Bechor behemah tehorah - why is it given to the cohen?

In this week's sedrah, the Torah says that it is a mitzva to give the bechor of a kosher domesticated animal to the cohen;


כָּל פֶּטֶר רֶחֶם לְכָל בָּשָׂר אֲשֶׁר יַקְרִיבוּ לַה' בָּאָדָם וּבַבְּהֵמָה יִהְיֶה לָּךְ... אַךְ בְּכוֹר שׁוֹר אוֹ בְכוֹר כֶּשֶׂב אוֹ בְכוֹר עֵז לֹא תִפְדֶּה קֹדֶשׁ הֵם אֶת דָּמָם תִּזְרֹק עַל הַמִּזְבֵּחַ וְאֶת חֶלְבָּם תַּקְטִיר אִשֶּׁה לְרֵיחַ נִיחֹחַ לַה'. וּבְשָׂרָם יִהְיֶה לָּךְ כַּחֲזֵה הַתְּנוּפָה וּכְשׁוֹק הַיָּמִין לְךָ יִהְיֶה.
"The firstborn of all living things which they (the benei yisroel) bring to Hashem whether from man or from animals shall belong to you (the cohanim)But the firstborn of an ox or the firstborn of a sheep or the firstborn of a goat you shall not redeem for they are holy. You shall sprinkle their blood on the mizbeach and you should burn their fat as a fire offering for a pleasing scent to Hashem. And their flesh will be to you like the chest [which is presented as a] wave offering and the right thigh [of a shelamim.]”

There are כ"ד מתנות כהונה - 24 gifts that are given to the cohanim. These include;
·         10 matanos that are given in the beis hamikdash (עשר מתנות במקדש). These are all parts of korbanos.
·         Four matanos that are given in Yerusholayim (ארבע מתנות בירושלים). These are; the hides of kodshei kedashim, bikkurim, the parts that are given to the cohen from the todah and eyl nazir and a bechor.
·         10 matanos that are given outside Yerusholayim (עשר מתנות בגבולים). These do not have the kedusha of a korban at all and include things such as terumah, gezel hager, reishis hagez, etc.

It is not clear what the basis of the obligation to give a bechor to the cohen is. Is it given to the cohen because it is the firstborn, similar to bikkurim and reishis hagez, as the passuk says it is the פטר רחם – the physical firstborn of the sheep or the cow? Or is it given to the cohen because it is a korban, similarly to the eser matanos ba'mikdash, as the passuk says הַיָּמִין וּכְשׁוֹק הַתְּנוּפָה כַּחֲזֵה – it is like parts from other korbanos that have to be given to the cohen?

The Brisker Rov z"l (Chiddushim al ha'Rambam, Hilchos Bechoros) brings a proof from the following gemara;

The gemara in Zevachim (9b) discusses the case of mosar ha’pesach. Mosar ha’pesach is a korban pesach that is left over after pesach, for example, an owner lost his korban pesach, bought a different one to replace it and then found the original korban pesach after shechitah of the new one. The halacha is that mosar ha’pesach is shechted with the intention that it should be a shelamim and this makes it into a korban shelamim.

The gemara suggests other korbanos that the mosar ha’pesach may be shechted as. One of the possibilities is that the mosar hapesach should be able to become a bechor;
אימא שחטיה לשם בכור ליהוי כבכור למאי הילכתא דלא ליבעי נסכים אי נמי דליתביה לכהנים
Let us say if he shechted it to be a bechor then it should become a bechor - what difference would this make? That it would not require nesachim or that it would have to be given to the cohanim [just as a bechor is given to the cohanim].” - The gemara subsequently rejects this suggestion based on a passuk.

At any rate you see that according to the hava aminah of the gemara that mosar ha'pesach can become a bechor, it would have had to be given to the cohanim, notwithstanding the fact that it is not actually a bechor. The Brisker Rov proves from this gemara that the reason that even a normal bechor is given to the cohen is because it is a korban, not because it is physically a peter rechem.

Temuras bechor
There is a machlokess between the Rambam (Temurah 3:2) and Tosafos (Zevachim 75b, d"h bechor eino niphdeh) concerning a temuras bechor. (This occurs where someone took a bechor and another animal and said that the second animal should become a bechor and be a korban instead of the actual bechor.) According to the Rambam the temurah of a bechor is given to the cohanim just like the original, according to tosafos the owner does not need to give it to a cohen because it is not actually a bechor.

The Brisker Rov asks on Tosafos as follows;
We can see from the case of the mosar ha'pesach that a bechor is given to the cohen because it is a korban, not because it is physically a peter rechem. If so, we should say that in the case of a temurah of a bechor that although the temurah is not a peter rechem, nevertheless, because it is a korban it should still be given to the cohen. How then can tosafos say that because it is only a temurah and not a real bechor that it remains the property of the yisroel?

Two causes
The Brisker Rov answers that there are two causes either of which can obligate the owner to give a bechor to the cohen:
·         Either if it is physically a peter rechem even although it is not a korban. For example, the gemara in Bechoros (9b) says that if a yisroel has a partnership with a non-Jew in an animal then it is mutar for the yisroel to use the bechor to do work with the animal and to shear it because it has no kedushah and nevertheless it still has to be given to the cohen.

Or

·         If it is a korban even if it is not physically a bechor as in the gemara’s hava aminah of mosar ha’pesach.

Both the Rambam and Tosafos agree that a bechor has to be given even if it is only a korban bechor and not a peter rechem as in the case of a mosar ha'pesach. However there is a difference between mosar ha'pesach and a temuras bechor. Although both of these korbanos have the kedusha of a bechor without being a peter rechem, the mosar ha'pesach  (in the hava amina of the gemara) is brought as a korban in the beis hamikdash, but a temuras bechor is not. As the mishna in Temurah (21a) says;
תמורת הבכור והמעשר ולדן ולד ולדן עד סוף העולם הרי אלו כבכור וכמעשר ויאכלו במומן לבעלים
“The temurah of a bechor and maaser, their children and their children’s children forever are like a bechor and maaser and are eaten with their mum to the baalim.” (The animal is left to graze until it gets a mum and is then shechted and eaten by their owner.)
The gemara derives this halacha from a passuk in this week’s sedrah;
רחמנא מעטינהו, לא תפדה קדש הם - הם קריבין ואין תמורתן קריבה
“The Torah excluded these from being brought as a korban – the passuk says ‘they shall not be redeemed because they are holy’ – [the word ‘they’ is extra to teach you that] they are brought as a korban but their temurah is not brought as a korban.”

Says the Brisker Rov – although the kedusha of a korban bechor alone is enough to cause it to be given to the cohen (as with the mosar hapesach), this is only where the animal can be brought as a korban to the beis hamikdash. However, in the case of a temuras korban, tosafos is of the opinion that although it has the kedusha of a bechor, nevertheless, because there is a chisaron in the kedushas ha'korban to the extent that it cannot be brought as a korban – it does not become the property of the cohen. According to the Rambam as long as the animal has the kedusha of a bechor it has to be given to the cohen, even if it can not be brought as a korban.

It comes out that both according to Tosafos and the Rambam the passuk in this week's sedrah means that if an animal is either a peter rechem or a korban bechor then it has to be given to the cohen. The machlokess between Tosafos and the Rambam only relates to a case where the animal is a korban and not a peter rechem and also there is a chisaron in its kedusha which causes it not to be able to be brought as a korban in the beis hamikdash. Is this sufficient to make it a gift to the cohen?

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