Every sacrifice has its time limit. For example, the shelamim, the peace-offering, which is shared among the Kohanim, the owner and those whom he invites, is eaten for two days and the night that is between them. However, after this limit is reached, whatever remains must be burned:
And that which remains (V’HANOTAR) of the meat of the offering, on the third day shall it be burned in fire (Vayikra 7:17).

Thus, any of the meat that has not been consumed by the end of the second day is called notar (remainder). In like manner, any sacrifice that is left over after its time limit is considered notar. In fact, the Torah prohibits the intentional leaving-over of any sacrifice past its time; it is tantamount to deliberately causing a physical defect in the animal (Ibid. 22:30; Rambam, “Laws of Invalidated Sanctified Things,” 18:9). Notar must be burned, but not until the third day, that is, during daylight hours (Sefer HaChinuch, ascribed to either R. Aharon HaLevi or R. Pinchas HaLevi of Barcelona, mid-13th Century, Commandment § 143, § 287).

Furthermore,
And if some of the meat of his shelamim offering will indeed be eaten (HEI’ACHOL YEI’ACHEIL) on the third day, it will not be accepted (LO YEIRATZEH); the one who offers it (HA’MAKRIV OTO), it shall not be considered for him (LO YEICHASHEIV LO); it shall be rejected (PIGGUL YIHYEH). And the soul that eats of it shall bear his iniquity (verse 18).
This means that for eating piggul (rejected sacrificial food) intentionally, one is punished with karet, spiritual excision, meaning death from Heaven (Kereitot 2a; Rambam, op. cit. 18:6). Piggul too must be burned (Sefer HaChinuch, loc. cit.).

At first glance, piggul seems to be sacrificial food eaten past its time-limit. According to this, it would be valid within its time-limit, but afterwards it becomes piggul. The problem with such an interpretation, however, is found in the declaration, the one who offers it (HA’MAKRIV OTO), it shall not be considered for him (LO YEICHASHEIV LO).

This suggests that piggul is invalid from the time it is offered. Is it possible that it was valid throughout the designated time, and subsequently eating it after the time limit invalidates it retroactively?!

What is piggul?

Rashi (quoting Torat Kohanim 8:1 and Zevachim 29a) says that the classification of piggul is conferred upon the sacrifice by the intention to eat it beyond its expiration time. This invalid intention renders the sacrifice defective immediately, and it must not be used, even within the allotted time. This law is implied in the words LO YEICHASHEIV LO, because CH-SH-V means “to think.” In addition, piggul occurs only if the sacrifice is valid in every other respect (see Sefer HaChinuch, Commandment § 144).

The repeated verb HEI’ACHOL YEI’ACHEIL (will indeed be eaten) refers to two kinds of “consumption”: that which is eaten by man, and that which is placed on the altar to smolder and burn. Consequently, any sacrifice can become piggul by the intention to eat it or place it on the altar after its deadline. And this can occur at any stage that is considered to be part of the process of “offering” (hakravah, based on the words in the verse HA’MAKRIV OTO). For a sacrificial animal, for example, that process has four stages: slaughtering, collecting the blood, carrying it to the altar and sprinkling it on the horns of the altar.

In the case of piggul, the explanation of the Torah sheb’al peh (Oral teaching) is rather different from the literal reading of the text. Rashbam says bluntly,
“The Sages have uprooted this from its simple meaning,”
and then he proceeds to record the Sages’ definition of piggul. Such is the immense power of the Torah sheb’al peh!

Thus, the intention, the state of mind – the kavvana – of the Kohen who attends to a sacrifice is so crucial to the offering that it can undo it. (It is interesting to note that, while Rashi and Rambam take this at face value – that the thought alone can invalidate – Tosafot suggest that piggul status is conferred only if the thought is expressed aloud in words. See Pesachim 63a, s.v. “Rabbi Meir” and Bava Metzia 43b s.v. “Ha’choshev.”)

Actually, there are three levels of disqualifying thoughts with regard to sacrifices:

1. Change of name ― such as offering as a peace-offering (shelamim) an animal consecrated as a sin-offering;
2. Change of place ― intending to eat the sacrifice outside its designated place.
3. Change of time.

Kavvana to change the name (in most cases) does not invalidate the sacrifice qua sacrifice, although the owner has not discharged his obligation thereby, and he must redo it. Change of place further disqualifies the sacrifice, although there is no penalty of karet. Change of time is piggul, as we have said, and carries with it the penalty of karet (Rambam, op. cit. 13:1,2; 15:1; 16:1).

Perhaps these three kavvanot correlate to three kinds of kedushah, or sanctity:
• holiness of designation, such as Kohanim and utensils for the Sanctuary
• holiness of place, such as the Land of Israel and the Temple Mount
• holiness of time, such as Shabbat and the festivals
(A similar division is found in Rav Avraham Yitzchak HaCohen Kook, 1865-1935, Orot HaKodesh II, pp. 303-304.) Sacrifices must be sanctified in all three dimensions. Perhaps also time is the most severely treated of the three kavvanot because time-sanctity is the most elemental, as it is the first type of holiness introduced into the world (Bereishit 2:3).

Kavvana is central to sacrifices, as Sefer HaChinuch (loc. cit.) explains:
“The purpose of an offering is to make people’s thoughts worthy and to form a conception in their soul, out of the activity of their hand, of the evil of sin and the goodness of upright, honest ways. Therefore, since its main reason concerns the thoughts, it is right that it should become disqualified by a thought about it that swerves from the upright, honest path in regard to any of its tasks.”