The Gemora asks (Daf Yomi: Gittin 36a) : Do the witnesses only have to sign on the Get because of “Tikun Ha’Olam” – “benefiting the world?” This is a Torah law! This is evident from the verse, “And it should be written in a document and signed!”
Rabbah says: The Mishna’s statement is needed according to Rabbi Elozar, who holds that the witnesses for the giving of the document cause the document to take effect. Even according to him, Chazal instituted that witnesses should also sign the Get because of tikun ha’olam. This is because there are times when the witnesses of the giving of the Get might have died or went overseas (and at least the witnesses signed will be able to contradict the ex-husband in case he claims that he did not divorce her).
Rav Yosef says: Even according to Rabbi Meir (who holds that the witnesses for the giving of the document cause the document to take effect), they decreed that witnesses should specify their names in a Get, due to tikun ha’olam. This is as the braisa states: Originally, people would sign, “I, So-and-so (without writing his name), have signed as a witness.” If there was a different document with the same handwriting that was verified to be authentic, this document would also be valid. If not, it is not valid. Rabban Gamliel said: They made a great decree when they instituted that witnesses should specify their names in a Get, due to tikun ha’olam.
The mefarshim ask on the Rambam in Hilchos Edus (3:4), who states that the requirement for witnesses to sign on a document is only mi’divrei sofrim (a Rabbinical obligation). The Gemora expressly states that this is a Biblical requirement!?
The Megillas Sefer answers that when the Gemora states that it is Biblically required, it is not being completely accurate, for the verse where this obligation is derived from is a verse in Yirmiyah. The Gemora only meant to ask that from the Mishna it would seem that the witnesses sign only because of Rabban Gamliel’s decree, when in truth, this was established generations beforehand!
The Pnei Yehoshua answers that it is only a Biblical requirement according to Rabbi Meir, who holds that the witnesses who sign the document are those who render it effective. However, the Rambam rules in accordance with Rabbi Elozar, who holds that the witnesses who observe the delivery of the document are those who render it effective. Therefore, the Rambam writes that the signatures are only a Rabbinical requirement.
The Nesivos Hamishpat, Chasam Sofer and others answer that the Rambam is only referring to proof documents, since the witnesses are obligated to testify in Beis Din so that the judges will have the ability to cross examine them. Testimony is valid only from the mouths of the witnesses, but not on the basis of any documents or writings. However, regarding a document that is made to affect something, either a marriage, divorce, sale etc., the Rambam will agree that the signatures of the witnesses are Biblically required.
Reb Chaim Brisker adds that a document, like a get, which later will be used as proof that the woman got divorced can still be Biblically valid. For once the document rendered an effect, it is as if it has been investigated in Beis Din, and would not any longer be disqualified because of the rule that testimony must come from their mouths and not from their writings.