Gemara

13b (Rav): If Reuven says to Shimon 'you have money of mine. Give it to Levi', and all three are present, Levi acquires the money.

Some gardeners who worked together calculated among themselves that one of them (Reuven) had extra money. They told him, in front of Ploni (the landowner), to give it to Ploni. They made a Kinyan (acquisition). Reuven later calculated by himself, and saw that he did not have too much.

Rav Nachman said that Reuven cannot retract, due to Rav's law, and the Kinyan. When he heard that Reuven had erred, he said that he can retract.

Bava Basra 6a (Mishnah): If Shimon claimed that Reuven owes him, and Reuven admitted, and Shimon demanded the money the next day, if Reuven says 'I paid you', he is exempt;

If Reuven says 'I do not owe you', he is liable.

Suggestion: This means 'I paid before the day due' (and he is not believed)!

Answer: No, it means 'I never borrowed from you.' This is like an admission that he never paid. (Since he admitted before that he owed, he must pay).

175a (Rabah): If a Shechiv Mera said '100 Zuz in my possession belongs to Ploni', and his orphans say 'He later told us that he paid Ploni', they are believed.

This is because later, he remembered that he had paid.

If he said 'give 100 Zuz to Ploni', and his orphans say 'later, he told us that he paid Ploni', they are not believed;

Had he paid, he would not have said 'give.' (This shows that he surely owes).

Rishonim

Rif and Rosh (1:17): A case occurred in which gardeners thought that Reuven had extra money of Ploni. B'Ma'amad Sheloshtan, they told Reuven to give it to him, and made a Kinyan. Reuven later calculated by himself, and saw that he did not have too much. Rav Nachman allowed him to retract. This is only when there are witnesses that they erred, or his colleague agrees. If there are no witnesses and his colleague disagrees, Reuven cannot retract. This is proper. If not, one could say about any document that he erred, and be exempt!

Question: Even if there are no witnesses that they erred, Reuven should be believed to say that he erred, Migo (since) he could say that he repaid! One who borrows with witnesses need not repay with witnesses.

Answer #1 (Ran DH b'Apei): Perhaps the Rif agrees. He merely teaches that the claim that he erred is not believed by itself. In a case when there is no Migo, e.g. he has been with witnesses from the moment he agreed to give it so we know that he did not pay, he is not believed.

Answer #2 (Rosh and Ran): He is not believed to say that he erred. This is like a Migo against witnesses, for one would not obligate himself before checking meticulously. Bava Basra 6a proves this. If Reuven admitted that he owes Shimon, and later said 'I do not owe' (I never borrowed), he is not believed to say that he erred, Migo he could have said that he paid later! Also in Bava Basra 175a, if a Shechiv Mera said 'give 100 Zuz to Ploni', and his orphans say 'later, he told us that he paid Ploni', they are not believed, even with a Migo. Had he paid, he would not have said 'give.' However, if his calculation or admission was not in front of witnesses, even if he admits that he was b'Ma'amad Sheloshtan or they made a Kinyan to acquire from him, he is believed to say that he erred. One is very careful before admitting only when there are witnesses. When not, he knows that he can retract.

Ran: The Rif says that Reuven can retract when 'his colleague,' i.e. Ploni, agrees. If the other gardeners agree, he is exempt according to the opinion that one who gave through Ma'amad Sheloshtan can pardon the debt. The opinion that says that he cannot pardon obligates Reuven. A witness (the other gardener) says that Reuven is exempt, and Ploni cannot swear to contradict him (he does not know). However, the oath to contradict a witness of payment is mid'Rabanan. One who cannot swear collects without an oath.

Poskim

Shulchan Aruch (126:1): If Reuven told Shimon 'you have my money. Give it for a gift, or to pay my debt, to Levi', b'Ma'amad Sheloshtan, Levi acquires it. Reuven or Shimon cannot retract, even if they are still involved in the matter.

Beis Yosef (DH u'Mah she'Chosav Rabeinu Af): Sefer ha'Terumos says that the Ramban holds that they cannot retract, even if they are still involved in the matter. R. Tam holds that they can; many argue with him.

Shulchan Aruch (13): Shimon borrowed money or took a deposit from Reuven. (Reuven said to give it to Levi and) Shimon agreed. Later, he said 'I perused my calculation, and saw that I did not have anything of Reuven. My admission was mistaken.' If he can verify this through witnesses, he is exempt;

If Reuven gave it to pay a debt and he cannot verify the error, if he agreed in front of witnesses and fixed a date to give it, before this time he is not believed to say that he erred or he was joking.

SMA (34) and Shach (53): If Reuven gave a gift, he can say that had he know that Shimon did not owe him, he would not have given.

SMA (36): This is even if he did not say 'you are witnesses against me.' One who obligates himself in a document need not say this. Every Kinyan is like a document. Ir Shushan disagrees. One can say that 'I was joking' only when another claimed from him. (Since he claimed what I do not owe, I likewise jested with him.) Here, Shimon could say to Reuven 'I jested with you' (since you claimed that I owe you), but this would not justify jesting with Levi.

Gra (34): He is not believed, for Ma'amad Sheloshtan is like saying 'give.'

Shulchan Aruch (ibid.): If he agreed not in front of witnesses, some believe him to say that he erred, Migo (since) he could have denied the entire matter or said that he paid, if it is after the time. The receiver's claim is against the giver.

Question: Why wasn't Shimon careful before admitting?

Answer (SMA 39): He reasoned, if I find that I erred, he cannot claim from me before the time, and after the time I will claim that I paid.

Shach (54): Even this opinion does not believe him to say that he was joking.

Shulchan Aruch (ibid.): Some say that he is not believed to say that he erred (Migo that he paid), for this is like a Migo against witnesses, for it is rare to err. People are very meticulous before admitting.

Beis Yosef (DH v'Im): The first opinion is like Sefer ha'Terumos. We do not follow him against Tosfos, the Rif, Rosh, and Ra'avad.

Shach (55): The Shulchan Aruch retracted from what he wrote in the Beis Yosef (rather, it is a Safek whom we follow), because many rule like Sefer ha'Terumos. However, the latter opinion is primary, like the Rema says.

SMA (40): 'Like a Migo against witnesses' suggests that even if there are no witnesses, he is not believed, for the Chazakah that one does not err is like witnesses. However, the Beis Yosef says so only when there are witnesses.

Rema: The latter opinion is primary. This is only if he admitted in front of witnesses. If not, he can say that he erred.