I would like to suggest an approach in the argument between R Yirmia and Abayee in Gitin 86. I think R Yirmia thinks that R. Elazar requires that witnesses that see the giving of the divorce to cause the validity of the document in itself. But Abayee thinks that there is no need for the document of divorce to have a category of a valid document. This distinction seems to be implicit in the very words of R. Yirmia and Abaye themselves. For on page 86b, the mishna says if there is a case where two documents of divorce to two different women were sent by one messenger, and those documents got mixed up. The law is that the messenger gives each document to each woman. R. Yirmia said this is not like R. Elazar who says the witnesses that see the divorce cause it to be valid. But here when the messenger gives the document, the witnesses do not know which document was written for either woman. That is there is no "for her sake". Abaye said R. Elazar does not require “Lishma” in the giving of the divorce, but only in the writing of it. The document is required to have been written for her sake, but it does not need the general category of a valid document.----------------------------I would like to suggest an approach in the argument between ר' ירמיה and אביי in גיטין דף פ''ו ע''ב. I think ר' ירמיה thinks that R. Elazar requires that witnesses that see the giving of the divorce to cause the validity of the document in itself. But אביי thinks that there is no need for the document of divorce to have a category of a valid document. This distinction seems to be implicit in the very words of ר' ירמיה and אביי themselves. For on page 86b, the משנה says if there is a case where two documents of divorce to two different women were sent by one messenger, and those documents got mixed up. The law is that the messenger gives each document to each woman. ר' ירמיה said this is not like ר' אלעזר who says the witnesses that see the divorce cause it to be valid,עדי מסירה כרתי. But here when the messenger gives the document, the witnesses do not know which document was written for either woman. That is there is no "for her sake". אביי said ר' אלעזר does not require לשמה in the giving of the divorce, but only in the writing of it. The document is required to have been written for her sake, but it does not need the general category of a valid document.----------------- I might mention that Rav Shach points out that according to the Rambam since the law is like R Elazar, documents do not need witnesses in order to be valid. {laws of divorce chaapter1 law 13} he also expresses surprise on the Shach in Shulchan Aruch chapter 66, law 6, that writes simply that one does not need witnesses in documents because to most rishonim one does need witnesses in a document for it to be valid. At any rate. It is possible that the Rambam is going here like Abaye who says R Elazar does not require the witnesses that see the act of divorce to know exactly for whom the document it is given. I.e., the document needs to be written for her sake there is no need for the giving of the document to be Lishma. --------I might mention that רב שך points out that according to the רמב''ם since the law is like ר' אלעזר, documents do not need witnesses in order to be valid. {laws of divorce chapter א' law 13} he also expresses surprise on the ש''ך in שלחן ערוך chapter 66, law 6, that writes simply that one does not need witnesses in documents because to most ראשונים one does need witnesses in a document for it to be valid. At any rate. It is possible that the רמב''ם is going here like אביי who says ר' אלעזר does not require the witnesses that see the act of divorce to know exactly for whom the document it is given. I.e., the document needs to be written for her sake there is no need for the giving of the document to be לשמה.