Gemara

(Beraisa) Question: What constitutes a Petzu'a Daka?

Answer: It is any man whose Beitzim were cut, even one of them, even if they were punctured, shriveled, or incomplete;

R. Yishmael the son of R. Yochanan ben Brokah says, I heard from Chachamim in Kerem b'Yavneh that anyone who only has one Beitzah is a Seris Chamah (due to sickness) and is Kosher (may marry).

Objection: This cannot be (due to illness)!

Correction: Rather, he is like a Seris Chamah, and is Kosher.

(Rav Yehudah): A Petzu'a Daka b'Yedei Shomayim is Kosher.

(Rava): This is why it does not say 'ha'Petzu'a' (connoting from the beginning), rather, "Petzu'a".

(Beraisa): Right after "A Petzu'a Daka will not marry" it says "A Mamzer will not marry". Just like a Mamzer is due to man's actions, also a Petzu'a Daka.

(Rava): The Torah forbids if any of them (the Ever, Beitzim, or Chutei Beitzim) is Petzu'a (bruised), Dach (crushed) or Krus (cut off).

Rishonim

The Rif brings the Gemara verbatim.

Ra'avad (brought in Sefer ha'Zechus): The Yerushalmi says that the Halachah follows R. Yishmael. This teaches that he argues with Chachamim, and that he discusses when a Beitzim was removed b'Yedei Adam. If often happens that someone has a bruised Beitzah and a doctor removes it and the man has children afterwards. Perhaps this is only when the left one is removed.

Rebuttal (Sefer haZechus): If R. Yishmael argues, surely the Halachah follows Chachamim; they did not accept what he heard from Chachamim in Kerem b'Yavneh. Ge'onim and the Rif do not rely on Pesak Halachah of the Yerushalmi even when there is no Pesak in the Bavli. Also, Rava disqualifies if any of the Ever, Beitzim, or Chutei Beitzim is bruised, crushed or cut off. He explains Chachamim of our Mishnah. BaHaG says that R. Yishmael discusses b'Yedei Shomayim. This is why he compares it to a Seris Chamah. He is Kosher, but he cannot have children. The same applies if the Beitzah was removed b'Yedei Adam; R. Yishmael merely reported the ruling of Chachamim in Kerem b'Yavneh on a case that occurred. Really, the Yerushalmi says that Chachamim Posel even b'Yedei Shomayim, unlike what the Ra'avad says. If one had a bruised Beitzah and a doctor removed it and he had children afterwards, they are Mamzerim. The Rambam was an expert doctor, and he disqualifies when it was b'Yedei Adam. The Rif did not rule because there is no argument. He did not rule about other matters, e.g. an Ever shaped like a quill, because it is not common.

Nimukei Yosef (DH Gemara): The Beraisa disqualifies a puncture Beitzah, even if nothing is missing. Therefore, it also mentions 'incomplete'. Tosfos says that a puncture is Posel only if it is Mefulash (goes from one side to the other). Rabeinu Yitzchak says that because the Bavli did not explain, we rely on the Yerushalmi, which requires that the right Beitzah remain.

Rambam (Hilchos Isurei Bi'ah 16:3): A Petzu'a Daka is one whose Beitzim were bruised. A Krus Shofchah is one whose Ever was cut off. Procreation depends on three elements - the Ever, the Beitzim, and the Chutei Beitzim, i.e. conduits in which the semen is cooked. If any of these three was bruised or cut off or crushed, the man is forbidden.

Rambam (7): If even one of the Beitzim or Chutei Beitzim was cut or bruised or crushed, or it is lacking or punctured, the man is forbidden.

Magid Mishneh: Some say that R. Yishmael discusses b'Yedei Shomayim. He is Machshir even when both are missing; he discussed when one is missing, for this is more common. The Rambam holds like this.

Rambam (9): Every Pesul we mentioned is when it was not b'Yedei Shomayim, e.g. it was cut by a man or dog or thorn. If one was born this way, or illness or boils atrophied one of the organs, this is b'Yedei Shomayim and he is Kosher.

Rosh (8:2): R. Yishmael is Machshir one who only has one Beitzah. Does he argue with our Stam Mishnah?! We cannot say that the Mishnah disqualifies when one was removed b'Yedei Adam, and R. Yishmael is Machshir when it was b'Yedei Shomayim. If so, even if both were removed b'Yedei Shomayim he would be Kosher! Also, we see men with one Beitzah father children. It is unreasonable to say that they are Mamzerim. R. Tam says that R. Yishmael also discusses b'Yedei Adam; it is worse when a Beitzah is bruised than when it is removed. We find that removal of the spleen does not make an animal Tereifah, but a puncture makes it Tereifah (Chulin 55a). When the Gemara says that if the Beitzim were cut off he is Pasul, this is only if both were cut off. Even though R. Yishmael says that one with only one Beitzah is a Seris Chamah, he can be healed and can have children. And even if R. Yishmael argues with Chachamim, we may rely in him because he heard from Chachamim in Kerem b'Yavneh, which is more reliable (Yevamos 42b). The Yerushalmi connotes that he is Kosher but cannot have children. It rules like R. Yishmael, on condition that (they are) Shleimin. This means that both were intact when one was removed, but if one was bruised and then removed he is Pasul. The Pesul of a bruised Beitzah does not return to be Kosher. Alternatively, 'Shleimin' is really two words, 'Shel Yamin', i.e. only if the right Beitzah remains he is Kosher. The Yerushalmi must say that R. Yishmael discusses when it was removed b'Yedei Shomayim; if it was b'Yedei Adam, since he cannot have children surely he is Pasul. Chachamim disagree and say that even b'Yedei Shomayim is Pasul. The Yerushalmi does not support R. Tam's ruling. R. Tam could say that our Gemara argues, and says that R. Yishmael discusses b'Yedei Adam. The Rif brought the Gemara without giving a ruling. We cannot determine his opinion. Perhaps he holds like R. Tam. However, he should have explained that there is no argument. It seems that he holds that R. Yishmael argues, so the Halachah follows Chachamim.

Rosh (ibid.): A Petzu'a Daka b'Yedei Shomayim is Kosher. Rebbi explains that this is from birth, or through lightning or hail. If it was through sickness, he is Pasul. The Yerushalmi supports this.

Poskim

Shulchan Aruch (EH 5:7): If even one of the Beitzim was cut or bruised or crushed, or it is lacking or punctured, the man is forbidden.

Beis Yosef (DH v'Chen Nir'eh): The Rif and Rambam did not specify. It seems that they hold that the Halachah does not follow R. Yishmael.

Rema: This is the primary opinion, unlike those who permit if the left Beitzah was removed intact. However, some are lenient like the latter opinion. It is good to be concerned for the stringent opinion regarding an Isur mid'Oraisa; they are they majority and the greatest Chachamim.

Shulchan Aruch (10): Every Pesul we mentioned is when it was not b'Yedei Shomayim, e.g. it was cut by a man or thorn. If one was born a Petzu'a Daka or Krus Shofchah or without Beitzim, or illness or boils atrophied one of the organs, the Rambam considers this b'Yedei Shomayim and he is Kosher. Rashi and the Rosh say that b'Yedei Shomayim is only from birth, or through lightning or hail; from sickness is like b'Yedei Adam, and he is Pasul. The Rosh says that the Yerushalmi supports this.

Rebuttal (Bach DH u'Mah she'Chosav Rabeinu): Rashi says that b'Yedei Shomayim is from birth, or through lightning or hail. The Rosh says that sickness is like b'Yedei Adam; Rashi (20b and 75a DH Seris) disagrees.

Chelkas Mechokek (5): It seems that the Shulchan Aruch is stringent. However, the Bach calls the Rosh's opinion 'an individual's opinion.'