A sin offering (chatat) is brought when one inadvertently violates a prohibition, that if violated deliberately would make him liable to karet. The Mishnah (3:1) deals with cases where the individual was made aware of the violation by other people. The second case is where two people provide conflicting accounts regarding whether the individual did indeed violate the prohibition. The Mishnah rules that he would need to bring an asham talui. The asham talui, about which we will learn next week, is the guilt offering that is brought in the case where one has a doubt whether they are indeed violated a prohibition that would obligate them to bring a sin offering.
The Tosfot R' Akiva Eiger writes that the Mishnah appears to imply that if two individuals present conflicting testimonies, it is not considered as if they are cancelled out and insignificant. Instead we find that both testimonies are adopted creating a situation of doubt.
The Tosfot R' Akiva Eiger directs us to the Machane Ephraim (Edut 8), who comments that this is indeed the opinion of the Rambam. The Ramban however maintains that in a case where two individuals present opposite testimonies, they cancel each other out and are disregarded. The Machane Ephraim cites our Mishnah in support of the Rambam.
The Machane Ephraim also cites the Mishnah in Taharot (5:9) as an additional proof. The Mishnah rules that if one person said an individual came into contact with a source of tumah and another person says he did not, then if the incident occurred in a private domain, the individual is deemed tameh. If however it occurred in the public domain, then the individual is tahor. The ruling is consistent with a case of safek tumah -- a doubt whether an individual became tameh. It is clear that the testimonies are not disregarded, but rather viewed as a case of safek.
The Tosfot R' Akiva Eiger however also directs our attention to the Shach (YD 127). The Shach cites the Yerushalmi (Yevamot 10:4) that deals with a case where there are conflicting testimonies regarding whether a woman was betrothed. The Gemara attempts to draw a proof from our cases, that we need to be concerned and that she would require a get if she wished to marry another. R' Yossi rejects the proof since the barrier to bring an asham talui is much lower. In other words, witness testimony is not required and even if one has internal doubts, he can bring an asham talui.
We can now defend the Ramban based on the Shach. It can still be argued that for legal matters where a single witness is significant, that if someone else testifies to the opposite, we completely disregard both. However in this case, since even a single witness testimony is not really required to bring an asham talui, the presence of two people that raise a doubt in the mind of the individual is enough to require an asham talui be brought.
How can we address the proof from Taharot? The Tifferet Yisrael (Taharot 5:9, Boaz 9) also raises that Mishnah as a difficulty against the Maharik that holds the same position as the Ramban. He adds however, that the Ran and Rashba have a more basic problem with that Mishnah and ask that in that case there is a chezkat heiter (the person was tahor before the question was raised) and everyone would agree that we would discount the single witness that states he is assur (tameh) in that case. The Tifferet Yisrael suggests that hilchot tumah is different since the Torah teaches that we disregard the chezkat tahara in a case of safek tumah be'resuht ha'yachid. Put differently, for safek tumah, the requirement to change his status, does not require witnesses to overrides the chazaka. One may suggest that Tifferet Yisrael implies that perhaps for hilchot tumah it is also different with respect to conflicting single witnesses.
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