Suppose there is an halachically prescribed, commonly-practiced action, which has been demonstrated scientifically to lead to death of the action's object and/or subject with a certain low probability (assume that this probability cannot be further reduced).

What does the probability have to be for us to stop performing that action?

Is the probability even relevant?

Does the answer depend on whether the action is d'Rabanan, halacha l'Moshe mi'Sinaj, or d'Oraita?

P.S.: This is not an "anti-" or "pro-something" question. This is a sincere attempt to better understand the halachic process. Please abstain from assigning a specific mitzvah to the question, as there isn't one. Thanks.

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    Actual mitzva de-oraita this could apply to: fighting in a milchemet mitzva. – Isaac Moses Jul 8 '13 at 21:31
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    @Isaac that is very likely a unique case with its own rules. – Double AA Jul 9 '13 at 4:57
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    Another mitzva d'Oray'sa this could apply to: mila (just the cutting). – msh210 Jul 9 '13 at 7:03
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    Also fasting on yom kippur. – Double AA Jul 9 '13 at 7:06
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    Heck, if someone did a scientific study on almost any mitzva, this could apply. There must be some low probability of dying from blowing shofar, after all, or from flapping at a bird to take her chicks. cc @Daniel – msh210 Jul 9 '13 at 7:08

(For torah mitzvot)

one. the mitzva that all males must leave their homes and go to Jerusalem 3 times a year (during the first temple era) leaving all towns and borders undefended seems to be in this category.

from a military perspective this is reckless and suicidal (long term high probability of danger) and would leaving them vulnerable to being encircled and easily defeated. Turns out that no foreign nation ever came up to take the land of the Jews during their festivals prior to the destruction of Jerusalem 400+ years later.

two. Likewise, the laws of shmita and yovel where every single plot of land in the entire country be left unworked simultaneously for 2+years (in yovel) seems to be dangerous practice and could lead to a famine.

conclusion: if the mitzva is dangerous and there's no other way to do it, and no built in exemption to the mitzva then the danger is not a deciding factor and you must do it.

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    I find your assertion that all cases of Pikuach Nefesh exempting one from a Mitzva to be individual built-in exceptions to be unsupported and unlikely. – Double AA Jul 9 '13 at 8:02
  • I'm not addressing the question whether pikuach nefesh is a stand alone exemption or a built in exemption. the point here is that if a mitzva has no way out like the two examples above (which are not like bris mila which has an exemption) then you must do it even if its dangerous. – ray Jul 9 '13 at 8:17
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    youre doing another thing though: you are extrapolating to all of torah from your two examples. – Double AA Jul 9 '13 at 9:03
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    Definitely not! Especially when both have explicit promises in the pasuk guaranteeing the Jews' safety. כל שני כתובים הבאים כאחד אין מלמדין – Double AA Jul 9 '13 at 9:40
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    If your answer is "God is in charge and just do what you are supposed to", then how do you explain the principle of Pikuach Nefesh? How do you know those who didn't work on Shabbat didn't survive because of those who did and had money to contribute to communal organizations? – Double AA Jul 9 '13 at 10:23

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