Menachem Kasher (1992, Torah Shelemah, additions to parashat Vayikra) quotes the Rama (16th century, Krakow) who presents 12 reasons for sacrifices. The first reason is from the Kuzari (see also Everett Fox 1995, p. 507, who quotes Smith 1927) that the sacrifice connects the giver with G-d through the food. Apparently, the idea is that the sacrifices are a shared meal that joins man with G-d as any regular meal joins people together. I find this difficult since there is no action of G-d by the sacrifices, and as Ehrlich (1900, p. 168) points out the sacrifices are eaten before G-d but not with G-d, see Shemot 18:12.
Reasons #2 and #8 are that sacrifices show a denial of idolatrous beliefs. Rambam (Moreh 3:46) writes that people used to worship sheep, goats and oxen, and hence he suggests that we are commanded to sacrifice these animals to show that we deny any divinity to these animals. (The Rambam does note that as these species are domesticated they are easy to obtain.) Ramban (on Vayikra 1:9) disputes this idea since then the point of sacrifices is only to deny beliefs of foolish people who worshipped the animals. Furthermore, sacrificing the animals is not a denial of the divinity of the animals but a form of honoring the animals. If the Rambam was correct, then we should just eat the animals. Ramban also points that one cannot claim that sacrifices are a “pleasant smell” because they show a denial of idolatrous beliefs since when Noah and Hevel offered their sacrifice nobody else existed, and the Torah records that G-d approved of their sacrifices, Bereshit 4:4, 8:21.
The 3rd reason is the juridical approach. Ramban (on 1:9, apparently quoting Ibn Ezra) writes that when a person pours blood on the altar one should think that he sinned to G-d and really his blood should have been poured on the altar. With this idea, it is G-d's kindness to spare the person and take the sacrifice instead. Yet, Hoffmann (1953, Introduction to Vayikra) points out that some sacrifices were not animals. Also, not all sacrifices were for sins and even when the sacrifices were due to sins the person was not supposed to die for their sins even had there been no sacrifice.
A variation on the 3rd reason is reason #11, that the sacrifice redeems or expiates a person from sins that did not entail cardinal punishment. Bekhor Shor (on Shemot 30:1 and Vayikra 2:13) suggests a further variation that the sacrifices show a person that he has been forgiven for his sins and this stops a person from sinning further. If there had been no sacrifices, then a person might have become discouraged and say, “well I have sinned already what harm is there in sinning again.” Yet, again this rationale of expiation might be applicable when the sacrifice is brought for sins but as pointed out by Hoffmann many sacrifices were not due to sins.
The 4th and 5th reasons are that sacrifices are to stop people from sinning because either the cost of the sacrifice is a financial penalty (#4) or because when one sees the dead animal one realizes how precarious is one’s own life (#5). The problem with reason #4 is that again many sacrifices are not based on sins, most sins do not require sacrifices, and even when sacrifices are due to sins many times they can be brought cheaply, as in Bemidbar 5:15. The problem with reason number five is any non-animal sacrifice and whether seeing a dead animal will really inspire a person to question the point of life. I have been told that for people who are accustomed to seeing blood and guts, the sight of the sacrificed animal would have no impact on them.
The 6th reason is that the sacrifices give a livelihood to the priests. Yet, while this is a result of the sacrifices, it is unlikely to be the reason for the sacrifices since there could have been just donations to the priests, like by the Levites.
The 7th reason is that the fire of the altar destroys the evil inclination within the person sacrificing the animal. How this happens is completely unknown to me.
The 9th and 12th reasons are that the sacrifices lead a person to a further dedication to G-d. I think the idea is that going through the whole process leads one to dedicate himself to G-d. Yet, is this different than other commandments? Maybe sacrifices are a particularly lengthy and physical process.
The 10th reason is Kabbalistic that the sacrifice is a process that unites the divine powers, the Sefirot, see Ramban on 1:9, "the true reason." After recording these 12 opinions the Rama adds a 13th opinion based on a connection with the creation of the world that is also mystical.
Hoffmann (1953, Introduction to Vayikra, pp. 59-67) presents a shorter list of four reasons for sacrifices. One approach is the “rational” approach of the Rambam (Moreh 3:32, also see Luzzatto on Vayikra 1:1). The Rambam writes that really G-d does not want there to be sacrifices, but when the Torah was given the people were so accustomed to religion involving sacrifices that G-d allowed for there to be sacrifices. With this idea, sacrifices do not appear to have any positive value, but the Rambam (Moreh 3:46) believes that there is some positive value to sacrifices since, as mentioned above, he thinks that they can eradicate idolatrous beliefs. Hoffmann rejects this approach since he claims it has no support in Chazal, though the Rambam (Moreh 3:32) argues that his view is supported by the prophets and by some Midrashim. (Maybe there is even a proof from the Torah for this idea, see our discussion below on 10:16-20, "An argument for the sake of heaven," https://lobashamayim.blogspot.co.il/2015/03/vayikra-1016-20-shemini-argument-for.html)
A second approach is anthropological that sacrifices are to propitiate G-d by giving G-d gifts. Hoffmann rejects this approach since the most important part of the sacrificial process was the sprinkling of the blood on the altar, and not the offering of the sacrifice itself. Also, G-d does not need our gifts.
The third approach is the juridical approach, mentioned above.
The fourth approach is the symbolic approach that the sacrifices symbolize a dedication to G-d, which corresponds to approaches nine and twelve above. Hoffmann argues that this approach can be seen in the sacrifices brought prior to Mount Sinai by Hevel, Noah, Avraham (the akedah) and Yaakov, that Hoffman suggests that each person was showing his belief and dedication to G-d. Hoffman argues that an oral dedication is not enough since actions are needed to show that the dedication is sincere. Yet, why is there a need to kill an animal to show a sincere dedication as opposed to some other action?
My guess is that to understand sacrifices, we need to understand the phrase "a pleasing smell" in 1:9. The phrase "a pleasing smell" connotes a good thing, but the use of the imagery of one of the senses, smell, suggests the idea of temporariness as senses give a temporary sensation but then are absent when the cause of the sensation is gone. Smells might be the least permanent of the senses since even when the cause of the smell is present, smells dissipate. This imagery of a "pleasing smell" then suggests that the sacrifices have at best a temporary effect on the person and/ or on G-d's view of the person.
What is this temporary effect? Here we enter the realm of speculation, but following the Rambam's approach (Moreh 3:32), in olden times, sacrifices were how people thought they were connecting to and establishing a relationship with G-d, and hence G-d allowed sacrifices since people then could not conceive of having a religion without sacrifices. The act of offering the animal was considered as giving something to G-d, and this gave the person bringing the sacrifice a feeling of being connected to G-d. The phrase a "pleasing smell" is then G-d's recognition that the person is offering the sacrifice to get close to and to worship Him, and hence the sacrifice is viewed positively. Yet, due to the temporary effect of the sacrifice, the sacrifice has no value in itself and the person is not considered intrinsically better or more religious since he/ she offered sacrifices. For example, I doubt that G-d decided not to curse the world again after the flood just because Noah offered sacrifices when he left the ark, Bereshit 8:21. However, when Noah offered sacrifices, this action was viewed positively by G-d since G-d knew that Noah was offering the sacrifices to thank G-d for saving him and his family from the flood. (This idea would be similar to reason number one of the Rama, though I doubt that people thought they were sharing food with G-d, and number four of Hoffmann, but it minimizes the value of the sacrifice.)
This idea would apply to the korban olah, to the minhah, which was a poor man's olah, and the shelamim sacrifices. It also could apply to a person who brings a sacrifice when he/ she sins accidentally, and who needs to "re-connect" with G-d, 4:31. This idea does not apply to the korban pesach, which is a re-enactment of the first korban pesach in Egypt. In Egypt, the sacrifice was necessary to get the blood to put on the doorposts, and the subsequent sacrifices are to remember that sacrifice. Possibly for this reason, the phrase "a pleasing smell" is never used in reference to the korban pesach since the bringing of this sacrifice is viewed positively forever.
Ehrlich, A. 1990, Hamiqra Kifshuto, Berlin: Poppelauer.
Fox, Everett, 1995, The Five Books of Moses: A new translation, New York: Schocken Books.
Hoffmann, David Tzvi (1843-1921), 1953, Leviticus, Jerusalem: Mossad Harav Kook.
Smith, Robertson, 1927, Lectures on the Religion of the Semites, 3rd edition, New York: Macmillan