Gemara

2a (Mishnah): If two are holding a garment, and each claims 'it is mine', each swears that he does not own less than half, and they divide it.

If Reuven says 'it is all mine' and Shimon says 'it is half mine', Reuven swears that he does not own less than three quarters, and Shimon swears that he does not own less than one quarter. Each gets like he swore.

8a: One might have thought that Shimon is like Meshiv Aveidah (one who returns a lost object), and he is exempt from swearing. The Mishnah teaches otherwise. Perhaps he schemes to avoid swearing. He knows that if he claims the entire object, he must swear, so he claims only half to be like Meshiv Aveidah.

110a: A document (of Mashkanta) said 'years' without specifying how many. Levi (the lender) says that it was for three years, and David (the borrower) says that it was for two.

(Rav Yehudah): If Levi already ate the Peros for three years, he must pay for the last year. When in doubt, we establish land to belong to the original owner (David);

(Rav Kahana): Our question is about the Peros, which are with Levi. The Chazakah favors him, he need not pay.

(Rav Yehudah): (Levi lent to David and took his land for Mashkanta.) If Levi says that the Mashkanta was for five years (and he lost the document), and David says that it was for three, Levi is believed, Migo (since) he could have said that he bought it (i.e. if he wanted to lie, he had a better lie to say).

Rav Papa: Rav Zvid and Rav Avira disagree. A buyer guards his document only for three years, but a lender is careful as long as he may eat the Peros. (Surely he did not lose it, rather, he is hiding it in order to eat extra Peros.)

Bava Basra 70b (Beraisa - judges of Bavel): If Levi brought a Shtar Kis (document of a business venture; half is a loan, and half is a deposit) against orphans, he swears (that their father never paid) and collects it all;

Judges of Eretz Yisrael say, he swears and collects half.

They hold that the father would be believed to say that the money was lost through Ones, which would exempt him from paying half (the deposit), therefore he would also be believed to say 'I returned it.' Therefore, we claim on behalf of the orphans, that perhaps their father paid half.

Rishonim

The Rif (1a) brings our Mishnah.

Rif and Rosh (66b and 9:40): The Halachah follows Rav Yehudah; Levi is believed (that the Mashkanta was for five years).

Rambam (Hilchos To'en 9:8): If Reuven says 'it is all mine' and Shimon says 'it is half mine', Reuven swears that he does not own less than three quarters, and Shimon swears that he does not own less than one quarter. Each gets like he swore. From here we learn to all who swear to receive, with a light or severe oath, that they do not swear like they claim, rather, like they receive, even if they claim more.

Magid Mishneh: The Rashba says that presumably, if they argue about something that can be divided, Reuven can take half, and afterwards swear that he does not own less than half of what remains in order to receive half of it. If the contested item cannot be divided, Reuven must swear that he does not own less than three quarters.

Rambam (Hilchos Sechirus 7:6): If Levi rented a field or took it for Mashkanta and ate the Peros for three years, and concealed the document and said 'I have rights to eat for five years', and the owner says that it was for three years, Levi is believed. If he wanted, he could say that he bought it, for he ate it for three years.

Rosh (1:1): Letter of the law, Reuven should receive half without an oath, and they should divide the other half with an oath. However, Beis Din makes him swear about three quarters to prevent any Rama'os (scheme) he might have in his heart. He cannot say 'why do you insist that I swear about three quarters? I swear according to your Da'as (understanding), and you intend that I swear without Rama'os!' One fears more when they remind him of the oath he transgresses than when he swears Stam (without specifying).

Tosfos (2a DH v'Zeh): Why isn't Shimon believed that half is his, Migo (since) he could have said that all of it is his? The Gemara (8a) said that this Migo would have exempted him from swearing, if not that we are concerned lest he schemes to avoid swearing. Rivam answered that we do not say a Migo to take from someone. Reuven is as Muchzak in the contested half as Shimon is. In Bava Basra 32b, Rabah ruled that a man can take through a Migo, because he could have been silent (and won his case). Rav Yosef holds that he had no Migo, because his first claim was false. We apply Migo even to keep one's property only when his first claim was true.

Ramban (Bava Metzia 2a DH vh'Omer): If Reuven says 'it is all mine' and Shimon says 'it is half mine', why isn't he believed with a Migo that he could have claimed all of it and received half? We say such a Migo in Bava Basra 70b! Some learn from here that one may not take through a Migo. I say that it is no proof, for he is not believed to receive his full claim. He admitted that half is not his; it is as if Reuven already received that half. We do not say that since he could have claimed about another garment (the half he conceded) that he should be believed to totally take this garment (the half that they argue about).

Ramban (Bava Basra 32b DH Amai): Some say that one may not take through a Migo. However, in Bava Metzia (110a) when a Mashkanta did not specify the number of years, we believe the lender, Migo he could say that he bought it (he had already eaten it for three years). Rashi explains that the original owner was Muchzak regarding all the Sefekos in the Gemara there, and even so, the lender takes the Peros through Migo.

Rivash (336): Even though Chezkas Karka supports David, Levi is believed through a Migo to keep what he has, and all the more so according to the Acharonim who gave clear proofs that we may take through a Migo.

Poskim

Shulchan Aruch (CM 82:12): If the borrower says that they stipulated that he will be exempt if he fulfills a certain Tenai, and the lender agrees but says that he did not fulfill it, the lender must bring a proof. If he cannot, the borrower swears Heses and is exempt.

Bach (19 DH v'Kashya): A grocer is believed to say that Moshe owed a tab (not a loan), for he could have said that he wrote a Pruzbul and lost it. Sefer ha'Terumos explains that this is because there is a Chazakah that one does not sin if he can achieve his goal without sinning.

Yam Shel Shlomo (Bava Kama 10:30): The Tur (CM 357) cites the Rambam, who says that Levi (a Nigzal) is believed to swear and take from Ploni things that are normally lent or rented, even without talk that he was robbed. This is wrong. The Rambam relies on what he said above, that there was talk that he was robbed. He also erred about the Rosh. When Moshe says 'I bought them', and Yosef says 'you stole them', he is not believed with a Migo that he lent or rented them, for we do not establish people to be thieves. Here, Levi does not say that Ploni stole them. Ploni himself says that he bought them! The Rosh holds like those who say that Levi is believed due to the Migo, even without talk that he was robbed. Even though one may not take through a Migo, like Tosfos and most Poskim say, here one may, for the Muchzak is unsure. Ploni bought from Almoni. He does not know whether Almoni stole it! Also, here it is not called taking through a Migo because Levi recognizes his Kelim and witnesses recognize them; it is as if Levi is Muchzak in them. If Levi would say 'I rented to you', and Ploni would say 'I bought from you', all say that Levi is believed, except for Rashi. All the more so we believe Levi through a Migo!

Rema: The lender is not believed with a Migo (that he could have denied that there was a Tenai), for we do not take money with a Migo. Some disagree and say that we take through a Migo.

Darchei Moshe (2): The Mordechai (Bava Metzia 216), Tosfos, Rosh and Nimukei Yosef say that we do not take through a Migo. The Rivash says that the Acharonim proved that we may take through a Migo, and even the opposing opinion uses Migo against Chazakah of land.

Shulchan Aruch (138:2): If Reuven says 'it is all mine' and Shimon says 'it is half mine', Reuven swears that he owns part and does not own less than three quarters, and Shimon swears that he owns part and does not own less than one quarter. Each gets like he swore. From here we learn to all who swear to receive, with a light or severe oath, that they do not swear like they claim, rather, like they receive, even if they claim more.

SMA (8): If Reuven would swear 'of the half that Shimon claims to own, I do not own less than a quarter', perhaps Reuven would intend for the half that Shimon concedes.

Gra (9): Perhaps Reuven's oath need not include 'I own part', for Shimon admits that Reuven owns half.

Rema: If they argue about something that can be divided, Reuven can take half, and afterwards each swears that he does not own less than half of what remains.