The death penalty does not fit under the commandment “You shall not murder.” I have understood that murder and killing are two different words in Hebrew, with the word “murder” being used in instances such as Cain and Abel, and when G-d is stating the punishments for such a crime. However, when G-d destroys Sodom and Gomorrah, for example, the word “kill” is used, not “murder”. If you could please explain the difference between the two, from the perspective of how the text differentiates, I would greatly appreciate it.
As in English there are two different words: “retzichah” for murder, and “harigah” for killing.
It is obvious that not all killing is murder, for the Bible itself imposes the death penalty for certain crimes! Jewish Law also says that if one sees person A about to murder person B, one is allowed to save B with lethal force—if necessary.
The modern death penalty is a complex issue, since the requirements are very different than those of Biblical law. Actually the Talmud says that a court that ordered the death penalty every seven years was called “murderous”—and one opinion says not seven, but seventy! I wouldn’t say the Bible comes down clearly on one side or the other, but in principle supports the concept that a death penalty is a valid detterent.