With the beginning of the fourth perek we learn about heseg yad. We have discussed that the value of an erech-vow is fixed; it is listed in the Torah and depends on the age and gender of the subject of the erech-vow. We now learn that if the person that made the erech vow cannot afford that amount of money, he pays whatever he can and thereby discharge himself of the obligation.
The Mishnah (4:1) comments that while the obligation varies with the financial standing of the one that made the erech-vow, in the world of sacrifices this is not the case. Concerning some korbanot, what one must bring also depends on the financial standing of the individual. One example is that of the metzorah. The Mishnah asserts that, unlike arachin, in the world of korbanot the korban is determined by the subject. The Mishnah explains that if one sees a poor metzorah and obligates himself to bring that individuals korbanot, then we consider the financial standing of the metzorah and not the individual how took upon himself to bring the korbanot.
R' Yehuda however responds that even in the world of arachin we can engineer a parallel case. One case would be if a wealthy individual made an erech-vow to bring his own erech, and a poor person declares that he wishes to take on that obligation. In such a case, R' Yehuda reasons, we would not look at what this poor person can afford. This is because he has taken upon himself what the wealthy person has obligated himself to pay. The ruling exactly parallels one that obligates themselves with bringing the korbanot of a poor or wealthy metzora.
The Rishonim differ in their understanding of this Mishnah. The Rambam appears to understand that R' Yehuda is not arguing with the Chachamim, rather adding to their explanation.
The Tosfot (17a, s.v. aval) however explains that the R' Yehuda and the Chachamim argue. In other words, even in a case where the poor person overheard the wealthy person making an erech-vow vow and the poor person responded by taking on the wealthy person's obligation, the Chachamim maintain that we would still consider what the poor person could afford when determining what the second person is obligated to pay.
According to the Tosfot how do we understand the position of the Chachamim? In both cases it appears that an individual is attempting to take on the obligation of another, and what the other person is obligated to bring depends on his financial status. Yet for korbanot the obligation of the one who made the neder is determined by the financial status of the subject (the first person), whereas for arachin, the standing of the one that made the neder is important (the second). What is the difference between korbanot and arachin?
The Chazon Ish (Kodshim p350, s.v. Arachin) explains that the difference between korbanot and arachin is that with the latter, the second person could have taken on the *erech-*vow directly themselves. That being the case, the second person is treated as if he made the original neder. Even though the second person stipulated that he wants to bring the first's obligation, it is not considered that this is a business obligation between two parties. Instead it is considered as a direct. obligation the second person is making to hekdesh. One can make such a commitment to hekdesh to pay what his friend owes, just like he can commit to donate any sum of money to hekdesh. Consequently, if the first person was wealthy and the second poor, the second is only obligated to pay what he can under the framework of an erech-vow and the first person must then pay what remains of his obligation. If however the first person was poor and the second wealthy, the wealth one must may the full amount of the erech-vow as any wealth person who makes an erech-vow, even if it is in excess of the amount the first person can afford.
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