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Answer:The main issue involved in this question is the definition of tochein (grinding). While the classic case is grinding wheat into grain flour, the gemara (Shabbat 74b) states that it is forbidden even to cut up vegetables into fine pieces. In the past [Mishpatim 5772, regarding making guacamole], we cited different opinions as to whether the Rashba’s leniency (Shut IV:75) that one may do the above soon before eating applies only when he leaves the vegetables in "slightly big pieces." We also cited Rav Moshe Feinstein’s opinion (Igrot Moshe, Orach Chayim IV:74) regarding mashing bananas that this is not grinding, as one does not create new fine particles, but just mashes the food into a softer form. On the other hand, the Chazon Ish (OC 57) rejected this distinction.
Skipping other possible leniencies mentioned in that context that can be applied to the potatoes you discussed, let us get straight to the leniency that applies to your potatoes that did not apply to guacamole. The poskim (see Rama, OC 321:19) understood from the Rambam (Shabbat 21:13) that one may take a food that was already made soft by cooking and further soften it by means of mashing. The Chazon Ish (OC 58:9) explains that the softness created by the cooking causes the additional mashing to be too trivial to be forbidden by the melacha of tochein. Contemporary poskim (Shemirat Shabbat K’hilchata 6:9; Orchot Shabbat 5:9) discuss your explicit case and say that it is permitted to mash soft, well-boiled potatoes on Shabbat for this reason.
However, the bad news is that you violated a rule of this leniency. That is that even when tochein does not apply, it is forbidden to use a utensil that is set aside for the mincing or crushing of food items (Shulchan Aruch, OC 321:10). A hand-masher seems to fit that bill; you should have used a fork. This stringency applies even to a food to which tochein does not even apply, such as cheese (ibid.), and even if one did the mincing right before the use (Mishna Berura 321:36; Shemirat Shabbat K’hilchata 6:2). The reason for this prohibition is that using such a utensil is uvdin d’chol (a weekday-like activity) (see Mishna Berura ibid.).
On the other hand, as far as what to with the potatoes after-the-fact, you were more stringent than halacha mandates. There is a broad machloket among the Tannaim as to the extent that the result of the violation of a melacha is forbidden, and there are too many opinions and permutations to address here (see Ketubot 34a and Shulchan Aruch, OC 318:1). We will address your case, where the violation was done b’shogeg (by mistake, e.g., not knowing the halacha). The Shulchan Aruch (ibid.) rules that it is forbidden to benefit from the work on Shabbat and permitted right after Shabbat. (There are opinions that can be relied upon if needed to be lenient even on Shabbat (Mishna Berura 318:7).) This indeed seems to fit along with your decision not to use the potatoes and your question. However, the Gra (ad loc.), accepted as halacha by the Mishna Berura (318:3) and many others, says that if that which was done by mistake was only a rabbinic prohibition, then there is no prohibition on the result after-the-fact. (An important exception to this leniency is if one left food on the fire on Shabbat without the proper precautions to avoid mistakes- see Shulchan Aruch, OC 253:2). Not only does the Gra’s leniency apply fully to this case, but it is further magnified by the fact that the rabbinical violation of uvdin d’chol is a weaker rabbinical prohibition than the average one. Therefore, despite your mistaken use of the hand-masher, you could have eaten the mashed potatoes even on Shabbat.
Bemare Habazak - Rabbis Questions (657)
Various Rabbis
46 - Hamapil for Those Who Take a Long Time to Fall Asleep
47 - Using a Hand Masher for Cooked Vegetables
48 - Removing a Licked Candy from Amongst Clean Ones on Shabbat
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