1) THE CASE OF "MANEH SHELISHI"
QUESTION: The Gemara cites a Mishnah in which Rebbi Yosi and the Rabanan disagree about the law in the case of "Maneh Shelishi": A Shomer was given two separate bundles of money to watch by two people. One person gave him 100 Zuz (one Maneh), and the other gave him 200 Zuz (two Manehs). Later, each depositor claimed that he was the one who gave 200 Zuz to the Shomer. Rebbi Yosi rules that all of the money is placed in escrow -- "Yehei Munach" -- until one of the depositors brings proof to his claim. The Rabanan rule that 100 Zuz is given back to each of them, and only the third Maneh ("Maneh Shelishi") is left in escrow.
The Gemara questions why the Rabanan do not rule that the Maneh Shelishi is also divided between the claimants. The Gemara answers that in the case of the Mishnah, it is possible that the garment belongs to both claimants, and therefore it is divided in court. In contrast, in the case of Maneh Shelishi, the third Maneh certainly belongs to only one of the claimants.
Why does the Gemara assume that the Maneh Shelishi cannot belong to both claimants? Perhaps the one who gave 200 Zuz gave half of a Maneh, or 50 Zuz, to the other person, who gave only 100 Zuz to the Shomer. Even though neither claimant makes such a claim, the possibility certainly exists that such a thing occurred. In fact, it is for this reason, as TOSFOS (2a, DH v'Yachloku) explains, that when a lender and a borrower come to Beis Din holding on to a Shtar together, Beis Din splits the debt written in the Shtar and requires the borrower to pay only half (and Beis Din does not rule "Yehei Munach"), since it is possible that the borrower indeed paid half of the money, even though neither the lender nor the borrower makes such a claim (but rather each one claims that the money is completely his).
ANSWERS:
(a) TOSFOS (2a, DH v'Yachloku) answers that it is not common for a person to give to someone else part of his money or item that is in the hands of a Shomer.
(b) The ROSH (1:1) writes that the reason Beis Din does not split the Maneh Shelishi according to the Rabanan is that the Shomer knew that the Maneh belonged to only one of them before the claimants brought the matter to court. According to the Rosh, the Gemara does not mean that it is impossible for both claimants to own the third Maneh, but rather there exists prior knowledge attesting to the fact that only one of them owns it. In the case of the Shtar held by both the lender and the borrower, there is no reason to assume that the Shtar definitely was paid or was not paid before the claimants brought the matter to court. It was possible that the Shtar was paid in half. This also seems to be the way the RAMBAN (2b, end of DH u'Lefikach) explains the Gemara. (See, however, the TUMIM 138:2, who understands the Rosh differently.)
2) THE POSSIBILITY THAT BOTH CLAIMANTS ARE TELLING THE TRUTH
QUESTION: After the Gemara explains how the Rabanan who disagree with Rebbi Yosi could agree with the ruling of the Mishnah, the Gemara asks whether or not Rebbi Yosi can agree with the ruling of the Mishnah. Rebbi Yosi rules, in the case of Maneh Shelishi, that all three Manos are taken away and put in escrow, since one of the two claimants definitely is lying. In the case of the Mishnah, Rebbi Yosi should rule that the garment is not divided between the two claimants.
The Gemara answers that Rebbi Yosi could agree with the Mishnah since it is possible that neither claimant is intentionally lying, but rather they both picked up the garment together, simultaneously.
At the time the Gemara asked its question according to Rebbi Yosi, it knew already that it was possible that the claimants picked up and acquired the garment together. It was for that reason that the Gemara said that the Rabanan agree with the ruling of the Mishnah that the garment should be split. Why, then, does the Gemara assume that it is less likely for Rebbi Yosi to agree with the ruling of the Mishnah than for the Rabanan to agree with it? (RASHBA)
ANSWER: The RASHBA answers that the difference between Rebbi Yosi and the Rabanan is as follows. The Rabanan are concerned only that the true owner not incur a definite loss. Rebbi Yosi, on the other hand, is interested in seeing that the liar ("Ramai") incurs a definite loss.
Therefore, according to the Rabanan, even though there might be a liar involved in the case of the Mishnah, nevertheless it is possible that there is no liar and the garment belongs to both of them, and neither one is losing. However, according to Rebbi Yosi -- who is interested in having the liar incur a loss -- even though it is possible that there is no liar, it is also possible that there is a liar and by splitting the garment Beis Din helps him gain. The Gemara answers that even Rebbi Yosi may agree with the ruling of the Mishnah since there is no certainty that there is a liar, but only a suspicion to that effect. Rebbi Yosi requires only that the object in doubt be taken away when it is known for certain that there is a liar among the claimants, but not when there is a doubt whether there is a liar.
It is evident from this explanation that the Rabanan are not concerned about whether or not there is a liar, but whether or not the true owner is incurring a loss. Even if one of the claimants certainly is a liar, Beis Din would divide the item if it is possible that the true owner is not sustaining a loss (for example, when each one claims that he made the entire garment Beis Din would split it, because perhaps they really own the garment together and not like either of them claims). This is the ruling of most Rishonim. However, RASHI (2a, DH Mekach u'Memkar) rules that when it is known that there is a liar, Beis Din does not split the garment. Rashi's words seem to be in accordance with the opinion of Rebbi Yosi and not that of the Rabanan!
The NACHALAS DAVID answers that Rashi maintains that according to the Gemara's conclusion, the Gemara no longer differentiates between whether or not it is possible that both claimants own the garment, according to the Rabanan. Rather, the Rabanan also are interested in ensuring that the liar does not gain (and not that the true owner does not lose), and the reason they divide the garment in the case of the Mishnah is that there is no certainty that there is a liar.
Support for this approach may be found in the words of the Gemara later on this Daf. The Gemara asks that according to both Rebbi Yosi and the Rabanan, Beis Din should rule "Yehei Munach" in the case of "Chenvani Al Pinkaso," because "there certainly is a liar." This implies that both Rebbi Yosi and the Rabanan determine whether or not to rule "Yehei Munach" based on whether or not there certainly is a liar.

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3) REQUIRING A PERSON TO SWEAR WHEN HE IS SUSPECTED OF STEALING
QUESTION: Rebbi Chiya maintains that when the lender claims that the borrower owes him 100 Zuz, and witnesses testify that the borrower owes 50 Zuz, and the borrower denies owing anything, the borrower must pay 50 and swear that he does not owe the other 50, similar to the Shevu'ah of "Modeh b'Miktzas."
Rebbi Chiya derives this Halachah through a Kal va'Chomer: if Hoda'as Piv (one's own admission) requires a person to swear, certainly witnesses require a person to swear.
The Gemara explains that had there been no Kal va'Chomer, one would have thought that only Hoda'as Piv requires the borrower to swear, but not the testimony of witnesses. The reason for this is that when a person is "Modeh b'Miktzas," it is possible that he denies owing the second half only in order to delay the repayment of the second half but not because he wants to default entirely on the loan. He intends to repay as soon as he has the money. It is for this reason that he admits to owing the first half. However, when he denies owing anything and witnesses testify that he owes half, Beis Din must assume that he has no intention to pay back the other half at all, and he is not merely trying to gain more time. For this reason, Beis Din should not force the borrower to swear, since once it is known that he is suspected of stealing someone else's money, he is also suspected of swearing falsely and his Shevu'ah will not clarify the matter (as Rashi explains in DH d'Leika).
Rebbi Chiya learns from a Kal va'Chomer not to follow this logic, but rather that the borrower must swear when witnesses testify that he owes half.
If the logic to exempt the borrower from a Shevu'ah is that since he is ready to steal he presumably is also ready to lie and swear falsely ("Migu d'Chashid a'Mamona, Chashid a'Shevu'asa"), then how can a Kal va'Chomer teach that the borrower must swear? Even if the testimony of witnesses is stronger proof than a person's own admission, the testimony of witnesses should not require the borrower to swear since he is assumed to be a thief! Only when a person's own admission makes him obligated to pay half should he be required to swear, since there is reason to assume that he is not a thief but that he merely is trying to gain more time in order to repay. (RAMBAN and Rishonim cited by the Shitah Mekubetzes)
ANSWERS:
(a) Many Rishonim disagree with Rashi's explanation of the Sugya for this reason. TOSFOS (DH b'Chulei) explains that even when a person is suspected of stealing, he is not suspected of swearing falsely. According to Tosfos, when the Gemara concludes that Rebbi Chiya's ruling is based not on a Kal va'Chomer but on a Tzad ha'Shaveh from Hoda'as Piv and Ed Echad, the Gemara's intent is to prove from Ed Echad that even when a person is suspected of stealing, Beis Din makes him swear in order to clarify whether or not he stole, for even a thief will not swear falsely. (In the case of Ed Echad, since the defendant denies the entire loan, there is no reason to assume that he merely is trying to gain time, but rather that he has no intention of ever paying back.)
When the Gemara initially assumed that Rebbi Chiya derives his ruling through a Kal va'Chomer from Hoda'as Piv and not from Ed Echad, why did the Gemara not immediately question the Kal va'Chomer that when witnesses testify against the borrower, he should not swear since he is suspected of being a thief and a thief might swear falsely? At that stage, the Gemara based the Kal va'Chomer on Hoda'as Piv, in which case the borrower simply may be stalling for time and is not a thief.
TOSFOS (DH Aval) and the TOSFOS HA'ROSH answer that the Gemara indeed could have rejected the Kal va'Chomer for this reason, but it provided a better reason for rejecting the Kal va'Chomer.
Rashi, however, does not accept this approach. Rashi writes that one who is suspected of stealing is suspected of swearing falsely. (See Rashi here, DH v'Hai; 2b, DH Aval Mekach u'Memkar; 4a, DH Tomar; see Tosfos here, DH b'Chulei.) According to Rashi, the reason why a person swears against an Ed Echad is that before a thief is caught lying in court, there still is a possibility that he will refrain from lying because of the need to make a Shevu'ah. In the case of Rebbi Chiya, since the thief was already caught lying with regard to the first fifty, he should not be believed with regard to the second fifty. (See TOSFOS here, DH d'Chashid, in the name of Rebbi Yehudah ha'Chasid.)
(b) The RAMBAN, RASHBA, and RITVA also disagree with Rashi. They write that a thief is not suspected of swearing falsely. The Gemara means that without a Kal va'Chomer, Beis Din would believe the borrower when he says that he does not owe the other fifty because of a Chazakah that "Ein Adam Me'iz Panav Bifnei Ba'al Chovo" -- a person is not so brazen to deny owing money to the person who did him the favor of lending him money. Rebbi Chiya learns from a Kal va'Chomer that if Hoda'as Piv can require the borrower to swear, then certainly witnesses can require the borrower to swear.
The CHEMDAS SHLOMO asks that this answer does not seem to address the question. How can a Kal va'Chomer from Hoda'as Piv teach that the borrower must swear? In the case of Hoda'as Piv, there is no Chazakah that the person will not be brazen; he might be denying the debt simply because he wants to gain more time to pay it all back. In contrast, when witnesses obligate a borrower to pay half, there is no basis to assume that the borrower is just stalling for time (since he did not admit that he owes half), and thus there should be a Chazakah that he is telling the truth. (This should be a Pircha on the Kal va'Chomer.)
From the words of the Ramban and Rishonim it seems that they answer this question as follows. In truth, even when a person is "Modeh b'Miktzas," he should be believed because a person would not be so brazen to deny owing the lender. The only reason why he is not believed is that since there is strong evidence (i.e. the Hoda'as Piv) which supports part of the claim of the lender, the Chazakah of the borrower is weakened and thus Beis Din looks for a way to circumvent the Chazakah. The Chazakah is bypassed by reasoning that since the borrower admitted to owing part, perhaps he merely is stall for time. Accordingly, from a Kal va'Chomer it can be derived that when two witnesses testify that a person owes half of the money, their testimony certainly should weaken the Chazakah, and Beis Din certainly should look for a way to bypass the Chazakah. In this case, Beis Din cannot bypass the Chazakah by saying that the borrower is stalling. Instead, Beis Din bypasses the Chazakah by saying that since the witnesses proved him to be a liar with regard to the first half of the money, he probably is lying with regard to the second half as well. Therefore, Beis Din makes the borrower swear.
(c) The RITVA explains how Rashi may understand the Kal va'Chomer. He suggests that the Kal va'Chomer teaches that although a person who lied in Beis Din is normally suspected that he might swear falsely, when a person denies a loan and the lender brings testimony that the person owes the money (or part of it), he is not suspected that he might swear falsely. The reason for this is that no one of sound mind would deny a loan when he knows that the lender has witnesses who will contradict his claim and force him to pay. Beis Din therefore must assume that the borrower is simply stalling for time ("Ishtamutei"), even though Beis Din normally assumes that a person who is "Kofer ba'Kol" is not "Ishtamutei." Rashi's assertion that one who is suspected of stealing is suspected of swearing falsely applies only to a person who attempted to steal when there were no witnesses who could contradict his claim (such as a case of "Kofer ba'Kol" where the lender has no witnesses, as Rashi mentions on 3b, DH v'Hai). This is also the way the RA'AVAD (cited by the Shitah Mekubetzes on 6a) explains (see Insights to 6:1 and 4:1:b). When a person is forced by witnesses in court to pay back a loan, Beis Din assumes that he was just stalling for time and that is why he is not suspected of swearing falsely.
According to this approach as well, the Kal va'Chomer must be understood the way the Ramban and Rishonim understand it (as explained in (b) above). The Kal va'Chomer is that once reason is found to assume that the borrower will not swear falsely because of Hoda'as Piv, certainly there should be reason to assume that the borrower will not swear falsely because of testimony of witnesses.
(d) TOSFOS RABEINU PERETZ answers that the Gemara means to say as follows. Without a Kal va'Chomer, Beis Din would not make a person swear because of testimony of witnesses; Beis Din would make a person swear only when there is strong reason to assume that the threat of a Shevu'ah will make him admit to the truth. Examples of this are "Modeh b'Miktzas" (where the person likely will admit since he merely is stalling for money) and a case of an Ed Echad (where the person likely will admit since the witness contradicts his statement). However, in the case of two witnesses who do not contradict him with regard to the other half of the money, there is no reason to assume that he will admit to the truth. The Kal va'Chomer teaches that, nevertheless, Beis Din must make the borrower swear because of the testimony of witnesses -- because they provide a stronger proof than Hoda'as Piv.
According to Tosfos Rabeinu Peretz, it is clear that the Gemara cannot ask a Pircha on the Kal va'Chomer from this logic.