Gemara

(Beraisa - R. Shimon ben Elazar): One may keep what he finds in a big encampment or thoroughfare, or any place where many people pass, for the owner despairs.

Question #1: Did R. Shimon ben Elazar say this only in a city that is mostly Nochrim, or even in a city that is mostly Yisre'elim?

Question #2: If he said so even in a city that is mostly Yisre'elim, do Chachamim disagree?

Question #3: If Chachamim disagree, is this only in a city that is mostly Yisre'elim, or even in a city that is mostly Nochrim?

Question #4: If you will say that Chachamim argue even in a city that is mostly Nochrim, does the Halachah follow R. Shimon?

Question #5: If you will say that the Halachah follows R. Shimon, is that only in a city that is mostly Nochrim, or even if it is mostly Yisre'elim?

24b - Answer (to Question #1 - Rav Asi): If one finds a barrel of wine in a city that is mostly Nochrim, he may keep it. (This is like R. Shimon, and he permits only when a majority are Nochrim!)

Rejection: Perhaps R. Shimon permits even when the majority are Yisre'elim. Rav Asi holds like R. Shimon only when the majority are Nochrim.

A man found four Zuz wrapped in a sheet and thrown in the river Biran. Rav Yehudah ruled that he must announce it.

Inference: The majority of people there are Nochrim. This shows that the Halachah does not follow R. Shimon, even regarding a majority of Nochrim!

Rejection: Most of the people who dam up the river and dig it out (to let the water flow) are Yisre'elim, therefore he does not despair.

Question (Rav Yehudah): If one found a wallet in the market of shredded wheat, what is the law?

Answer (Shmuel): He may keep it. If a Yisrael came and gave a Siman, he must return it.

This means that he must go beyond the letter of the law and return it.

(Rav Nachman): If one found a wallet in the market of shoemakers (some say, Chachamim), he may keep it, even if a Yisrael came and gave Simanim. Even if the loser is screaming that it is his, he is like one screaming over his house that burned or his ship that sank.

R. Ami found slaughtered chicks between Tiverya and Tzipori. Rav Asi, R. Yochanan or Chachamim in the Beis Medrash permitted them to him.

Rishonim

Rif: The questions were not resolved. The Sugya permits when most are Nochrim, and obligates to take and announce when most are Yisre'elim.

Rambam (Hilchos Gezeilah 11:6): In a city that is half Yisre'elim and half Nochrim, one who finds an Aveidah takes and announces it. If a Yisrael gave a Siman, he gives it to him.

Rambam (7): If most of the city are Nochrim, if he found it in a place where mostly Yisre'elim are found, he must announce it. If he found it in a big encampment or thoroughfare, or a Beis ha'Keneses or Beis Medrash where Nochrim are always found, or any place where many people are frequent, he keeps it. This is even if a Yisrael gave Simanim, for he despaired when he dropped it, for he assumed that a Nochri would find it. Even though it is the finder's, one who wants to go in the good, straight path and go beyond the letter of the law will return it to a Yisrael who gives Simanim.

Rosh (2:7): The Rif says that since Rav Asi rules like R. Shimon ben Elazar when most are Nochrim, but not when most are Yisre'elim, the Halachah follows this. The Gemara knew that mostly Nochrim are in the markets of shredded wheat and of Chachamim. This is why it did not try to prove from there that the Halachah follows R. Shimon ben Elazar even where most are Yisre'elim. We do not force one to go beyond the letter of the law. The Ra'avad rules like R. Shimon ben Elazar even where the majority are Yisrael. He learns from the slaughtered chicks that were permitted. We cannot say that most of the slaughterers were Yisre'elim but most of the people there were Nochrim, for people slaughter their own chicks! Rather, even though most of the people were Yisre'elim, they were permitted.

Gra (CM 259:7): If Rav Asi permitted chicks even though the majority were Yisre'elim, this contradicts his ruling about the wine!

Rashash (24b DH Sham): Rav Asi ruled about the wine, and R. Asi ruled about the chicks. Tosfos (Chulin 19a) says that Rav Asi and R. Asi are different! We follow R. Asi, for he ruled in an actual case.

Poskim

Shulchan Aruch (CM 259:3): If one found an Aveidah in a place where Yisre'elim are found, he must announce it, for the owner did not despair. Even if the city is half Yisre'elim and half Nochrim, or even mostly Nochrim but he found it in a place where mostly Yisre'elim pass, he must return it.

Beis Yosef (DH u'Mah she'Chosav Rabeinu): A Mishnah in Machsirim (2:8) is stringent when exactly half are Yisre'elim.

Beis Yosef (DH u'Mah she'Chosav Iy): We learn from the money wrapped in a sheet and thrown in the river that one must return it if the majority of the people who pass by are Yisre'elim.

SMA (6): If the majority of the city are Nochrim, we are stringent only for a place where mostly Yisre'elim pass, but not if half Yisre'elim pass. Likewise, if the majority of the city are Yisre'elim, we are lenient only where mostly Nochrim pass. A majority (of the city) overrides what is closer (the place it was found) only when it was not found in the close place, and presumably it came from the majority (of the city).

Rebuttal (SMA): In Bava Basra 24a, Amora'im argue about whether we follow the majority or what is closest. Rashi says that the former opinion follows the majority of the world, and not from what is closer. This is the Halachah. If so, here we should follow the majority of the city! I say that here, since we can clarify the matter through announcing, we rely on the majority only for despair; the owner despairs if the majority nearby are Nochrim. When there is no despair, but the majority of possible losers are Nochrim, one must announce to see if a Yisrael lost it. Tosfos (Bava Basra 23b DH Chutz) says like this.

Shulchan Aruch (ibid): If most of the city are Nochrim, or even if most are Yisre'elim but where he found it mostly Nochrim pass, he is exempt.

Beis Yosef (DH u'Mah she'Chosav Aval): The Gemara said that one keeps money found in a Beis ha'Keneses if mostly Nochrim are found there. We must say that the city is mostly Yisre'elim, for if not one may keep money found anywhere in the city!

Shach (2 and 260:12): We require a recognizable majority of Nochrim. This is why the Gemara (26a) discusses three Nochrim who rented from a Yisrael.

Shulchan Aruch (ibid): This is even if he knows that a Yisrael lost it and it has a Siman, for surely the owner despaired. This refers to something for which we may assume that he knew immediately when it fell.

Beis Yosef (DH u'Mah she'Chosav Afilu: Rav Nachman said that one may keep the Aveidah even if a Yisrael came and gave Simanim.

SMA (7): We hold that Ye'ush she'Lo mi'Da'as (one who would despair if he knew that he lost the item) is not despair.

Rema: Some say that one does not despair from Seforim even in a place that is mostly Nochrim.

SMA (8): Normally, only Yisre'elim buy Seforim. The loser does not despair, for he thinks '(even if a Nochri finds it,) the Yisrael who buys (from the finder) will announce it, and I will give a Siman.'

Nimukei Yosef (Bava Kama 41b DH Yishava): Perhaps one does not despair if his Seforim were stolen even by a Yisrael, for he knows that a Yisrael will get them, for Nochrim do not buy Seforim. We find that one does not despair of something lost in a river if Yisre'elim dam it and dig it out.

Shulchan Aruch (5): Even though letter of the law, in a place that is mostly Nochrim he need not return it even if a Yisrael gives Simanim, it is proper to go beyond the letter of the law will return it to a Yisrael who gives a Siman.

Rema: If the finder is poor and the loser is rich, he need not go beyond the letter of the law.

Shach (3): The Mordechai says so in the name of Avi ha'Ezri. Avi ha'Ezri and Ra'avan force a rich finder to return it.

Gra (15): The Gemara said that he must return it, for we force him to go beyond the letter of the law. 'He is like one screaming over his house that burned' applies when the finder is poor and the loser is rich.