Arachin, Chapter 1, Mishnah 2. The opening chapter of Masechet Arachin maps out who is included in the laws of erech and who is left out, both as the one who declares the vow and as the person whose value is being pledged. Our mishnah takes up the case of the nochri, the non-Jew, and asks how he stands in relation to the two kinds of pledges we deal with in this masechet: erech, the fixed sums the Torah assigns according to age and gender, and damim, a person's actual worth as he would be valued on the market.
Two Words in One Verse
The Torah's section on arachin begins with a command aimed at a defined audience: "dabber el benei Yisrael," speak to the Children of Israel, and then "ve'amarta aleihem," and you shall tell them. That framing suggests the mitzvah was handed to Israel and to no one else. Yet the verse goes on with the words "ish ki yafli neder," a man who pronounces a vow, and the term "ish" is understood as a broadening one, drawing the nochri into the halachah. A single verse thus holds a narrowing phrase and a widening phrase side by side, from which it follows that the non-Jew must have some partial share in the laws of erech. What our mishnah argues about is which half of that share belongs to him.
The Machloket
"Hanochri, Rabbi Meir omer: ne'erach aval lo ma'arich." According to Rabbi Meir, a Jew who pledges the erech of a non-Jew has made a binding vow, yet the non-Jew has no power to pronounce such a vow himself. Were he to declare an erech, about his own person or about a Jew, nothing whatsoever would take effect.
Rabbi Meir's reasoning has a precedent to lean on. We already met, in the previous mishnah, a group whose members can have their erech pledged by others but cannot pledge anyone themselves: the cheresh, the shoteh and the katan. Since the verse both includes and excludes the nochri, and we are forced to choose which side of the law he lands on, it is most natural to slot him into that existing category.
The Bartenura points out that the argument could just as easily have run the other way. There is a second precedent available: the tumtum and the androgynos, who are able to make an erech vow but cannot themselves be the subject of one. Why not compare the nochri to them instead? Rabbi Meir answers that a comparison to three categories of people carries more weight than a comparison to two.
"Rabbi Yehudah omer: ma'arich aval lo ne'erach." Rabbi Yehudah rules the opposite way. A nochri is capable of declaring an erech vow and thereby obligating himself to pay the fixed sum set for some Jew, yet no valid erech vow can be made concerning him, not even by a Jew. Why? Because the Torah's erech works through brackets, set amounts determined by age and gender, and Scripture laid out those brackets with respect to Jews only.
Counting the Categories
Rabbi Yehudah therefore lines the nochri up with the tumtum and the androgynos rather than with the cheresh, shoteh and katan, and he answers Rabbi Meir's counting argument head on. The cheresh, shoteh and katan are not really three separate categories at all. All three are disqualified for one and the same reason: they lack da'at, the mental capacity that a vow requires. Functionally they are a single group.
A tumtum and an androgynos, on the other hand, are fully in possession of da'at, and they really do form two independent categories, since the doubt surrounding each of them is a different sort of doubt. In the case of the tumtum, the organs are concealed by a covering of skin, so we have no way of knowing which he has. In the case of the androgynos, both sets are present, and the question is whether we relate to him as a man or as a woman. Two distinct uncertainties yield two distinct categories, and on that count, Rabbi Yehudah maintains, the comparison tips toward their side.
Where Both Agree
"Zeh vazeh modim shenodrin venidarin." On vows of damim, actual value, Rabbi Meir and Rabbi Yehudah stand together. A non-Jew may pledge the market value of another person, and his own market value may be pledged by someone else. The exclusion drawn from the verse applies to erech alone and does not spill over into other forms of vowing. The Torah grants a non-Jew the ability to vow in general, as we see from the laws permitting him to bring certain korbanot, and it is only with regard to erech that Scripture limits his participation.