The Mishnah teaches that if a woman borrows ingredients for her challah from a neighbor on Yom Tov, the resulting challah is restricted in its movement. It can only be transferred within the combined and shared area where both of their techum Rosh Hashanah (halachic travel limits) overlap. This is because, since the neighbor contributed water and salt, they are considered to have a partnership in the challah, and her stake limits its movement to the shared techum.
The Gemara questions this, citing Hacham Meir, who suggests that the borrowed ingredients, such as water, should become nullified (batel) within the majority of the flour. If nullified, they should not be significant enough to affect the techum. Abaye substantiates this, explaining that while there is a monetary obligation to repay the borrowed items, the halachic discussion on Yom Tov concerns whether the water and salt affect the prohibition (isur) of techum. Since nullification (bitul) applies to prohibitions, the challah should be nullified and not subject to techum laws. The Gemara offers three reasons why the Mishnah states that the water and salt are not nullified.
The first reason, given by Abaye, is a preventative decree (gezeirah). While the water and salt should ideally be nullified in the flour, if we permit nullification in this case, people might mistakenly apply it to a situation of actual partnership (shutafut) in challah. In a true partnership, where individuals explicitly declare themselves partners, everyone agrees there is no nullification, and the challah must be moved only to a joint area. The concern is that people might learn from the case of borrowed ingredients (where one gave a portion) and incorrectly assume they can move the challah to their individual techum in a true partnership. Therefore, the Mishnah rules against nullification in the borrowed ingredients case as a gezeirah to prevent error in partnership cases.
Rabbah offers a second reason, specifically for the case of borrowed spices (tavlin) mentioned in the Mishnah. If someone borrows spices and adds them to a pot (kedirah), the pot's movement is also restricted to the overlapping techum. Rabbah explains that spices are not nullified because they impart taste (ta'am). Anything that gives taste is not subject to nullification, as its presence is evident and significant. According to the Shi (a commentary), Abaye and Rabbah are not in dispute; Abaye addresses the challah case (a gezeirah against partnership), and Rabbah addresses the pot case (due to taste). However, the Tosafot learns differently, stating that Abaye's gezeirah applies to both challah and pot, and Rabbah's reason of "taste" also applies to both, as salt gives taste to dough and water is essential for its coagulation. Thus, according to Tosafot, Abaye and Rabbah are in disagreement, with each offering an explanation applicable to both cases.
Rav Ashi provides a third, simpler explanation: the prohibition (isur) in question, regarding techum, is temporary. The restriction on moving the challah or pot only applies on Yom Tov. After Yom Tov, the techum laws no longer apply, and the item can be moved freely. There is a principle that nullification (bitul) does not apply to something that will eventually become permissible (davar sheyesh lo matirin). Since the isur of techum will naturally expire, we do not apply bitul. Tosafot adds that this principle typically applies to items of the same species. Here, salt and water are considered integral to the challah, making them part of one species for this rule. This principle, davar sheyesh lo matirin, applies even to rabbinic prohibitions, as the isur techum is rabbinic.
The Gemara then delves into the specific components of the Mishnah's ruling. The Mishnah states that if one borrows water, there is no problem, implying a leniency. Yet, the Mishnah does not explicitly state this leniency for salt. The Gemara asks why water is singled out. It then cites a Braita from Rabbi Yehudah who states that salt, when mixed into dough or a pot, is nullified. This contradicts the implication that salt poses a problem. The Gemara resolves this by distinguishing between types of salt: melach sidomit (fine salt) is nullified and poses no techum problem, while melach istrokanit (thick salt) is not nullified. The Mishnah's leniency for water refers to thick salt, while Rabbi Yehudah's leniency refers to fine salt.
The Braita then states that water is not nullified in a pot because it is evident. This contradicts Rabbi Yehudah, who permits water in both dough and a pot. The Gemara resolves this by distinguishing between the consistency of the pot's contents: if the pot is thick, the water is not evident and is nullified; if it is thin (like soup), the water is evident and not nullified. Thus, Rabbi Yehudah's ruling on water depends on the pot's consistency, and his ruling on salt depends on its fineness.
The next Mishnah discusses the halachic status of a burning coal (gahelet) versus a flame (shalhevet). It presents five distinctions: 1. Regarding techum: A gahelet follows the techum of its owner. A shalhevet, however, can go anywhere, even beyond the owner's techum, because it is not tangible. 2. Regarding consecrated items (hekdesh): Benefiting from a consecrated gahelet incurs the prohibition of me'ilah (misuse of consecrated property), requiring a sin offering. Benefiting from a consecrated shalhevet is forbidden initially (lechatchila), but if one did benefit, it does not incur me'ilah. 3. Regarding idolatry (avodah zarah): A gahelet designated for avodah zarah is forbidden. A shalhevet of avodah zarah is permissible, even initially. 4. Regarding Shabbat: Carrying a gahelet from a private domain to a public domain on Shabbat makes one liable. Carrying a shalhevet is exempt. 5. Regarding vows (neder): If one vows not to benefit from a friend, they are forbidden to benefit from their friend's gahelet but are permitted to benefit from their shalhevet, as a shalhevet is not considered tangible.
The Gemara questions the distinction between hekdesh and avodah zarah regarding a shalhevet. Why is benefiting from a shalhevet of hekdesh forbidden initially, but a shalhevet of avodah zarah is permissible even initially? Both are generally forbidden. The Gemara explains that avodah zarah is generally repulsive to people, so there is no rabbinic decree (gezeirah) that if one uses the flame, they might come to use the coal. People naturally distance themselves from avodah zarah. However, hekdesh is not repulsive; on the contrary, it is sacred. Therefore, a gezeirah was made on the shalhevet of hekdesh, lest one come to use the actual gahelet. Tosafot clarifies that while hekdesh is less desirable than ordinary items (chulin), it is not repulsive compared to avodah zarah.
The Gemara then addresses the Shabbat law, where carrying a shalhevet is exempt, yet a Braita states that carrying even a tiny shalhevet makes one liable. Rav Sheishet reconciles this by explaining that the Braita refers to a shalhevet carried on a splinter (kisam). Since the splinter itself is too small to incur liability for carrying wood (which requires enough wood to cook an egg), the liability must be for the shalhevet, which is considered significant when attached to something. Abaye argues that a flame on a small splinter is not significant, as it will quickly extinguish. He suggests the Braita refers to a shalhevet on a vessel (keli) smeared with oil, making the flame substantial. The Gemara then asks why one would not be liable for carrying the vessel itself. It explains that the vessel is considered cheap or too small to meet the minimum measure for carrying on Shabbat. Thus, the liability is solely for the significant shalhevet.
The Mishnah's ruling that carrying a shalhevet is exempt must therefore refer to a shalhevet not attached to anything tangible. The Gemara asks how one can carry an unattached flame. It explains that the case refers to a flame on the ground that is fanned or blown from one domain to another. Since the shalhevet is not tangible, one is exempt from liability for carrying it on Shabbat.
The next Mishnah discusses wells. A privately owned well (bor shel yachid) means its water is bound by the owner's techum. A city well (bor shel benei ha'ir) follows the techum of the city, allowing water to be moved 2,000 cubits in any direction. Wells built for pilgrims from Babylon (olei Bavel) follow the techum of the person who draws the water (ha'mimaleh). Rashi clarifies that olei Bavel wells are considered ownerless (hefker), and one acquires hefker by picking it up. Once drawn, the water belongs to the drawer and is bound by their techum. If they lend it to a friend on Yom Tov, it still follows the drawer's techum. The Gemara suggests the Mishnah implies that the water from olei Bavel wells is acquired retroactively (berirah) by the one who draws it, making it theirs from before Yom Tov. This is a stringency (lachumra) to limit its movement if lent to another.
Rabbah poses a contradiction to Rav Nachman. The Mishnah states that a private well's water follows the owner's techum. However, another Braita states that water from flowing rivers and gushing springs follows the techum of anyone who possesses it. Rav Nachman resolves this by distinguishing between stationary water (like a private well), which has a fixed techum, and flowing water, which has no fixed techum and can be moved by anyone who takes it.
Regarding olei Bavel wells, there is a dispute: Rav Nachman says if one draws water for a friend, it follows the friend's techum. Rav Sheishet says it follows the drawer's techum. Their dispute hinges on how olei Bavel wells are viewed. Rav Sheishet holds they are ownerless (hefker). When one picks up an ownerless item for a friend, the friend does not acquire it (as one cannot acquire an ownerless item for another if it causes a loss to a third party). Therefore, the water belongs to the drawer, and its techum follows the drawer. Rav Nachman holds that olei Bavel wells are a partnership (shutafut) of all Israel. When one draws water for a friend, they are taking the friend's share, so the water belongs to the friend and follows their techum.
The Gemara challenges Rav Nachman's view that olei Bavel wells are a partnership. A Braita states that if two people vow not to benefit from each other (hareini alecha herem), they are still permitted to drink from olei Bavel wells. This implies the wells are ownerless, not a partnership, because if they were partners, their mutual vow would forbid them from benefiting from each other's share in the well. The Braita lists other items considered ownerless (like the Temple Mount) and others considered partnerships (like city streets and synagogues). The Gemara then asks how Rav Nachman can maintain his view. Rav Nachman replies that the permission to drink from olei Bavel wells in the case of vows is because when one drinks, they can retroactively declare (berirah) that they are drinking from their own share of the water, not their friend's. However, bathing in the well would be forbidden, as one would be using all the water, including the friend's share.
The Gemara then questions whether Rav Nachman actually holds of berirah. It introduces two laws: 1. The half-shekel tax: Every Jew must give a half-shekel for public offerings. An extra fee (kalbon) is added to cover the money changer's commission. Even if two people give a whole shekel together, each must pay a kalbon. However, a father paying for two sons only pays one kalbon. 2. Animal tithes (ma'aser behemah): This applies only to individually owned animals, not to animals owned by partners. This is derived from a verse about firstborn animals. The Gemara then discusses brothers who inherit animals. If they inherit collectively (tefisat ha'av), it's considered individually owned (by the "father's estate"), so they pay one kalbon and are liable for ma'aser behemah. If they divide the inheritance by monetary value, it becomes a partnership, and they are liable for individual kalbons but exempt from ma'aser behemah. If they divide it one-for-one (e.g., a lamb for a lamb) and then decide to be partners again, Rav Nachman says it's a new partnership, making them liable for individual kalbons and exempt from ma'aser behemah. This is because he does not hold of berirah to retroactively say each received what was intended for them by the father. This contradicts his earlier use of berirah regarding the olei Bavel wells.
The Gemara resolves this by affirming that everyone agrees olei Bavel wells are ownerless (hefker). The dispute between Rav Nachman and Rav Sheishet then becomes about who acquires the water when one draws it for a friend. Rav Sheishet says that even if one intends to draw for a friend, the friend does not acquire it (as it's like finding a lost item for someone else, which is not valid if it harms a third party). Thus, the drawer, by picking it up, acquires it for themselves, and the water follows their techum. Rav Nachman says that if one draws for a friend, and the friend cannot acquire it, then the drawer also does not acquire it for themselves (as their intention was not for themselves). Therefore, the water remains ownerless until the friend receives it, at which point the friend acquires it, and it follows the friend's techum.