Gemara

101b (R. Yochanan): If Reuven tells Shimon 'I owe you 100', he must pay;

Reish Lakish says, he need not.

Question: If Reuven said (to witnesses) 'Atem Edai (you are witnesses against me)', why would Reish Lakish exempt? If Reuven did not say 'Atem Edai', why would R. Yochanan obligate?

Answer: He did not say this. Rather, he said 'I owe you 100 in a document';

R. Yochanan says, the matter of a document is potent. It is as if he said 'Atem Edai.' Reish Lakish says, it is not potent.

Question (against Reish Lakish - Mishnah): If a man married a woman and agreed to feed her daughter for five years, he must feed her for five years.

Suggestion: The case is like above.

Answer: No, it discusses a document of committal (like parents who pledged to give certain amounts to their children just before Kidushin was done).

Question (Mishnah): If Reuven wrote to a Kohen 'I owe you five Sela'im' (for Pidyon ha'Ben) he must pay him, and his son is not redeemed. (The document obligates him!)

Answer: There, the Torah obligated him. He wrote a document to clarify to which Kohen he will give the redemption money. (Chachamim decree that his son is not redeemed, lest people say that one may redeem through a document.)

Suggestion (Rava): R. Yochanan holds like R. Yishmael (who obligates one who accepted to be an Arev (guarantor) below the signatures on a document, and Reish Lakish holds like Chachamim (who exempt).

Rejection: R. Yishmael can hold like Reish Lakish. R. Yishmael obligates an Arev to pay, for the Torah does. Here, there is no Torah obligation!

Rishonim

Rif: We asked from our Mishnah of feeding his wife's daughter and Pidyon ha'Ben, in which there was no prior obligation. We say that R. Yochanan holds like R. Yishmael, who obligates an Arev below the signatures. This shows that R. Yochanan and Reish Lakish argue about one who accepted a new obligation. The Halachah follows R. Yochanan, who obligates even if he did not say 'Atem Edai', and all the more so if he said it, and all the more so if a Kinyan (Chalipin) was done. The Yerushalmi says that R. Yochanan and Reish Lakish agree that if one wrote a document thinking that he was liable and it was found that he is not liable, he is not liable. We are not concerned for this, for it is unlike the Bavli.

Rambam (Hilchos Mechirah 11:15): If Reuven obligates himself to Ploni unconditionally, even though he did not owe to him anything, he is liable. This is like a gift; it is not Asmachta. If Reuven wrote in a document 'I owe 100 to you' even though there are no witnesses, he must pay. This is even if both admit and the witnesses know that he did not owe anything. He obligated himself and decided to make himself liable like an Arev. The Ge'onim ruled like this.

Magid Mishneh: The Rambam explains that he comes to obligate himself. He does not say that the one who admitted later denied owing. The Rambam says that a document helps without witnesses according to the opinion that Edei Mesirah Karsei (the witnesses who saw it given make it valid). Alternatively, the one who obligated himself wrote it in his handwriting; it helps to collect from Bnei Chorin, even if it was given without witnesses. If it was in another's handwriting; and it was not given in front of witnesses, it is invalid. The Ramban and Rashba disagree. If there was no prior debt, we would not ask why Reish Lakish exempts, rather, why R. Yochanan obligates! Later, we answer that he obligates himself through a document.

Ran (DH v'Hacha): We do not discuss one who admitted to an existing debt. No one would argue about this. A Mishnah (Bava Basra 175b) teaches that one collects with a document in Kesav Yado. Rather, he comes to obligate himself. R. Yochanan holds that a document is as strong as saying Atem Edai and admitting to an existing debt. It would have been more appropriate to say 'it helps like a Kinyan'. It mentions Atem Edai because this was mentioned above. Reish Lakish holds that one cannot obligate himself through a document. A proof of this is that we challenged him from the Mishnayos of feeding a daughter and Pidyon ha'Ben, and we did not answer that those documents had witnesses. This would have been a good answer, for no other Mishnah teaches about obligating oneself through a document.

Rosh (12:2): Rashi explains that we discuss one who admitted 'I owe you', but he did not sign. R. Tam explains that he did not admit; he wrote in his handwriting 'I owe you' and obligated himself through the document. Even though Metaltelim are not acquired through documents, since he wrote an expression of Chiyuv, he decided absolutely to obligate himself. Meshichah is needed for specific Metaltelim, but a document suffices for obligation and debts. The Rif agrees.

Question (Hagahos Ashri): According to Rashi, why can't he say 'I was joking'? When we asked from Pidyon ha'Ben, we should have answered that there, he signed the document!

Answer (Drishah 1): Really, 'I was joking' applies only when there was a claim against him. Rather, Hagahos Ashri asks why he can't say that he made a false admission, lest people think that his children will inherit great wealth.

Beis Yosef (CM 40 DH ha'Omer): According to Rashi, if the recipient agrees that he did not lend anything, or if witnesses testify that he did not owe him before giving the document, the document does not obligate him.

Poskim

Shulchan Aruch (CM 40:1): If Reuven obligates himself to Ploni unconditionally, even though he did not owe to him anything, he is liable. If he wrote in a document 'I owe 100 to you' even though there are no witnesses, he must pay.

Beis Yosef (DH v'Nir'eh): R. Tam says that if a borrower wrote in his handwriting 'I owe to you 100' and gave it in front of witnesses, it is a loan with a document. It is no worse because it is in his handwriting. Even though the text is unlike a document, it suffices because it contains an admission and was given in front of witnesses. The Rambam agrees.

Bach (3): The Tur explains that R. Tam obligates him only if he (or witnesses) signed the document or it is in his Kesav Yado. If not, it does not help, even if it was given in front of witnesses. He can say 'I was joking.' The Mordechai and Hagahos Ashri agree. Rashi holds that Kesav Yado or giving it in front of witnesses suffices.

Rebuttal (Shach 5): Since we rule that Edei Mesirah Karsei, all validate any document given in front of witnesses. The Tur (Sof Siman 69) says that it may be used to collect from sold property! It is unreasonable to distinguish between an existing debt and a new obligation. The Beis Yosef says that the Rambam agrees with R. Tam's law. The Bach inferred from Hagahos Ashri's question against Rashi, that if he did not sign it, he can say 'I was joking.' Perhaps Rashi explains the Sugya even according to the opinion that Edei Mesirah are not Karsei, for surely Reish Lakish holds like this opinion. R. Tam disagrees; Reish Lakish holds that all agree that one cannot accept a new obligation through a document.

Drishah (1): If he gave a Kesav Yado but did not sign it or give it in front of witnesses, Rashi and R. Tam hold that it is invalid. It seems that the Rambam would be Machshir, but perhaps he merely cited the Gemara.

Rema: All the more so if one writes 'I received such and such from the money you owe to me' he pardoned it, even if we know that he did not receive.

Source: Ritva (56a DH R. Yehudah), cited in Darchei Moshe (1).

SMA (3): Even a verbal pardon or admission that he was paid is valid.