We have discussed previously that certain melachot are permitted on Yom Tov for ochel nefesh – food. The Mishnah (2:5) records a debate regarding heating water for washing one's hands and feet. Beit Shammai forbid the practice unless the water is fit for drinking, whereas Beit Hillel rule leniently. We shall attempt to understand this debate.
The Bartenura explains that for Beit Shammai kindling a fire is only permitted for food and not for washing. Beit Hillel however maintain that since the melacha was permitted for food, it is permitted for other benefits - mitoch she'hutra le'tzorech, hutra nami she'lo letzorach (mitoch for short).
Given that Beit Shammai and Beit Hillel argue about the principle of mitoch, the Tosfot Yom Tov explains that according to Beit Shammai, it is not enough for the water to be drinkable. One must drink from that hot water using the remainder for washing their hands and feet, since the heating is only permitted for consumption.
The Tosfot R' Akiva Eiger comments whether the water is drinkable is not relevant to mitoch. Instead it is more relevant to the principle of "ho'il" (that we discussed in connection to eiruv tavshilin). Recall that according to Raba, even though on a biblical level one is not allowed to cook from Yom Tov to Shabbat, nevertheless since (ho'il) it is possible for guests to come during the remainder of the day, cooking at the time is not biblical prohibited. That being the case, since Beit Shammai require the water to be drinkable, it implies that they maintain the principle of ho'il. Consequently, it is not necessary that one drink from the heated water since the ho'il alone permits the melacha.
The Tosfot R' Akiva Eiger however cites the Rashba who explains that since Beit Shammai do not maintain the principle of mitoch, they would certainly disagree with ho'il. He however cites the Tosfot that states explicitly that Beit Shammai maintains the principle of ho'il. The Gemara in Pesachim (46b) records the debate regarding ho'il with Raba maintaining the principle and Rav Chisda rejecting it. The Gemara (47b) cites a Beraita that accords with Beit Shammai as a difficulty for Raba. The Beraita discuss the prohibitions that are violated if one cooks gid ha'nasheh in milk on Yom Tov. One of those listed is kindling. The Gemara comments that according to Raba since one could use the fire for a permissible use, they should not be liable for that prohibition. The Tosfot concludes that based on the argument, according to Raba who maintains the principle of ho'il, he understands that it is universally accepted. Consequently, we return to the original question, according to Beit Shammai, we can suggest that the reason why it is permitted when the water is drinkable is based on the principle of ho'il and he would not require the person drink from that water. The Tosfot R' Akiva Eiger leaves the matter requiring further analysis.
The Tifferet Yisrael attempts to defend the position of the Rashba. He explains that there are different types of ho'il and the Tosfot differentiate between a ho'il that is shechi'ach (common) and one that is not. The ho'il the relies on the possibility that guests might arrive is weak. It depends on the likelihood of the third party arriving. That type of ho'il, the type that is our Mishnah, is the type that the Tosfot reject. It is that weaker type that the Rashba maintains that if Beit Shammai reject mitoch they would certainly reject ho'il. This however is different to the ho'il discussed in Pesachim. With respect to kindling, the ho'il used (one could use the kindled fire for cooking) is immediately available. It is that type of ho'il that the Beit Shammai would accept. Consequently, since Beit Shammai would reject ho'il in our case, the only way he could heat the water is if it was for consumption, and he drank some water as the Tosfot Yom Tov contends.
In defence of the Tosfot R' Akiva Eiger, Rashi's explanation of our Mishnah presents of difficulty for the Tifferet Yisrael. When explaining the position of Beit Shammai, Rashi does not mention the melacha of cooking, but rather the melacha of havarah – kindling! Therefore, even if we accept the distinction of the Tifferet Yisrael, both cases are dealing with kindling – both cases are dealing with the same "category" of ho'il! Consequently, the question of the R' Akiva Eiger stands. Beit Shammai would indeed maintain ho'il in our case!
The Sefat Emet however answers that even according to the opinions that maintain the principle of ho'il, that does not mean that they can be relied on le'chatchila. In other words, the Gemara in Pesachim was explaining that based on ho'il, one will no longer have violated a biblical prohibition. Granted that that may be the case, one cannot rely on ho'il to permit any practice from the outset. Consequently, it explains why Beit Shammai does not rely on ho'il and only allows heating the water if the person will drink some of it.
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