Gemara

(Mishnah): If a woman miscarried, but does not know whether or not a child came out, she is Safek Yoledes Zachar or Nekevah, Safek Nidah.

Kidushin 39a (Rav Asi): A tradition from Moshe from Sinai forbids Orlah in Chutz La'aretz.

Question (R. Zeira - Mishnah): Safek Orlah in Eretz Yisrael is forbidden. In Chutz La'aretz, you may buy it, as long as you don't see the seller picking Vadai Orlah.

Answer (Rav Asi): The tradition permits a Safek and forbids Vadai.

Rishonim

Rambam (Hilchos Shechitah 5:3): Even though all laws of Terefos are a tradition from Sinai, since the only when explicit in the Torah is Drusah, Chachamim were stringent about it, and any Safek about it is forbidden. Regarding the other seven Terefos, some Sefekos are permitted.

Rambam (Hilchos Mikva'os 8:6): If there is Safek whether the connection between two Mikva'os is big enough, they do not join, because the source of Tevilah is from the Torah. We are stringent about all such matters, even though the Shi'ur is a tradition from Moshe from Sinai.

R. Shimshon (on Mikva'os 6:7): The Tosefta (Mikva'os 5:4) says that anything with a source from the Torah but the Shi'ur is mid'Rabanan, a Safek about it is Tamei.

Perush ha'Mishnayos: This does not contradict what I said that Shi'urim are a tradition from Sinai, for anything not (explicitly) written is called mi'Divrei Sofrim.

Tosfos (29a DH Teshev): She is concerned for Tum'as Yoledes Nekevah, even though there is a Sefek-Sefeka. If we would exempt her due to the Sefek-Sefeka, we would also be lenient if she sees blood on days 34 and 41, to say that perhaps it was not a male, so a Sefek-Sefeka says that she did not begin Nidah now. These leniencies contradict each other. However, regarding one who does not know when she gave birth, we are stringent even though there are several Sefekos.

Poskim

Beis Yosef (YD 294 DH u'Mah she'Chasav uv'Chutzah): The Tur says that in Eretz Yisrael, Safek Orlah is forbidden, and in Chutz la'Aretz, Orlah is only a tradition from Moshe from Sinai, therefore we are lenient about a Safek. This is wrong. Regarding other a tradition from Sinai, we forbid a Safek. This is clear from the Gemara's question, and the answer, that a special tradition permits Safek Orlah in Chutz la'Aretz. Perhaps the Tur really wrote 'it is a Halachah (tradition) that we are lenient about a Safek', and scribes erred and wrote 'Hilkach (therefore) we are lenient about a Safek.' However, if so he did not need to mention the Isur in Eretz Yisrael.

Pri Chodosh (3): Tosfos holds that when there are contradictory leniencies in Sefek-Sefekos, we are stringent about both of them. However, since we are lenient about a Safek mid'Rabanan, we can be lenient even if there is Tartei d'Sasrei regarding two people. This is when the matter is not evident, e.g. a Safek whether it was day or night. If a matter comes in front of us, we are not lenient about both of them, for this would make Divrei Chachamim look ludicrous.

Sha'ar ha'Melech (Hilchos Mikva'os 10:6 DH ul'Inyan): We say that Safek Eruv (Techumim) is Kosher. Surely, one may not go 2000 Amos from his Eruv and 2000 Amos from his house. Even though each of these is a Safek mid'Rabanan, this is Tartei d'Sasrei. In any case he transgresses! The case of two who told a person to be Me'arev for them is different, for there, there are two people, like the Pri Chodosh wrote. Does 'Safek Eruv Kosher' mean that one may go 2000 Amos from his house and lose (the Heter to go) 2000 Amos from his Eruv? Or, perhaps he may go 2000 Amos from his Eruv, but he may not go 2000 Amos from his house. According to the first Perush, both should be forbidden, for they are Tartei d'Sasrei. When a Sefek-Sefeka leads to Tartei d'Sasrei, Tosfos says that we are stringent in both ways, for there is no reason to be lenient about one of them more than the other. The same applies to a single Safek about a mid'Rabanan law, for it is like a Sefek-Sefeka about a Torah law. The Bartenura rules like the Rambam in Mikva'os 2:3 (to be lenient about a Safek about Mayim She'uvim, even without a Chazakah), but regarding Eruv he requires a Chazakah, like Tosfos. This is because without a Chazakah we are stringent because it is Tartei d'Sasrei.

Sha'ar ha'Melech (ibid., Klal 4): Tosfos holds that Terumah of all Peros other than grain, wine and oil is mid'Rabanan. Why was R. Akiva stringent to take Ma'aser Sheni and Ma'aser Oni from an Esrog because he was unsure about which is Rosh Hashanah for trees (Rosh Hashanah 14a)? We are lenient about a Safek mid'Rabanan even when it has a source mid'Oraisa! Rather, if he would be lenient about both, he would not tithe it at all, and this is Tartei d'Sasrei. The Ran (Pesachim 23a) says similarly about reclining (at the Seder). It was not decided whether one must recline for the first two cups or the last two, therefore all require reclining. We cannot say Safek mid'Rabanan l'Kula. This would uproot the Mitzvah of reclining. There is no reason to be lenient about two of them more than the others. However, the Mishneh l'Melech (Megilah 1:11) says that the Ran said so only regarding reclining, for the Safek is about what Chachamim enacted. A Safek about which cities were surrounded by a wall from the days of Yehoshua is different. The Ran says that he reads on the 14th and he is exempt on the 15th, for mid'Rabanan l'Kula. There, Chachamim's enactment remains. mid'Rabanan l'Kula exempts them on the 15th, only if they read on the 14th. If so, it should have sufficed for R. Akiva to separate one tithe! The Ran holds that Ma'aser of Peros is mid'Rabanan. I say that a Safek Mitzvah mid'Rabanan is unlike a Safek Isur mid'Rabanan. For the latter, we must be stringent about both, for there is no reason to favor one over the other. We do not say so about a Safek Mitzvah mid'Rabanan. Ma'aser pertains to a Safek Isur, for one may not eat without tithing.

Question: Why don't the Poskim discuss the Isur of Chamoso after the wife died? According to the Rambam, there is still Kares, so Kidushin does not take effect. According to the Ramban and Rashba (Yevamos 98b), there is not even a Lav, only an Isur Arur, so Kidushin takes effect!

Answer (Noda bi'Yehudah EH 2:148, partially cited in Pischei Teshuvah EH 173:2): Perhaps the Halachah follows R. Yishmael, like the Rosh brings from R. Chananel. And even if the Halachah follows R. Akiva, perhaps R. Akiva agrees that there is Kares after the wife died, like the Rambam says. Therefore we are not concerned for Kidushin or Zikah (to require Chalitzah), due to the Sefek-Sefeka. However, if one married a convert, after she dies he may marry her mother, for this is a Safek about a mid'Rabanan law. (Perhaps the Halachah follows R. Akiva.)

Note: It seems that the Noda bi'Yehudah holds that we can be lenient about a Sefek-Sefeka for a Torah law, even if this leads to a contradictory leniency about a law mid'Rabanan.

Chavos Ya'ir (192): The Rambam calls a tradition from Moshe from Sinai 'mi'Divrei Sofrim.' The Kesef Mishneh brought supports for this from Medrashim which call Shi'urim 'mi'Divrei Sofrim', even though Shi'urim are a tradition from Sinai. I say that the Tur holds that even though it is considered mid'Oraisa, we are lenient about a Safek. The Gemara asked 'if Vadai is Asur, how can we be Mezalzel (belittle) a Safek'? (Note: Also the Taz had this text. It is not in our text.) It did not ask 'how can we permit a Safek'? The question was only why we allow him to pick. This is why also the Tur forbids this. We do not permit Safek Kidushei Kesef (which is not explicit in the Torah) due to the severity of Eshes Ish. Alternatively, marrying a woman in this Safek (due to another man) belittles the Isur, similar to the case of Orlah.

Noda bi'Yehudah (2 YD 146): We are lenient about a Safek about a matter that is primarily a tradition from Sinai. Teshuvas (ha'Rashba) 263, attributed to the Ramban says that laws of excommunication are not mid'Oraisa, for if so, Chachamim could not (choose to) be lenient or stringent about them. Rather, they are a tradition. This shows that we are lenient about a Safek regarding laws known from tradition.

Be'er Yitzchak (YD 1 Anaf 5): If one says 'I know that I specified to give a certain amount to Hekdesh, but I do not know how much' (he must give an amount that surely, he did not pledge more than this). If he is unsure whether or not he pledged at all, he gives the smallest amount (he might have pledged), for it is a Sefek-Sefeka. If an enactment was made recently, it is considered mid'Oraisa, and we are stringent about a Safek. If it was from previous generations, it is considered mid'Rabanan and we are lenient about a Safek. The Noda bi'Yehudah (2 YD 146) says that for a Tzibur that made a Cherem, it is mid'Oraisa. For later generations, which did not make the Cherem, it is like a tradition. It is no more stringent than a tradition from Sinai, for which we are lenient about a Safek.

Shivas Tziyon (48): Also the Shach (YD 294:19) is stringent about every tradition from Sinai. Why didn't the Beis Yosef mention the Rambam, who says that if the Ikar is not from the Torah, but it is a tradition from Sinai, we are lenient about a Safek? The Beis Yosef himself (Kesef Mishneh, Reish Hilchos Ishus) brought the Tosefta in Mikva'os, which connotes like this! Also Be'er Yakov (YD 294:29) holds that a tradition from Sinai is totally mid'Oraisa, and we are stringent about a Safek. He holds that the Rambam says that regarding the other Terefos, we are lenient about a Sefek-Sefeka. The Rambam holds that the Torah permits every Safek, therefore a Sefek-Sefeka is permitted (like a Safek mid'Rabanan). He was bothered by the Darchei Moshe's question, why Ula says that all eight Terefos are a tradition from Sinai (Chulin 43a). "U'Vasar ba'Sadeh Treifah" explicitly forbids Drusah! Rather, the tradition forbids a Safek, therefore Sefek-Sefeka is forbidden mid'Rabanan. This is difficult. The Rambam in Hilchos Mikva'os explicitly says that the Torah permits a Safek about Shi'urim, which are a tradition from Sinai, unless the source is mid'Oraisa. The Beis Yosef has a good proof against the Rambam.

Rebuttal (Shivas Tziyon): The Rambam said that when the Ikar is mid'Oraisa, we are stringent about a Safek, for the tradition merely explains the verse. The Torah discussed Orlah in Eretz Yisrael. In Kidushin we asked that the tradition in Chutz la'Aretz explains the verse, so we must be stringent about a Safek. The Taz (294:13) says that the tradition Stam forbids Orlah in Chutz la'Aretz. We infer that a Safek is permitted, for if not, the Torah would have Stam forbidden Orlah, without mention of Eretz Yisrael. Similarly, we must say that the tradition about Drusah (even though it is explicit in the Torah) teaches that we are stringent about a Safek about it, but we are lenient about a Safek about other Terefos.