GEMARA

(Beraisa - Rebbi): Why does it say "Nefesh Asher Tiga... v'Nivlas Chayah... Behemah"? Behemah was already included in Chayah!

Answer: This is extra, to learn a Gezeirah Shavah "Behemah-Behemah" from eating Kodshim when Tamei (also our verse discusses this).

Makos 22a (R. Hoshaya): One who mates (even with its own species) Pesulei ha'Mukdashim (a blemished Korban that was redeemed, or Ma'aser or Bechor, which need not be redeemed) is lashed. It is like two species, Chulin and Kodshim.

(R. Yitzchak): One who conducts (works with) Pesulei ha'Mukdashim is lashed. Even though it is one animal, the Torah considers it like two species.

Bechoros 33a: Three verses mention Tzvi v'Ayal (a deer and a wild goat). One of them teaches the laws of R. Yitzchak and R. Oshaya.

Bava Kama 54b (Mishnah): The following apply to all Behemos (domestic animals), Chayos (wild animals) and fowl... working with or crossbreeding diverse species.

We learn about working with diverse species from a Gezeirah Shavah "Shor-Shor" from Shabbos. We learn about crossbreeding diverse species from a Gezeirah Shavah "Behemah-Behemah" from Shabbos.

55a - Question (Rachbah): May one use a goat and Shibuta (a fish) to pull together?

Since goats never go in the sea, and fish never go on the land, it is permitted. Or, since he works with them, it is forbidden.

Mishnah (Kilayim 8:1): One may raise and keep Kilai Behemah. It is forbidden only to crossbreed them.

Mishnah (2): One may not plow, pull or lead diverse species, whether they are both Behemos or Chayos or one of each. This is whether they are Tahor or Tamei or one of each.

RISHONIM

Rambam (Hilchos Kilayim 9:7): If one works with two Behemos or Chayos and one was Tahor and one was Tamei, he is lashed.

Rambam (8): One is liable for any Tahor species with a Tamei species, whether they are Behemos or Chayos or one of each. Mid'Rabanan, one may not work with any two species that one may not mate together (even if both are Tahor or Tamei).

Rambam (11): The Torah considers Pesulei ha'Mukdashim like two bodies. It was Kodesh, and now it is Chol, so it is like a Tamei and Tahor animal together - "Kol Behemah Teme'ah Asher Lo Yakrivu..." Therefore, one who plows with it or mates it is lashed.

Rebuttal (Ra'avad): Bechoros 33a considers it like a Behemah and Chayah, for it is like Tzvi and Ayal, but it does not consider it Tamei.

Perush ha'Mishnayos (Kilayim 8:2): Since the (first) Mishnah said that the only Isur of Kilai Behemah is to crossbreed them, our Mishnah explains that this is only for two Chayos or two Behemos and the rest of what it details. However, if one is Tahor and one is Tamei, there is another Isur in addition to crossbreeding, i.e. one may not plow, pull or lead them. Mid'Rabanan, this is forbidden with any two diverse species.

Radvaz (8): The Mishnah supports the Rambam. If there were no difference between (which combinations of animals are forbidden for) mating and plowing, one Mishnah would have taught both of these together. Rather, first it taught the Isur of crossbreeding, then it lists combinations of animals, then it teaches the Isur of working together. Semag supports the Rambam from a Tosefta, in which R. Meir forbids tying together Tamei animals, and Chachamim permit. Surely all agree that tying connects them (this is like working together), but Chachamim permit because both are Tamei! In any case the Mishnah is not difficult for the Rambam. Even if it forbids in every case, the Isur is mid'Oraisa only when one is Tamei and one is Tahor. Rachbah asked about a goat and Shibuta, for Shibuta is Tamei. Even if you will say that it is Tahor, he asked about whether there is an Isur mid'Rabanan. The Rambam explained that the Torah equated Pesulei ha'Mukdashim to a Tamei and Tahor animal. It says Tzvi v'Ayal just to teach that it may be eaten in Tum'ah (therefore, it needed to discuss Tahor species).

Rosh (Hilchos Kilayim 5): The Rambam holds that the Gezeirah Shavah "Shor-Shor" from Shabbos teaches that every animal and Chayah is like an ox or donkey, but the Isur is only if they are like an ox and donkey, i.e. one is Tamei and one is Tahor. If both are Tahor or both are Tamei, the Isur is only mid'Rabanan. The Mishnah includes whether both are Tamei or both Tahor or one of each. This shows that we do not distinguish. The Mishnah discusses various laws that apply to Behemos and Chayos. It seems that the same law applies to all of them. In Makos we say that one who mates or conducts Pesulei ha'Mukdashim is lashed, for it is like two species, Chulin and Kodshim. R. Tam explains that it is like a deer and wild goat. Bechoros 33a proves this. It says that one of the three verses that mention Tzvi v'Ayal teaches the laws of R. Yitzchak and R. Oshaya. The Rambam is forced to say that Kodesh and Chulin is like Tahor and Tamei. It is difficult to say that this obligates lashes. The Sifri says that one is liable for any diverse species. "Ox and donkey" exclude a man who plows with an animal. This is the only Heter it found, for the Torah forbids any two different animals!

Rosh (Teshuvah 2:16): Rachbah asked if one may use a goat and Shibuta to pull together. Shibuta is Tahor; in France, they eat it. (Rachbah asked only because one is a fish, but he does not exempt two Tahor species!)

Tosfos (Avodah Zarah 39a DH v'Simanech): Shibuta is Tahor, like it says in Kidushin (41a) that Rava salted Shibuta to honor Shabbos. We see from Rachbah's question that it is the sea creature that corresponds to a goat.

Shnos Eliyahu (Kilayim 9:8): "Behemtecha Lo Sarbi'a Kilayim" connotes all Behemos, and Chayos are included. "Lo Sacharosh b'Shor v'Chamor Yachdav" forbids only like an ox and donkey, i.e. one is Tahor and one is Tamei. This is like the Rambam.

Note: It seems that the Gra retracted. In his Perush on Shulchan Aruch (below) he rules like the Rosh.

Da'as Zekenim mi'Ba'alei ha'Tosfos (Devarim 22:10): The Torah forbids working with an ox and donkey because the ox chews its cud and the donkey is pained when it hears the ox eat.

Meshech Chachmah: This is like the Rambam, who forbids only Tamei and Tahor. One must reconcile this with the Yerushalmi, which forbids riding on a mule (because it comes from two species). In Moreh Nevuchim (3:49), the Rambam explains that the Torah merely distances us from crossbreeding any two species. This is unlike what he wrote in Mishnah Torah. A crossbreed of Tamei and Tahor is unlikely to produce offspring!

Note: The Meshech Chachmah could have asked from the Bavli, which forbids working with Pesulei ha'Mukdashim, even though the reason of Da'as Zekenim mi'Ba'alei ha'Tosfos does not apply. According to his reason, perhaps 'Tahor' and 'Tamei' refer to animals that do and do not chew the cud, respectively. If so, a camel would have the law of a Tahor animal. The reason does not apply when the animals work with food that it can eat (since one must let them eat). Also the Ramban (Devarim 22:8) says that the Isur to work with Kilayim is due to the Isur of crossbreeding. This explains the side to permit a fish with a goat, since fish never go on the land and there is no concern lest they mate.

POSKIM

Shulchan Aruch (YD 297:10): One may not do Melachah with two species, e.g. to plow or pull a wagon, whether they are Tahor or Tamei or one of each, whether they are Behemos or Chayos or one of each.

Gra (21): The Shulchan Aruch did not say that he is lashed, for the Rambam holds that he is lashed only for a Tamei and Tahor species. The Rosh refuted this, and all Poskim hold like the Rosh.