2. Vaisheshika Darshana
Historically, Vaisheshika system has been closely associated with the Nyaya  school of logic. The Vaisheshika school  was founded by Sage Kanaada (Kana-ad, literally, atom-eater).  It postulates an atomic pluralism in terms of  which all objects in the physical universe are reducible to a certain number of  finite atoms. God is regarded as the fundamental force who causes consciousness  in these atoms. The basic text is Kanaada’s Vsisheshika  Sutras.

The logic of  Vaisheshika
Being associated with the school  of logic, Vaisesika texts use logical arguments  to prove that the world is made of finite number of indivisible atoms (paramanus). Later, Vaisesika  philosophers developed a theory to explain the properties of materials as the  interaction of different types of atoms that make up the material. These  materials are called padarthas. According to them the functioning of atoms  was guided or directed by the will of the Supreme Being. They accept the  existence of God called Ishwara or Maheshwara which is the Supreme Intelligent  Being under whose will and guidance this world is created, sustained and  dissolved.

The starting point of the creation is the Will of  God. The first product of the Divine Will is Brahma who is the chief architect  of creation. Brahma proceeds with further creation in accordance with the  totality of the unseen merits and demerits of the individual souls by setting  in motion the atoms to combine with one another causing the world. The process  of dissolution is in the reverse order where Brahma gives up his body and  Ishwara takes charge of the process of dissolution. The whole world is then  reduced to the primary state of padarthas.

Therefore this system is a theistic form of  atomism suggesting that creation is not a process of chance but a choice executed  by God in a well planned manner according to the karmas of the individual jivas  for the proper realization of their ultimate perfection. Over the centuries, the school  merged with the Nyaya system of Indian philosophy to form  the combined school of Nyaya-Vaisesika because  of their closely related metaphysical theories.

3. Samkhya Darshana
Samkhya (or Sankhya),  is regarded as the oldest of the orthodox philosophical systems in Hinduism. The sage Kapila is traditionally considered to be the founder of  the Samkhya school. His text is called Samkhya  Sutras.  However, the earliest  available and reliable text of classical Samkhya is the Samkhya Karika,  written by Ishvara Krishna.

Its philosophy regards the universe as consisting of  two eternal realities: purusha and prakrti. It is therefore a strongly dualist and enumerationist philosophy, characterized by a worldview that  sees the universe as an evolving mixture of distinct dualities (light/dark,  male/female, etc). Historically, the Samkhya school has been closely associated  with the Yoga school of philosophy.

The Metaphysics of Samkhya
Metaphysically, Samkhya maintains a radical duality  between spirit/consciousness (Purusha) and matter (Prakrti). All  physical events are considered to be manifestations of the evolution of Prakrti,  or primal nature (from which all physical bodies are derived). Each sentient  being is a Purusha, and is limitless and unrestricted to its body. Bondage arises when the Purusha is misled as to its own identity and confuses  itself with the physical body. The spirit is liberated with the realization  that it is distinct from and not restricted to physical matter.

The evolution of primal nature is also considered to  be purposeful - Prakrti evolves for the spirit in bondage. The spirit  itself is only a witness to the evolution. The evolution obeys cause-and-effect  relationships, with primal nature itself being the material cause of all  physical creation. The cause and effect theory of Samkhya is called Satkaarya-vaada,  and holds that nothing can really be created from or destroyed into nothingness  - all evolution is simply the transformation of primal nature from one form to  another.

The purushas (souls) are many, conscious and devoid of  all qualities. They are the silent spectators of prakrti (matter or nature),  which is composed of three gunas (dispositions): satva, rajas and tamas  (steadiness, activity and dullness). When the equilibrium of the gunas is  disturbed, the world order evolves. This disturbance is due to the samyoga or  effective contact between the purusha and prakrti.

The very purpose of evolution of the prakrti into the  world is to give the purusha a chance for liberation. But it is the same  prakrti and its evolution, the world that binds purusha once more. The main  cause of the bondage of purusha and the resultant suffering in the world is  ignorance - nondiscrimination between himself (as pure consciousness or  sentient) and prakrti (the unconscious or insentient entity).

The evolution ceases when the purusha or spirit  realises that it is distinct from primal nature or prakrti. When such viveka dawns purusha, the sentient, pure  conscious entity separates himself from the prakrti, the insentient matter. This  destroys the purpose of evolution, thus stopping Prakrti from evolving for Purusha.

Liberation (kaivalya),  then, consists of the realisation of the difference between the purusha and the  prakrti which can be achieved by following the Eight steps of Yoga (ashtanga yoga) wherein the purusha or  the Soul is the object of meditation.