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"By the testimony of two witnesses or three witnesses shall the person be put to death" (Devarim 17:6). At least two witnesses are required to provide testimony in beit din. The significance of the Torah adding "or three witnesses" is discussed in the Mishnah (1:7).
The Mishnah (1:7) first teaches that a set of witnesses has the same legal force irrespective of the size of the group. Just as three witnesses can testify to render two as false witnesses, two witnesses can render three witnesses false. R' Shimon adds that for a set of witnesses to be considered edim zomemin such that they receive the reciprocal punishment, all of the witnesses need to be found false. In other words, other witnesses must testify that these "witnesses" were with them at a different location at the time of the supposed incident. The same is true even for a large set. Every witness in the group needs to be found false in this manner to be considered edim zomemin and receive the reciprocal punishment. Note that the additional witness affords the group a leniency in this regard.
R' Akiva however adds that the third witness in the group is really coming to add a stringency, such that he would share the same punishment as the other false witnesses. Exactly what R' Akiva means is the subject of debate.
Rashi (5b) explains that none of the opinions in the Mishnah are arguing with regards to halacha. In other words, while R' Akiva agrees with the first two opinions, the pasuk was not needed to teach these points since they are self evident. Instead, the novelty is that even though this third witness is not really needed (considering that only two witnesses are required) nonetheless since they are all found false, he would also receive the reciprocal punishment. To be clear, he is not arguing regarding the law. For the reciprocal punishment to be administered, he agrees that all the witnesses need to be found false.
The Nemukei Yosef however cites the Riva who explains that R' Akiva argues with R' Shimon. In other words, if only two of the three were found to be false, those two could indeed be killed (if it were a capital case) with third witness set free. That is also the Ritva's first explanation, which he maintains is the simple reading of the Mishnah.
The Ritva however also suggest that perhaps we can understand debate between R' Shimon and R' Akiva as being where the third witness came after the other two, and they were all found false. R' Shimon would treat the third as being separate and exempt, while R' Akiva maintains that he is punished along with the other two.
The Nemukei Yosef however, also cites the Ri ben Geiut who explains that if only two were found false, then they could all be considered zomemin and be punished. Nevetheless, the Nemukei Yosef concludes that the halacha is like R' Shimon.
The Tumim (38, s.v. Omnam) however asks, according to the Maharitz Geiut, what if this third person was telling the truth? He might not have known that the other two were false witnesses. Why should he be punished?
The Tumim answers, that it must be that the Maharitz Geuiut maintains that the witnesses must see each other to be defined as single testifying group. Considering that they presented as witnesses together and two have been found to be false witnesses it is clear that this third person is lying. Granted that he has not be found to be an eid zomem, nevertheless this is the stringency of the pasuk according to R' Akiva, that since he associated himself with them, he bears their punishment.
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