that the signing must be performed for her sake? If it is in accordance with the opinion of Rabbi Meir, he requires signing for her sake; however, he does not require that the writing must be for her sake. As we learned in a mishna (21b): One may not write a bill of divorce on anything that is attached to the ground, e.g., a leaf attached to a tree. However, if he wrote it on something that is attached to the ground, and then he detached it, signed it, and gave it to her, it is valid. This indicates that the essential stage of writing a bill of divorce is when it is signed by witnesses. The Gemara says that this is Rabbi Meir’s opinion, as an unattributed ruling in the mishna typically follows the opinion of Rabbi Meir.

If it is in accordance with the opinion of Rabbi Elazar, who disagrees with Rabbi Meir and requires that the writing must be for her sake, he does not require that the signing must be for her sake. And if you would say that actually the mishna is in accordance with the opinion of Rabbi Elazar, and when Rabbi Elazar does not require signing for her sake, he means by Torah law, whereas by rabbinic law he requires that bills of divorce must be signed for her sake; but that is untenable, as the Sages listed three bills of divorce that are valid by Torah law but are invalid by rabbinic law, and when he disputes that ruling Rabbi Elazar does not require that the signing must be for her sake.

As we learned in a mishna (86a): Three bills of divorce are invalid ab initio, but if the woman married another man after having received one of these bills of divorce the offspring is of unflawed lineage. In other words, she is not considered to be a married woman who engaged in sexual intercourse with another man, which would render their child as one born from an adulterous relationship [mamzer]. And these three are: A bill of divorce that the husband wrote in his handwriting but there are no signatures of witnesses on the document; and if there are the signatures of witnesses on the document but there is no date written on it; and if there is a date written on it but it has only one witness signed on it. These are the three invalid bills of divorce concerning which the Sages said: And if she married, the offspring is of unflawed lineage.

The mishna continues: Rabbi Elazar says: Even though there are no signatures of witnesses on the document, but he gave it to her in the presence of two witnesses, it is a valid bill of divorce. And on the basis of this bill of divorce the woman can collect the amount written to her in her marriage contract even from liened property, as Rabbi Elazar maintains that witnesses sign the bill of divorce only for the betterment of the world. If no witnesses sign a bill of divorce the husband could contest its validity at any time by denying that he wrote it. In any case, it can be seen from this mishna that according to Rabbi Elazar the signatures of the witnesses are not an essential part of a bill of divorce. Consequently, it does not need to be signed for her sake, even by rabbinic law.

But rather, you can say that the mishna is in accordance with the opinion of Rabbi Meir, and when Rabbi Meir does not require that the writing must be for her sake, he meant by Torah law, whereas by rabbinic law he does require that the writing must be for her sake. However, the Gemara raises a difficulty against this explanation as well: But didn’t Rav Naḥman say that Rabbi Meir would say: A bill of divorce need not be written for her sake, and even if a husband found a bill of divorce in the garbage, and the names of the man and woman in the bill of divorce are the same as his name and that of his wife,