Among the six Darshana Sutras, Sāṅkhya can be said to be oldest one which is written by Kapila. Most of people read or refer Sāṅkhya Karika to study Sāṅkhya philosophy probably because it is the oldest surviving work on Sāṅkhya.

Searching about Sāṅkhya Sutras, we can find original text from Sanskrit Wikisource or from Vedic Reserve site. I want to know whether this available Sutras are those which are written by Kapila or not. On some source I found that It is Sāṅkhya Pravachana Sutras (सांख्य प्रवचन सूत्र). And according to some source, Sāṅkhya Pravachana Sutras are modern work and is not original Sāṅkhya Sutras written by Kapila whereas some says it is another name of Sāṅkhya Sutras.

So, I am looking for an answer which shed some light on

  • Whether Sāṅkhya Sutras and Sāṅnkhya Pravachana Sutras are the same text or different.
  • If they are different then the Sutras which we have (linked above) are Sāṅkhya Sutras or Sāṅkhya Pravachana Sutras.
  • If it's later one then are the original Sutras written by Kapila available or lost?

Good question, but a real answer is lost in the sands of time. Chandradhar Sharma in his work A Critical Survey of Indian Philosophy (https://archive.org/details/IndianPhilosophyACriticalSurvey), chapter entitled Sankhya:

Tradition regards Kapila as the founder of this system. But Sankyha-pravachana-sutra which is attributed to him is generally regarded by scholars as a work of the fourteenth century A.D., because it has not been referred to by the earliest writers of the other schools, because it criticizes the rival systems and because it wants to revive theism. So far as theism is concerned, we maintain that the original Sankhya was theistic. But the fact that the work has been ignored and Ishvarakrshna's Karika has been referred to instead by the earlier writers, as well as the fact that it criticizes other systems goes against this work being a work of Kapila himself. As Ishvarakrsna himself speaks of Kapila, Asuri, and Panchashikha, it seems probable that these were historical personages whose works have been lost. Kapila certainly flourished before Buddha and he must have composed Sankhya-sutra which work was lost long ago. Ishvarakrsna's Sankhya-Karika seems to be the earliest available and the most popular work of this system. Besides this we have Gaudapada's Sankhya-Karika-bhasya, Vachaspati Mishra's Tattva-Kaumudi and Vijnana-bhiksu's Sankhya-pravachana-bhasya.

In his work, A History of Indian Philosophy, Volume 1, Surendranath Dasgupta writes in Chapter 4 (https://www.wisdomlib.org/hinduism):

The Samkhya system is ascribed to a mythical Kapila, but the earliest works on the subject are probably now lost.

Dasgupta goes into greater details as to the later works in Chapter 7, same volume. He writes:

A word of explanation is necessary as regards my interpretation of the Samkhya-Yoga system. The Samkhya karika is the oldest Samkhya text on which we have commentaries by later writers. The Samkhya sutra was not referred to by and writer unitl it was commented upon by Aniruddha (fifteenth century A.D.). Even Gunaratna of the fourteenth century A.D. who made allusions to a number of Samkhya works, did not make any reference to the Samkhya sutra, and no other writer who is known to have flourished before Gunaratna seems ot have made any reference to the Samkhya sutra.

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