The Big One,
I don’t think you understood my point in the comments on that section. My point was not that it was my personal assessment that the Jewish murderers should be executed. Such a psak is way, way above my Torah knowledge and experience.
Rather my point was that people should not be quick to criticize the posek that did take that position because such a concept, of executing Jews for high-profile serious crimes against non-Jews, even when normal halacha would not allow such an execution is found in Chazal.
The case that I pointed to, was the Gemara in Yevamos 79a in which David HaMelech executed the children/grandchildren of Shaul HaMelech for Shaul’s crimes against the Givonim. This was done without eidim and hasra and, more strikingly, in violation of a mefurash pasuk that children cannot be killed for the crimes of their father. Still the Gemara says ???? ????? ???
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Rashi says that the Chillul Hashem here is that if David does not punish the children of Shaul the nations of the world will criticize Klal Yisroel for not allowing the Givonim their justice.
This Gemara only provides support for such executions when the alternative is widespread, among the nations of the world, Chillul Hashem. Not for every Chillul Hashem. So yes, the fact that it is “news” informs this position and the fact that the Gentiles will perceive a lack of severe punishment as an indication that Jews discriminate severely against non-Jews.
I think that Israel should pass a law allowing for the death penalty for terrorism. If there is a way under the law on the books to execute the terrorists that murder the three Jewish boys, I would support that as well.
On your last question, are you referring to execution by a Bais Din or the death penalty in secular court? Bais Din cannot judge capital crimes in the absence of the lishkas hagazis and the Sanhedrin. So I would certainly not support such a position as it is in violation of the Torah.
If you are referring to the death penalty in secular court, I would not support that either because such executions would not work to stop mishkav zachor and because doing so would cause, not prevent, a worldwide Chillul Hashem.