1)PARTIAL ADMISSION TO A DOCUMENT THAT WITNESSES SAY WAS PAID
1.(R. Aba): If Shimon brought a loan document against Levi and says that he did not collect any part of it, and Levi says that he paid half, and witnesses testify that he paid it all, Levi swears that he paid half, and Shimon collects half from Levi's Bnei Chorin (unsold property). He cannot collect from Meshubadim (what Levi sold), for the buyer can say 'witnesses testified that it was paid!'
2.Bava Metzia 4b: If a loan document says 'Sela'im' (this implies at least two), the lender claims five, and the borrower (Yehudah) admits to three, R. Akiva exempts Yehudah from swearing, like a Meshiv Aveidah (one who returns a lost object, for he could have said two). R. Shimon ben Elazar obligates him to take the oath of Modeh b'Miktzas (partial admission).
3.Bava Basra 128b (R. Aba): Only there, R. Akiva considers him like a Meshiv Aveidah, for there are no witnesses. Here, Levi admitted to half due to fear of the witnesses, therefore he must swear.
4.Objection (Mar bar Rav Ashi): Just the contrary! Even R. Shimon ben Elazar obligates swearing Modeh b'Miktzas only there, for witnesses do not support him. Here, witnesses support Levi (he could have denied owing anything), so he is like a Meshiv Aveidah, and he does not swear.
5.(Mar Zutra citing Rav Ashi): The Halachah follows R. Aba.
1.The Rif and Rosh (57a and 8:26) bring our Sugya.
2.Rif (Shevuos 18a): Even R. Akiva considers him to be a Meshiv Aveidah only when there is no document. Here, there is a document, so he fears.
i.Nimukei Yosef (57a DH Afilu and Ran 18a DH Garsinan): Why must he swear that he paid at least half? Witnesses say that it was paid! It is because he contradicted the witnesses. We do not consider it as if there were no witnesses at all, and say that he is not believed even with an oath, like a regular case of a document. Perhaps the witnesses remember the payment better than he does. It is not utter contradiction. We do not totally rely on the testimony, nor on the document. Rather, due to the Safek we consider it as if there were no witnesses and no document, and he swears Modeh b'Miktzas.
ii.Hagahos Ashri: Mar bar Rav Ashi holds that R. Shimon ben Elazar obligates swearing if he admitted before the witnesses testified. Then, it is not like Meshiv Aveidah. Even if he knew that witnesses will testify that he paid all of it, if he admitted before they testify, it is not Meshiv Aveidah.
3.Rambam (Hilchos Malveh 14:4): If Shimon brought a loan document against Levi and says that he did not collect any part of it, and Levi says that he paid half, and witnesses testify that he paid it all, Levi swears that he paid half and he pays half, for he admitted partially. He is not like a Meshiv Aveidah, for he was afraid of the document. Shimon collects the half only from Bnei Chorin, for the buyer can say 'I rely on the witnesses. They disqualified the document!'
4.Rambam (Hilchos Malveh 7:7): If David admitted 'I owe 100 to Reuven', and later said 'I remembered that I paid the debt that I admitted to. Here are witnesses', we follow their testimony. He does not contradict the witnesses. He is not like one who says 'I never borrowed.'
i.Magid Mishneh: I know of no source for this, but it is reasonable. Some ask from the above law (14:4). Levi should be believed to say 'I remembered that I paid', for witnesses say so! They answer that Levi could say so. The Gemara and Rambam discuss when he does not say so. However, the Rambam should have explained this! Rather, there, there is a document, and if not for the witnesses, he would not have been believed at all. Here, he is liable only due to his admission. This requires investigation.
1.Shulchan Aruch (CM 82:13): If Shimon had a validated loan document against Levi, and Levi says that he paid half, and Shimon says that he did not pay anything, and witnesses testify that he paid it all, he (Levi) swears, and Shimon collects half from Bnei Chorin.
i.Beis Yosef (DH To'an): The Tur explains 'there, there are no witnesses' about the third Sela that Yehudah admits to, for the document connotes only two. Here, there are witnesses on the document who say that he owes the entire amount. It seems that the Rambam and Rif agree. R. Yerucham (Meisharim 6:5 (24a)) says that some Gedolim say that if witnesses came before Levi said that he paid half, he is Meshiv Aveidah and he is exempt form swearing. It seems that the Rashbam agrees, for he says that the witnesses testified after Levi said that he paid half. He also says that Meshiv Aveidah is when there are no witnesses, e.g. when the document says 'Sela'im' (which connotes two), and the witnesses do not know more than this. Here, since witnesses testified in the end like one of them, we can say that the borrower feared lest they support the lender, and therefore he admitted to half. This is like Tosfos.
ii.SMA (50): Also the Tur holds that if witnesses came before he said that he paid half, he is Meshiv Aveidah and he is exempt form swearing. The Halachah follows this.
iii.Bach (23 DH Aval): The Rambam holds that even if witnesses came before he said that he paid half, he is not Meshiv Aveidah. Since there is a Chazakah that if he paid, he would have taken back the document, he fears to say that he paid it all, lest Beis Din not heed the witnesses against a strong Chazakah, and obligate him to pay everything. If Shimon claimed against Levi without a document, and Levi has witnesses that he paid, all agree that he is Meshiv Aveidah. He knows what the witnesses will say, for he brought them to Beis Din! He has no fear, not of a document or of witnesses. The Rif's text (in Shevuos) says 'even R. Akiva considers him to be a Meshiv Aveidah only when there is no document. Here, there is a document, so he fears.' This is unlike the Rashbam's text, which says '... when there are no witnesses. Where there are witnesses, he fears.' Even though the Rosh brought the Rashbam's text, the Tur rules like the Rif and Rambam. He did not bring the opinion of the Rashbam and Rosh at all, for it is difficult why the Gemara mentioned the document at all. The Rashbam and Rosh hold that he fears lest the witnesses testify like the lender says!
iv.Rebuttal (Shach 37): Also Agudas Ezov says so, but this is wrong. The Tur says that he is not a Meshiv Aveidah, since he admitted only due to the document. If the witnesses already testified, he need not fear the document! We need not say that the Tur argues with the Rosh and did not even bring his opinion. The Gemara mentioned the document, for without a document obviously he need not swear! The Ran explains that when there is a document, the witnesses, who were partially contradicted, help to disqualify the document. The Chazakah (had you paid, I would not have the document) helps to contradict the witnesses. When there is no document, they are not contradicted at all, and he need not swear.
v.Note: Levi must pay half due to his admission, but this is not considered contradiction of the witnesses.
vi.Beis Yosef (DH Kosav): Sefer ha'Terumos asks why the lender does not swear (and collect), like a regular case of a document in which Levi claims that he paid. There, Shimon swears and collects it all. There is different. We do not believe Levi, for there is a Chazakah that had he paid, he would have taken back the document! Here, he says that he paid half, so this is why Shimon still has the document. The Ri mi'Gash says that here, since witnesses say that he paid it all, they disqualified the document. Now, it is like a Milveh Al Peh (a loan without a document). Levi swears and pays only half. One is not believed against a document.
vii.Shach (39, b'Sof): Sefer ha'Terumos' first words are astounding. He holds that even without witnesses, we believe a borrower who says that he paid half, for Shimon's possession of the document does not refute this. The Gemara (Bava Basra 170b, Bava Metzia 103a) clearly says that he is not believed!
viii.SMA (51): Levi swears mid'Oraisa due to Modeh b'Miktzas, for it is considered a Milveh Al Peh. This is why Shimon collects only from Bnei Chorin. However, the testimony does not exempt Levi, for his admission is like 100 witnesses.
ix.Shach (39): If after they testify, Levi says 'I remembered that I paid', he is believed (CM 79:3). The Magid Mishneh held that it is different when there is a document, but the Tur does not distinguish.
MODEH B'MIKTZAS (Bava Kama 107)