superior to Yavneh, because any place close to Jerusalem that could see and hear and reach it could blow the shofar, whereas for Yavneh this can only happen in a beit din. The Gemara (Rava, Rav Huna, and friends) goes nuts about what "in a beit din" means. In the physical presence of the beit din? Just at the time that the beit din meets? (And what if the beit din sits longer than its appointed time? Is it while the beit din is physically seated, or during the fixed time when they're supposed to be seated? Teiku!!! Stalemate!) Is there a difference between individuals blowing shofar for themselves vs. a communal shofar blowing? Is there a difference between shofar on Rosh Hashanah and shofar for the yovel? We explore every possible permutation, for much of an amud (30a).
But before that, we ask the obvious question: why is blowing shofar on Shabbat a problem in the first place? After all, it's not melacha (forbidden labor). R. Levi b. Lachma says in the name of R. Chama bar Chanina that the exemption on Shabbat comes from the Torah -- "shabbaton zichron teru'ah" refers to Rosh Hashanah on Shabbat, while "yom teru'ah" refers to Rosh Hashanah on a weekday. While this distinction between teru'ah and zichron teru'ah may have been preserved in the liturgy, the Gemara actually knocks it down! If no-shofar-on-Shabbat is really a Torah commandment, then why did they do it in the Temple?! Rather, it's just a rabbinic fence: everyone has to hear the shofar and not everyone knows how to blow it, so someone might carry a shofar through the public domain to bring it to a skilled shofar blower, thus violating Shabbat, so the rabbis somehow overturned a Torah requirement. And the same rationale applies to lulav and megillah. Lame. (Especially lame for lulav! I can see how shofar and megillah require skilled labor, but lulav???)
To conclude with a story about our hero R. Yochanan ben Zakkai: One time Rosh Hashanah fell on Shabbat, and RYbZ said "Let's blow the shofar." They said "Wait a second, let's talk about it first." He said "Let's blow the shofar first, and then we can talk about it." They blew the shofar and they said "Now let's talk about it." RYbZ said "There's nothing to talk about! The shofar has been blown and what's done is done."
While this story may seem heroic in the context of letting Judaism evolve (rather than discussing everything to death before being willing to take any action), RYbZ's actions can be seen as either heroic or despicable depending on your view of the issue at hand. As an exercise, ask yourself whether RYbZ's method of creating "facts on the ground" is justified for each of the following scenarios: evolving Jewish ritual practice, building settlements in the West Bank, same-sex marriage in Massachusetts, same-sex marriage in San Francisco, invading Iraq, getting rid of the Senate filibuster, bulldozing the runway at Meigs Field.