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As I discuss in this question, by far the most popular school of Hindu philosophy is the Vedanta school, which bases its tenets on the doctrines laid out in the Brahma Sutras, a work by the sage Vyasa that summarizes and systematizes the philosophical teachings of the Upanishads. (You can read the Brahma Sutras here.) Now in Adhyaya 3 Pada 1 Sutra 25 of the Brahma Sutras:

aśuddhamiti cet, na, śabdāt

If it be argued that rites (invoking killing of animals) are unholy, we say, no, since they are sanctioned by scriptures.

As I discuss in this question, most commentators on the Brahma Sutras agree that in this Sutra, Vyasa is saying that animal sacrifice in Vedic Yagnas is not a sin. But while the Vedanta school is unequivocal in its support for animal sacrifice, other schools of Hindu philosophy had different views. In this excerpt from his Sarvartha Siddhi, the Sri Vaishnava Acharya Vedanta Desikan discusses the Samkhya school's view that animal sacrifice is a minor sin:

In this regard the Sāṅkhyas think so: “The prescription about the killing of the animal victim in the Agnīṣomīya says that the killing is a subsidiary to the ritual. But the sentence ‘One should not perform any violence’ encompasses also the violence within the Agnīṣomīya because the word ‘violence’ works without any restriction. And in this way this violence is the cause of something evil but this is easy to be atoned (parihṛ-), since it is Vedic”. In this regard the confutation has been said in the Śārīrakaśāstra: “Although the killing of the animal victim within the Agnīṣomīya causes a major sufferance, it cannot be said to be ‘violence’. In fact, there is [also] not violence when a physician, etc., cut or cauterise, etc., for the sake of heal a tumour, etc. Nor is the scolding of one’s child or pupil by the parents, [teachers], etc. a form of violence. Only a violent act not conformable to the Śāstras and performed by someone causing much sufferance is violence. In this regard, by contrast, although there is separation from the vital breaths, there is no violence, because of the compliance to the Śāstra. Instead, there is protection (rakṣā), because through the interruption of the body of the animal victim, which results in evil, [the sacrifice] causes for that very animal the attainment of a a special body which is conform to the enjoyment of upmost pleasure”. Having in mind this all he said Because of the mention of what is beneficial for the animal. With the mention of the mantra ”You do not indeed die, nor are you injured, you go in the divine with easy paths” (na vā u etan mriyase na riṣyasi devāṃ ideṣi pathibhis sugebhis, ṚV 1.162.21, found also in Rāmānuja’s Gītābhāṣya). it is said that the animal obtains a specific place.

The Shariraka Shastra, by the way, refers to Ramanujacharya's Sri Bhashya, the Sri Vaishnava commentary on the Brahma Sutras. But I'm interested in the part in bold. My question is, did the Samkhya school believe that animal sacrifice in Vedic Yagnas is a sin "that's easy to be atoned"?

It's clear that they thought that animal sacrifice was a sin; here is what verse 2 of Ishwara Krishna's Samkhya Karika, the defining work of the Samkhya school, says in the course of describing the flaws of pursuing happiness through Dharma:

dṛṣṭavadānuśravikaḥ sa hyaviśuddhi kṣayātiśayayuktaḥ ।
tadviparītaḥ śreyān vyaktāvyaktajñavijñānāt ॥

The [means of happiness revealed by the Vedas] is like the evident one, It is linked with impurity, destruction and inequality. Other than that is better,—proceeding from the right cognition of the Manifest, Unmanifest and the Knower.

The word "impurity" refers to the notion that pursuing happiness through Dharma involves killing animals; here is what Gaudapada's Samkhya Karika Bhashya says:

Linked with impurity, because of the slaughter of animals. As it is said: “According to the injunction in the aśvamedha, six hundred animals, minus three, are employed (i.e., slaughtered) at midday.”

But what Samkhya works say that this sin is minor and easily remedied?

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Yes, the Samkhya school does believe animal sacrifice is a minor sin that's easily remedied. Here's what the Advaita philosopher Vachaspati Mishra in this excerpt from the Tattva Kaumudi, his commentary on Ishwara Krishna's Samkhya Karika:

[The means of happiness revealed by the Vedas] is "impure" because sacrifices like soma yagna, etc. are performed by the sacrifice of animals and destruction of corn, etc. Bhagavan Panchashikhacharya says "It is slightly mixed (with impurity), remediable, and bearable." "Svalpahsankarah" means the admixture of the slight sin, productive of evil, caused by the slaughter of animals etc with the principal merit born of the performance of sacrifices like Jyotishtoma, etc. By "Saparihara" is meant that the evil is removable by certain expiatory rites. But, if due to inadvertence, expiatory rites are not observed, then, it, also bears fruit at the time of the fruition of the principal karma. As long as these evil effects are produced so long they are borne with patience; hence it is qualified as "sapratyavamarsha". Adepts who are immersed in the huge lakes of heavenly nectar obtained by the performance of virtuous deeds bear patiently the spark of the fire of misery brought about by sin.

Vachaspati Mishra is quoting the ancient Samkhya philosopher Panchashikha, who was Kapila's shishya's shishya. On a side note, I find the reference to corn interesting; I posted a question on it here.

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