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Samkhya and Yoga are one of the six Astika Darshanas of thoughts in Sanatana Dharma (the other four being Nyaya, Vedanta, Mimamsa and Vaisheshika).

Both Darshanas are said to very closely related. Both philosophies posit the universe consisting of two independent entities i.e. Purusha (consciousness) and Prakriti (matter) which bond together to form a Jiva, which in turn leads to the emergence of buddhi (intellect) and ahamkara (ego). Both Darshanas are concerned with breaking the bonds between Purusha and Prakriti through Kaivalya which leads to Moksha. The two Darshanas also rely on three pramanas mainly i.e. pratyaksa (perception), anumana (inference) and sabda (testimony). In fact, some of the arguments by Vyasa in the Brahma Sutras against the Samkhya Darshana directly apply to the Yoga Darshana as well. The only difference I could find between the two philosophies was that Samkhya denies the existence of Ishvara while Yoga accepts the existence of Ishvara.

My question is, apart from existence or nonexistence of Ishvara, what are the other philosophical differences between these two Darshanas?

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This is answered by Bhishma to Yudhishthira in theShanti Parva of the Mahabharata

Yudhishthira said: O sire, what the difference is between the Sankhya and the Yoga system of philosophy. O foremost one of Kuru's race, everything is known to thee, O thou that art conversant with all duties!

Bhishma said: The followers of Sankhya praise the Sankhya system and those regenerate persons that are Yogis praise the Yoga system.....Both those systems of science, O king, have my concurrence and are concurred in by those that are good and wise. If practised duly according to the instructions laid down, both would, O king, cause a person to attain to the highest end.

Yudhishthira said: If the vows, the compassion, and the fruits thereof recommended in both systems be the same, tell me, O grandsire, for what reason then are not their scriptures (in respect of the paths recommended) the same?

The primary difference is that while Samkhya emphasized on the need of viveka to discriminate between the real and the unreal (purusha vs prakriti), Yoga emphasized on the need of samadhi to do the same.

As discussed below,

Right knowledge allows us to discriminate the true subject or soul (Purusha) from Object (Prakriti) and from all of its products. In Samkhya, this discriminatory knowledge is achieved through a purely intellectual process; later, in Yoga, it is achieved through a long process of mental, moral, and physical discipline.

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