Gemara

(Beraisa): "Min ha'Tzon" excludes a Tereifah (for Korbanos).

Question: A Kal va'Chomer should teach this! A person may eat a (Chulin) Ba'al Mum, yet a Ba'al Mum may not be offered. A person may not eat a Tereifah, all the more so it may not be offered!

Sotah 29a: "If meat (of Korbanos) touches anything Tamei, it will not be eaten" - if it became Vadai Tamei, it may not be eaten. If it is a Safek, it may be eaten;

Contradiction: "Every Tahor person may eat meat (of Korbanos)" - if he is Vadai Tahor, he may eat. If he is Safek, he may not eat.

Resolution: When an involved party has understanding, we are stringent about a Safek. When no involved party has understanding, we are lenient.

Chulin 84b (Beraisa - Yosef): Bris Milah overrides Shabbos if we know that it is the eighth day. If we are not sure, it does not override even Yom Tov;

Kisuy does not override Shabbos, even for a definite Chayah or bird. All the more so, it does not override Yom Tov for a Safek Chayah!

114b (Rav Ashi): "Do not eat any abomination" - if the Torah forbade something, one may not eat the result.

115a - Question: If so, it should be forbidden to eat crossbred animals!

Answer: The Torah forbids them to the Mizbe'ach. We infer that they are permitted to people.

Question: If Oso v'Es Beno are slaughtered on the same day, the latter should be forbidden (it was slaughtered b'Isur)!

Answer: The Torah forbids Mechusar Zeman to the Mizbe'ach (including Oso v'Es Beno, which may not be slaughtered yet). We infer that people may eat it.

Rishonim

Rambam (Hilchos Tum'as Mes 9:12): All these and similar Tum'os are mid'Rabanan. Mid'Oraisa, only one Vadai Tum'ah is Metamei. Every Safek about Tum'ah, forbidden food, Ervah and Shabbos is mid'Rabanan. Even so, a Safek about a Chiyuv Kares is Asur mid'Oraisa, for one brings an Asham Taluy for it.

Maharit (DH v'Tu): In Beitzah (8b), the Gemara forbids using oven ash to cover the blood of a Kvi slaughtered on Yom Tov, for he planned only for Vadai Chayos. If the Torah is stringent about a Safek, he should plan even for a Safek! Also, the Gemara says that we forbid to slaughter on Yom Tov, lest one permit its blood. People will think that during the week, Chachamim would tell him to toil to cover the blood (due to Safek), but not on Yom Tov. If the Torah were stringent about Sefekos, also on Yom Tov he should toil!

Rebuttal #1 (Pri Chodosh YD 110 Beis ha'Safek DH Od Hochi'ach): In any case, mid'Rabanan one must cover the blood of a Kvi! We must say that since the Chiyuv is only due to Safek, the ashes are not prepared. This is whether the Chiyuv is mid'Oraisa or mid'Rabanan! If blood of a Behemah became mixed with blood of Vadai Chayos or birds on Yom Tov, Chachamim exempted from covering if it will entail additional toil (Beitzah 8b)!

Rebuttal #2 (Chavas Da'as YD 110 Beis ha'Safek DH u'Mah): Chulin 84b makes a Kal va'Chomer. Vadai Bris Milah overrides Shabbos, but Safek does not override Yom Tov. Vadai Kisuy does not override Shabbos, all the more so, a Safek does not override Yom Tov! Tosfos says that even if the Kal va'Chomer does not apply (when he prepared dirt beforehand), people will err and make this Kal va'Chomer, and assume that if we cover the blood of a Kvi, it must be a Vadai Chayah.

Maharit (DH v'Tu): A Beraisa permits Tum'as Kohanim only for Vadai relatives, but not for a Safek. Why must the Torah teach about Safek? If a Safek is normally permitted, and here it is forbidden, this is not difficult. Those who say that we are normally stringent about a Safek hold that the verse teaches that one is lashed, for Tum'as Kerovim was permitted only for Vadai. Alternatively, one might have thought that the Mitzvah of Tum'as Kerovim applies even to a Safek.

Pri Chodosh (YD 110 Beis ha'Safek DH v'Im Tomar d'Tanya): The verse is needed for when a Chazakah says that he should be Mitamei, e.g. his wife was Safek divorced.

Maharit (DH u'Mah): Even if the Torah is lenient about a Safek, it must teach that we follow the majority for when there is Chezkas Isur, and to teach that we follow the majority even to be stringent.

Question (Kreisi u'Pleisi, Beis ha'Safek DH v'Hinei Yesh): In Rosh Hashanah 13a, the Gemara asked how Bnei Yisrael offered the Omer upon entering Eretz Yisrael. Perhaps it grew a third with the Nochrim! According to the Rambam, what was the question?

Answer (Chavas Da'as Sof 110 Beis ha'Safek): The Rambam learns from Sotah 29a. The Gemara assumed that "meat that touches anything Tamei will not be eaten" and "every Tahor person may eat meat" discuss Vadai Tum'ah and Taharah. There was nothing extra in these verses. This shows that the Torah discusses Vadai, not Safek. This also reveals a difference between action and passivity. When the Torah says 'do not eat this', e.g. pork or Chelev, it forbids only Vadai pork or Chelev, but a Safek is permitted. When it says to do an act, e.g. to marry a Besulah or take an Esrog or eat Matzah, one must do so Vadai. He cannot use a Safek. A Korban must be Tam, i.e. Vadai Tam. A verse was needed for Mamzer to permit when one was mixed with one, e.g. children of a Bas Yisrael and a Mamzeres became mixed. Alternatively, if she went to the Bo'el, the Isur is fixed. Normally, the Torah forbids in this case. Alternatively, the verse permits marrying (both) a Bas Yisrael and a Mamzeres.

Rebuttal (Merumei Sadeh Sotah 29a DH Eima): The Gemara said that the Torah forbids only a Vadai Mamzer or Vadai Tamei (meat) only due to extra verses (Kahal and veha'Basar). If not, we do not say that the Torah discusses only Vadai!

Question (Beis Efrayim EH 2, and Mahari Asad and Imrei Baruch in Otzar Meforshim in Friedman Shulchan Aruch): Menachos 5b did not need a verse to forbid offering a Tereifah. Since a person may not eat it, all the more so it may not be offered. If the Torah permits Safek Tereifah to people, we need a verse to disqualify offering a Safek Tereifah!

Yehudah Ya'aleh (OC 175:3 - Ben ha'Mechaber): We can ask similarly about Chulin 115. We suggested that "do not eat any abomination" should forbid eating Kil'ayim and Oso v'Es Beno. We answered that since they are forbidden to the Mizbe'ach, this implies that people may eat it. According to the Chavas Da'as, people may eat Safek, so "mi'Mashkeh Yisrael" forbids only Vadai to the Mizbe'ach. The verses that forbid Kil'ayim and Oso v'Es Beno to the Mizbe'ach are needed to forbid Safek. If so, we may not infer that they are permitted to people! How can Chavas Da'as explain why is one liable Asham Taluy for Safek Chelev, if not like the Kesef Mishneh? His question from Sotah is not difficult for the Kesef Mishneh. Eating Tamei Kodshim is a Lav. We learn from Mamzer that a Safek is permitted. A Tamei who eats Kodesh is Chayav Kares. We learn from Asham Taluy that a Safek is forbidden.

Beis Efrayim (OC 56): The Rambam holds that the Torah permits even an even Safek because Heter has precedence. Even if if the Chazakah of Heter was weakened, we have no source to be Mechadesh an Isur. It is as if there is a Chazakah of Heter. People challenged the Rambam, for the Gemara learned that we follow the majority from the head of an Olah (we may not dissect it to ensure that the animal is not a Tereifah. The Rambam holds that even a Safek Tereifah is permitted!) I answer that in such a Safek, when the Torah commanded to bring a Kosher animal for an Olah, if there were a Safek that it is Tereifah, we would not be Machshir an even Safek just because we favor the Heter. The Safek is not about the Heter, rather, about whether or not one was Yotzei. The same applies to many Mitzvos Aseh.