Gemara

(Mishnah - R. Akiva): The rule is, if we know that an animal previously gave birth (or miscarried, even if the first child is a male, the Kohen gets nothing). If we know that it did not give birth before, the Bechor belongs to the Kohen. If we do not know whether it gave birth before, the owner eats it when it gets a Mum.

21b (Rav): If one buys from a Yisrael, the first child born is a definite Bechor. Had the mother given birth already, the seller surely would have told the buyer, for such an animal is worth more.

(Shmuel): The first child is a Safek Bechor. Perhaps the mother already gave birth. The seller did not tell the buyer, for he assumed that the buyer intends to slaughter it (it will not bear offspring).

(R. Yochanan): The child is Vadai Chulin. Had the mother not given birth yet, the seller would have told the buyer (that the first child will be a Bechor).

Bava Kama 114b (Rav Ashi): L'Fi Tumo is valid only for Edus Ishah (testimony that a man died, to permit his wife to remarry).

Question (Ravina): It is believed about who owns a swarm of bees!

Answer (Rav Ashi): Ownership of bees is only mid'Rabanan.

Yevamos 111b: A Nochri was saying 'who is from Chivai's house? Chivai died!' Rav Yosef permitted his wife to remarry.

112a (Beraisa): If a Nochri selling fruit said 'it is Orlah, or it is fourth year produce', his words have no effect, for he intended only to praise his fruit.

Rishonim

Rosh (Bechoros 3:3): Rashi says that if one bought from a Yisrael, the child is a Vadai Bechor, for surely he would have said if the mother already gave birth, to show that it is worth more. I.e., the danger of dying in the first birth already passed. If so, a Nochri is not believed even if he said so, for he does not speak Emes. Even if (it seems that) he said so l'Fi Tumo (unaware of the consequences), he is not believed, for he knows that this makes his animal worth more. However, perhaps it is worth more because it is exempt from Bechorah. (If so, a Nochri would be believed l'Fi Tumo, for he does not know this.)

Terumas ha'Deshen (130): The Rosh connotes that we do not rely on l'Fi Tumo of the Nochri only because he intends to praise his animal, but if we knew that he does not, we would rely on him. However, in Yoreh De'ah the Tur wrote Stam that we do not rely on him. In Bava Kama we say that Edus Ishah is the only Torah law for which we rely on l'Fi Tumo.

Poskim

Shulchan Aruch (YD 316:1): If one buys an animal from a Nochri and does not know whether it already gave birth, if it had a child, it is a Safek Bechor. Even if the Nochri said l'Fi Tumo that it already gave birth, he is not believed.

Shulchan Aruch (3): An animal with milk is exempt, for most animals do not have milk until they give birth.

Rema: Some say that we do not rely on milk. The Acharonim rule like this, and this is the custom in these lands. However, if there is another reason to permit, or the Nochri speaks l'Fi Tumo without intent to make it worth more, we rely on this to permit. This refers to cows, in places where we did not hear that they have milk before giving birth. Goats often have milk before giving birth, so we do not rely on this, even if it is a Sefek Sefekah, e.g. it gave birth to two (and we do not know which was born first).

Shach (2): The Levush and Bach say that he would say that it already gave birth, for an animal that already gave birth before has better milk. The Drishah says that surely he is not believed l'Fi Tumo when he praises his animal. Rather, even when he does not praise it, a Nochri is believed l'Fi Tumo only for Isurim mid'Rabanan.

Zichron Yosef (YD 19): A case occurred in which one bought two old sheep with milk from a Nochri who said that they have many offspring. Surely he is not believed, for he praised his animals. One of them gave birth to two males, and the other to one male, and we know which was first only through a (Nochri) shepherd. Even though each of them is a Safek, we do not permit due to a Sefek Sefekah (perhaps the mother already gave birth), like the Shach (110:63) and Taz (110:5). The shepherd is no better than Mesi'ach (one who speaks) l'Fi Tumo. Perhaps he is worse, for here many shepherds know that Yisre'elim sell pregnant animals due to the Isur of the firstborn. All three lambs are Safek Bechoros. However, if one can show that in this land sheep do not have milk before giving birth, then Mesi'ach l'Fi Tumo would help. E.g two Yisre'elim could ask the neighbors to resolve their wager, i.e. 'I said that the sheep had given birth four times, and he said that it gave birth only once or twice', like Chavos Ya'ir (36) brings. It seems that even if one can establish the firstborn only through one who was there at the birth, the shepherd is believed to permit the one born second, just like a midwife is believed to say which baby was born first or which was born to the Kohen (Kidushin 73b, CM 277:12). Normally, one witness is not believed about money. She is believed as long as there is no one else who knows. If so, presumably a (Nochri) shepherd is believed here for the same reason.

Taz (4): A case occurred in which a Nochri (Tony) owed money to Reuven. Tony showed him a cow with a calf nearby, and said that he will give the cow alone for eight gold coins of the debt. Reuven said 'it is old. This is probably its sixth or seventh child. I would pay more for a younger animal.' Tony said 'it is not young, but it is not so old. This is only its fourth child.' Are we concerned for Bechorah? Seemingly, we do not rely on l'Fi Tumo. However, Bechoros 21b shows that it is exempt. Shmuel and R. Yochanan have reasons to argue with Rav (and say that (perhaps) it already gave birth). When there is no other reason, all agree that an owner praises his animal as much as possible! Here, if the cow never gave birth, Vadai the Nochri would have said so! He is not believed to praise his animal l'Fi Tumo, but he is believed l'Fi Tumo when he does not praise it. l'Fi Tumo is believed only for Edus Ishah. Here there is even more reason to believe him! A scribe is believed to disqualify a Sefer Torah that he wrote only when his admission causes himself a (big) loss (Gitin 54b). Here also, Tony wanted to make his cow seem younger. Had it not given birth, surely he would have said so. Do not say that in Gitin he is believed merely to make it a Safek. The Gemara connotes that he is believed Vadai. When he causes himself a small loss, he is not believed even to make a Safek, for the Sefer Torah is not in his hands. Maharik (121) says that a once, a judge promised a Nochri that if he tells the truth he will not be punished. The Nochri said that he killed Ploni, and they permitted Ploni's wife. We rely on documents made in Nochri courts, for the judges fear to ruin their reputation. This would suffice for Gitin, if not that divorce does not apply to Nochrim. All the more so we may rely on a Nochri that he would not falsely incriminate himself! Even if he trusted the judge's promise, he should have been careful, especially since Nochri judges promise in order to get people to tell the truth, and do not fulfill their promises! Do not say that here, Tony feared to say that it never gave birth, due to the danger of a first birth. If so, he should have said that it gave birth only once!

Note: Perhaps he feared to say so because it looked old and he would not be believed, or the Yisrael would suspect that if it had not given birth, it must be sick! Also, perhaps he schemes to admit partially to make it seem that he tells the truth (see Bava Metzia 4b)!

R. Akiva Eiger (YD 15): Mesi'ach l'Fi Tumo does not help for something with a source in Torah. This is unlike the Maharshal said about eggs. The Rema relies on Mesi'ach l'Fi Tumo only for cows, which normally do not have milk before giving birth, but not for goats. This is based on the Terumas ha'Deshen. We rely on Mesi'ach l'Fi Tumo for an Isur mid'Rabanan only if the Isur was not Muchzak (Shach 98:2). The Torah exempts milking goats from Bechorah, for the majority do not have milk before giving birth. Chachamim were stringent to consider it an even Safek. Since Bechorah is mid'Oraisa, we are stringent even when the concern is mid'Rabanan. The Terumas ha'Deshen (79) said so about eating eggs bought on Yom Tov right after Shabbos. He does not rely on Mesi'ach l'Fi Tumo, for the Isur of Hachanah (if they were born on Shabbos) is mid'Oraisa, even though in this case it is mid'Rabanan. (Most eggs are from before. Chachamim were stringent because Yesh Lo Matirim, they are permitted the next day.)

Chavos Ya'ir (37): One may not join Mesi'ach l'Fi Tumo with having milk to permit, unless the Nochri had no benefit at all to say so. Then, we rely on even a Mesi'ach l'Fi Tumo who says what he heard another say l'Fi Tumo. We learn from Edus Ishah. Surely, it is like when one speaks l'Fi Tumo. The Shach (98:2) says that we rely on l'Fi Tumo even for an Isur mid'Oraisa if the matter will become known. Regarding l'Fi Tumo, we do not distinguish permitting from forbidding, like we find at the end of Yevamos. Only regarding Edus Ishah we require that the Nochri begin the dialogue. A proof is that we give a Nochri cook to taste, and rely on what he says, even for an Isur mid'Oraisa!

Chasam Sofer (YD 308 DH v'Im): When the Nochri begins to speak l'Fi Tumo and he is believed, he is believed even what he answers to questions while engaged in the matter. However, once he left, if we begin to ask him (and all the more so if he never began), we cannot believe him.