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The week we began masechet Arachin. If someone declares that they want to give the erech of a person, the amount that he must donate to the Beit HaMikdash depends on the age and gender of that person, with the values described in the Torah. Note that this is different to if a person wants to give the demei (value) of a person. In that case the value depends on the value of the subject of the neder.
The second Mishnah records the debate regarding nochrim. R' Meir's opinion is that they can be ne'erach (be the subject of an erech-vow) but no maarich (make an erech-vow), whereas R' Yehuda maintains that the opposite is true. The Gemara explains the debate is based on the pasuk that introduces the laws of arachin. The pasuk opens by saying, "Speak to Bnei Yisrael..." implying that the laws apply exclusively to Bnei Yisrael. Yet the pasuk continues relating to an "ish" (person) who makes the *erech-*vow. The term "ish" is understood to be broader, thereby including nochrim. It is understood that one term refers to the maarich and the other the ne'erach. The debate is which term applies to each case.
The Gemara initially explains R' Meir and R' Yehuda each point to cases where more people are relevant to both the maarich and ne'erach to support their positions. Rava however continues that the halacha should follow R' Meir's opinions. This is not because of the rationale provide in the Gemara, but rather based on the pasuk, "It is not for you and us to build the house of Hashem" (Nechemia 4:3). The pasuk is understood to exclude nochrim for contributing to the Bedek HaBayit (Temple treasury). That therefore aligns with R' Meirs position that they can be ne'erach but not maarich.
The Minchat Chinnuch (350:9) assumes that the above cited pasuk is the reason behind the position of R' Meir. Note however that the pasuk only excludes nochrim from contribution to the bedek ha'bayit. Nochrim can however volunteer to bring korbanot. That being the case the Minchat Chinnuch suggests that if the nochri declared that he wanted to bring the erech of himself or another person to be used for a korban, then perhaps it would work.
The Gemara however continues by asking what R' Yehuda would do with the pasuk. Rava explains that really nochrim could have contributed. In the times of the Nechemya, the nochrim's intention was to sabotage the construction of the Beit HaMikdash, by taking responsibilities, and not deliver -- rifyon yadaim. That is why, at the time, they did not want their involvement.
The Tosfot (s.v. Ela) comments that when the Gemara explained that pasuk is due to rifyon yadaim that was only to explain the position of R' Yehuda. According to R' Meir however, the original understanding must be maintained, in order that Rava's conclusion that halachha accords with R' Meir be preserved.
The Tosfot however ask that if that we as the case, how then could the Mishnah teach that nochrim can nodrim. The simple understanding is that they can volunteer korbanot and donate to the bedek ha'bayit. He suggests that perhaps Rava retracted from his original position that the pasuk support R' Meir and instead everyone agrees that the pasuk is motivated by rifyon yadaim. This understanding would not work with the Rambam who ultimately ruled like R' Meir, presumably because of the first statement of Rava.
The Chazon Ish (30:4) however prefers the first answer of the Tosfot and explains that when the Mishnah states that nochrim can nodrim, it is only referring to korbanot and not the bedek ha'bayit.
The Shitah Mekubetzet however provides a different explanation. Firstly, the conclusion is that everyone agrees that the pasuk is motivated by rifyon yadaim. Consequently, nochrim can donate to the bedek ha'bayit. When it comes to arachin however, R' Meir understands that they still cannot maarich due to the pasuk by arachin -- "Bnei Yisrael". (This would presumably exclude them from all types of arachin.) Nevertheless the pasuk cited by Rava still supports the notion that halacha should follow R' Meir. Not because it is the source for his position, but rather it demonstrates that there are contexts in the world of making dedications that apply to an yisrael and not a nochri.
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