Gemara

Question (Ravina): If (on Shabbos, two animals were available for a Chatas Tzibur, and after slaughtering the second,) the first was found to be lean in the intestines, what is the law?

If it depends on intent, he is liable. (Since he did not know that the first is lean, he had no permission to slaughter);

If it depends on the action done, he is exempt (since it was a Mitzvah to slaughter the second.)

Version #1 - Answer (Rav Ashi): Rabah and Rava agree that in such a case he is liable!

If (on Shabbos) Reuven heard that a child was drowning in the sea and he set a trap to catch fish and fish were trapped, he is liable;

(Rabah): If the child was saved in the trap and fish were trapped, he is exempt;

(Rava): He is liable.

Rabah assumes that since he heard that a child was drowning, surely he also intended to save the child. Had he not heard, all agree that he is liable.

Version #2 - Answer (Rav Ashi): Rabah and Rava argue about your question:

If Reuven heard that a child was drowning and he set a trap to catch fish and fish were trapped, he is liable;

(Rabah): If the child was saved and fish were trapped, he is exempt;

(Rava): He is liable.

Rabah exempts, for he says that it depends on the action done. (He saved the child. This is a Mitzvah). Rava is Mechayev. He says that it depends on intent.

Yoma 84b (Beraisa): We oversee Piku'ach Nefesh on Shabbos. In all the following cases, it is praiseworthy to be zealous. One need not ask permission from Beis Din.

If one saw a child who fell into the sea, he sets a trap to lift him, even if he traps fish.

If a child fell into a pit, he uproots a ring (of earth around the pit) and raises him, even though he fixes a step (to enter and leave the pit).

If a door was locked in front of a child, he breaks it and removes the child, even though he intends to break off boards (or chips) that he needs.

One may extinguish or block a (dangerous) fire, even though he lowers coals (which he can use after Shabbos).

We needed to teach all of these cases... One might have thought that when a door was locked in front of a child, it suffices to jingle nuts (on the other side), and this will assuage the child.

Nazir 23a (Mishnah): If a woman accepted Nezirus, and she did not know that her husband annulled her Nezirus, and she drank wine or became Teme'ah, she does not receive 40 lashes;

R. Yehudah says, she receives lashes mid'Rabanan.

Rishonim

Rif and Rosh (Shabbos 40a and Yoma 8:15) If a door was locked in front of a child, one breaks it and removes the child, even though he breaks off boards (or chips) that he needs.

Ran (DH v'Af): In every clause it says 'he need not ask Reshus from Beis Din' to teach that even though he also does a Melachah that he needs, it is permitted.

Ran (Shabbos 38a DH Ha): The Rashba learns from the Yerushalmi that if one needs to lock his house, he may intend also to trap a deer inside. This is astounding. I say that even if he does not intend, if he knows that a deer will be trapped it is forbidden. We say that R. Shimon agrees about a Pesik Reishei (an inevitable consequence)! Rather, the Yerushalmi means that if one locked his house, and afterwards found out that he trapped a deer, he need not open his house. The Yerushalmi then discusses Piku'ach Nefesh, even though it is different. There, one may intend for Melachah along with saving the life. This is because the Melachah (of saving) is a Mitzvah. Therefore, Chachamim permitted to intend for a Melachah of Reshus with it, lest one refrain from his Chiyuv of Piku'ach Nefesh. Regarding the deer, the Yerushalmi said 'he intended to lock, and locked it, and the deer.' It said differently about Piku'ach Nefesh, i.e. 'he intended to raise the child and to catch fish.'

Rambam (Hilchos Shabbos 2:16): We oversee Piku'ach Nefesh on Shabbos. One need not ask permission from Beis Din. One who is prompt to save a life is praiseworthy. If one saw a child who fell into the sea, he sets a trap to lift him, even though he also traps fish. If one heard that a child fell into the sea, and he set a trap to lift him, and he only trapped fish, he is totally exempt.

Lechem Mishneh: The Gemara did not mention this case. The Rambam says so from reasoning. Since he set his trap to raise the child, he did a Mitzvah. Why should it matter that he caught fish? He is totally exempt.

Rambam (ibid.): If he intended to trap fish, and raised the child and caught fish, he is exempt. Even if he had not heard that a child fell in, since he raised the child with the fish, he is exempt.

Ra'avad: Rabah and Rava argue about this in Menachos. Rava is lenient. He says that it depends on his action. The Rambam rules like Rava, even though he is a Talmid with respect to Rabah.

Magid Mishneh: In our texts, Rabah is lenient. Even according to the Ra'avad's text, one can say that the Halachah follows Rava, for he is Basra. We say that the Halachah does not follow a Talmid against his Rashi only when they argued in person, e.g. 'Rava said to Rabah...' When they argue like Stam differing opinions, perhaps the Halachah follows Basra. The Rashba says so.

Or Some'ach: In this case, he is lashed mid'Rabanan. The Rambam (Hilchos Nedarim 12:18) says so about one who did not know that her father annulled her vow. Since she intended to transgress, she is lashed mid'Rabanan. This is like R. Yehudah (Nazir 23a).

Rambam (2:17): If a door was locked in front of a child, one breaks it and removes the child, even though he breaks off pieces useful for Melachah.

Lechem Mishneh: Only in this case, the Gemara mentioned that he intends (for benefit while saving). Why did the Rambam omit this? It seems that if he intends, surely it is forbidden. The Rambam explains that the Gemara means that his intent is evident from his action. To save the child, it would suffice to break the door. Surely, he broke it into many pieces for the sake of Melachah. Even so, it is permitted. In the other cases, his intent could not be evident through his actions.

Rambam (Hilchos Nedarim 12:18): If a girl did not know that her father annulled her vow (and intended to transgress it), since she intended to transgress, she is lashed mid'Rabanan.

Mishneh l'Melech: This is like R. Yehudah. Tosfos (Nezirus 21b DH l'Olam) says that the first Tana argues, and holds that if one did not transgress, he is not lashed mid'Rabanan. Presumably the Halachah follows the first Tana.

Eshel Avraham (OC 329:8): If one did not know that a child fell in the river, and he intended to trap fish, and he also saved the child, according to Tosfos he did not transgress. He did a Mitzvah. The Rambam would agree. This is relevant to testimony. One who is liable lashes mid'Rabanan is Pasul for testimony.

Me'iri (84b DH Mefakchin): The Yerushalmi says that it is permitted to intend to save and catch fish. This means that one who does so is exempt. Surely one may not intend also for Isur!

Mordechai (Shabbos 463): Regarding all the cases brought, the Gemara knew when there is danger, e.g. lighting a Ner and breaking a door for a child. We are not as expert about eating as a sick person. If he says that there is no danger if he does not eat (on Yom Kipur), one may not feed him. the same applies to Chilul Shabbos.

Poskim

Shulchan Aruch (OC 328:13): One who is zealous to be Mechalel Shabbos for a mortal danger, this is praiseworthy, even if he fixes with this another matter. E.g. he set a trap to save a child who fell into the river, and it also trapped fish. The same applies to all similar cases.

Magen Avraham (8): If a door was locked in front of a child, one breaks it and removes the child, even though he breaks off wood useful for Melachah, for perhaps the child will be frightened and die. We do not say that he can jingle nuts from the outside. This is from the Gemara. Hagahos Mordechai connotes that one should not be lenient about this.

Rebuttal (Eliyahu Rabah 13): (The Mordechai is not stringent.) Also R. Yerucham permits.

Eshel Avraham: If he intended, it is forbidden, but he is exempt, even though he could have merely broken in a destructive way (which is always exempt on Shabbos, and he broke in a constructive way). This requires investigation, for Shabbos is Nidcheh (for Piku'ach Nefesh. It is not totally permitted!) It seems that he is exempt because his primary intent is to save the child.

Machatzis ha'Shekel (DH v'Lo): It seems that if he has an axe to break the door, he may not break off pieces of wood.

Tosefes Yom ha'Kipurim (84 DH Ra'ah): Rava obligates one who intended for the child and for fish. The Beraisa in Yoma exempts! He must say that he is exempt if he intended primarily for the child, and liable if he intended primarily for the fish. Alternatively, we do not permit to intend for both. If he did, Rabah and Rava argue about whether he is liable.

Birkei Yosef (6): Really, the Beraisa in Yoma did not explicitly say that he (intentionally) traps fish (rather, fish got caught). The Gemara explained it to mean that he intended to trap, to explain the Chidush that he need not ask Reshus. Rava can explain differently. I agree with the first answer of Tosefes Yom ha'Kipurim, that it depends on his primary intent. His second answer, which forbids intent for both, is difficult. The Ran permits this! The Lechem Mishneh says that the Rambam forbids. Since the Yerushalmi permits, and there is no proof from the Bavli, why should he forbid?

Mishnah Berurah (38): We permit even if the one who saves needs the ring, boards or chips, because he does not intend for this.

Sha'ar ha'Tziyon (17): Some Rishonim are lenient. R. Akiva Eiger brings the Ran, who is lenient. Bahag's text in Yoma permits intent (for benefit) in every case. The Roke'ach says that even if he intends also for Melachah, this is praiseworthy. The text of the Rif and Rosh was 'even though he breaks chips.' This is why the Rambam did not mention intent. (The Lechem Mishneh missed this.) R. Yerucham says that he does not intend for Melachah, but in any case he needed the chips. Also the Me'iri forbids intent for Melachah. Clearly, all forbid doing an extra action for the sake of Melachah.