Chullin, Chapter 8, Mishnah 4. This chapter is devoted to the laws of basar bechalav, meat and milk, and here the Mishnah draws the precise lines: which combinations of meat and milk are forbidden on the level of Torah law, and which fall outside that prohibition entirely.
The classic case
The Mishnah begins with the straightforward pairing: "basar beheima tehorah," flesh taken from a kosher domesticated animal, joined together with "bechalav beheima tehorah," milk drawn from a kosher animal as well. The ruling has two parts. "Assur levashel": placing the two in a pot together is prohibited. "Ve'assur behana'ah": once they have been cooked, no benefit of any kind may be taken from what results. This is the paradigm case of basar bechalav on the level of Torah law, the model from which the entire prohibition is defined.
When one of the two is not kosher
The Mishnah now moves to the mixed pairings. First, "basar beheima tehorah," kosher flesh, cooked "bechalav beheima temei'ah," in milk that came from a non-kosher animal, camel's milk for example. Then the reverse: "basar beheima temei'ah," flesh of a non-kosher animal, cooked "bechalav beheima tehorah," in kosher animal's milk. In each of these the halachah is "mutar levashel u'mutar behana'ah." Since one of the two ingredients is inherently not kosher, what sits in the pot never qualifies as basar bechalav: cooking it is permitted, and so is deriving benefit from it.
Of course, nobody is suggesting that this food may be eaten. One of its components is non-kosher, and eating it is out of the question for that reason. The Mishnah's point is narrower: the specific prohibitions generated by basar bechalav, namely cooking and deriving benefit, do not attach here.
Rabbi Akiva: wild animals and birds are outside the Torah prohibition
A dispute now opens. Rabbi Akiva rules: "chayah ve'of," a wild kosher animal such as a deer and likewise a bird, "einam min haTorah" - neither of them is governed by the Scriptural prohibition. By Torah law, then, venison or poultry simmered in milk could be cooked and even consumed.
He anchors this in a count of verses. The command "Lo tevashel gedi," do not cook a kid, "bachalev imo," in the milk of its mother, is written by the Torah on three separate occasions, "shalosh pe'amim." Every one of those occurrences performs an act of exclusion: "perat lechayah, u'le'of, u'livheima temei'ah." A gedi is a domesticated creature, so the first mention screens out the chayah, the undomesticated animal; the second screens out fowl; the third screens out flesh of a non-kosher animal. For Rabbi Akiva, all three stand outside the Torah-level prohibition.
Rabbi Yose HaGelili: read the verse alongside its neighbor
Rabbi Yose HaGelili holds otherwise, and he produces a derivation that draws the wild animal inside. He notes that a single verse carries two commands back to back. It opens with "Lo tochlu chol neveilah," no neveilah may be eaten, meaning an animal whose slaughter was not valid. It then continues, "vene'emar," the Torah goes on to say, "Lo tevashel gedi" (a kid is not to be cooked) "bachalev imo" (in the milk of its mother). Their placement one beside the other is itself an invitation to learn the one from the other.
From that pairing a principle emerges: "et she'assur mishum neveilah," whatever flesh is capable of taking on the prohibition of neveilah, is precisely the flesh that is "assur levashel bechalav," barred from being cooked with milk. Every kosher animal, whether it lives in the barn or in the field, becomes a neveilah if its shechitah was performed improperly. Consequently every kosher species, the chayah included, comes under the laws of basar bechalav.
What the principle screens out is the non-kosher species. Neveilah status never attaches to such a creature, because shechitah has no relevance to it to begin with. So in the view of Rabbi Yose HaGelili as well, meat of a beheima temei'ah is not part of the prohibition on the d'oraita level.
The problem of the bird
Yet as formulated the rule reaches further than intended, since fowl too can be rendered neveilah. The Mishnah itself presses the objection: "of, she'assur mishum neveilah," a bird, which certainly does become forbidden as a neveilah when slaughtered improperly, "yachol yehei assur" - might it as well be prohibited, "levashel bechalav," to be cooked with milk? If the yardstick is susceptibility to neveilah, poultry in milk should be barred by Torah law.
To this the Mishnah answers: "talmud lomar: bachalev imo." The verse specifies "in its mother's milk," and that phrase does the excluding: "yatza of, she'ein lo chalev imo." The bird is removed, because a bird has no mother's milk; a bird's mother produces no milk at all. So the final definition according to Rabbi Yose HaGelili has two conditions together: the flesh must be capable of becoming a neveilah, and its mother must be a producer of milk. Only such flesh is included in the Torah's prohibition of basar bechalav.