One who intended to declare produce to be Terumah and he said 'Maaser' or vice-versa; or if he intended to declare an animal to be an Olah offering and he said 'Shelamim' or vice-versa; if he intended to vow that he will not enter a certain house and he mentioned the wrong house, he has not said anything unless his mouth and heart (i.e. his intention) are the same.

(Gemara): (Mishnah in Maseches Nazir) Beis Shammai say that mistaken Hekdesh is still Hekdesh. And R. Yirmiyah said that if he intended to say that 'this animal is Chulin' and he said 'Olah', it is a valid consecration.

(R. Yosi disagrees): Beis Shammai is referring to when he said, "The first black ox that comes out of my home should be Hekdesh'' and a white ox came out first, it is Hekdesh. (Beis Shammai said that he intended that the next ox that comes out should be Hekdesh, but he assumed that it would be black. However, if he intended to say 'Chulin' and he said 'Hekdesh' even Beis Shammai say that it is not Hekdesh.)

Question: Does our Mishnah follow Beis Hillel or even Beis Shammai?

Answer: According to R. Yirmiyah, who said that Beis Shammai's opinion is that even when he had no intention to make Hekdesh, it is Hekdesh, the Mishnah does not follow Beis Shammai. According to R. Yosi, all agree that if he simply made a mistake over the words, it is not Hekdesh.

(Baraisa): The pasuk states (Vayikra 5:4), "(Or if a person swears, expressing) with his lips'', but not with his heart. I might have thought to exclude even one decided in is heart, but the pasuk used the word, "to express''.

(Shmuel): One who decided in his heart does not need to keep it unless he also expressed it with his lips.

Question (Baraisa): The pasuk says (Shemos 35:5), "...every generous hearted person'' - this is one who decided in his heart (to donate to the Mishkan). Perhaps it's referring to one who expresses in his lips? When the pasuk states (Devarim 23:24), "Keep that which comes through your lips'', that refers to expression of the lips, so what is the meaning of 'every generous hearted person'? It includes even one who decided in his heart. This is against Shmuel who said that one who decided is only obligated when he actually expressed it...?

Answer: Shmuel was discussing bringing a sacrifice for a false Shevuah.

(Mishnah): A gentile's and a Kusi's Terumah and Maaser are valid and their consecration to Hekdesh is valid.

(R. Yehuda): A gentile's vineyard does not have Kerem Revai (the laws relating to 4th year produce).

(Chachamim): It has Kerem Revai.

The Terumah of a gentile can prohibit a mixture into which it falls and if a non-Kohen would accidently eat it, he must pay the extra fifth. R. Shimon exempts.

(Gemara) (Baraisa) (Rebbi): When a gentile brought out produce from his house (claiming that it is Terumah), it is treated with the stringencies of Tevel and Terumah.

(Rabban Shimon ben Gamliel): It is certain Terumah.

(Rebbi): If he took out what he claimed was Maaser Rishon, it is treated with the stringencies of Tevel and Maaser Rishon.

(Rabban Shimon ben Gamliel): He must only separate from it Terumah Gedolah.

If he took out what he claimed was Maaser Sheni, it is treated with the stringencies of Tevel and Maaser Sheni.

(Rabban Shimon ben Gamliel): He must only separate from it Terumah Gedolah and Maaser Rishon.

(R. Yosi b'R. Bun): Rebbi was concerned that perhaps he separated from one species for another species. Rabban Shimon ben Gamliel was only concerned that the gentile separated Maaser before Terumah so that it was still obligated in Terumah Gedolah. (Similarly in the case of Maaser Sheni, he was concerned that the gentile separated it before Terumah and Maaser Rishon.

The Mishnah taught that the Terumah of a gentile can prohibit a mixture into which it falls and if a non-Kohen would accidently eat it, he must pay the extra fifth. R. Shimon exempts.

(R. Zeira): I said before R. Abahu in the name of R. Yochanan - Over which case do they disagree? Over a gentile's Terumah of his own granary, but if he merely bought produce from a Jew (and then separated from it Terumah), even R. Shimon agrees that a non-Kohen would need to pay the extra fifth.

(R. Abahu in the name of R. Yochanan to R. Zeira): They also disagree over that case.

Question: If so, there is a question over the opinion of R. Shimon - R. Shimon said that the separation of a gentile exempts his produce from Tevel on a Torah level, even if he bought it from a Jew...?

Answer: Even though a gentile's Kodshim are valid on a Torah level; nevertheless, R. Shimon exempts them, as is taught...

(Mishnah in Zevachim): For the Kodshim of gentiles, one would not be liable for the prohibitions of Pigul, Nosar and Tameh and one who slaughtered them outside of the Temple courtyard is exempt. This is the opinion of R. Shimon. R. Yosi says that one would be liable.

They wanted to suggest that R. Shimon only disagrees over adding a fifth, but he agrees that it would prohibit a mixture. But they discovered a Baraisa that teaches that he disagrees in both cases.