1) THE POWER OF A WRITTEN ADMISSION
OPINIONS: The Gemara quotes the Mishnah in Bava Basra (175b) that states that if a person claims money from his friend and backs up his claim with a written admission from his friend, he may use the note to collect only from properties that have no lien from someone else. He certainly may not collect from properties that have already been sold by the person who owes him money.
What is the claim of the defendant in this case?
(a) TOSFOS (DH Hotzi) quotes the RIF who says that the Gemara is discussing a case in which the defendant totally denies the claim, saying that it never even happened. If, however, the defendant admits that he owed the money but claims that he already paid it, he is totally exempt.
This differs from an ordinary loan document. When one produces a loan document stating that a borrower owes him money, the borrower cannot claim that he already paid back the loan. This is because the lender has a valid claim: "If you paid back the loan, then why do I still have the loan document?" The Rif says, however, that the lender can make such a claim only when he has an ordinary loan document, but not when he has merely a written admission. This is also the opinion of the RAMBAM (quoted here by the RITVA).
(b) TOSFOS (ibid.) quotes RABEINU YITZCHAK who argues with the Rif. He rules that whenever a person who is owed money has a written admission attesting to his debt, the borrower cannot claim that he paid back the loan without showing some type of evidence.
It seems that Rabeinu Yitzchak's ruling is more logical. After all, why should a person who wrote a an admission of debt not collect that promissory note when he pays back the lender? Why should the lender not be able to claim, as he may claim regarding a legal document, that had the borrower indeed paid back the loan he would have taken back the written admission?
1. The SHACH (CM 69:14) answers in the name of the MAGID MISHNAH that the reason why a borrower does not mind leaving his written admission in the hands of the lender hand is that he knows he has a way to protect himself if the lender is deceitful and tries to collect the money again. He simply can sell all of his property. Since the written admission cannot be used to collect from any property with a previous lien on it or property that was previously sold, by getting rid of his property quickly he can avoid having to pay back the debt twice.
2. The Shach (ibid.) gives another answer in the name of the RAMBAN. In general, a borrower does not suspect that a lender will collect again dishonestly using the loan document. However, he still must take back a real loan document because if he does not, people will not buy his fields. Even though he trusts the lender, the buyers of his fields will be worried that the lender will act dishonestly and collect twice, causing them to lose their fields. This, in turn, will cause people to buy the borrower's fields only at a low price. He therefore must ensure that he receives his loan document in return upon paying his loan. However, this suspicion does not apply to a written admission, because the buyers do not care if he leaves his written admission with the lender; even if he does, it cannot negatively affect them since the lender cannot collect from property that has already been sold by the borrower. Accordingly, the borrower may sell his properties at a normal price and leave his note with the lender whom he trusts. This is why the Rif and others say that a lender cannot claim, "If you paid back the loan, then why do I still have the loan document?" with regard to a written. (Y. Montrose)

21b----------------------------------------21b

2) WHEN TWO JUDGES RECOGNIZE THE SIGNATURE ON A CONTRACT
OPINIONS: Rav states that if three judges convene together as a Beis Din in order to verify the signatures of witnesses on a document, and two of them recognize the signatures, those two judges may testify that the signatures are authentic in front of the third judge who is not familiar with the signatures. This implies that after their testimony, they may write a document stating, "We have verified and upheld this document with three [judges] who are sitting [together], as it has become known to us that these are indeed the signatures of the witnesses" (see RASHI DH v'Chasam).
Why is this a valid authentication of the signatures? Beis Din (three judges) did not receive testimony from two witnesses. Why is this a valid form of testimony in front of Beis Din?
(a) The ROSH derives from here that testimony verifying a document does not need to be given in front of three judges at once. The two witnesses may testify in front of all three judges separately if this is convenient. The judges may then convene, confirm with each other that they each heard the same testimony validating the document, and then write that the document has been validated.
(b) The TESHUVOS HA'RAMBAN (end of #91) disagrees with the Rosh. He explains that testimony verifying a document must be done in front of three judges. In the case of the Gemara here, the testimony is being done in front of three judges, as the two witnesses are also judges. While generally the law is that "Ein Ed Na'aseh Dayan" -- "A witness does not becomes a judge," this applies only to Torah law. The procedure of verifying documents is mid'Rabanan, as according to Torah law documents do not need to be verified. Accordingly, witnesses may become judges, and it is as if their testimony was said in front of all three judges. (Y. Montrose)