Overview of Hindu philosophy
Hinduism is not comparable to Christianity or Islam in that it's not a single coherent religion. In fact it would be more accurate to think of Hinduism as a civilization comparable to western civilization. Both Hindu civilization and western civilization contain multiple distinct strands of philosophical and religious thought, many of them diametrically opposed to each other.
The study of western philosophy is different from the study of Indian philosophy in that in western philosophy, the philosophers are taken as individual contributors and analysis is usually in chronological order considering how one philosopher was influenced by his predecessors and how he influenced his successors. In Indian philosophy the philosophers aligned themselves to particular schools of thought and argued against philosophers of different schools. In the course of these debates the maxims of the various schools were tweaked and modified or deleted so they could survive the intellectual war. The analysis of Indian philosophy is therefore more centred around the parallel evolution of the various schools than focused on individual philosophers. It is effectively the tracking of millennia long arguments and counter arguments between the various schools. As an artefact of this context, most Indian philosophical literature exists in the expositional form of hypothetical debates with proponents of rival schools.
Before the arrival of Buddhism in the 6th Century BC, Hindu philosophy seemed to have reached a dead end.
1. On the one hand there were the hymns and rituals of the Vedas with little scope for expansion of thought.
2. On the other hand there was the final conclusion of the Upanishads that held that Brahman was the answer to everything and everything else was false and illusory. Under this perspective there were no other worthwhile questions of the same magnitude worth exploring.
3. Finally there were the materialists of the Carvaka school of thought which rejected the authority of the Vedas and concepts like 'the soul', reincarnation and Moksha. According to this school of thought, the point of life was to enjoy it. Along with this group of non-orthodox thought (Nastik) we can also club the deterministic school of Ajivakas (we have no free will and therefore there is no good or bad) and the seemingly nihilistic school of Ajita Kesakambali (there is no other world, nor is this one real, there is no good or bad and we are all going to die)
The arrival of Buddhism and Jainism challenged the orthodox Vedic thinking and forced adherents to come up with counter-arguments. As a result of these debates various different schools of thought emerged. By the 3rd Century AD (the Golden age of the Guptas) there were roughly 9 distinct traditions.
The first 6 were derived from the Vedas and accepted their authority.
1. Samkhya (or Kapila Samkhya) - A dualistic school of thought that did not believe in the existence of God. According to this school the Universe is made of Purusha (consciousness) & Prakriti (mind/matter). Liberation occurs when Purusha stops mis-identifying itself as Prakriti and realizes it is distinct.
2. Yoga (or Patanjali Samkhya) - This is almost identical to the Samkhkya school of thought except that in Yoga there is a God (Ishwar). Yoga practices can unify Purusha & Prakriti. There are seven different schools of Yoga:
i) Raja Yoga (8 steps including meditation, breath control, physical asanas, etc)
ii) Jnana Yoga (philosophical insight can lead to liberation - similar in this respect to Vedanta)
iii) Karma Yoga (using everyday work as a mechanism for achieving enlightenment)
iv) Bhakti Yoga (devotion to God)
v) Tantra yoga (pycho-spiritual teachings)
vi) Mantra yoga (using the psycho-acoustical properties of words to concentrate the mind)
vii) Hatha Yoga (preparatory steps for Raja Yoga such as physical yoga poses)
3. Purva Mimamsa - Principles on how to interpret the Vedas so that sacrifices can be done properly
4. Vedanta - The Advaita Vedanta of Adi Shankaracharya believes that both the Atman (individual consciousness) and Brahman (universal consciousness) are actually the one and same. The universe is non-dualistic and any experience of separation is as a result of 'Maya' (illusion) which ends with enlightenment. There are also dualistic schools such as Vishishtadvaita of Ramanuja, Dvaita of Madhavacharya, Dvaitadvaita of Nimbarka, Shuddhadvaita of Vallabhacharya, Acintya Bheda Abheda of Chaitanya Mahaprabhu. These non-dualistic schools interpret the Upanishads in a way that allows for a God separate from the material Universe and also from the individual consciousness. These dualistic schools allowed for Vaishnavist/Bhakti worship of Krishna/Vishna as personifications of Brahman.
5. Nyaya - Deals primarily with the cultivation of logic, in particular which sources of knowledge are valid (inference, comparison, perception and testimony) and what are the mistakes one can make through them that would result in false knowledge. Nyaya differs from western analytical thought in that it uses this understanding specifically for the purpose of spiritual liberation.
6. Vaisheshika - Is a school of atomism that speculates on what elements matter, consciousness, etc are made up of.
Post the Gupta age, Samkhya eventually got absorbed into Yoga. Vaisheshika merged into Nyaya, which itself survived till the 17th Century as Navya Nyaya. Out of the original 6 astik schools, most of the existing strands of thought today centre around Yoga and the various Vedantic schools. Mimamsa lost prominence as a philosophical school of thought but still shows up in today's India in the various Hindu rituals and sacrifices.
Between the 2nd and 8th Centuries new theistic Shaivite schools of thought (Pashupata, Shaiva Siddhant, Kashmir Shaivism) were added to the mix. Shaivites disdained what they felt was Vaishnavites servitude to the supreme being. They felt that the supreme being was not separate but something they could merge with. Shaivites feel that the soul possesses the attributes of the Supreme Deity when it becomes liberated from the 'germ of every pain'. The Tantric tradition of spiritual practices related to ecstatic union and use of spiritual energy is primarily derived from Samkhya and Vedantic thought but with a number of unique innovations and is often closely related to Shaivite traditions of merging with the supreme being.
Apart from the original 6 astik (orthodox) schools that existed in the Gupta age, there are also 3 main nastik (non-orthodox) schools which reject the authority of the Vedas but are still considered part of Hinduism
1. Buddhist - Originally an agnostic/atheistic school, Buddhism rejected rituals and the caste system
2. Jain - Exponents of Ahimsa (non-violence). Influenced orthodox schools in ending animal sacrifice
3. Carvaka - Atheist materialist philosophy which rejects the concept of karma, rebirth, etc. One school of Carvakists believed there was no such thing as a soul and the other school believed that there was a soul but that it was destroyed on the death of the body. They were highly critical of orthodox schools of thought and described the Vedas as suffering from the three faults of untruth, self-contradiction and tautology.
Apart from Carvaka materialism, the other schools, for all their differences have some major points of agreement
1. Karma & rebirth
2. Mukti (liberation from rebirth)
3. The soul - Buddhists don't believe in a soul but Nyaya believes it is characterless, Samkhya describes it as pure consciousness and Vedanta describes it as being Sat Chit Ananda (pure being, pure consciousness, pure bliss)
In the 15th Century Sikhism was also founded and is also considered a part of the Hindu civilization. It seems to bear the influence of Islam in that it is a monotheistic faith that believes in one true God but it also has many concepts of Hinduism such as Maya and Karma.
Modern Indian philosophy was developed during British occupation(1750-1947). The philosophers in this era gave contemporary meaning to traditional philosophy. Some of them were Bal Gangadhar Tilak, Swami Vivekananda, Rabindranath Tagore, Sri Aurobindo, Mahapandit Rahul Sankrityayan, Swami Sahajanand Saraswati, Ananda Coomaraswamy, Ramana Maharshi, Mahatma Gandhi and Sarvepalli Radhakrishnan.
Among contemporary Indian philosophers, Osho and J. Krishnamurti developed their own schools of thought. Pandurang Shastri Athavale, U. G. Krishnamurti and Krishnananda are other prominent names.