הַפֶּסַח שֶׁשְּׁחָטוֹ שֶׁלֹּא לִשְׁמוֹ, וְקִבֵּל וְהִלֵּךְ וְזָרַק שֶׁלֹּא לִשְׁמוֹ, אוֹ לִשְׁמוֹ וְשֶׁלֹּא לִשְׁמוֹ, אוֹ שֶׁלֹּא לִשְׁמוֹ וְלִשְׁמוֹ, פָּסוּל. כֵּיצַד לִשְׁמוֹ וְשֶׁלֹּא לִשְׁמוֹ, לְשֵׁם פֶּסַח וּלְשֵׁם שְׁלָמִים. שֶׁלֹּא לִשְׁמוֹ וְלִשְׁמוֹ, לְשֵׁם שְׁלָמִים וּלְשֵׁם פָּסַח:
If one did not slaughter the Pesach lishmo (as such, for its own sake) [as when he slaughtered it as a peace-offering], or if he received [its blood in the sprinkling bowl], or brought [the blood to the altar] or sprinkled [the blood on the altar] not lishmo; or lishmo and not lishmo [as when he slaughtered it lishmo and received the blood not lishmo]; or not lishmo and lishmo, it is invalidated. [We are hereby apprised that thought obtains from one (sacrificial) function to another (i.e., if he thought while performing one function to perform another with an unfit thought, e.g., if he thought: "I shall slaughter it lishmo to sprinkle its blood lo lishmo"), the offering is immediately invalidated, even if he did not perform the second function with that unfit thought. And this is how our Mishnah is to be understood, viz.: "Or [if he thought, while slaughtering, to sprinkle the blood lo lishmo] and [he sprinkled it] lishmo, it is unfit. The fact that lo lishmo renders the Pesach offering unfit is derived from (Exodus 12:27): "And you shall say: 'It is a Paschal sacrifice'" — It must be sacrificed as a Paschal offering. And "it" ("hu") connotes a categorical requirement (which, if not observed, invalidates the offering)]. "Lishmo and not lishmo": How so? Leshem Pesach and leshem shelamim (peace-offering). "Shelo lishmo and lishmo". How so? Leshem shelamim and leshem Pesach. (See above).
Tosefta Pesachim
One who slaughtered [the Passover offering] for its purpose but completed [the rituals associated with the sacrifice] for a different purpose -- it is valid because [a sacrifice] is rendered valid through the slaughter. How is it "slaughtered for those who cannot eat it" (Pes. 5:3)? [This applies where] he slaughtered for a sick person or for an elderly person who cannot eat an olive's-bulk. How is it [slaughtered] for "those who are not registered" (ibid.)? [This applies where] he slaughtered it for members of a different collective. [If] he slaughtered for [both] circumcised and uncircumcised, or for [both] impure persons and for pure persons, it is valid. Abba Shaul disqualifies it, and it is logical that it should be disqualified, since [a person's unfit status] at the time [of the sacrifice] disqualifies [a sacrifice], and an uncircumcised person is disqualified *and an impure person is disqualified (following the GR"A). Just as "the time" (i.e., where the butcher both intends that sacrifice be eaten in its proper time and not at its proper time, see Minchat Bikkurim) makes it [disqualified under the principle of] "the part is like the whole," so too an uncircumcised person makes it [disqualified under] "the part is like the whole." Or perhaps look at it this way: Since an impure person and an uncircumcised person are disqualified, just as [partial] impurity does not cause [application of the principle] "the part is like the whole," thus so too a [partially] uncircumcised person does not cause [application of the principle] "the part is like the whole." Let us see to what case it is similar: We derive a matter that does not apply to every offering (i.e., lack of circumcision), from a [different] matter that does not apply to every offering (i.e., impurity), and it is proven from "time," which [also] does not apply to all offerings. Or perhaps look at it this way: We derive a matter which does not permit exception to a general prohibition, from a [different] matter which does not permit an exception to a general prohibition, and it is not proven from impurity, which does permit an exception to a general prohibition.
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