Arachin, Chapter 5, Mishnah 2. This mishnah and the two after it map out the ways in which a pledge of market value (damim) parts company with a pledge of erech, the sum the Torah fixes according to age and gender. Mishnah 1 discussed a man who consecrated how much one of his limbs weighs. Now the subject shifts: our case is a man who consecrates to hekdesh how much one of his limbs is worth.
The mishnah begins with the declaration "Demei yadi alai" - "my arm's value rests upon me." He has committed the market price of that arm to the Temple treasury. And how is the figure arrived at? "Shamin oto kamah hu shaveh beyad vekamah hu shaveh belo yad" - the man himself is priced twice over: once as a slave who has that arm, and once as a slave who lacks it. Whatever separates the two prices is what hekdesh collects from him.
Where a Vow of Damim Is Stricter
"Zeh chomer bindarim mib'arachin" - here the damim pledge carries a severity that the erech pledge lacks. Had this man consecrated instead the erech of that same arm, his words would have attached to nothing whatsoever and he would owe not a coin. Because he consecrated its market price, however, the declaration holds him, and he must pay whatever that arm turns out to be worth.
The principle behind it: market value vows have a far wider reach. They can attach to almost anything that has a price. An erech vow, by contrast, must be made on a whole person; it cannot be pinned to one limb of the body.
Where a Vow of Erech Is Stricter
"Vechomer ba'arachin minedarim" - and in the opposite direction, arachin can be the stricter of the two, more stringent than nedarim, pledges made by market value. "Keitzad" - in what way?
"Ha'omer erki alai" - a man declares, "my erech rests upon me," binding himself to hand hekdesh the sum the Torah fixes for a person of his age, and then "vamet" - he dies with the pledge still unpaid. "Yitnu hayorshin": the obligation is charged against his estate, and those who inherit from him pay it.
"Demai alai vamet, lo yitnu hayorshin" - but had he said, "my market value rests upon me," and died before anyone assessed him, those who inherit owe nothing. Why? A damim commitment becomes an actual debt only once beit din prices the man and names a figure. A corpse cannot be priced, "she'ein damim lametim": there is no slave price attached to one who has died. No debt ever came into existence, so the heirs have nothing to discharge.
Here we see the reverse stringency. An erech obligation is automatic and objective, with no room to maneuver. The moment a person pronounces it, the fixed sum becomes a debt. A damim obligation is created only at the moment of assessment, and if death intervenes first, no debt was ever born.
Erech on a Single Limb
The mishnah now spells out the rule it relied on above, that erech does not attach to a part of the body. "Erech yadi" - one who consecrates the erech of one hand, or "erech ragli alai" - the erech of one foot, "lo amar kelum": his words are empty and accomplish nothing. The Torah binds an erech to a whole living person, never to some individual part of him.
"Erech roshi ve'erech kevedi alai, noten erech kulo" - by contrast, one who consecrates the erech of his head, or that of his liver, must pay the erech of his entire self.
"Zeh haklal: davar shehaneshamah teluyah bo, noten erech kulo" - this is the rule: anything upon which the soul depends carries the erech of the whole. A person cannot survive without his head or his liver, so pledging such a part is treated as though he pledged his entire body, and he pays his full erech.
But when he pledges the erech of a limb he could live without, such as an arm or a leg, the vow remains a vow on a limb alone. Individual limbs have no connection to the mechanism of arachin, the declaration does not take hold, and he owes nothing.