Gemara

Question: Perhaps we should expound "ha'Shoretz" as if it said "ha'Mashritz (which breeds)," to exclude the Achbar that develops from earth (it is not Tamei)!

Answer: A Chuldah is Tamei, just like an Achbar. Just like everything called Chuldah is Tamei, also every Achbar, even one that develops from earth.

Objection: We can learn oppositely!

Just like a Chuldah procreates, also an Achbar. This excludes one that comes from earth.

Shabbos 12a (Beraisa - R. Eliezer): If one kills a Kinah (louse) on Shabbos he is (liable) like one who killed a camel;

(Beraisa): One who delouses his clothes (on Shabbos) may roll the lice between his hands and cast them down, but he may not kill them;

Aba Sha'ul says, he may cast them down, but he may not roll them.

(Rav Huna): The Halachah is, one may roll lice and throw them. It is dignified to do so (not to kill them), even during the week.

Rabah and Rav Sheshes used to kill them. Rava would cast them into a vessel of water.

(Beraisa - R. Shimon ben Elazar): Beis Shamai forbid killing lice on Shabbos;

Beis Hillel permit.

107b (Rav Yosef): Chachamim (of R. Eliezer) exempt one who kills a louse on Shabbos, for they do not reproduce (sexually).

Both of them learn from rams;

R. Eliezer says, just like they were killed (for their skins, for the Mishkan), one is liable for killing anything;

Chachamim say, just like they reproduce, one is liable for anything that reproduces.

Objection (Abaye): Lice reproduce!

It was taught that Hash-m feeds the entire world, from Karnei Re'emim (the biggest animals) to Beitzei Kinim (lice that just hatched).

Answer: 'Beitzei Kinim' is the name of a species.

Question: A Pir'osh (flea or louse) reproduces, yet R. Yehoshua exempts!

Answer (Rav Ashi): He is exempts only for trapping it. All agree that one is liable for killing it.

121b (R. Yehoshua ben Levi): One may kill any damager on Shabbos.

Question (Rav Yosef - Beraisa): Five animals may be killed on Shabbos - a fly in Mitzrayim, a wasp in Ninveh, a scorpion in Chadayev, a snake in Eretz Yisrael, or a rabid dog anywhere.

This cannot be R. Yehudah. He obligates for Melachah she'Einah Tzerichah l'Gufah (one does not benefit from the Melachah. He would permit only for mortal danger, and then any animal could be killed)!

Rather, it is R. Shimon, and he permits only these five!

Answer #2 (Rav Yosef): The case is, they are pursuing him.

(R. Yanai): I kill wasps. All the more so I kill snakes and scorpions!

Perhaps he permits (to trample them) only l'Fi Tumo (as if he is unaware);

(Rav Sheshes): One may trample a snake l'Fi Tumo.

(Rav Katina): One may trample a scorpion l'Fi Tumo.

Rishonim

Rif (Shabbos 5a): Beis Hillel permit killing lice on Shabbos.

Ran (Shabbos 5a DH Amar): R. Eliezer holds like Beis Shamai. We hold like Beis Hillel. This is why Rav Huna and Rav Sheshes killed lice. We discuss Kinim. Rabanan permit killing it, because it does not reproduce. All forbid Pir'osh.

Ran (DH u'Veis): Lice do not reproduce. They breed from man's skin. R. Shimon ben Elazar teaches that Beis Shamai and Beis Hillel argue about them.

Rambam (Hilchos Shabbos 11:2): If vermin reproduce from male and female, or develop from earth, like Pir'oshim, one who kills them is liable like one who kills an animal. If vermin develop from excrement or rotting Peros or similar things, e.g. worms of meat or in legumes, one who kills them is exempt.

Rambam (3): One may kill lice on Shabbos, for they are from sweat.

Rosh (Shabbos 1:29): Rabah and Rav Sheshes would be Mekate'a the lice. This is like Rav Huna said, that it is honorable not to kill them. Rashi explains that was on Shabbos. People rely on this to kill lice even when delousing clothing on Shabbos. We must say that this is the Chidush of Rabah and Rav Sheshes. Surely one may kill (head) lice on Shabbos, since the Halachah follows Beis Hillel! However, how can they argue with both Tana'im (Aba Sha'ul and Chachamim) of the Beraisa, who forbid killing lice from clothing? Perhaps (Rabah and Rav Sheshes) discuss killing head lice. The Chidush is that we do not decree to forbid Kinim due to Pir'oshim, since Pir'oshim are not commonly found in the head.

Ramban and Rashba (Shabbos 12a DH Ha and DH mid'Amrinan): One is liable for what reproduces. This is why one is liable for killing a Pir'osh on Shabbos.

Ramban (ibid.): R. Tam says that a Kinah is a Pir'osh. Shabbos 107b refutes this. Some say that a Pir'osh reproduces. Some say that it is Albergos. Even though it develops from earth and does not reproduce, one is liable for it like for something that reproduces. We learn from rams to exempt what does not reproduce, but only for things like lice, which develop from sweat, or worms that develop from wasteheaps and things that decay. The Rambam holds like this. I say that surely one is liable for a mouse that develops from earth, since its species reproduces, even though it itself is sterile. We exempt only species that do not reproduce at all, like Albergos. L'Chatchilah one may trap and kill them, for it is in the category of lice.

Rashba (12a DH v'Pir'osh): Some say that Pir'osh is the black species called Borgos in Arabic. Some say that Borgos does not reproduce, for it develops from earth. Therefore, R. Chananel (12a DH Lo) explained that Kinah is Pir'osh. We find that in Makas Kinim, they came from the earth. However, this cannot be the Pir'osh mentioned on 107b, for it reproduces, and all forbid killing it on Shabbos. Perhaps that Pir'osh reproduces; it is not Borgos. Presumably, Borgos is lice, like the Ramban says, for one may delouse without a Ner (e.g. during the day) on Shabbos (12a). Borgos are common like lice. If it were forbidden to kill them on Shabbos, we should forbid delousing lest one kill Borgos! Rather, one may trap and kill it.

Shiltei ha'Giborim (Shabbos 5b:1): Women who kill Pir'oshim rely on the Ramban and Rashba. We let them do so.

Rebuttal (Eliyahu Rabah 26): Chalilah to allow this. All the other Poskim say that one is Chayav Chatas for this!

Poskim

Shulchan Aruch (OC 316:9): On Shabbos, one may not kill a Pir'osh, which is called Borgos in Arabic

Beis Yosef (DH Asur): Even though the Halachah follows R. Yehoshua who exempts for killing a Pir'osh, it is forbidden (mid'Rabanan).

Beis Yosef (DH u'Mah she'Chasav v'Asur): The Tur connotes that one may not kill it even if it is on his skin. Even though one may kill any other damager that is running after him (121b), other damagers bite stingingly, unlike Pir'oshim. However, the Mordechai permits killing all other damagers, even without danger, if they are running after him. R. Tam says that the same applies to a Pir'osh and similar things. He holds like R. Shimon, who exempts for Melachah she'Einah Tzerichah l'Gufah. To prevent pain, it is permitted, like R. Shimon permits bursting a scab to let the pus out (107a) or extinguishing a coal so people will not be damaged.

Mishnah Berurah (35): Borgos is a black (flea) that jumps.

Gra (DH v'Asur): The Shulchan Aruch is unlike R. Tam, who permits other damagers The Rambam holds that one who kills it is liable!

Mishnah Berurah (38): Even if a Pir'osh is biting him, he may not kill it.

Levush: One may not kill a Pir'osh. It develops from earth, like other Sheratzim. One may not kill it even if it is biting him. It is unlike others damagers. One may kill snakes and scorpions that are chasing him, even if they do not kill, for their nature is that they can harm.

Rema: One may kill a Kinah.

Kaf ha'Chayim (75): A Pishpesh (bedbug; it gives a nauseating smell when it is crushed) has the same law as a Pir'osh. However, we may be more lenient about removing it when it is on the outside of his garment, if one cannot shake it off, since its bite hurts much more, and it hides in garments and bites. Also Pesach ha'Dvir says so.

Bi'ur Halachah (DH Asur): The Mechaber holds that fleas are Pir'osh. He did not say that one is liable, for if they are biting him, killing them is Einah Tzerichah l'Gufah.

Bi'ur Halachah (DH Lehargah): The Pri Megadim asked why one is liable for a Pir'osh. It is not a Briyah (creation, for which one who kills it is liable), for it nurtures from rotting Peros! It is difficult to say that the Mechaber considers this something that develops from earth. I answer based on the Rambam (Hilchos Ma'achalos Asuros 2:13), who says that worms that develop in attached Peros are called Sheretz. However, even what develops from excrement and rotting Peros is called Sheretz! Why does the Pri Megadim say that the latter is not a Briyah? The Rambam says that Pir'osh does not reproduce. The Gemara explicitly says that it does! The Ramban and Rashba answered that Pir'osh is a different species. Since it is from earth, it is as if it reproduces. This is very difficult. Rather, the Rambam holds like he wrote in Sefer ha'Mitzvos (Lav 179), that even what does not come from male and female can reproduce (via eggs). This includes what develops in Peros or from earth. He excludes only what develops from rotting things. Those are called Romesh (swarming), but not Sheretz, which connotes multiplying. Even though the Gemara says that the mouse that develops from earth does not reproduce, we need not say (like the Ramban) that whatever develops from earth does not reproduce. The Ramban disagrees with the Rambam there in Sefer ha'Mitzvos. How does the Ramban explain the question about Kinim? They come from sweat, so surely they do not reproduce! The Ramban brought a proof from hens. If it warmed itself in the dirt, the resulting eggs cannot form a check, since they were without a male. Chickens are different, for their nature is to reproduce through male and female.

Shulchan Aruch (10): Damagees that do not bite and kills, e.g. snakes and scorpions in a place where they do not kill, one may kill them only if they are chasing him. One may trample them l'Fi Tumo, even intentionally, but he makes it look as if he does not intend.