Gemara

(R. Yitzchak): If Reuven claims that he lost two wallets tied together, and that Shimon found them, and Shimon says that he only found one, Shimon must swear. If Reuven claims that he lost two oxen tied together and that Shimon found them, and Shimon says that he only found one, Shimon need not swear.

This is because wallets do not come untied by themselves, but oxen do.

If Reuven claims that he lost two oxen tied together and that Shimon found them, and Shimon admits, but claims that he returned one of them, Shimon must swear.

Question: Doesn't R. Yitzchak agree that an enactment for Tikun ha'Olam exempts one who finds an Aveidah from swearing?!

Answer: R. Yitzchak holds like R. Eliezer ben Yakov;

(Beraisa - R. Eliezer ben Yakov): Sometimes one swears due to his own claim. If Reuven says 'Shimon's father deposited one Maneh by me, and I returned half', he must swear;

Chachamim say, he is exempt, like Meshiv (one who returns an) Aveidah.

Question: Doesn't R. Eliezer ben Yakov exempt Meshiv Aveidah?

Answer #1 (Rav): A minor (Shimon) claims that Reuven owes the full Maneh.

Question (Mishnah): We do not swear due to the claim of minor.

Answer: Rav meant, Shimon is an adult, but in his father's affairs he is (ignorant) like a minor.

Question: If so, why does R. Eliezer ben Yakov say that Reuven swears due to his own claim? He swears due to Shimon's claim!

Answer: Rather, they argue about Rabah's teaching);

(Rabah): The Torah requires one who makes a partial admission to swear, because one is not brazen enough to lie and deny his creditor's claim. He would like to deny the whole claim, but he lacks the audacity to do so. For this reason, he would prefer to admit to the entire claim. He does not, for he cannot pay the whole claim now. He is stalling until he can pay it all. The Torah imposes an oath on him so he will admit to the whole claim.

R. Eliezer ben Yakov says that likewise, one cannot be brazen to deny the claim of his creditor's son. Therefore, he is unlike Meshiv Aveidah (so he swears).

Chachamim say that one cannot be brazen to deny his creditor's claim, but he can be brazen against his creditor's son. Since he could have denied the whole claim, but did not, he is like Meshiv Aveidah (and need not swear).

Rishonim

Ba'al ha'Ma'or (25a): The Mishnah says 'one who finds a Metziah (does not swear)', not 'one who returns a Metziah.' This teaches that the owner has a Vadai claim against him, and even so, the enactment exempts the finder from swearing. We say that R. Yitzchak holds like R. Eliezer ben Yakov. We have no proof to reject Chachamim, who are the majority. The Mishnah is unlike R. Yitzchak and R. Eliezer. Shmuel avoids establishing the Mishnah like an individual. The Halachah follows Shmuel in monetary laws. The Rif initially ruled (in Kesuvos) like Chachamim, then retracted to rule like R. Eliezer. If so, he should have brought R. Yitzchak's law here! All the Ge'onim rule like Chachamim.

Rebuttal (Rosh 5:4 and Milchamos Hash-m): The Gemara said that R. Yitzchak holds like R. Eliezer ben Yakov. R. Chananel says that we retract from this. Really, even R. Eliezer ben Yakov exempts Meshiv Aveidah. He argues only about whether or not one can be brazen to a child (claiming what was due to his father). R. Yitzchak's teaching is rejected. This is why the Rif did not bring it, even though he rules (Shevuos 23a) like R. Eliezer. It seems that they explain 'they argue about Rabah's law' like the Ri, that we discuss when an adult heir claims. Therefore, it is unlike an Aveidah.

Hasagos ha'Ra'avad: In Shevuos, the Rif rules like R. Eliezer. Perhaps he retracted. The Gemara asks there 'what is the difference between the father and the son?' This is when the son says that the borrower admitted to his father just before his father died. When the son's claim is Safek, and one need not swear against it. In the Yerushalmi, R. Aba obligates swearing when David (the owner) claims that Levi found two oxen, and Levi says that he already returned one. R. Yochanan says that the Torah exempts when Levi claims that he found only one, and the enactment was to exempt when he says that he returned one! R. Yitzchak obligates when he says that he returned one, for it is like wallets; David is Vadai, for wallets do not come apart by themselves. Since our Gemara says that R. Yitzchak holds like an individual, and R. Yochanan argues with him, the Halachah does not follow R. Yitzchak and R. Eliezer.

Rebuttal (Milchamos Hash-m and Sefer ha'Zechus): The Halachah follows R. Eliezer ben Yakov even against a majority, unless the Gemara explicitly rules unlike him. We do not follow Amora'im of the Yerushalmi when they argue with Amora'im of the Bavli.

Poskim

Shulchan Aruch (CM 267:27): One who finds an Aveidah does not swear, due to Tikun ha'Olam. If we will say that he must swear, he will leave the Aveidah, to avoid swearing. Even if he found a wallet, and the owner says that he lost two tied together and it is impossible that he found one without the other tied to it, he does not swear.

SMA (42): If David says that he saw Levi pick up both of David's wallets, the laws of Aveidos and Metzi'os do not apply. This is like regular claims, and Levi must swear that he found only one.

Rebuttal (Taz): This is no different from when Levi says that he returned one of them. This is also like a regular claim (David is sure that he did not), yet Chachamim were concerned lest people ignore Aveidos lest they need to swear. Also here, Levi does not know that David sees him. If we will require him to swear, people will fear this and will not take Aveidos to return them. When Levi says that he returned one of them, he could have done so in front of witnesses, nevertheless Chachamim were concerned (lest people refrain from taking Aveidos). All the more so they are concerned here (one who finds a wallet has no way to protect himself from a Shevu'ah if the owner will claim that he saw him pick up two)!

Pischei Teshuvah (4): The Tur (Sa'if 29, and also in Kitzur Piskei ha'Rosh) exempts even when the finder claims that he returned one and the owner denies this. The Levush says the same. It seems from the Tumim (88:22) that this was written in the Shulchan Aruch, and was omitted during the printing.