Arachin, Chapter 5, Mishnah 3. This chapter continues to examine the exact wording a person uses when he makes a pledge to hekdesh, and how the placement of a single word can change the entire obligation. Here the Mishnah presents four formulations, two involving erech (the fixed value set by the Torah according to age and gender) and two involving damim (a person's actual market value), and it closes with a general rule that ties them all together.
Half of my erech
"Chatzi erki alai": "Half of my erech is upon me." He pledges half of his erech value, and that is exactly what he pays. Take a male of twenty five years old, whose erech according to the Torah is fifty shekalim. He pledged his erech and then cut it in half, so he gives twenty five shekalim to hekdesh.
The erech of half of me
"Erech chatzi alai": "The erech of half of me is upon me." Here he pays his full erech value. Notice the difference in what he has halved. In the first case he halved the sum of money; here he has halved himself, and then pledged the erech of that half.
The rule behind this was already established in the mishnah before: whenever a vow is attached to a limb or organ without which one cannot stay alive, it is treated as if the whole person had been pledged. There is no surviving with only half a body intact. So when he speaks of the erech of half of himself, his words reach his entire self, and the full fifty shekalim are due.
Half of my damim
"Chatzi damai alai": "Half of my value is upon me." He gives half of his value. Since this is a damim pledge rather than an erech pledge, we do not use the Torah's fixed table. We assess him as he actually is, according to what he would fetch were he sold as a slave in the market, and he pays half of that figure.
The damim of half of me
"Demei chatzi alai": "The value of half of me is upon me." He gives his full value. Once again he has divided his body rather than the money, and a person cannot survive on half a body. His words amount to pledging his whole self, so he owes his entire market value.
The general rule
"Zeh haklal": this is the principle that governs all such cases. "Davar shehaneshamah teluyah bo, noten demei kulo": one who pledges the value of a limb or organ upon which life depends gives his full value. Half a body clearly belongs in that category. Whoever pledges the value of half of himself has, in the language of vows, offered all of himself, and hekdesh collects accordingly.