Judaism has two "Torahs" or Torot The Written Torah and the Oral Torah The Written Torah is quite in favor of capital punishment The Oral Law is largely opposed - though not entirely.

What is certain is that Talmudic Judaism opposs an "eye for an eye" in a physical sense. The best understanding is this is a legal idiom denoting "just compensation" The Pentateuch has numerous capital offenses. While Talmudic Law makes it almost impossible to implement. The beauty of this tension is that Judaism is reluctant to execute, BUT it does reserve this right. For example, the State of Israel has banned capital punishment but had no compunctions executing the evil Adolf Eichmann.

This, in my opinion, is the paradigm for the Torah approach. That is many crimes deserve capital punishment from a sense of rooting out evil. Or - from a spiritual perspective - many crimes are deemed worthy of capital punishment, as an act of treason towards Our Heavenly Ruler. However, we humans are too imperfect to use this authority, and so we reserve it for only the most extraordinary cases. It must meet several severely limiting criteria. Thus, from even a Talmudic perspective, Nuerenberg,and similar major crimes would justify capital punishment.

Shalom
RRW

Sources

Mishnah Makkot 1:10

1) A sanhedrin that executes once in seven years, is called murderous.

One) Rabbi Eliezer b. Azariah Says: once in seventy years.

Two) Rabbi Tarfon and Rabbi Akiva say: “Had we been members of a sanhedrin, no person would ever be put to death.

Three) Rabban Shimon ben Gamaliel remarked: “They would also multiply murderers in Israel.”

Section three: This famous piece of mishnah testifies to some of the Rabbis’ deep hesitations with regards to the death penalty. As we have seen throughout tractate Sanhedrin and tractate Makkoth, convicting a person of a capital crime is no easy matter. The person must be warned beforehand and then the crime has to be explicitly witnessed by two valid witnesses. Therefore, the first opinion in our mishnah, concludes that a court that executes once every seven years is a murderous court. Since the laws of testimony are so strict, any court that executes more often than this is assumed to be illegally suspending the laws and is therefore, in a sense, engaging in murder itself. Rabbi Elezar ben Azariah says that once in seventy years already makes a court murderous. Rabbi Tarfon and Rabbi Akiva brag that had they been on a sanhedrin no one would have ever been executed. At the end of the mishnah Rabban Shimon ben Gamaliel, the political leader of the Jews at the time, notes a sound of caution. The Rabbinic tendency to be overly lenient on executing murderers can take its toll on society. In his opinion the attitudes of the other Rabbis cause the numbers of murderers to rise.

 One of the first things the Torah tells us about human beings is that we are created in God’s image, b’tzelem elohim. This concept is not to be understood in a physical manner, but in a more abstract way. We share with our Creator something unique that defines us as humans and distinguish us from the rest of the creatures on the planet. 

Some feel that the current Jewish response to the death penalty mirrors the liberal trends that the majority of Jews have tended to follow in our society.  In reality, the admittedly liberal Jewish approach to punishment for capital offenses dates back to the time of the Talmud.

I am glad you asked about how “Jewish” values can inform us regarding the death penalty.  If one read only the Hebrew Bible, the “eye for an eye” phrasing of the “lex talionis”, or the principle of retributive justice that appears three times in the Torah (Exodus 21:22, Leviticus 24:19, and Deuteronomy 19:21) is quite clear, and there’d be no question about it.  However, those who follow Judaism – as opposed to ancient Israelite religion – also would have been bound by the decisions of the Talmudic scholars who refused to justify the death penalty except in very rare circumstances.

The Mishnah, in Makkot 1:10, puts forth the following oft quoted reference to the death penalty.  “The Sanhedrin who executes a person once in seven years, is considered ‘pernicious’ (often translated “cruel”).  Rabbi Eliezar ben Azariah said: Even one who does so once in seventy years is considered such.  Both Rabbi Tarphon and Rabbi Akiba said: If we were among the members of the Sanhedrin, a death sentence would never occur.  To which Rabbi Shimon ben Gamaliel said: Such scholars would only increase bloodshed in Israel.”

Those Jews who favor a stiff death penalty based on non-Jewish thinking will – justifiably – point to the statement above of Rabbi Gamaliel to confirm Judaism’s acceptance of the death penalty.  However, the tradition when reading rabbinic texts is that the anonymous ruling is the one that stands (there are exceptions, but this is not one of them), and that those rulings that have authorities cited represent the minority viewpoints.

So if one were to read this section of Mishnah one might conclude that where the death penalty is not favored, it certainly is not prohibited by any means.  And this is probably the correct reading.

The system of justice of the modern state of Israel does, for example, permit the death penalty, but for only one offense: a “crime against humanity”, and has only carried out one such sentence in its 62 year history, that of Adolph Eichmann in 1962.  All other capital offenders in Israel have prison terms as punishment, even those convicted of terrorism.

By the way, the Rabbis of the Talmud recognized early on the futility of carrying out an “eye for an eye” kind of justice.  They realized that this was not true justice, so I might humbly disagree with the premise in your question.  If one disabled a fellow’s eye or hand, the Rabbis thought, there was no use or purpose of disabling the perpetrator’s eye or hand.  Rather, they thought, there should be some kind of compensation for such an injury, and this usually took the form of money or bartered goods.  So even in ancient Israel, there was rarely the literal punishment of “an eye for an eye”.