The Mishnah (3:9) teaches that if during a fast day decreed due a lack of rain it starts raining, then depending when it begins to rain, the fast can be broken. According to the first opinion, it is only if begins to rain prior to sunrise, whereas according to R' Eliezer the cut-off is midday.
The Tifferet Yisrael notes that our Mishnah appears to contradict the ruling in the Gemara (Taanit 10b). There the Gemara rules that if one is fasting for someone who is unwell, and the person recovers, the fast must nevertheless be completed. How do we explain the Gemara's ruling considering our Mishnah?
The Tifferet Yisrael explains that there is a difference between a public fast day and a private fast. Regarding a public fast, it is considered as if Beit Din stipulates that if it rains, then fast will end early. Regarding a private fast, even though it is clear that the only reason the individual is fasting is due to this misfortune, since it was not stipulated explicitly, it is considered "devarim she'balev" and insignificant in this context. The Aruch HaShulchan (O.C. 569) adds that it follows, that if the individual did articulate at the time they took on the fast that it would end if the trouble ended, then the stipulation is effective.
The Tifferet Yisrael's explanation is the answer of the Rosh. Before the Rosh however provides this answer, he first cites this question and a different answer in the name of the Raavad. The Raavad answers that the cases are different. In our Mishnah the concern is that it has not yet rained. Once an adequate amount falls, there is no longer a need for fasting. In the case of other troubles, after the reprieve, one still needs to pray for divine mercy that it will not return. The Beit Yosef cites the Ran who, based on the Raavad's logic, maintains that not one would be required to complete all fasts that they committed to, and not just the one they are engaged in at that moment. The Rosh however finds the Raavad's explanation inadequate and therefore provides the distinction cited above.1
Rashi however appears to provide a different explanation as to why an individual must completed the fast even if the situation changes. He explains that stopping the fast early would be as if one is giving Hashem an ultimatum: "if this trouble passes I will fast, where as if not, I will not." The Tifferet Yisrael cites R' Yeshaya Pick who explains that the logic presented above appears to be reversed and Rashi instead should read that ultimatum is: "if the trouble passes I will not fast, but if it does I will".
The Tifferet Yisrael however wishes to preserve the reading of Rashi. Before explaining, he adds that Rashi maintains that if the person unfortunately dies because of the illness, the person fasting must still complete the fast(s). The Tifferet Yisrael questions the source of Rashi's position. He therefore explains that in the case where the person recovered, there is no need to explain why the fast must be completed. As we explained earlier, since the one fasting did not stipulate at the outset that he would stop if the person recovered, he must complete his vow. The situation that requires explaining is where the sick person passes away. In that case, one might think that it should be considered as if he accepted the fast in error.2 The Tifferet Yisrael however notes that in Rashi's explanation he does not say "if he is saved" (hitzil); instead the language of "avrah" is used ('passed'). In other words, if the person died and the one fasting stopped his fast, it would appears as though he was asserting that if trouble passes eventually, then he will happily fast, otherwise, if the person succumbs to illness, then he will not. The Tifferet Yisrael explains that such an approach is inappropriate as one needs to praise Hashem for both good and bad and accept Hashem's Will in all circumstance.
1 The Beit Yosef however also cites that Terumat HaDeshen who explains that if the tzibur fasted past midday and then heard that the matter was resolved already the day before, then they would be able to stop their fast. This is because since in reality, there was no reason to fast already from the outset, it is considered as though their acceptance of the fast was in error. The Beit Yosef writes that this would also be the law for an individual and in a similar situation they would not be required to complete the fast.
2 See the previous footnote which includes a case where we do consider it as if the vow as accepted in error.
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