What is the logic of this opinion? What could possibly invalidate the Get
when witnesses sign the Get she'Lo Lishmah? Granted, when an invalid witness
signs the Get, then there is justification for the Chachamim to invalidate
the Get, lest people mistakenly infer from the fact that this person signed
the Get that he is a valid witness (and use him as a witness for other
matters). However, when a Get is signed she'Lo Lishmah, what possible mishap
could result from it for which the Chachamim should invalidate the Get? (The
witness himself is a valid witness for all other matters, and he signed in
attestation of what actually occurred; he merely did not sign Lishmah.)
Certainly, mid'Oraisa there is no reason for a Get not to be valid, since
the Torah does not require Edei Chasimah in the first place.
(a) TOSFOS (DH Modeh) explains that the Rabanan invalidated a Get that is
not signed Lishmah, because people might learn from it that the Kesivah also
does not need to be Lishmah. Even though the Get was already written, they
will assume the next time they write a Get that they do not need to write it
Lishmah. (People will not realize that the Edei Chasimah are entirely
extraneous to the validity of the Get.)
(b) The RASHBA suggests that it could happen that if the Edei Chasimah did
not sign Lishmah, the Get is not valid mid'Oraisa. For example, in a case
where the Get was handed over in front of Edei Mesirah (witnesses who see
the giving of the Get) but those witnesses are no longer available (they
died or left the country), then the onus of validation falls on the Edei
Chasimah. Rebbi Elazar (3b) says that the Get can be validated through the
Edei Chasimah in such a case. How, though, do the Edei Chasimah prove that
the Get was delivered in front of witnesses (Edei Mesirah)? The answer is
that since the Get was not forged, we assume that everything about the Get
was done in the proper manner.
The Rashba says that when the Get is validated through the Edei Chasimah,
their signatures and testimony become an integral part of the Get, since
Beis Din will authenticate the Get based on their signatures. Therefore,
just like every important part of the Get must be written Lishmah, the
signatures -- through which the Get is being authenticated -- must also be
written Lishmah! The signatures, in such a case, are considered part of the
Kesivah.
This is why Rebbi Elazar says that when witnesses are signed on the Get
she'lo Lishmah, the Get is invalid mid'Rabanan. The Chachamim were afraid
that at a later time we would rely on the Edei Chasimah to validate the Get,
in which case the Chasimah will have had to be Lishmah.
(c) The Rashba points out that according to the RIF, the Edei Chasimah who
are not signed Lishmah might invalidate the Get *mid'Oraisa*. The Rif
maintains that according to Rebbi Elazar, although it is the Edei Mesirah
who empower the Get to be effective ("Edei Mesirah Karti"), Edei Chasimah
can also make the Get valid without Edei Mesirah. (See TOSFOS, DH d'Kaima
Lan.)
The Rashba suggests that according to the Rif, Rebbi Elazar will require
that both the Edei Mesirah and Edei Chasimah be Lishmah, since they are both
of equal importance. (The Rashba concludes that he does not favor this
approach, since, if Edei Chasimah are included in the words "v'Kasav Lah,"
then every Get should require Edei Chasimah, and how could Rebbi Elazar
permit writing a Get without Edei Chasimah?)