Āstika and nāstika
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Āstika ("there is, there exists") and nāstika ("not āstika") are concepts used by the Brahmanical tradition to classify and contrast Indian philosophies. Āstika has been defined in one of three ways; as those who accept the epistemic authority of the Vedas, as those who accept the existence of ātman, or as those who accept the existence of Ishvara. In contrast, nāstika are those who deny the respective foundational definitions of āstika.
The various definitions for āstika and nastika philosophies has been disputed since ancient times, and there is no consensus. Buddhism is considered to be nāstika, but the Gautama Buddha is considered an avatar of Vishnu in some Hindu traditions. The most studied Āstika schools of Indian philosophies, sometimes referred to as orthodox schools, are six: Nyāyá, Vaiśeṣika, Sāṃkhya, Yoga, Mīmāṃsā, and Vedānta – all schools of Hinduism. The most studied Nāstika schools of Indian philosophies, sometimes referred to as heterodox schools, are four: Buddhism, Jainism, Cārvāka, and Ājīvika – last two are also schools of Hinduism. This orthodox-heterodox terminology is a construct of Western languages, and lacks scholarly roots in Sanskrit. Recent scholarly studies state that there have been various heresiological translations of Āstika and Nāstika in 20th century literature on Indian philosophies, but quite many are unsophisticated and flawed.
Astika and Nastika do not mean "theism" and "atheism" respectively in ancient or medieval era Sanskrit literature. In current Indian languages like Hindi, āstika usually means "theist", while nāstika means "atheist". However, the terms are used differently in Hindu philosophy. For example, Sāṃkhya is both an atheist and āstika (Vedic) philosophy.
As used in Hindu philosophy the differentiation between āstika and nāstika does not refer to theism or atheism. The terms often, but not always, relate to accepting Vedic literature as an authority, particularly on their teachings on Self (Soul). The Veda and Hinduism do not subscribe to or include the concept of an almighty that is separate from oneself i.e. there is no concept of 'god' as in the Christian or Islamic sense. As N. N. Bhattacharyya writes:
The followers of Tantra were often branded as Nāstika by the political proponents of the Vedic tradition. The term Nāstika does not denote an atheist since the Veda presents a godless system with no singular almighty being or multiple almighty beings. It is applied only to those who do not believe in the Vedas. The Sāṃkhyas and Mīmāṃsakas do not believe in God, but they believe in the Vedas and hence they are not Nāstikas. The Buddhists, Jains, and Cārvākas do not believe in the Vedas; hence they are Nāstikas.— N. N. Bhattacharyya
Manusmriti, in verse 2.11, defines Nastika as those who revile "Vedic literature based on two roots of science of reasoning (Śruti and Smriti)". The 9th century Indian scholar Medhatithi analyzed this definition and stated that Nastika does not mean someone who says "Vedic literature are untrue", but rather one who says "Vedic literature are immoral". Medhatithi further noted verse 8.309 of Manusmriti, to provide another aspect of the definition of Nastika as one who believes, "there is no other world, there is no purpose in giving charity, there is no purpose in rituals and the teachings in the Vedic literature."
Manusmriti does not define, or imply a definition for Astika. It is also silent or contradictory on specific rituals such as animal sacrifices, asserting Ahimsa (non-violence, non-injury) is dharma in its verses such as verse 10.63 based on Upanishadic layer of Vedic literature, even though the older layer of Vedic literature mention such sacrifices unlike the later layer of Vedic literature. Indian scholars, such as those from Samkhya, Yoga, Nyaya and Vedanta schools, accepted Astika to be those that include Śabda (शब्द, Aptavacana, testimony of Vedic literature and reliable experts) as a reliable means of epistemology, but they accepted the later ancient layer of the Vedic literature to be superseding the earlier ancient layer.
Definition without reference to Vedas
In contrast to Manusmiriti, the 6th century CE Jain scholar and doxographer Haribhadra, provided a different perspective in his writings on Astika and Nastika. Haribhadra did not consider "reverence for Vedas" as a marker for an Astika. He and other 1st millennium CE Jaina scholars defined Astika as one who "affirms there exists another world, transmigration exists, virtue (punya) exists, vice (paap) exists".
The 7th century scholars Jayaditya and Vamana, in Kasikavrtti of Panini tradition, were silent on the role of or authority of Vedic literature in defining Astika and Nastika. They state, "Astika is the one who believes there exists another world. The opposite of him is the Nastika."
Similarly the widely studied 2nd-3rd century CE Buddhist philosopher Nagarjuna, in Chapter 1 verses 60-61 of Ratnāvalī, wrote Vaiśeṣika and Sāṃkhya schools of Hinduism were Nastika, along with Jainism, his own school of Buddhism and Pudgalavadins (Vātsīputrīya) school of Buddhism.
Definition based on belief in Atman
Astika, in some texts, is defined as those who believe in the existence of Atman (Soul, Self, Spirit), while Nastika being those who deny there is any "soul, self" in human beings and other living beings. All six schools of Hinduism classified as Astika philosophies hold the premise, "Atman exists". Buddhism, in contrast, holds the premise, "Atman does not exist". Asanga Tilakaratna translates Astika as "positivism" and Nastika as "negativism", with Astika illustrated by Brahmanic traditions who accepted "soul and God exists", while Nastika as those traditions, such as Buddhism, who denied "soul and God exists".
Classification of schools
Several Indian intellectual traditions were codified during the medieval period into a standard list of six orthodox systems or ṣaḍdarśanas (also spelled Sad Darshan), all of which cite Vedic authority as their source. Nyaya, Vaisheshika, Samkhya, Yoga, Mimāṃsā and Vedanta are classified as āstika schools:
- Nyāyá, the school of logic
- Vaiśeṣika, the atomist school
- Sāṃkhya, the enumeration school
- Yoga, the school of Patañjali (which assumes the metaphysics of Sāṃkhya)
- Mimāṃsā, the tradition of Vedic exegesis
- Vedanta or Uttara Mimāṃsā, the Upaniṣadic tradition.
These are often coupled into three groups for both historical and conceptual reasons: Nyāyá-Vaiśeṣika, Sāṃkhya-Yoga, and Mimāṃsā-Vedanta.
The main schools of Indian philosophy that do not base their beliefs on the Vedas were regarded as heterodox by Brahmins:
The use of the term nāstika to describe Buddhism and Jainism in India is explained by Gavin Flood as follows:
At an early period, during the formation of the Upaniṣads and the rise of Buddhism and Jainism, we must envisage a common heritage of meditation and mental discipline practiced by renouncers with varying affiliations to non-orthodox (Veda-rejecting) and orthodox (Veda-accepting) traditions.... These schools [such as Buddhism and Jainism] are understandably regarded as heterodox (nāstika) by orthodox (āstika) Brahmanism.— 
Tantric traditions in Hinduism have both āstika and nāstika lines; as Banerji writes in "Tantra in Bengal":
Tantras are ... also divided as āstika or Vedic and nāstika or non-Vedic. In accordance with the predominance of the deity the āstika works are again divided as Śākta, Śaiva, Saura, Gāṇapatya and Vaiṣṇava.— 
Jains themselves have been branded nāstika or not accepting the Vedas, and they in turn have accused many non-Jains of being nāstika. According to Jainism, nastikavada is a system of beliefs that are nāstika in nature. Jains assign the term nastika to one who is ignorant of the meaning of the religious texts or those who deny the existence of the soul.
Although Buddhists have been branded by orthodox or mainstream Hinduism as Nastika, the Buddhists themselves have branded only the Cārvākas as nastika. For example, Nagarjuna wrote in his Ratnavali, that nastikya (nihilism) leads to hell while astikya (affirmation) leads to heaven. Further, the Madhyamika philosopher Chandrakirti, who was accused of being a nastik, wrote in his Prasannapada that emptiness is a method of affirming neither being nor non-being and that nihilists are actually naive realists because they assume that things of this world have self-existent natures, whereas Madhyamikas view all things as arising dependently within the context of casual conditions.
There were also Buddhists that were accused of believing in ideas outside of the Buddha's teachings, and they were called nastika in the "Bodhisattvabhumi" (a section of the Yogacarabhumi by Asanga) and the scripture also declared they should be subject to isolation so their views do not infect the rest of the Buddhist community. Like the Manusmriti, the Bodhisattvabhumi also criticizes the nastika for reliance on logic only.
According to the Sallekha Sutta, belief leading to evil conduct is of three kinds, and natthika ditthi (nastikavada or nihilism), is one of them (the others being ahetuka ditthi or accidentalism and akiriya ditthi or the view of inaction).
According to Buddhist texts, Astikavada is also known as Sabbathikavada.
- Monier-Williams 2006
- Flood 1996, pp. 82.
- Flood: "These schools [such as Buddhism and Jainism] are understandably regarded as heterodox (nāstika) by orthodox (āstika) Brahmanism."
- Andrew J. Nicholson (2013), Unifying Hinduism: Philosophy and Identity in Indian Intellectual History, Columbia University Press, ISBN 978-0231149877, Chapter 9
- GS Ghurye, Indian Sociology Through Ghurye, a Dictionary, Ed: S. Devadas Pillai (2011), ISBN 978-8171548071, page 354
- Wendy Doniger (2014), On Hinduism, Oxford University Press, ISBN 978-0199360079, page 46
- Literature review of secondary references of Buddha as Dashavatara which regard Buddha to be part of standard list:
- A Dictionary of Asian Mythology By David Adams Leeming p. 19 "Avatar"
- Hinduism: An Alphabetical Guide By Roshen Dalal p. 112 "Dashavatara" ""The standard and most accepted list found in Puranas and other texts is: ... Rama, Krishna, Buddha, Kalki."
- The Illustrated Encyclopedia of Hinduism: A-M p. 73 "Avatar"
- Hindu Gods and Goddesses By Sunita Pant Bansal p. 27 "Vishnu Dashavatara"
- Hindu Myths (Penguin Books) pp. 62-63
- The Book of Vishnu (see index)
- Seven secrets of Vishnu By Devdutt Pattanaik p. 203 "In the more popular list of ten avatars of Vishnu, the ninth avatar is shown as Buddha, not Balarama."
- A Dictionary of Hinduism p. 47 "Avatara"
- Gavin D. Flood (13 July 1996). An Introduction to Hinduism. Cambridge University Press. p. 116. ISBN 978-0-521-43878-0.
- Flood 1996, pp. 82, 224–49
- For an overview of this method of classification, with detail on the grouping of schools, see: Radhakrishnan & Moore 1989
- For instance, the "Atheist Society of India" produces a monthly publications Nasthika Yugam, which it translates as "The Age of Atheism".
- Chatterjee, Satischandra; Datta, Dhirendramohan (1984), An Introduction to Indian Philosophy (Eighth Reprint ed.), University of Calcutta, pp. 5, footnote 1,
In modern Indian languages, "āstika" and "nāstika" generally mean "theist" and "atheist", respectively. But in Sanskrit philosophical literature, "āstika" means "one who believes in the authority of the Vedas". ("nāstika" means the opposite of these). The word is used here in the first sense. The six orthodox schools are "āstika", and the Cārvāka is "nāstika" in both the senses.
- "By Sāṃkhya reasoning, the material principle itself simply evolves into complex forms, and there is no need to hold that some spiritual power governs the material principle or its ultimate source." Francis Clooney, CJ, "Restoring 'Hindu Theology' as a category in Indian intellectual discourse", in Flood 2003
- Apte 1965, pp. 240
- Bhattacharyya 1999, pp. 174
- George Williams (2003), Handbook of Hindu Mythology, Oxford University Press, ISBN 978-0195332612, page 65
- Sanskrit: Manusmriti with six scholar commentaries VN Mandlik, page 1310
English: Manusmriti 10.63 Berkeley Center for World Religion, Peace and World Affairs, Georgetown University
- P. Haag and V. Vergiani (Eds., 2009), Studies in the Kāśikāvṛtti, Firenze : Società Editrice Fiorentina, ISBN 978-8860321145
- Markus Dressler and Arvind Mandair (2011), Secularism and Religion-Making, Oxford University Press, ISBN 978-0199782949, page 59 note 39
- Ernst Steinkellner (1991), Studies in the Buddhist Epistemological Tradition: Proceedings of the Second International Dharmakīrti Conference, Vienna, Volume 222, Austrian Academy of Sciences Press, ISBN 978-3700119159, pages 230-238
- C Sharma (2013), A Critical Survey of Indian Philosophy, Motilal Banarsidass, ISBN 978-8120803657, page 66
- Dae-Sook Suh (1994), Korean Studies: New Pacific Currents, University of Hawaii Press, ISBN 978-0824815981, page 171
- John C. Plott et al (2000), Global History of Philosophy: The Axial Age, Volume 1, Motilal Banarsidass, ISBN 978-8120801585, page 63, Quote: "The Buddhist schools reject any Ātman concept. As we have already observed, this is the basic and ineradicable distinction between Hinduism and Buddhism".
- Asanga Tilakaratna (2003, Editors: Anne Blackburn and Jeffrey Samuels), Approaching the Dhamma: Buddhist Texts and Practices in South and Southeast Asia, Pariyatti, ISBN 978-1928706199, pages 128-129;
God, states Tilakaratna, in Brahmanic traditions is Parama-atma (universal soul, Ishvara, Brahman)
- Flood 1996, pp. 231–2
- Flood 1996, pp. 82
- Banerji 1992, pp. 2
- Page i, Forms of Indian Philosophical Literature and Other Papers by V.S. Kambi
- P. 163 Mahāvīra: His Life and Teachings by Bimala Churn Law
- P. 173 Unifying Hinduism: philosophy and identity in Indian intellectual history By Andrew J. Nicholson
- P. 101 A Critical Survey of Indian Philosophy By Chandradhar Sharma
- P. 187 Zen and the Art of Postmodern Philosophy: Two Paths of Liberation from the Representation Mode of Thinking By Carl Olson
- P. 174 Unifying Hinduism: philosophy and identity in Indian intellectual history By Andrew J. Nicholson
- P. 227 Studies in the Buddhist epistemological tradition: proceedings of the Second International Dharmakīrti Conference, Vienna, June 11–16, 1989
- P. 123 Sallekha Sutta: A Discourse on the Refinement of Character By Mahasi Sayadaw, Sobhana
- Apte, V. S. (1965), A Practical Sanskrit Dictionary
- Banerji, S. C. (1992), Tantra in Bengal (Second Revised and Enlarged ed.), Delhi: Manohar, ISBN 81-85425-63-9
- Bhattacharyya, N. N. (1999), History of the Tantric Religion (Second Revised ed.), New Delhi: Manohar, ISBN 81-7304-025-7
- Flood, Gavin (1996), An Introduction to Hinduism, Cambridge: Cambridge University Press, ISBN 81-7596-028-0
- edited by Gavin Flood. (2003), Flood, Gavin, ed., Blackwell companion to Hinduism, Blackwell Publishing, ISBN 0-631-21535-2
- Monier-Williams, Monier (2006), Monier-Williams Sanskrit Dictionary, Nataraj Books, ISBN 1-881338-58-4
- Radhakrishnan, Sarvepalli; Moore, Charles A. (1989) , A Source Book in Indian Philosophy (Princeton paperback 12th ed.), Princeton University Press, ISBN 0-691-01958-4