Nyaya and Vaisheshika Systems:
The first twin systems are the Nyaya and the Vaisheshika systems. The two systems are allied together. The Vaisheshika system outlines the scheme of the ontological categories and describes their nature, the origination and the dissolution of the world. The Nyaya System examines the logical explanation, apparatus of human knowledge, the criterion of truth and falsehood, the nature and function of knowledge, its instruments, their limits defects and problems relating to the validity or knowledge. Rishi Gautam wrote the famous Nyayasutra on which an excellent commentary was written by Vatsyayan followed by many othrs. The initiator of Vaisheshika darshan was Kanada whose Vaisheshika sutras were followed by many other explanatory works like Bhasha Parichcheda by Vishwanatha.
The Sankhya System is considered to be the oldest Indian Philosophical system. There are references to this system in the Upanishads, the Gita, and the Mahabharata. The word Sankhya has two meanings; the knowledge and number. Maharshi Kapila is the originator of the system. The two important source books for the system are Isvara Krishna’s Sankhyakarika and the Vachaspati’s Tattva Kaumudi. This system contains elaborate discussions on Purush and Prakriti.
The Yoga System:
Amongst all the systems of Astika school, the Yoga System of Maharshi Patanjali is the most widely known and popularly appreciated system of thought. The system of Yoga is a psychosomatic process for training the mind and keeping the body under control. The source and significantly single inspiration for Indian psychology is the Yoga Sutras of Patanjali. The date assigned to Patanjali is the second century B.C. The Yoga system is considered to be complementary to the Sankhya. If Sankhya is the theory; yoga is its practical side. The Yoga System enables one to realize kaivalya (liberation), i.e., his true nature.
The Mimamsa System:
Among the philosophical systems, the Mimamsa and the Vedanta are exclusively based on the authority of the Vedas. The word Mimamsa means an enquiry. This system holds that the Vedas issue commands and have ritual actions for the purport. This also prescribes certain actions and prohibits certain others. The prime purport of the Vedas is to command duties and prohibit some acts. It is a list of do’s and don’ts. The System is pragmatic in approach.
The Vedanta System:
What is living and vital in Indian Philosophy today is the Vedanta system in its various forms. The Vedanta is the crowning edifice of all the systems. The other philosophical systems are mainly studied as accessories to the study of Vedanta and not as ends in themselves. There are different branches of Vedanta which have grown from the interpretation of the triple text: (i) the Upanishads, (ii) the Gita, (iii) the Vedantasutras. All the commentators claim alike that the systems of philosophy, they have built, are in complete accord with the total unitary import of the three texts, that these texts should have lent themselves to a variety of interpretations even contradictory to one another, is the most amazing nature of these scriptures and their inexhaustible significance. The branches of this system are, the system of Advaita Vedanta (non-dualism) of Shankara, the system of Dvaita Vedanta (dualism) of Madhva, the Dvaitadvaita Vedanta of Nimbarkacharya and Vishistadvaita (qualified non-dualism) of Ramanujacharya.