Question
Does the Bhagavad Gita declare that caste is based on birth?
Answer
Does the Bhagavad Gita declare that caste is based on birth?
Yes it does, according to all ancient and orthodox Vedic commentators.
First, from chapter 1:
1.41 - When unrighteousness prevails, O Krishna the women of the clan become corrupt; when women become corrupt, there arises intermixture of castes.
adharmābhi-bhavāt kṛṣṇa praduṣyanti kula-striyaḥ | strīṣu duṣṭāsu vārṣṇeya jāyate varṇa-saṅkaraḥ || 41 ||
...
1.43 - By the crimes of the clan-destroyers who bring about intermingling of castes, the ancient traditions of the clan and caste are destroyed.
doṣair etaiḥ kula-ghnānāṁ varṇa-saṅkara-kārakaiḥ | utsādyante jāti-dharmāḥ kula-dharmāśca śāśvatāḥ || 43 ||
These verses are saying that when society stops following Dharma, women become corrupt, and when women become corrupt, they will approach any and many men, and their children will be mixed caste or of unknown caste or even without caste like a Mleccha.
The same concept is found in the Vedas and there is even a sutra for it in Jaimini's Purva Mimamsa Sutras, which are commented upon by Shabaracharya:
Adhyaya 1, Pada 2, Sutra 13:
On account of the failings of women, (there can be no certainty regarding one's caste); specially as the son belongs to the progenitor.
Shabara's commentary on that sutra:
Another example of a Vedic text stating what is contrary to direct facts, cited by the Opponent is - "We do not know if we are Brahmanas or non-Brahmanas" (Maitrayaniya Samhita 1.4.11 of the Krishna Yajur Veda). This is auxiliary to the injunction "When the pravaras [ancestral lineages] are being recounted, one should say the deities are our fathers" (Ibid.), which stands in need of justification; and the meaning of the eulogistic passage is that "Even a non-Brahamana would become a Brahmana by the recounting of pravaras [and hence it is necessary for the Brahmana also to recount his pravaras, as one can never be sure of one's brahmanahood (due to possible caste intermixing)"]. It is difficult to know if one is really a Brahmana; - and this is what is figuratively spoken of as "we do not know", and the difficulty in knowing it for certain is due to "the failings of women", and also to the fact that "the son belongs to the progenitor"; this is also indicated by the advice "May you guard this dynastic line with great care." - Apastamba Dharma Sutra 2.6.13.6
The Vedic verse is basically saying, "We don't know if we are Brahmanas or non-Brahmanas, therefore, one should say that their ancestral lineage is the Devas", which admits that caste is based on birth and ancestry.
The Mahabharata says the same thing,
... by uniting themselves with women of other castes, led not by considerations of righteousness but by uncontrolled lust, cause numerous mixed castes to come into existence whose occupations and abodes depend on the circumstances connected with the irregular unions to which they owe their origin.
So all these verses show that the Vedas, Mahabharata, and Bhagavad Gita all unanimously declare that caste is based on birth.
What about Gita verses like 4.13 and 18.41 that are cited by Hindu reformists to try to show that the Gita supports a behavior based caste system?
4.13 - The social system of four castes was generated by Me according to division of Gunas and Karma. Though I am the generator, know Me as a non-agent and immutable.
18.41 - The duties of the Brāhmaṇas, Kṣatriyas; Vaishyas and the Śūdras O Arjuna, are distinctly divided according to their inherent dispositions
brāhmaṇa kṣatriya viśāṃ śūdrāṇāṃ ca paraṅtapa | karmāṇi pravibhaktāni svabhāva prabhavair guṇaiḥ || 41 ||
The word guna in these verses is actually referring to bodily gunas, and not mental gunas. The bodies of the people of the different castes have different gunas, which determines their inherent, genetic predispositions by nature, as this answer shows.
The medieval Vedantic scholar Vedanta Desikan has said,
Owing to the preponderance of such qualities as sattvam, in the body, a man is entitled to be called a Brahmin, a kshatriya, and the like. But this is different from the praise of being a Brahmin that is often given in certain passages, owing to the quality of sattvam and the like in the mind.
Here is Ramanujacharya's commentary for Gita verse 18.41:
Svabhava = nature = own or inherent nature, of Brahmanas, etc. This nature means the past karma that has been the cause of determining the serveral births as Brahmana, etc. The gunas like sattvam, etc are born of this.
...
Duties, varying according to the qualities born of the natures of Brahmanas, etc., are assigned by the Shastras; i.e., the Shastras ddefine that such are the qualities possessed by Brahmanas, etc., such the duties proper to their station, and such their occupations, etc.
So in conclusion, the Bhagavad Gita declares that caste is based on birth.
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