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The Mishnah records several debates between Admon and the Chachamim. One of these (13:4) is where one person claims his friends has jugs of oil in his possession and the friend admits that he was entrusted with empty jugs only. The issue is whether this constitutes a partial admission -- modeh be'miktzat -- such that the friend would be required to make a shevuah that that is indeed all that he was entrusted with. Admon maintains that the original claim included the jugs. Consequently, this case is one of partial admission. The Chachamim however argue that the original claim was only regarding the oil, with the jugs a reference to the quantity. Even though monetarily it might be a partial admission, the admission is regarding a different type to what was claimed. This would then be similar to a case where the claim was that he owed wheat, and the admission was that he owed barely. Such cases are not considered modeh be'miktzat.
The Mishnah ends with Rabban Gamliel stating that he sees the logic in Admon's position. The Tosfot (Shevuot 40a) however finds the position taken by Rabban Gamliel difficult. This is because Rabban Gamliel maintains that the partial admission need not be of the same type as the claim. Rabban Gamliel would require a shevuah even if the claim was for wheat and the admission was for barely. Consequently, whether in our Mishnah the claim for barrels of oil included the barrel is not important for Rabban Gamliel since even if it did not, he would require a shevuah. Why then was Admon's logic important to Rabban Gamliel?
The Tosfot answer that it would be important in the case where the claim was for ten barrels of oil, and the admission of for five. Admon's position is that "barrels of wine" also implies the barrels. Consequently, the admission for five barrels of oil, even after the shevuah, would obligate this person to return not just that quantity of oil, but barrels also.
Tosfot R' Akiva Eiger (Shevuot 6:3) however finds this explanation difficult. Granted the according to Admon we can accept that the claimant's intention was to include the barrels in order to obligate him to make a shevua. Nevertheless, to say with certainty that that is the intention to obligate the other party in his admission to return the barrels as well, is not so clear.
The Tosfot R' Akiva therefore suggests that it is important for the case where the claim was for ten barrels of oil, and the admission was for a quantity of oil that fills ten barrels. According to Admon since the claim also implied barrels, then this would qualify as a case of modeh be'miktzah since it is a partial admission. According to the Chachamim however it would be a full admission since the claim never implied the barrels.
The Tosfot R' Akiva provides another case where the position of Admon is important for Rabban Gamliel. That is, whether the jugs were of equal value to their contents. The claim was once again regarding jugs of oil, whereas the admission was only to having jugs. According to Admon there is a partial admission. According to the Chachamim, the value of the admission was equal to the value of the claim. Consequently, it would not be considered a case of modeh be'miktzat.
The Shitah Mekubetzet (108b, s.v. ve'hiksha) explains that Rabban Gamliel also requires the admission to be part of the claim. In the case where the claim was for wheat and the admission for barley, he obligates a shevuah since the claim for wheat does not discount barely. Even if it was only barely that was really taken, the claimant may not have been discerning with the type of grain when making his claim, since he was dealing with grain and more focused on the value. Returning to our case however, according to the Chachamim, since the claim does not imply the barrels, it is as if the claim explicitly excludes the jugs. Consequently, even Rabban Gamliel would agree that according to the Chachamim's understanding, it is not a case of modeh be'miktzat. According to Admon however, since the claim included the barrel, Rabban Gamliel would require a sheuvah.
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