Bharat has a very rich intellectual and spiritual tradition spanning more than 3000-5000 years. The intellectual, as well as the, spiritual corpus of the sub-continent is captured in the 4 Vedas.

What do the Vedas contain?
The Vedas contain the mystical/spiritual experiences of various Rishis. Most of these are in the form of mantras addressed to a deity or devata. The Veda also has a detailed description of rituals called Yajnas to attain. Apart from these, there are a large body of texts called the Upanishads most of which appear at the end of each Vedic recension (Of course there are exceptions) that discuss esoteric spiritual doctrines, like self-realization. Also discussed are a multitude of topics like morals/ethics for everyday living, Astronomy, Grammar, Ayurveda, Linguistics, Mathematics, Yoga and Spirituality. These spiritual ideas have been encapsulated into what is known as Darshanas.

Darshanas or knowledge systems
Many sages and thinkers had various views on what the Veda had to say in finality. As discussed above, these views over time started to crystallize into concrete systems of thought called “Darshanas”. The Sanskrit word Darshana literally means view or insight. 

The Darshanas discuss various subjects, starting from physical sciences, logic, and philosophies of language, to theories of sound propagation etc. But mainly their focus is on alleviating or removing the pain of existence by applying epistemology, teleology, soteriology etc. In this article, I’ll be discussing those darshanas that rely on the 4 Vedas, or in other words, those that consider vedas as the pramana.

Note that the view Darshana is not same as the word Philosophy. “Philosophy” in the western tradition, is mainly intellectual and is done as an academic exercise, divorced from any spiritual underpinnings. It does not seem to concern itself with teleological problems, AKA in the Vedic tradition as attainment of Moksha or relief from existential problems. A darshana discusses existential problems and proposes solutions for the same. So, I will refrain from using the term “Philosophy” here.

There are 6 Astika Darshanas 

1. Nyaya also called Anvikshiki or logic
2. Vaisheshika, the study of matter discusses physical phenomenon
3. Sankhya, enumeration or counting of various tattvas and through this separation of existence from matter, through intellectual enquiry alone.
4. Yoga, a practical application of Sankhya to attain kaivalya or
   apavarga(Moksha)
5. Poorva Mimamsa, a hermeneutical system concerned with interpretation of Vedic statements, used for correct performance of Vedic rituals and to attain the fruits of those performances
6. Uttar Mimamsa, popularly known as Vedanta now, concerned with the relation of the Jivatma and paramatma and how can apavarga or Moksha be attained

All these 6 Darshanas are based on the authority of the Veda and hence called “Astika” as they accept the statements of the Veda like the existence of the Atma, Dharma etc. Note Astika does not mean the acceptance of a god as commonly understood. Some Darshanas do not accept a god or just barely mention his existence. This article is just a primer or an introduction to each Darshana and does not go into detail of each. That would need a separate article of its own. Neither is the concept of pramanas introduced here. It will be done in detail in another article. Each darshana is now being discussed. Note that it is difficult to historically attribute one person as the founder of a darshana and the sutras and commentaries are attempts to codify/systematize thoughts crystallized over centuries.

Nyaya
Codifiers/pioneers/commentators
Sage Gautama wrote the Nyaya Sutras, and his school can be called prachina or ancient school of Nyaya. Rishi Vatsyayana wrote a commentary for the same. Gangesha Upadhyaya and Raghunath Shiromani later developed what is called Navya Nyaya which is in vogue now. Tatvachintamani was composed by Gangesha which discussed Navya Nyaya principles. Annam Bhatta was another person who wrote the work called Tarka sangraha, which fuses Nyaya and Vaisheshika discussed below.

Core tenets

The Nyaya system (Literally meaning “Rules” or “Justice”) concerns itself with epistemology or what is called “Pramana” and logic, called syllogism in the west. Sage Gautama in the Nyaya sutras discusses the 16 categories called “Padaartha”. These sutras are called “Praachina Nyaya” or ancient Nyaya, which is different from Navya Nyaya in vogue at present. Naiyayikas (People who follow the Nyaya Darshana) hold that human suffering is due to the mistakes/defects produced by actions with the “wrong knowledge”. According to them, moksha is the gaining of the right knowledge thus being able to avoid pain in the future. Thus, this theory is based on realism.

Nyaya has contributed the “Five-part syllogism” as to how does one arrive at an inference, that involves

Nyaya has contributed the “Five-part syllogism” as to how does one arrive at an inference, that involves 

1. Pratijna, the statement to be proved
2. Hetu, the reason
3. Udaharana another similar example to the Pratijna
4. Upanaya reaffirmation
5. Nigamana or conclusion

All this to be discussed in detail later. Note the Dvaita Vedanta school is heavily reliant on the Navya Nyaya or “New school of Nyaya” 

Vaisheshika
Codifiers/pioneers/commentators
Rishi Kanaata Kashyapa wrote the Vaisheshika sutras. One Shankar Mishra wrote a commentary for this

Core tenets
The Vaisheshika darshana is a naturalistic system. Vaisheshika accepts 7 categories of substances unlike Nyaya. The Vaisheshikas propose that the physical universe is reducible to the paramanu, the smallest atom. The entire universe is built up by a combination of various atoms. Worldly experiences arise from the spatial arrangement of atoms, their number etc. Many interesting phenomena like gravity, the absorption of water by plant stems etc are taken up for discussion. The Vaisheshikas propose that Moksha can be attained by a complete understanding of the worldly experience. The Vaisheshika sutras even advocate following the meditative practices of the “Yogachaara” school of Buddhism for Moksha.

In the 13th century after the CE Nyaya and Vaisheshika fused into a single school called Navya Nyaya resulting in the classical Nyaya darshana. This was the accomplishment of one Gangesha Upadhyaya of Mithila desha, though his book Tattvachintamani. Navya-Nyāya developed a sophisticated language and conceptual scheme that allowed it to raise, analyze, and solve problems in logic and epistemology.

Sankhya

Codifiers/pioneers/commentators

Sage Kapila was supposed to be the founder of this system and has written the Kapila Sankhya sutras. Ishvara Krishna composed a Vartika or a word-by-word commentary.

Core tenets 

This darshana views reality composed of 2 independent principles

1. Prakriti, nature or matter, including the human mind 
2. Purusha is the witnessing conscious entity. It is independent of matter and above the experience of the senses or the mind

When prakriti is in an unmanifested state, the 3 gunas Satva, Rajas and Tamas are in equilibrium. But due to some reason if prakriti comes into contact with purusha, mayhem starts and prakriti manifests into 23 tatvas.

1. Intellect
2. Ego
3. Mind
4. The five sensory capacities known as ears, skin, eyes, tongue and nose
5. The five action capacities known as hasta, pada, bak, anus, and upastha
6. The 5 subtle tanmatras, which are the seeds for the gross elements like space, earth, fire, water, air etc 

Thus all human experiences can be considered as the interaction between prakriti and purusha. Ignorance of the Purusha that it is unattached with matter is the cause for suffering. Moksha consists of understanding that the purusha is independent of prakriti.

Sage Kapila is supposed to have composed the Sankhya sutras and Ishvara Krishna supposed to have composed a Karika for this.

Note that there are both theistic and atheistic schools of Sankhya. Generally, the Sankhya Sutras and Karika do not accept a god but accept mature individuals who attain to the level of gods. The Bhagavata purana teaches a theistic version of Sankhya adding “Ishvara” or God to the 23 evolutes of prakriti. Note that advaita and Vishistadvaita vedantas owe their existence to the sankhya darshanas as they accept many aspects of material creation. Advaita especially relies on sankya for the ideas of Avidya, gunas and the idea that moksha can be attained with intellectual enquiry alone.

Yoga

Codifiers/pioneers/commentators

Rishi Patanjali wrote the Patanjali Yoga sutras, for which, Rishi Badarayana wrote a commentary. There are other acharyas like Adinatha, the founder of the Hatha yoga school who wrote the Hatha Yoga pradeepaka.

Core tenets

This is one of the most presently popular darshanas especially in the west. Note there are different schools of Yoga like the Shaivite school, schools from various Agamas etc. But specifically, when Yoga is meant as a darshana, it is based on the yoga sutras of Patanjali. This is also popularly known as the Ashtanga yoga school, or the yoga of 8 limbs. The theoretical frame for the yoga sutra is Sankhya and the definition of moksha in yoga is the same as in Sankhya. The eight limbs are

1. Yama 2. Niyama 3. Asana 4. Pranayama 5. Pratyahara 6. Dharana 7. Dhyana 8. Samadhi

The 1st two limbs mostly prescribe the ethical and moral purity one needs to follow like, non-covetousness, control of senses, charity etc. Patanjali accepts an Ishvara, and he is characterized by his syllable “OM”. Ishvara pranidhana or dedication to Ishvara is one of the steps mentioned as part of Niyama. Note that Patanjali though mentions an Ishvara, he never mentions him as the bestowing moksha.

The 3rd step is the most popular one, again especially in the West where Yogahas become synonymous with Asana. Various complex poses are taught in the west, which are not mentioned by Patanjali. They are found in the Hata Yoga pradeepaka or the Geeranda Samhita, basically Hata yoga texts, which again are purificatory texts to make the aspirant fit for Ashatanga yoga. Patanjali only prescribes “Sukhasana” or just a comfortable pose for meditation.

The 4th step is pranayama which involves breath control.
The 5th step involves withdrawal of the senses.
The 6th step sublimating the mind such that it can contemplate steadily on the goal, without breaking. Just as when oil is poured the oil flows steadily without a break.

The 7th step is focusing the mind on the purusha. The last step is when the mind has ceased its vacillations and the Purusha alone shines forth, separated from Prakriti. This is the state of Moksha or apavarga or Kaivalya. At this stage the sadhaka is freed from the cares of worldly existence.

Note Patanjali Yoga sutras also discusses about various yoga siddhis or powers to be attained but those are distractions to the main goal.

Poorva Mimamsa

Codifiers/pioneers/commentators

The main pioneer for this school is Rishi Jaimini, the disciple of Rishi Vyaasa. He composed the Poorva Mimamsa sutra. Shabara Swamin, Kumarila, Bhatta and Prabhakara have written commentaries for the Poorva Mimamsa sutras.

Core tenets

This darshana is a hermeneutical school that concerns itself with the correct performance of various rites prescribed in the Veda to attain various fruits like heaven, progeny, wealth. Rishis Jaimini is the pioneer of this school, having composed the Poorva Mimamsa sutras. Among the four human purushartas or goals, this darshana concerns itself with a deeper enquiry of dharma. This school postulates that through Dharma one can attain higher regions of experience thus reducing the pain of earthly existence.

This darshan has developed sophisticated rules based on grammar and logic along with its own rules for sentence interpretation. Mimamsa is especially concerned with correct sentence formation. Whereas grammar or Vyakarana is concerned with the origin of words.

Note that Jaimini does not care much to discuss about moksha in the poorva mimamsa sutras or does not postulate the need for a God to disburse the fruits of vedic karma to their performers.

According to this school Moksha is an extreme state of absence of pain. Moksha can happen only when the individual soul has zeroed down its karmic balance. Thus, one should continue to perform his mandated Vedic rite without expecting fruits to keep sin at bay and avoid performing karma with desire. Thus, when the resultant karmic balance is zero, one attains moksha, a state where one is not born again.

After Jaimini and in the medieval times, many theistic schools of Poorva mimamsa came into being. Like Vedant deshikas “Seshvara mimamsa” etc. This school has a sophisticated language theory. This has resulted in this school being used in artificial intelligence. One such application is the usage of the tenets of this darshana to teach unmanned cars ethics, using what is called deontic logic. For more info, check here.
 

Uttara Mimamsa or Vedanta
Codifiers/pioneers/commentators

Sage Badarayana composed the Brahma sutras. Shankara codified the Advaita school, Ramanuja the Vishishtadvaita school and Madhvacharya the Dvaita school. All the 3 acharyas wrote commentaries on the Brahma sutras, Geetha, and some Upanishads.

Core tenets
This is also a very popular darshana in modern times, especially advaita Vedanta. This darshana mainly talks about Moksha based on the Upanishads, Brahma sutra and the Bhagavat Geetha called prasthana trayam. There are 3 main schools of Vedanta.

A) Advaita:

The most famous proponent of this darshana is Shankaracharya. He wrote a commentary from an Advaitic perspective for the Brahma sutras, Upanishads and the Geetha. Note that advaita existed even before Shankara. For example, it is evident from the Vaakypadiya text from Bartruhari the celebrated grammarian that, even Vaiyakaranas or grammarians followed advaita with some differences from the Shankara school. This school considers the Jivatman(Individual self) and the paramatman(Supreme self) to be one. Moksha is the realization by the Jiva that it is not limited and is not different from the paramatma in terms of consciousness. As per the Shankara school, worldly experiences happen due to the misidentification of the individual self with the body. Moksha can be attained now in this life by realizing that one is not the body but the eternal atman.

On losing one’s identity with the body one enters a state of tranquillity. Advaita can be theistic or atheistic as moksha is not dependant on an Ishvare. Shankar prefers a theistic approach, where the grace of God is needed to realize one’s own self as the “parabrahman”. Texts like the Yoga Vasishta explicitly state that such a realization is one’s own effort

B) Vishistadvaita

Ramanuja was the main proponent of this school and wrote commentaries for the Brahma sutra, Geetha and the Upanishads from a Vishitadvait perspective. But through the compositions of the Azhwars or vaishnavite saints, called Divya prabhandam, the school existed earlier than Ramanuja. This school is a theistic school of Vedanta as it posits that Ishvara can only bestow moksha. According to this darshana, the Jiva is an amsha of the paramatma, just like small sparks are an amsha of the main fire source. This school of Vedanta prescribes sharanagati or surrendering to Ishvara and a lifelong service to him. After the present life is over, the devotee reaches vaikuntam and enjoys the bliss of the lord, still maintaining his distinct identity with Ishvara.

C) Dvaita

This too is a theistic school and presupposes a God that can give Moksha. The main acharya of this school is Madhvacharya who again wrote a commentary on the Prasthana trayam from a Dvaitic point of view. This school is heavily based on Nyaya. This school consider the Jiva and paramatma to be entirely different. It mainly teaches the differences between matter, individual Jivas and paramatma. Moksha according to this school can be attained with the grace of Hari and Krishna Bhakti. After the present life ends the devotee attains the abode of Ishvara and each devotee enjoys bliss in proportion to the capability of the Individual jivas, the separation between Jiva and Ishvara intact.

Note each school of Vedanta has different sub sects and the purpose of this article is not to discuss those.

Conclusion
As stated in the introduction, the purpose of this article is to give its reader a brief introduction to the various Indian knowledge systems or  schools of thought. The fundamental difference between Indian and western knowledge systems is that western philosophy is academic while our knowledge systems are spiritual in nature and character. Therefore, if you belong to any particular school of thought, you are encouraged to embody its core tenets and principles.