Chullin 2:7 - 2:8

ורבי אליעזר פוסל – if the animal belongs to a heathen. For even though it is a Jew who is performing the slaughtering, it benefits the thought-processes of the heathen, since the unexpressed thought of the heathen is directed to idolatry.

חצר כבד – the large lobe of the liver

אמר רבי יוסי קל וחומר – Since there is no benefit for the thought-processes of its owner, since a Jew performs the slaughter.

ומה במקום שמחשבה פוסלת – that is, with regard to Holy things, as it states (Leviticus 7:18): “[If any of the flesh of his sacrifice of well-being is eaten on the third day, it shall not be acceptable;] it shall not count for him who offered it. It is an offensive thing [and the person who eats of it shall bear his guilt”]. It [the Biblical verse] is read “he shall not think” -that is to say, he should not think about eating it outside of the appropriate time since it will be a rejected sacrifice in consequence of an improper intention in the mind of the officiating priest.

אין הכל הולך אלא אחר העובד – as it is written (Leviticus 7:18) “it shall not count for him who offered it” – but the owners are not invalidated by their thoughts for the individual who offers it is the priest.

מקום שאין המחשבה פוסלת – The Gemara (Hullin 39b) explains our Mishnah in that it should [understood] in this manner: just as thought-processes invalidate [something offered] in Holy matters through four forms of service, everything follows only [the thought-patterns of] the individual worshipper. Whereas concerning Hullin–ordinary meat, thought-processes only invalidate in two areas, does it not follow that everything follows after [the thought-processes of] the ritual slaughterer? In the place where thought-processes invalidate those sacrifices offered in the realm of the holy things with regard to four acts of divine worship: ritual slaughter, reception of the blood, sprinkling of the blood and the carrying of the portions of the sacrifice to the altar ascent, on which of these that he thought that on the condition that he would eat from the sacrifice at an inappropriate time, does it make the sacrifice rejected in consequence of an improper intention in the mind of the officiating priest? But even though there is this stringency, the thought-processes only follow after the individual worshipper. Regarding Hullin–ordinary meat, in the matter of idolatry, thought-processes do not invalidate in four aspects of worship but rather in only two: in slaughter and in sprinkling [of the blood]. And regarding these, it is written [in these verses] (Exodus chapter 22, verse 19): “Whoever sacrifices to a god [other than the LORD alone shall be proscribed]” [and] (Psalms 16 verse 4): “I will have no part of their bloody libations; [their names will not pass my lips].” But reception of the blood and the carrying of the portions of the sacrifice to the altar ascent are not written–mentioned in these verses. But burning on the altar, even though it is connected to idolatry, it is, however, not worship to lose an animal because of the burning of its fats on the altar for idolatrous worship where it is not slaughtered and where its blood is not sprinkled for idolatrous purposes, for even inside, the sacrifice is not invalidated if he thought about the eating of meat at the time of the burning of the fats, and since we found a leniency in thought-processes outside [the altar], it is the law that we can be lenient in this and that the matter will not be dependent upon anyone other than the actual slaughterer. And the Halakha follows [the opinion] of Rabbi Yosi.

השוחט לשם הרים וכו' שחיטתו פסולה – an idolatrous offering does not prohibit one from deriving benefit from it, since all of these [things] are not done for idolatrous [purposes], as it is written (Deuteronomy chapter 12, verse 2): “[You must destroy all the sites at which the nations you are to dispossess worshiped] their gods, whether on lofty mountains [and on hills or under any luxuriant tree],” and not on the mountains of their gods. But however, it is prohibited to eat it, because it is similar to slaughter for the sake of idolatrous [purposes] by exchanging something [of their own in its place]. And specifically if he said: לשם הרים, לשם גבעות–in honor of mountains, in honor of hills (which is the language used in the Mishnah), but if he [the person making the offering] said: to the angel appointed on the mountains and on the hills, this is considered the sacrifices of the dead and it is prohibited to derive benefit [from them].