Gemara

13a (Beraisa): To plead his case, a Kohen may go through a Beis ha'Pras. Its Tum'ah is mid'Rabanan. He may become Tamei (mid'Rabanan) to learn Torah or marry a woman.

R. Yehudah says, if he can find a Rebbi here, he may not become Tamei to learn elsewhere.

R. Yosi permits this, for perhaps he will learn better from the Rebbi there. Yosef ha'Kohen followed his Rebbi to Tzidon (in Chutz la'Aretz) to learn.

(R. Yochanan): The Halachah follows R. Yosi.

48b (Mishnah): One may not pass under an Asherah. If he did, he is Tamei (for surely something under the tree was offered to idolatry).

This is like R. Yehudah ben Beseira, who says that something offered to idolatry has Tum'as Ohel.

(Mishnah): If the foliage was overhanging a Reshus ha'Rabim and he passed under it, he is Tahor.

This is R. Yochanan's text. R. Yitzchak ben Elazar's text is 'he may pass under it.' They do not argue. If there is another path (no longer than this), one may not pass under. If there is no other path, it is permitted.

Chagigah 25b (Mishnah): Beis Shamai and Beis Hillel agree that one may check a Beis ha'Pras to go through to bring Pesach, but not to eat Terumah.

(Rav Yehudah): He checks it by bending down and blowing the earth before each step (to clear away any small bones that might be there).

(R. Chiya bar Aba): If many people walked through a Beis ha'Pras, it is Tahor regarding Korban Pesach. Chachamim did not apply their stringency if it will cause one to transgress (not bringing Pesach, which is) an Isur Kares;

Mo'ed Katan 5b (Rav Yehudah bar Ami): If many people walked through a Beis ha'Pras, it is Tahor.

Berachos 19b (Beraisa): If an Avel (mourner) was returning from burying his Mes on a Tamei path, Kohanim may accompany him, even if there is also a Tahor path, because of his honor.

Question: "Ein Chachmah...l'Neged Hash-m" -- wherever desecration of Hash-m's name is involved, we do not honor an important person!

Answer (R. Aba): The path is a Beis ha'Pras.

Rishonim

Rif (Avodah Zarah 3b, Hilchos Tum'ah (after Menachos) 2b) and Rosh (Sof Hilchos Tum'ah): A Kohen may not enter a Beis ha'Pras, i.e. a field in which a grave was plowed. If he is going to a Mitzvah, e.g. to get married or learn Torah, or to plead his case, and there is no alternative path, he may go through it.

Nimukei Yosef (Sof Hilchos Tum'ah) and Rashi (Pesachim 92b DH she'Nidash): Since many people have walked over the field after the grave was plowed, surely all bones stuck to their sandals and none remain.

Rashi (Nidah 57a DH she'Nidash): The bones stick to people's sandals and get crushed to less than the size of a barley seed.

Rif and Rosh (Avodah Zarah 3b and 1:12): The Halachah follows R. Yosi who permits even if he can find a Rebbi here, for perhaps he will learn better from the Rebbi there. Yosef ha'Kohen followed his Rebbi to Tzidon to learn.

Ran (21a DH Haysah): One may not pass under an Asherah due to Tum'as Avodah Zarah.

Rambam (Hilchos Avodah Zarah 9:12): All of these Tum'os due to Safek are mid'Rabanan.

Note: Perek 9 discusses concern for a cemetery when three graves are found, a Tamei mound that became mixed with Tahor mounds, and a pit in which a Safek Nefel was cast. Perek 8 discussed a grave lost in a field, and the coming Halachos discuss a field in which a grave was plowed.

Rambam (ibid.): Mid'Oraisa, only Vadai Tum'ah is Metamei. We are concerned for Sefekos about Tum'ah, forbidden food, Arayos and Shabbos only mid'Rabanan. However, the Torah forbids a Safek about something punishable by Kares when b'Mezid, for one brings Asham Taluy for such a Safek.

Rebuttal (Ra'avad): We are stringent about a Safek mid'Oraisa, and lenient about a Safek mid'Rabanan. These Safek Tum'os are permitted mid'Oraisa because they are Sefek-Sefeka (two doubts).

Defense (Kesef Mishneh): The Rambam holds that it is a mid'Rabanan stringency to be stringent about a Safek mid'Oraisa. The Ra'avad himself agreed to this in Hilchos Kil'ayim (10:27)!

Rambam (Hilchos Evel 3:13): If a Kohen became Tamei through a Beis ha'Pras or Chutz la'Aretz, he is lashed mid'Rabanan.

Rosh (Kesuvos 2:5): The Yerushalmi (Kil'ayim 40b) says that we are not particular about Mesim or Kil'ayim in the Beis Medrash. This means that it is optional for a Kohen to remain in Ohel ha'Mes for the sake of Talmud Torah. The Bavli permits only Tum'os mid'Rabanan, e.g. Beis ha'Pras.

Rosh (Hilchos Tum'ah 6): Rav Hai Gaon's text in Berachos suggests learning from a Mes Mitzvah, which overrides Tum'as Kohen and Nazir, that Kavod ha'Briyos overrides a Lav mid'Oraisa. This is rejected, for Kohen and Nazir are not Shavah b'Kol (they apply only to certain people). In any case, we should learn that it overrides all Isurim of Tum'ah. This is unlike the Sugya earlier, which said that it overrides only Tum'ah mid'Rabanan, e.g. a Beis ha'Pras.

Perush ha'Mishnayos (Ohalos 17:1): The Tum'ah of the two kinds of Beis ha'Pras are mid'Rabanan.

R. Shimshon (Ohalos 17:3 DH O she'Nimtza and 18:3 DH Chutz): It is a fine to consider a field in which a grave was plowed to be Tamei. This applies to a Yisrael who plowed his own field, but not if one plowed another's field or if a Nochri plowed his own field. If a grave was lost in a Reshus ha'Yachid, we are stringent mid'Oraisa. Many Gemaros say that a Beis ha'Pras is mid'Rabanan. This is when a grave was plowed, or it was lost in a Reshus ha'Rabim.

Panim Me'iros (2:152 DH Aval): Tosfos (Shabbos 15b DH Al) agrees that a grave lost in a Reshus ha'Yachid is mid'Oraisa. Perhaps Rashi (DH Al) says that it is mid'Rabanan because the Gemara never distinguished.

Poskim

Shulchan Aruch (YD 142:9): One may not pass under an Asherah if there is another path. If there is no other path, he runs under it.

Beis Yosef (DH u'Mah): Tosfos (48b DH Iy) says that 'there is no other path' refers to a path as short as the path under the Asherah. If not, there is always another path!

Shach (20): The Gemara connotes that it is permitted only if it steals from the Rabim.

Gra (20): The Shulchan Aruch cites the Rambam. He omitted 'if it steals from the Rabim', for he explains this to mean that the road is underneath it, and this is included in 'there is no other path.' The Ra'avad explains 'it steals from the Rabim'to mean that the road preceded the idolatry.

Shulchan Aruch (369:1): A Kohen may not become Tamei by entering a field in which a grave was plowed and we do not know where.

Shulchan Aruch (372:1): A Kohen may enter a Beis ha'Pras (a field in which a grave was lost and plowed) only if he needs to get married or learn Torah, and there is no other path. This is even if he could learn elsewhere. If an Avel goes through it, a Kohen may go through it to console him.

Magen Avraham (OC 224:7): The Shulchan Aruch (372:1) does not permit even Tum'ah mid'Rabanan in order to see the honor of kings. The Rambam permits this for seeing even Nochri kings, or to console Avelim. Tosfos says that for other Mitzvos a Kohen may pass through a Beis ha'Pras only if he blows on the ground.

Aruch ha'Shulchan (1): He may go through if necessary for any Mitzvah, e.g. Bikur Cholim.

Shulchan Aruch (ibid.): Similarly, he may become Tamei through a Tum'ah mid'Rabanan to make claims against Nochrim, for this is like saving his money from them. The same applies to every similar case.

Rema: If a Kohen was lying naked and found out that he is in Ohel ha'Mes, a Tum'ah mid'Oraisa, he must leave immediately. He may not wait to dress himself. If he is in a Beis ha'Pras or Chutz la'Aretz, a Tum'ah mid'Rabanan, he dresses himself first, for Kavod ha'Briyos is great (and overrides mid'Rabanan laws). If he was sleeping in Ohel ha'Mes, one must wake him so he will leave.

Shach (2): This is only for Tum'as Ohel mid'Oraisa. Tum'ah that comes through a window a Tefach by a Tefach, or 'Sof Tum'ah Latzeis' is only mid'Rabanan.

Magen Avraham (343:2): This is wrong. Tum'ah that comes through a window a Tefach by a Tefach is mid'Oraisa. The Beis Yosef citing the Rambam, Toras ha'Adam (Kohanim 38), Tosfos (Yevamos 103b DH Kivan, Nidah 57a DH Ilan), Sukah 18a, and all the Mishnayos in Ohalos say so. The Beis Yosef brings an opinion that Sof Tum'ah Latzeis is mid'Oraisa, so a Kohen must remove his son from there if the son has understanding.

Pischei Teshuvah (3): Some say that the Shach says only that Sof Tum'ah Latzeis is mid'Rabanan.

Aruch ha'Shulchan (2): All laws of Tum'ah are a tradition from Sinai.

Shach (3): When the Kohen is sleeping he transgresses b'Shogeg. Even though he does no action, it is Asur mid'Oraisa. One need not wake him if the Isur is mid'Rabanan.

Gra (DH Aval): Tosfos Berachos (20a DH Shev) says that the Gemara concludes that Kavod ha'Briyos overrides even Tum'ah mid'Oraisa, since the Isur of Tum'ah is not Shavah b'Kol. However, Rashi's opinion is primary; Kavod ha'Briyos does not override Tum'ah mid'Oraisa. (Rather, the Torah never forbade Tum'ah regarding a Mes Mitzvah.)

R. Akiva Eiger (Teshuvah 2:18): Do not say that since Kohanim are Temei'im nowadays, they need not be concerned for Tum'os mid'Rabanan, e.g. Sof Tum'ah Latzeis. This is wrong. The Ra'avad exempts them even mid'Rabanan. The other Poskim obligate them even mid'Oraisa!