Masechet Beitzah focuses primarily on Yom Tov. We have learnt that, unlike Shabbat, the Torah permits certain melachot required for food on Yom Tov (ochel nefesh). The masechet addresses the scope of that permit. One melacha discussed that catches the Rishonim by surprise is the grinding.
The Mishnah (1:7) records the following debate. Beit Shamma maintains that spices can be pound with a pestle made of wood while salt can only be ground using a jug. The Bartenura explains that since the spices cannot be ground in advance, a small change (shinui) from the regular method is sufficient. With respect to salt however, since the flavour would not diminish if it were ground before Yom Tov, a greater shinui is required. Beit Hillel however maintains that for spices, no shinui is required and a stone pestle may be used, while for salt, a small shinui, using a wood pestle, is sufficient.
The difficulty raised with this Mishnah is that the pounding of spices is the derivative of the melacha of tochen (grinding) and one of the melachot that are forbidden on Yom Tov. The Ran cites the Yerushalim that it is prohibited on a biblical level. The Torah places the instruction to guard the matzot and the permission to perform the melacha for ochel nefesh near one another. The Yerushalmi therefore learns that only those melchot that are performed from the time one needs to guard the matzot are permitted; from kneading onward. How do we understand this Mishnah? How can a shinui help to permit a biblical prohibition? Furthermore, even according to those opinions that understand that grinding on Yom Tov is prohibited on a Rabbinic level, it would not be permitted even with a shinui if the melacha could have been performed prior to Yom Tov.
The Pnei Yehoshua initially suggest that the pounding of spices is different. For the melacha of grinding in general, for wheat or dyes, the raw products are not usable until they are ground and then mixed with water. Spices however are used for adding flavour and that purpose can be achieved prior to their pounding. Consequently, the action in our Mishnah is not really a melacha.
The Pnei Yehoshua however rejects this suggestions since most poskim agree that if one chopped their vegetables finely, they would be violating the biblical prohibition of performing the melacha of grinding.
The Pnei Yehoshua therefore reverts to the explanation of the Ran (in the third perek) that the melachot that were prohibited despite the justification of ochel nefesh are those that are generally performed and left for a while. This would include picking a fruit from the tree, despite wanting to eat it immediately, since we are focusing on the action itself. When pounding spices, the result of the melacha is used immediately one's food. He also cites the Raavad who makes the same distinction but adds that it is the activities in the former category that would be performed by an aved for his master. Since pounding spices to added to one's food immediately does not resemble avdut, the Chachamim were lenient.1
1 The Maggid Mishnah (Yom Tov 1:5) however explains that they we are lenient with those things that were machshir food, improved food and not eaten on their own. The Lechem Mishnah (3:12) asks that the logic appears to be reversed. Why would the machshir be more lenient that with ochel nefesh itself. The Chatam Sofer (Beitzah 14a) explains that the intention is not that the spices are a machshir alone. The spices are ochel nefesh themselves and they act as a machshir for other ochel nefesh. For ochel nefesh we explained that melechot that are for a number of days (harvesting, grinding, etc) are not permitted. We find that for machshirin, even those melachot are permitted (in certain ways - see 3:7). Consequently since this is a machshir and ochel it affords further leniencies
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