1) SANCTIFYING HALF OF THE AMOUNT OF A MINCHAH
QUESTIONS: Rebbi Yochanan maintains that sanctifying half of the flour of the Kohen Gadol's daily Minchas Chavitin in one vessel, and half in another vessel, is ineffective. The entire amount must be sanctified in one vessel, even though it will be divided later and half offered in the morning and half towards evening. The Gemara asks that Rebbi Yochanan seems to contradict himself, because he rules elsewhere that if a person separates half of the minimum amount of a Minchah with intention to add to it later, that half is sanctified.
The Gemara answers that when the person intends to add more flour later ("Da'ato l'Hosif"), the law is different. In such a case, half of the flour may be sanctified by itself. The Gemara proves this from the ruling of Rebbi Yosi who says that although a Kli Shares must be full in order to be Mekadesh its contents, when the person has intention to add to it later, it is Mekadesh its contents even when it is not yet full.
What is the Gemara's question on Rebbi Yochanan in the first place? Rebbi Yochanan clearly states in his second ruling that when a person separates half of the minimum amount of a Minchah "with intention to add to it" later, that half is sanctified. That case clearly differs from the case of the Minchas Chavitin, where the Kohen has no intention to add to the flour in each vessel later. What does the Gemara add when it answers that "Da'ato l'Hosif" is different?
Moreover, what does the Gemara prove from Rebbi Yosi's ruling? Rebbi Yosi merely reiterates the ruling of Rebbi Yochanan, but he does not explain what the difference is between a Minchas Chavitin that was sanctified in halves and a case of "Da'ato l'Hosif," in which case sanctifying half of the Minchah is effective.
ANSWERS: To answer these questions, it is necessary to understand how "Da'ato l'Hosif" works to allow a partial amount of a Minchah offering to become Kadosh. There are two ways in which it may work. One way is that it gives half of a Minchah a degree of being fit for being offered. Since there will be more flour added later, the half that is there now is not viewed as an independent amount, but rather it is viewed as a half of a whole Minchah, and thus it has a certain degree of validity for being offered (even though it cannot actually be offered until it contains the entire amount).
A second way that "Da'ato l'Hosif" works is that even though it is not considered fit to be offered, since the person is in the middle of the process of being Mekadesh a whole Minchah the Kidush takes effect even when only half of the flour is present. It is viewed as one long process of Kidush, and every part of the Minchah that enters the vessel becomes Kadosh.
When the Gemara asks that Rebbi Yochanan seems to contradict himself, the Gemara understands that "Da'ato l'Hosif" works to be Mekadesh half of a Minchah in the first way described above. The Gemara reasons as follows. If a partial amount of flour can become Kadosh because it is fit to be offered as part of more flour that will be added later, then it must not be necessary to fulfill all of the conditions of the Korban for the Kidush process. As long as "Da'ato l'Hosif" gives it a status of eligibility, to some degree, to be offered (by allowing it to be viewed not merely as a small amount of flour, but rather as half of a larger amount), that suffices to make it Kadosh. Consequently, a Minchas Chavitin should also be able to become Kadosh in halves, since each half is fit to be offered even without "Da'ato l'Hosif." (The Chavitin does not need to be "half of a whole amount" in order to be considered fit to be offered, since this amount is always the amount that is offered on the Mizbe'ach.) Even though it is missing the conditions for being offered (i.e. being Mekadesh the entire Minchah before beginning the Hakravah), the Kidush nevertheless should be effective, since Kidush takes effect as long as the flour is fit, to some degree, to be offered.
Accordingly, the Gemara is asking that if Rebbi Yochanan says that "Da'ato l'Hosif" is enough to be Mekadesh half of the flour by giving it a status of eligibility to be offered, then the Chavitin also should be able to be sanctified in halves (even without "Da'ato l'Hosif"), since each half has a status of eligibility to be offered.
The Gemara answers that the way that "Da'ato l'Hosif" works to be Mekadesh half of a Minchah differs from the way the Gemara assumes in its question. The logic is not that the partial amount is considered fit to be offered. Rather, the logic is that since the Kidush process is going to be completed (by adding more flour later), the Kidush itself takes effect immediately, even on a partial amount of flour. However, this logic applies only when there is actual intent to add more flour later to the partial amount. When one sanctifies the Chavitin in halves, even though each half is fit to be offered, the Kidush process is not going to be concluded. The Kohen has no intention to add more flour to the vessel; this is the end of the Kidush process. When the Gemara answers that "Da'ato l'Hosif" is different, it means that "Da'ato l'Hosif" works by making the Kidush take effect now due to the eventual completion of the Kidush process. That is the difference between the two rulings of Rebbi Yochanan; in the case of the Chavitin, the Kidush process will not be completed later, while in the case of sanctifying half of a Minchah, the Kidush process will be completed later.
The MINCHAS AVRAHAM quotes the BRISKER RAV who explains the proof from the ruling of Rebbi Yosi as follows. Rebbi Yosi is discussing a Kli Shares that is used for measuring. Therefore, when it is not full, it does not measure, and it cannot be Mekadesh its contents. Giving its contents a status of eligibility to be offered does not help, because the problem is not with the Minchah inside of the Kli, but with the Kli itself. Rebbi Yosi says that, nevertheless, when the person offering the Minchah intends to add more flour later, the Kli is Mekadesh its contents. The reason for this must be that since, when the Kli becomes full, it will effectively be measuring its contents and the Kidush will be able to take effect, the Kidush begins as soon as the flour begins to enter the Kli. Placing the flour into the Kli is considered the start of one long act of measuring.
Accordingly, Rebbi Yosi's ruling serves as a basis for the Gemara's answer by proving why "Da'ato l'Hosif" is effective. It works to be Mekadesh the partial amount of a Minchah because the rest of the flour will be added eventually, and thus the Kidush process begins now. In contrast, no more flour will be added to the Chavitin, and thus the Kidush does not take effect in halves. (Mordechai Zvi Dicker)

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2) EATING "KODSHIM" IN THE "HEICHAL"
OPINIONS: Rebbi Yehudah ben Beseira teaches that if Nochrim besiege the Azarah with arrows and other artillery, making it impossible for the Kohanim to enter the Azarah in order to eat Kodshim, the Kohanim may enter the Heichal and eat Kodshei Kodashim there. He derives this from the verse, "ba'Kodesh ha'Kodashim Tochlenu" -- "in the Kodesh ha'Kodashim you shall eat it" (Bamidbar 18:10). (See Insights to Zevachim 63:1 for whether this verse permits the Kohanim to eat Kodshim only in the Heichal, or even in the Kodesh ha'Kodashim.)
The Torah teaches that no one is permitted to enter the Heichal for no valid reason (Vayikra 16:2). However, to enter the Heichal in order to eat Kodshim seems to be a valid reason and should not be included in the prohibition against entering the Heichal for no reason. What, then, prevents the Kohanim from eating Kodshim in the Heichal in the first place, such that a special allowance is needed, and how does the danger posed by Nochrim permit it?
(a) The MINCHAS CHINUCH (184:6) understands that once the Torah permits entering the Heichal during a siege in order to eat Kodshim, it must be that entering the Heichal in order to eat Kodshim is not prohibited, even when there is no siege. However, the Gemara (9a) teaches that another factor prevents one from eating there unless there are extenuating circumstances ("b'She'as ha'Dechak"): it is improper for a person to eat in the presence of his master. Therefore, l'Chatchilah, Kohanim may not enter the Heichal to eat Kodshim, not because this is a transgression of entering the Heichal for no reason, but because it is improper.
The Minchas Chinuch writes that, according to his approach, if a Kohen would enter the Heichal in order to eat Kodshim at a time when Nochrim are not besieging the Azarah, he would not be punished with Malkus, and he would fulfill the Mitzvah of eating Kodshim. Since "b'She'as ha'Dechak" he is permitted to eat Kodshim in the Heichal, he is not considered to be entering the Heichal with no purpose, and although it is improper to eat in the Heichal, he still fulfills the Mitzvah.
(b) The BRISKER RAV explains the allowance to eat in the Heichal in a different manner. RASHI (DH Hekifu) writes that the siege of the Nochrim creates an actual threat to life, a situation of Piku'ach Nefesh, to anyone standing in the Azarah. Rashi implies that it is only because of the threat to life that one is permitted to enter the Heichal. Without a threat to life, entering the Heichal to eat Kodshim is included in the prohibition against entering the Heichal for no reason (Vayikra 16:2).
However, if entering the Heichal to eat Kodshim is included in the prohibition, then why should it be permitted in a case of Piku'ach Nefesh? The Kohanim certainly are permitted to enter the Heichal to protect their lives, but they also can escape from the Azarah completely and thereby save their lives. Why are they allowed to enter the Heichal?
The answer is that when there is nowhere else to eat the Kodshim (due to the danger of the artillery falling in the Azarah, and since eating Kodshim outside the Azarah is forbidden), entering the Heichal to eat the Kodshim is permitted as part of the Avodah. The Avodah requires that the Kohanim enter the Heichal in order to eat the Kodshim, and thus it is not considered an entry for no reason.
Therefore, according to the Brisker Rav, when there is no threat to life, the Kohanim are prohibited to enter the Heichal and eat Kodshim there because doing so constitutes entering the Heichal for no reason, and they will be punished with Malkus for doing so. Only when there is a danger to life, entering the Heichal is no longer considered unnecessary for the Avodah and it is permitted. (Mordechai Zvi Dicker)

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