As distributed by the RCA
Every legal system has a principle that the ends justify the means. The question however is, which ends and which means. If a woman is in labor and her husband is rushing her to the hospital at three o’clock in the morning on the highways where there are no other cars, the police will radio ahead to let the husband pass through all the red lights so that the woman would arrive in the hospital on time. The halacha considers the mitzvah of “v’chai bohem” (the mitzvah of pikuach nefoshosh) of supreme importance and it takes precedence over almost all of the other mitzvos in the Torah. Sick or elderly people whose life might possibly be endangered by fasting on Yom Kippur are required to eat. Likewise, if one’s life may be in danger we all know that we must violate Shabbos by driving to the hospital even if there is only a sefek sefeka of a sakonah and even though driving a car on Shabbos constitutes a melocha d’oraisa.
The halacha however, has three exceptions to the rule where pikuach nefesh does not take precedence. One of the three is murder. We may not kill one person in order to save the life of another person. We may not make calculations that the life of one individual is more valuable than the life of another individual (see Mishnah end of seventh chapter of Oholos and see Gemorah Pesochim 25B). Even if one individual is on a respirator and his chances for survival are very slim, and even if he survives he will not live that many added years, and another person is in need of the respirator whose chances of survival are much better and will probably live many more years, the halacha declares that we have no right to make such calculations. Even if the individual on the respirator is a goses, the din is still the same. One who kills a goses b’yidei shomayim, is given the death penalty (Sanhedrin 78A).
The Rash in his commentary on the last Mishna in the eighth chapter of Terumos, quotes a passage from the Talmud Yerushalmi which has been codified both by the Rambam (Yisodei Ha’torah 5:5) and by the Shulchan Aruch ( Yoreh Deah 157:1 in the Ramoh). The Yerushalmi states that if murderers surround and capture the city and threaten to kill all the people in the city unless they will hand over on person whom they will kill, this is not permitted. The Kesef Mishna in his commentary on the Rambam points out that this Yerushalmi is adding a chidush that even if the situation is such that at the end of the day, we will be saving more lives by killing the one person, the halacha still forbids this act of murder. Even if the murder is only in the form of Gram R’zicha, which would not deserve a death penalty, the halacha still does not permit it.