Sāṅkhya is the study of material elements. That’s what normally in the west is called metaphysics. In short, the Sāṅkhya system includes analytical knowledge that enables one to distinguish between matter and spirit.
The original Saṅkhya system was introduced during the reign of Svayambhuva Manu, at the beginning of the current day of Brahma by Lord Kapila, the son of Devahuti. This original system explains the material elements, as well as the workings of the universe, studies the causes of suffering for the jivas, and so on, leading ultimately to the process of devotional service to the Lord. This original philosophy of Saṅkhya is explained in the third canto of Srimad Bhagavatam.
Later, however, an impostor Kapila appeared, propounding another philosophy with the same name. This atheistic Saṅkhya studies the material elements (prakrti) and accepts the existence of the soul (purusa) without accepting the existence of Isvara, or God. According to this atheistic Saṅkhya philosophy, the entire material manifestation is simply based on a principle of cause and effect that has its ultimate cause on prakrti.
In Vaishnava philosophy we accept this this material world is not false, but illusory. Although temporary, the material manifestation factually exists and everything that exists should be used in Krsna’s service. When we do that, we understand that ultimately there is no material world. Since everything is a transformation of Krsna’s energy, everything is connected with Him, and everything is ultimately spiritual. However, under the influence of Maya, we try to separate things from Krsna, and that’s what makes them material. As long as we are under the false concepts of “I” and “Mine”, we live in the material illusion, and as soon we start seeing everything in connection with Krsna and using everything in His service we become liberated, even if still technically living in this world. In other words, there is a delicate balance between the ideas of this world being real and illusory.
However, other Indian schools of thought have other ideas.
The philosophers of the Advaita school (Mayavadis), for example, accept the principle of Vivartavada, the idea that the material manifestation is ultimately unreal, and is caused simply by illusion. For example, I may see a rope on the road and mistake it for a snake. In this case, the rope is not factually transformed into a snake, the appearance of the “snake” is just caused by my misconception. As soon as the mistake is clarified, I understand that there is no snake. Similarly, according to the Mayavadis, this world is unreal and becomes possible only because of illusion.
The Sankhya philosophy, on the other hand, follows the view of Parinamavada. Their idea is that there is a factual transformation of the cause into the effect, just like a slab of stone into a statue, wood into furniture, or milk into yogurt. In other words, their opinion is that the material manifestation really exists, it is not just an illusion.
Carvaka Muni was of the opinion that atoms are the material causes of everything, an opinion that is also shared by Buddhists, Jains, and so on. The Sankhya philosophy is a little more evolved, believing that prakrti, the subtle aggregate of material energy is the ultimate material cause, producing both the gross material elements, as well as the subtle components, such as mind, intelligence, the three material modes, and so on. Apart from prakrti, there is purusha, or consciousness, which is the collective of all souls, who interact with prakrti.
Sankhya philosophers believe that the conscious souls are completely different in nature from the inert material energy. Originally they are separated, but when they somehow come closer, the chain of transformations in the material nature that leads to the creation and eventual destruction of the universe is started.
In the process of creation, prakrti gives origin to different subtle energies, which are gradually transformed into gross energies, which in turn give origin to atoms and finally to different material objects. During the process of dissolution, the opposite happens, with physical objects being broken into atoms, which in turn dissolve into the gross energies, which dissolve into the subtle energies, and everything ultimately dissolves back into prakrti, the unmanifested. Between the two stages, many material manifestations appear due to the influence of the three modes of material nature, goodness, passion, and ignorance. According to the Sankhya philosophy, these three modes are the cause of everything we experience in this world, being characterized by pleasure (goodness), pain (passion), and indifference (ignorance). A woman, for example, can be simultaneously the cause of pleasure for her husband, pain to another man who was rejected by her, and indifference to people who don’t know her. All these three different attitudes come from the three gunas or three material modes.
In Vaishnava philosophy, we also study the interaction between matter and spirit due to the influence of the three gunas. The main difference is that in Sankhya there is no reference to God, which makes the explanation very materialist and incorrect in some points. For example, because Isvara, or God, is not accepted, the three material modes are considered the ultimate cause of the cosmic manifestation. According to this idea, the three modes originally exist in a state of equilibrium in prakrti, and when this equilibrium is somehow disturbed, they become distinct and start to act as three separate forces. When separated, the gunas are constantly reacting to each other and this becomes the cause of the whole material manifestation. Pradana or prakrti is the origin of the gunas, and the gunas are the cause of everything else, therefore prakrti is the ultimate cause of everything.
According to them, the whole cosmic manifestation is experienced by the souls, purusha, which is the intelligent principle that guides it. All the material objects that come from prakrti, which are by nature pleasurable, painful, or neutral, have no meaning if they are not experienced by some intelligent force. That intelligent force is purusha, the collective of all souls. Both the prakrti and the purusha are eternal, and when they become close the material manifestation happens, and when in the stage of material bondage, the soul performs actions and both enjoy and suffer under the influence of the three modes. When the soul finally understands he is distinct from matter, he eventually becomes free, going back to his original transcendental state.
The Sankhya philosophy is based on studying the different material elements and interactions between them with the goal of finally becoming free from material influence. The study of buddhi, or intellect, is given especial importance. Buddhi pocesses eight qualities: virtue (dharma); knowledge (jnana); detachment (vairagya); excellence (aisvarya); nonvirtue (adharma); ignorance (ajnana); attachment (avairagya); and imperfection (anaisvarya). The first four manifest under the influence of sattva-guna, and the other four manifest when buddhi is overpowered by ignorance. The soul identifies with buddhi, the material intelligence, and thus experiences what the material intelligence is experiencing. Through knowledge, however, the soul can eventually understand he is transcendental to it.
This conditioning of the soul by material intelligence is also studied in Vaishnava philosophy. In the 5th canto of Srimad Bhagavatam, we have the description of the allegory of King Puranjana. In this allegory, the soul is described as the king and the material intelligence as the queen, both living in the city of the body. The helpless condition of the soul while living under this false identification is described in the following verses:
“When the Queen drank liquor, King Purañjana also engaged in drinking. When the Queen dined, he used to dine with her, and when she chewed, King Purañjana used to chew along with her. When the Queen sang, he also sang. Similarly, when the Queen cried, he also cried, and when the Queen laughed, he also laughed. When the Queen talked loosely, he also talked loosely, and when the Queen walked, the King walked behind her. When the Queen would stand still, the King would also stand still, and when the Queen would lie down in bed, he would also follow and lie down with her. When the Queen sat, he would also sit, and when the Queen heard something, he would follow her to hear the same thing. When the Queen saw something, the King would also look at it, and when the Queen smelled something, the King would follow her to smell the same thing. When the Queen touched something, the King would also touch it, and when the dear Queen was lamenting, the poor King also had to follow her in lamentation. In the same way, when the Queen felt enjoyment, he also enjoyed, and when the Queen was satisfied, the King also felt satisfaction.” (SB 4.25.57-61)
In this way, the view of the Sankhya philosophy more or less describes the interactions between the souls and the material nature that are also explained by Lord Kapila in the original Sankhya, but because they don’t accept the existence of God, their theory is incomplete. Their concept of liberation is also nihilistic, with the souls just returning to an unmanifested state, where there is no activity.
By the time of Vyasadeva, the atheistic Saṅkhya philosophy was already popular, therefore we can find mentions of it in some of his works, where some of its incorrect ideas are refuted.