Gemara

(Rav): One who eats a k'Zayis of Sheratzim (rodents) is lashed. The Torah forbids "Achilas" Sheratzim, i.e. a k'Zayis.

Question (R. Yosi b'Rebbi Chanina's Beraisa): "V'Hivdaltem Bein ha'Behemah... v'Lo Seshaktzu Es Nafshoseichem... Hivdalti Lachem Letamei" begins with eating ("v'Lo Seshaktzu") and ends with Tum'ah. This teaches that just like k'Adashah (the volume of a lentil) is the Shi'ur of Tum'ah for Sheratzim, it is the Shi'ur (to be liable) for eating.

Answer: R. Yosi's teaches about a dead Sheretz. (It is Tamei; we equate eating to Tum'ah). Rav discusses a live Sheretz (which is Tahor).

R. Yochanan praised R. Yosi's teaching.

Question: A Mishnah teaches that a limb of any size is Tamei, and R. Yochanan taught that he is lashed only if he ate a k'Zayis!

Answer (Rava): The verse ("v'Hivdaltem... ") discusses Muvdalim (things that are different, i.e. the eight Sheratzim mentioned in the Torah that are Metamei).

Avodah Zarah 69a - Question: If a mouse fell into vinegar, what is the law?

Answer #1 (Rav Hillel): A case occurred, and Rav Kahana forbade the vinegar.

Rejection (Rav Ashi): He forbade because Imretutei (the mouse was decimated into tiny pieces; alternatively, the wool came off).

Answer #2: The Halachah is, whether a mouse fell into beer or vinegar, 60 times is needed, like (standard) Isurim of the Torah.

Makos 16b (Rabah bar Rav Huna): If one ground up nine ants and completed the quantity of a k'Zayis with a Chai (live or intact) ant, he is lashed five times for eating a Briyah (full creation) and once for eating a k'Zayis of Neveilah.

Yevamos 114b: Had the Torah taught only that one may not feed Sheratzim to minors, one might have thought that this is because the Isur applies to Mashehu (any amount).

Rishonim

Rosh (Chulin 7:35): A complete Briyah is not Batel, but if it was diced or part was cut off, it is not called a Briyah, and it is Batel in the majority. If one ground up nine ants and completed the quantity of a k'Zayis with a Chai ant, he is lashed six times. This shows that when they are diced, they are not considered a Briyah and a k'Zayis is required. Even though Ever Min ha'Chai of any size is Tamei, for eating one is lashed only for a k'Zayis. Eating is unlike Tum'ah. In a Teshuvah, the Rif said that for any kinds of Sheratzim found in a pot, whether they fell into hot or cold, if part was detached from the Sheretz, it forbids up to 60 times its volume, like other Torah Isurim. A Gaon was asked about a mouse that fell into oil of the Beis ha'Keneses. He answered that if the oil was hot, if there was more than 60 times the volume of the mouse, one may eat the oil, and all the more so one may burn it. If the oil was cold, one strains off the mouse and one may eat the oil; we do not require 60. Likewise, if part of a Chatichah ha'Re'uyah Lehiskaved fell off after it fell in a pot, it lost its importance and it is Batel like other Isurim. If Parech nuts and pomegranates of Badan are split, they can be Batel (Gitin 54b). A Tosefta teaches that a piece is not Batel in 1000 pieces, and it forbids the gravy if it is Nosen Ta'am. If it dissolved, it forbids if there is Nosen Ta'am. Therefore, if part was cut off any piece of the mixture, it is permitted and the others are forbidden.

Rashi (Avodah Zarah 69a DH Imretutei): The mouse was Imretutei, i.e. cut into small pieces. The Isur to eat is ka'Adashah, like its Tum'ah. We are concerned lest one swallow a piece of Sheretz with the vinegar.

Rebuttal (Ran Avodah Zarah 32b DH ha'Hu Imretutei): Indeed, in Me'ilah we say that one is liable for ka'Adashah of a Sheretz. However, why is this relevant? Even regarding other Isurim, one must be concerned for less than a k'Zayis, for we hold like R. Yochanan, who says that the Torah forbids Chetzi Shi'ur! Also, if this is the reason to be stringent, why did Rav Kahana forbid it? One can strain it! Rather, Imretutei means that the wool came off. Since we see that it delayed a long time (in the vinegar), we must be concerned lest the sharpness of the vinegar caused the mouse to give beneficial taste. Even though vinegar and beer are cold, since it delayed, this is pickling, which is like cooking.

Mordechai (Avodah Zarah 855): Ra'avan wrote that if a mouse fell into beer or vinegar, even though it improves it, it is Batel in 60, like other Isurim. This is if it is intact. If Imretutei, it is forbidden, lest one taste from it in ka'Adashah. If one strains it with a garment, it is permitted. There is no difference whether it is removed whole or in pieces, as long as all was removed.

Tosfos (Zevachim 72v DH v'Livatlu): Even though Ever Min ha'Chai is not Batel, in our Mishnah the mixture is not forbidden due to Ever Min ha'Chai, rather, due to a Chatas that must die or an ox sentenced to be stoned. Even if it is whole, it is not considered a Briyah, like a Nevelah, Chelev or blood. One is not liable for eating a whole Nevelah of a Tahor bird if there is less than a k'Zayis of meat. However, the Torah forbids a whole Tamei bird of any size. Likewise, Gid ha'Nasheh and Ever Min ha'Chai are Briyos. It is as if the Torah specified 'of any size.'

Tosfos (Makos 16b DH Risek): One ant was Chai, i.e. whole. Surely it was dead. If not, it would not join to a Shi'ur for Nevelah! Why must it be whole? One is liable for a k'Zayis of Sheratzim! It must be whole for the Isurim of Sheratzim, regarding which it does not say 'Achilah', to apply.

Tosfos (Makos 17a DH v'Rabanan): Anything that loses its name when it is cut, it is a Briyah. Sometimes a partial Nevelah is called Nevelah, but a Gid (ha'Nasheh) loses its name when it is cut.

Tosfos (Yevamos 114b DH Mishum): Rashi explains that the Isur of Sheratzim is Mashehu, i.e. ka'Adashah. This is wrong. In Me'ilah, it says that one is lashed for a k'Zayis! Also in Makos we say that the Shi'ur for ants is a k'Zayis. Rather, the Isur is Mashehu, i.e. one is lashed for an ant of any size, because it is a Briyah.

Gra (YD 104:6 LIkut): In Me'ilah we say oppositely! For Muvdalim, one is lashed for ka'Adashah! There is no proof from ants, for it is not Muvdalim. Perhaps Tosfos asks because the same verse (that forbids feeding minors) mentions "Kol Holech Al Gachon Ad Kol Marbeh...", which are not Muvdalim.

Poskim

Shulchan Aruch (YD 104:1): If a city mouse fell into beer or vinegar, it is a Safek whether it improves the taste. If it fell into cold beer or vinegar, if it was taken out intact, if it did not delay there 24 hours, it is permitted. If it fell into hot beer or vinegar, or even into cold but it delayed there 24 hours, whether it was taken out whole or cut into small pieces, and he can strain it so nothing will remain, or whether it totally dissolved and became liquid and no (solid) substance remained, it is permitted if there was 60 times as much as the mouse. If it was cut into small pieces, and one cannot strain it, e.g. the beer or vinegar is mixed with a thick food, all is forbidden and there is no Bitul. We are concerned lest he encounter a small amount of Isur unknowingly.

Beis Yosef (DH u'Mah she'Chasav v'Im): The Tur permits if it was totally dissolved, for if any substance remained, even ka'Adashah, one is liable for a Sheretz of this size. Even less than ka'Adashah is forbidden, for the Torah forbids Chetzi Shi'ur.

Rema: Only regarding a Sheretz we are concerned lest there is a piece that cannot be removed. Regarding other Isurim, we are not concerned.

Gra (6): Rashi says that the mouse was cut into small pieces. The Isur to eat is ka'Adashah, like its Tum'ah, like it says in Me'ilah. Toras ha'Bayis and the Ran challenged Rashi, because the Torah forbids Chetzi Shi'ur. Also, one can strain it. The Shulchan Aruch answers the second question. It is forbidden even if there is 60. In the Gemara, Reish Lakish does not forbid due to Nosen Ta'am li'Fgam, but he forbids if it was cut. The Rema answered the first question. The Maharshal and Shach explain that the mouse itself is Batel even in a majority, for anything that stands by itself is considered a dry mixture. The stringency is because it is a Briyah. Even though a shredded Briyah is Batel, here since the Shi'ur is ka'Adashah, it is like a Briyah. The Taz and Pri Chodosh challenged this, for even if it is big, if it is not whole, it is not a Briyah! Rather, the Isur is not Batel if it is recognized, like the Yerushalmi says. Likewise, if the Heter is recognized, it is not Mevatel Isur. This is why Bitul is only for mixtures of wet and wet or dry and dry. The Shulchan Aruch teaches that if it dissolved, this is wet in wet. If it was cut, this is dry in wet, i.e. if it is a thick food, e.g. a thick gravy. It is considered wet because it cannot stand by itself. It is not Batel even in 1000, for one can feel the Isur with his hands, so it is recognizable. Rashi holds like Tosfos in Zevachim, that anything that for which less than a k'Zayis is forbidden is a Briyah in the Shi'ur that is forbidden, e.g. a Gid. The teaching of an ant is not difficult. Only regarding Muvdalim (the eight Sheratzim) one is liable for ka'Adashah even if it is not a Briyah. Rashi is correct. Even though Tosfos wrote unlike this in Makos, rather, like the Rosh, the opinion of Tosfos in Zevachim is primary. Also, we can say that here Rashi teaches that an Ever of any size is forbidden.