Q: What is Samkhya-Yoga and does it agree with Hinduism?
A: This is an excellent question that gets into the Metaphysical concepts of Hinduism and some of its varying schools (six major schools). It can be difficult to discuss these things in a simple way as there are many new words and concepts involved. What can complicate this kind of discussion as well is that there are some “schools with schools” or variations on the themes within each of the philosophical schools that promote these ideas. Hence, one may find some variation from teacher to teacher or school to school. The helpful key to understanding this form of Hindu teaching is to remember that Hinduism is not a large block of authoritative and singular practice and belief, rather a varied collection of beliefs united by a few key ideas. Let me start by stating that “Yes, it is a part of Hinduism.”
This is the teaching that is connected to the darsana known as the Samkhya, hence the name. Most of the Puranas also contain a chapter or more on Samkhya-yoga as a path to salvation. It is somewhat an alternative or different school from Vendata as it is not based upon statements of scripture (acc. to Vendanta) and does not rate sruti any higher than reason itself. It also does not recognize the theistic notion of the existence of a deity above purusa and prakriti. Yet both Vedanta and Samkhya accept Pantajali-yoga as a veritable form of purification.
Samkhya offers freedom from misery and says it offers a means to terminate the pain through a dualistic realism. It assumes two beginning realities: prakriti (prakrti) and purusa, the female and male, matter and spirit. It is dualistic in the sense that they exist in polarity from one another. In the existential world they are mixed. Purusa, or consciousness is pulled to experience changes of prakriti as it exists in some mixture of the three gunas of matter: lightness, passion, and darkness. Because of purusa (originally many), the original equilibrium of prakriti (originally one) is disturbed and a change begins. This change begins with intellect and then moves to individualization. Samkhya would disagree with the teaching of one spirit pervading all and offers the idea that there are true individual and plural purusas. The persons who can free themselves from prakriti and who are able to differentiate and discern purusa from prakriti are then able to separate from the body, leaving prakriti inactive and finding therefore, true freedom in this separation. The spirit which was connected to matter is not freed from the cause of its misery and restlessness. The separation of purusa from prakriti is its freedom.
The actual process of discriminating the differentiation of purusa from prakriti and to achieve this freedom is accomplished in yoga (e.g. Pantanjali’s Yoga Sutra). In this yoga, misery is identified in four forms: egoism, attachment, aversion, and love of the material world. To combat these mistakes and problems is the solution: meditation. This meditation destroys the impurities of the mind through the practice of the 8 practices of yoga: yama and niyama-moral commands, asana-body postures, pranayama-breath control, pratyahara-separation from the senses, dharana-concentration, dhyana-meditation, and samadhi-inner mindfulness.
In summary, there is an existential process from the combination of spirit (purusa) and matter (prakriti). When a person suffers and seeks freedom from misery, yoga can provide the reversal of this combination process and lead to the separation of the spirit from matter and produce true contentment in aloneness.
This is a basic description of Samkhya-yoga. I hope this is helpful to you.