1) THE CASE OF THE BLACK OX AND WHITE OX
QUESTION: The Mishnah discusses the dispute between Beis Shamai and Beis Hillel in the case of an object that was sanctified in error as Hekdesh ("Hekdesh Ta'us"). In the specific case in which they argue, a person says that he consecrates "a black ox, which will be the first to come out of my house." A white ox then exits the house first. Beis Shamai says that the Hekdesh takes effect. Beis Hillel says that it does not take effect.
The Gemara initially assumes that Beis Shamai maintains that the Hekdesh takes effect on the white ox. How, though, can it take effect on the white ox if the person specifically said that he wanted the black ox to be Hekdesh? Rav Papa suggests that Beis Shamai means that the Hekdesh takes effect on the first black ox to leave the house (after the white ox). Beis Hillel says that it is not Hekdesh because the person's wording implied that the black ox should become Hekdesh only if it is the first ox to leave the house.
The Gemara concludes (according to Tosfos) that both Rav Papa and Abaye agree that Beis Shamai rules that the white ox is Hekdesh, because had the person known that the white ox would leave the house first he would have made the white ox Hekdesh.
What is the basis for the assumption that the person would have made the white ox Hekdesh had he known that it would leave the house first? All he said was that "a black ox, which will be the first to come out of my house," should be Hekdesh! (ARZEI HA'LEVANON, fn. 1)
ANSWERS:
(a) The ARZEI HA'LEVANON answers that it is obvious that, according to Rav Papa, the Mishnah is discussing a case in which the person later explicitly said that he would have wanted the white ox to become Hekdesh had he known that it would exit first (as Abaye mentions on 31b). The Gemara's question was that even if he later explains that this is what he meant, his explanation should be ignored because it contradicts the words he spoke earlier (since he said "black ox"). This seems to be the intention of TOSFOS (33a, end of DH Ta Shema).
(Although, normally, one may consecrate an object as Hekdesh in his mind (b'Machshavah) by simply deciding that the object is Hekdesh (Shevuos 26b), when he articulates his intent but says the wrong words he prevents his Machshavah from effecting Hekdesh. See Insights to Pesachim 63:2.)
The Arzei ha'Levanon cites support for this approach from the words of TOSFOS RABEINU PERETZ (32b) who explains that in the case of the six people walking along the road, in which Beis Shamai rules that each one is a Nazir because "Nazir Ta'us Havi Nazir," each person is a Nazir only if he explicitly says that "had I known that the person I saw from afar is not the one I thought he was, I still would have accepted upon myself to be a Nazir."
(b) However, TOSFOS RABEINU PERETZ there cites the RI ME'IVRA who explains that even if the Nazir does not state explicitly that he wants to be a Nazir in any case, he still becomes a Nazir. Presumably, in the case of the Mishnah as well, the person does not need to explain afterwards that had he known that the white ox would exit first he would have made it Hekdesh. (When Abaye says that the man said, "Had I known that a white ox would exit first...," his words are Lav Davka; if he does not say that statement, it is still assumed that this is his intention.)
If he said specifically that he wants the black ox to be Hekdesh, why is it assumed that he wants the white ox to be Hekdesh? Apparently, the answer is that it may be assumed (based on an "Umdena") that the person's main intention was that the first ox to exit the house should become Hekdesh, because he had no way of knowing that a black ox would exit the house first. (Even according to Abaye, who explains that in this case an ox already left the house and the owner identifies it as his black ox based on the sound of its hoof-steps, the owner knows that there is a significant margin of error in his ability to identify the ox. The same reasoning applies in the case of the six people on the road: the people who accepted to become Nezirim were aware of the margin of error in their guesses.)
Why are his words not interpreted to mean that the first black ox of all the black oxen to exit the house will be Hekdesh (as Rav Papa originally suggests)? The answer is that Rav Papa himself says that this explanation is not viable because the person should have said "b'Rishon" and not "Rishon."

31b----------------------------------------31b

2) THE KORBANOS OF A NAZIR WHOSE NEZIRUS WAS ANNULLED
QUESTIONS: The Mishnah states that when a person makes a Neder to become a Nazir and separates animals for his Korbanos of Nezirus, and then he has a Chacham annul his oath of Nezirus ("She'eilah"), the animals are Chulin.
TOSFOS explains that since he is not a Nazir, the animal he sanctified as a Chatas Nazir is not needed as a Chatas, and therefore the animal is not Kadosh.
(a) Tosfos explains why the animal designated as a Chatas is not Kadosh. A Chatas may be offered only due to an obligation. When a person who has no obligation to offer a Chatas says, "This animal is a Chatas," the animal does not become Kadosh. Why, though, are the animals designated as an Olah and Shelamim not Kadosh? The Gemara earlier (24a) teaches that if a woman separates animals for the Korbanos of her Nezirus and then her husband annuls her Nezirus, the Olah and the Shelamim remain Kadosh (even according to the view that the husband's Hafarah is "Meikar Akar"). The woman's acceptance of Nezirus shows that she wants to bring Korbanos (as a Nedavah) even if her Nezirus, for whatever reason, will be annulled and she will not be able to bring the animals as Korbanos of Nezirus (see Insights to 24:1). Why does the same logic not apply to the case of the Mishnah here, in which a Chacham annuls the Neder of Nezirus? When the Nazir accepts upon himself Nezirus, he shows that he wants to make the animals Kadosh, and thus they should be Kadosh for a Nedavah even if they cannot be offered as Korbanos of a Nazir!
Tosfos asks a similar question with regard to the Chatas Nazir. In the case of the husband's Hafarah, the woman's Chatas is left to die, but in the case of the Chacham's Hatarah, the Nazir's Chatas becomes Chulin. The answers which Tosfos suggests do not apply to the Olah and Shelamim. Tosfos' first answer is that it is only Rebbi Elazar ha'Kapar who maintains that the Chatas is still Kadosh after Hafarah. This answer explains only why the Chatas is Kadosh after Hafarah but not why the Olah and Shelamim are Kadosh after Hafarah. Although the Gemara earlier (19a) mentions a logical reason for why the Olah of a Nazir Tamei should depend on the statement of Rebbi Elazar ha'Kapar, that reasoning does not apply to the Olah of a Nazir Tahor. The Gemara there says that the Olah of a Nazir is not brought as a "gift" ("Doron") but rather it is a unique obligation of a Nazir on which the atonement of a Nazir depends. Hence, according to Rebbi Elazar ha'Kapar, the Olah of a Nazir Tamei also remains Kadosh. As Tosfos points out (24a, DH veha'Olah), this reasoning applies only to a Nazir Tamei. The Olah and Shelamim of a Nazir Tahor are offered as a "Doron"! Why, then, are they Kadosh after Hafarah? It must be that since they are brought as a "Doron," when the Nazir voluntarily accepts Nezirus upon himself it is as if he voluntarily commits himself to bring the Olah and Shelamim as well. Therefore, he has in mind that even if it turns out later that he is not a Nazir, he still wants to bring the Olah and Shelamim voluntarily as a Nedavah. The same logic should apply in the case of She'eilah!
Tosfos' second answer is that in the case of the husband's Hafarah, the Neder took effect for one moment (see Insights to 22:1), and thus the Chatas remains Kadosh. This answer does not apply to the Olah and Shelamim, since their Kedushah (after Hafarah) is unrelated to the Nezirus which took effect for one moment. The Kedushah of the Shelamim is not that of a Shalmei Nazir but that of an ordinary Shalmei Nedavah (even though it is eaten for only one day and not two days; see Insights to 24:1). Why, then, in the case of She'eilah are the Olah and Shelamim not Kadosh?
(b) This question is even stronger according to Beis Shamai, who maintains that Hekdesh made in error ("Hekdesh Ta'us") remains Hekdesh. Even if the person would not have sanctified the animals had he known that the Chacham would annul his Nezirus and he would not need the Korbanos, nevertheless the animals should remain Kadosh because Hekdesh made in error is Hekdesh! The Mishnah, however, implies that the Olah and Shelamim do not remain Kadosh once the person's Nezirus is repealed. (The RAMBAM (Hilchos Nezirus 9:8) apparently understands that the Mishnah indeed refers only to the Korban Chatas; see KEREN ORAH here. However, the other Rishonim do not differentiate between the Korbanos, and they imply that all of the Nazir's Korbanos become Chulin according to Beis Shamai.)
ANSWERS:
(a) There is a basic difference between Hafarah and She'eilah (Hatarah). In the case of Hafarah, the woman who made herself a Nazir still wants to be a Nazir. Her husband revoked her Nezirus against her will. Since she intended to accept Nezirus and the obligation to bring the Korbanos of Nezirus, it is assumed that she intended to bring the Korbanos as a Nedavah even if she cannot bring them as Korbenos Nezirus. In contrast, when a person has a Chacham annul his Neder, he shows that he did not want to accept Nezirus in the first place. In that case, it is assumed that he wanted neither the Nezirus nor the Korbanos or responsibility for the Korbanos, and he did not intend to bring the Korbanos as a Nedavah in the event that they could not be brought for the Nezirus. This is the reason why the Olah and Shelamim are not Kadosh according to Beis Hillel in the case of She'eilah.
(b) According to Beis Shamai, who maintains that "Hekdesh Ta'us" remains Hekdesh, why are the Olah and Shelamim not Kadosh? Apparently, Tosfos relies on what he writes later (32b, DH v'Im Lav; see Insights there), where he explains that there are different levels of error. There is a Ta'us, an error, which is a total error, and there is a Ta'us which is a partial error. When a person seeks to annul his Nezirus (with She'eilah) because later developments cause him to regret his acceptance of the Nezirus, Beis Shamai rules that She'eilah of Nezirus is like She'eilah of Hekdesh and does not work. She'eilah is effective only because it renders a Neder into a Ta'us, but a Nazir Ta'us remains a Nazir according to Beis Shamai.
However, another type of Ta'us involves a greater degree of error: a person accepts upon himself Nezirus based on the assumption which unexpectedly turns out to be false (for example, a person accepts Nezirus based on the assumption that he has animals to bring as his Korbenos Nezirus, and then he discovers that his animals were stolen). Tosfos writes that in such a case even Beis Shamai agrees that the person is not a Nazir. Such an error is able to cause the annulment of the Nezirus even according to Beis Shamai.
The same distinction applies in the case of a person who designated animals as Korbanos under the assumption that he was a Nazir, and then he repealed his Nezirus (with She'eilah). Since he designated the animals only because he thought he was obligated as a Nazir to bring them, and now it turns out that he was not a Nazir and was not obligated to bring them, even Beis Shamai agrees that he is not Nazir and is not obligated to bring the Korbanos.
When Tosfos writes that after the Nazir annuls his Nezirus with She'eilah, he is like a person who thought he was obligated to bring a Chatas and then discovered that he was not obligated, Tosfos does not mean that the reason the Hekdesh does not take effect is that one cannot voluntarily bring a Chatas. Rather, Tosfos means that the Hekdesh does not take effect because he consecrated the animal based on a mistaken assumption -- that he was obligated to bring the Korban. The same applies to the Olah and Shelamim. (If not for the fact that this type of Ta'us removes the Hekdesh, even the Chatas would be Kadosh with Kedushas Olah, according to Beis Shamai. Since he wanted to make the animal Hekdesh, some form of Hekdesh must take effect, and if the Kedushah of Chatas cannot take effect, the Kedushah of Olah takes effect instead.)
This is also the intent of the Gemara with regard to Temurah (32a). Even Beis Hillel agrees that Temurah takes effect b'Ta'us, such as when a person says, "This animal shall be Temurah for the first animal," and then he repeals (with She'eilah) the Kedushah of the first animal. In such a case, the second animal (the Temurah) loses its Kedushah. The reason it loses its Kedushah is not that it no longer has an object from which to draw its Kedushah (because a Temuras Olah can be made even when no Olah is present). Rather, the reason it loses its Kedushah is that this Ta'us involves a much greater degree of error. (According to this approach, when Tosfos (31a, DH Mi she'Nadar) writes that according to Beis Shamai, the Nazir in the case of the Mishnah here did not actually do She'eilah to annul his Nezirus, but rather he went to a Chacham to determine whether he used the correct wording, Tosfos could also explain that the Nazir was Sho'el on his Nezirus but his She'eilah was based on a mistaken assumption, an absolute Ta'us.)

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