Gemara

(Mishnah): If a Kosher animal nursed from a Tereifah, the (contents of the) stomach is forbidden.

If a Tereifah nursed from a Kosher animal, the stomach is permitted, because the milk is just gathered there.

The Halachah is, one may curdle with the stomach of a Kosher animal that nursed from a Tereifah. It is like Pirsha (a secretion, or waste).

Avodah Zarah 39b: Honey of Nochrim is permitted. We are not concerned lest the Nochri mixed in (Isur), for this would make it spoil!

Bechoros 6b - Question (Rav Acha): Chachamim learn (to forbid camel milk) from "Gamal... Gamal." R. Shimon learns from "Es ha'Gamal." If not, we would permit;

Why do we not learn from Sheratzim (that what comes from something forbidden is forbidden)?

(Beraisa): "Ha'Teme'im" forbids their brine, soup (the water in which they were cooked), and Kipah (spices and shredded meat that accumulate at the bottom of the pot).

Answer #1: We cannot learn from there. In a milking animal, (what normally comes out as) menstrual blood is converted into milk. It is a Chidush that (even Tahor) milk is permitted;

One might have thought that since a Chidush permits Tahor milk, also Tamei milk is permitted. The verse teaches that this is not so.

Question: This is like R. Meir, who holds that a nursing woman (or animal) does not (normally) have Dam Nidah because it turns to milk;

R. Yosi holds that it is because her limbs are perturbed by the birth, and do not return to normal until 24 months. How can he answer?

Answer #2: Normally, anything that comes from a living being is forbidden. Since the Torah permits milk, one might have thought that it permits even milk of Teme'im. Therefore, the verse is needed.

Question: What is the source that Tahor milk is permitted?

Answer #1: We learn from "v'Dei Chalev Izim l'Lachmecha l'Lechem Beisecha v'Chayim l'Na'arosecha" (that one may subsist on milk)!

Rejection: Perhaps the verse teaches that one will sell the milk (to Nochrim)!

Answer #2: "(David brought) v'Es Aseres Charitzei he'Chalav" (to the leader of 1000 men in the war. Surely, it may be eaten!)

Question: Perhaps he brought it to him to sell!

Answer: In war, one does not sell food to the enemy!

Answer #3: "Eretz Zavas Chalav u'Devash" - Eretz Yisrael would not be praised for something forbidden to eat!

Answer #4: "U'Lechu Shivru b'Lo Chesef uv'Lo Mechir Yayin v'Chalav."

Temurah 31a (Abaye): All permit a chick that comes from an egg of a Tereifah. Before it develops, it putrefies. It is like earth (the Isur goes away).

Rishonim

Ramban (Hilchos Bechoros 4a DH Beitzas): Some say that if a Tahor egg were Asur, also the chick that comes from it would be forbidden, for what comes from Tamei is Tamei. Rather, since Tahor birds are permitted, also the eggs are permitted. This is wrong. We say in Temurah that the chick of a Tereifah is permitted, for it develops only after it decays into earth. We could have said the same about the egg of a Tahor bird.

Chasam Sofer (YD 70 DH v'Nora'os): I cannot understand this opinion. Even if they overlooked the Gemara in Temurah, we could say that the egg is forbidden due to Ever Min ha'Chai, and when it becomes a bird, we slaughter the bird to permit it!

Rosh (Bechoros 1:5): Milk is like Ever Min ha'Chai, and the Torah permitted it. We learn that milk of Tahor animals is permitted from "Eretz Zavas Chalav", or from "u'Lechu Shivru... v'Chalav." Eggs of Tahor birds are permitted, even though they come from a living being. We learn from "Tikach Lach" - the Mitzvah applies when you may take the eggs to eat, and not (only) for your dog. Even though two verses permit things that come from a living being, it is considered a Chidush, since they are not in the same matter.

Rosh (Chulin 8:52): If a Tereifah animal nursed from a Kosher animal, its stomach is permitted, for the (Kosher) milk is gathered there. The Gemara says that it is a mere Pirsha, i.e. congealed milk in the stomach. The Mishnah forbids what Kosher animal nursed from a Tereifah when the milk is clear. It is pure milk.

Rosh Berachos (6:35): Some say that musk is sweat of a Chayah. It is more correct to say that it is from a certain Chayah with a hump in its throat. Something like blood gathers there, and becomes musk. The Ramah forbade eating it, due to concern for blood. R. Yonah says that perhaps we can permit, for it is a mere Pirsha. Even though initially it was blood, we are not concerned. It depends on what it is now. This is like Isur that dissolved in honey. It is transformed to honey, so we permit it like honey. The same applies to musk. Since it is no longer blood, now it is permitted, even if it improves the taste of the food. R. Yonah's proof (from honey) needs a proof.

Ran (Avodah Zarah 16b DH Misrach): The Isur (mixed with honey) decays, and does not mix. Others say that it is normal to mix others things in honey, and they dissolve into it and are transformed to honey, so there is no concern. Before it dissolves, it is spoiled and permitted. This is like we say in Temurah, that a chick that comes from a Tereifah egg is permitted. Before it develops, it putrefies. It is like earth.

Poskim

Shulchan Aruch (YD 81:5): Milk of Tahor Behemos and Chayos is permitted.

Pleisi (7 DH v'Hinei): What was the Gemara's rejection 'perhaps it is to sell?' If milk is forbidden due to Ever Min ha'Chai, it is forbidden also to Nochrim! If the Nochri has enough milk of his own (so it is not Lifnei Iver), he would not buy from the Yisrael! According to Chachamim, the Hava Amina to forbid blood was due to Ever Min ha'Chai. According to R. Meir, it was also due to blood. The rejection was only according to R. Meir. Even if we say that the Torah permitted the Isur Ever Min ha'Chai, perhaps the other Isur still applies. Isurim due to Ever Min ha'Chai are more lenient, for they are permitted through Shechitah (Chulin 69a. I did not find this - PF.) Indeed, "Eretz Zavas Chalav" proves that it is not Ever Min ha'Chai. (If it were forbidden, one could not sell it to Nochrim. If so, why is Eretz Yisrael praised for it?) What was the proof from Charitzei Chalav? Perhaps the milk was from after Shechitah! The proof is according to R. Meir, that there is no Isur due to blood. We hold like Chachamim, therefore the Rosh mentioned only Zavas Chalav.

Note: Even if it is forbidden to Nochrim, presumably they may feed Isur to their children! One could sell milk to a Ger Toshav, who will feed it to his children!

Retraction (Pleisi DH Ach): If a Nochri has many milking animals, one may sell to him even if it is forbidden to him. Also, most Poskim hold that the Torah permits cooked blood. If so, even if milk were Asur because it comes from blood, cheese is permitted because it was cooked! If so, there was no proof from cheese.

Minchas Shlomo (2:111): The Noda bi'Yehudah asked that those who hold that the Torah permits cooked blood say so because it cannot be offered on the Mizbe'ach. If so, all the more so milk that comes from blood is permitted! This is a great difficulty. Perhaps the Heter is primarily because cooking changes the blood. Since it becomes Pasul for the Mizbe'ach, we consider it a new entity.

Question (Magen Avraham 216:3): R. Yonah permits musk (and Isur mixed into honey), because it becomes Heter. This is difficult, for in Bechoros, we say that milk is a Chidush, since it came from blood. This shows that it depends on the origin! We do not learn from a Chidush! Do not say that musk is a mere Pirsha, and not a food. If so, all would permit it, like a Kosher animal that nursed from a Tereifah. One may curdle in its stomach. R. Yonah says that it is a mere Pirsha, i.e. it is not blood. We permit a chick that hatches from a Tereifah egg, for until it spoils, it does not develop. When it (starts to) develop, it is like mere dirt. If not for this, it would be Asur, like its origin!

Chak Yakov (OC 467:16): R. Yonah says that if meat or Neveilah dissolved in honey, it is transformed to honey. The law depends on its current status. One may not rely on this, like the Rosh and Shirei Keneses ha'Gedolah say. It is unlike the Yerushalmi. The Chidush of milk does not disprove R. Yonah. One might have thought that it is totally forbidden, for it comes from blood, so it is still like blood, even though its appearance changed. It did not change to Heter. If Isur put in honey turns to honey, it changed to Heter. Why should it be unlike other honey? It has the same taste and appearance. With difficulty, one could say the same for musk.

Bach (216:2 DH v'Nir'eh): The Rosh would agree (to permit musk) if we knew that the Isur becomes Pirsha. However, we cannot know this without prophecy! Perhaps the Isur gave taste to the Heter, and Ta'am k'Ikar is forbidden mid'Oraisa!

Taz (2): There is a clear proof for R. Yonah from the Rosh in Chulin. He says that if a Kosher animal nursed from a Tereifah and the milk congealed, it is permitted, for it is a mere Pirsha. Also here, what hardened on the animal is Pirsha (and is permitted). There is no difference between (congealing) in the animal or on the animal. Both of them are Pirsha.

Mishbetzos Zahav: The Pri Chodosh (Teshuvah 10) permitted to put musk in a food, for it is like earth. Some say that if there is more than one part in 60 (of Stam Isurim), even though it is added for taste, it is forbidden only mid'Rabanan. This is a Safek about a mid'Rabanan law, so we are lenient. L'Chatchilah we are not Mevatel Isurim, but this is only mid'Rabanan. Even though who say that something added for taste is not Batel mid'Oraisa, if we consider its initial status it is Batel in 60, for it does not give taste. Now it became a spice and gives much taste. The Torah did not forbid this taste.