Contrary to popular belief, there is no single religion called "Hinduism". "Hinduism" is the blanket term Westerners use to designate all the religions that developed on the Indian subcontinent except Buddhism, Jainism, and Sikhism. The term "Hindu" is Persian, and derived from the Greek name for the Indus (Sanskrit Sindhu) river, Indos (from which we get the word "India"). Originally it simply meant "People of, and beyond (i.e. East of), the Indus river". The Moslem invaders of the eleventh and thirteenth centuries used the term to designate those Indians who would not convert to Islam, and who were not Buddhists. This Islamic use of the word was not as a religious label, but a term of separation from Islam and Buddhism. Only in the sixteenth century was the word first used by European merchants and missionaries to refer to the non-Moslem majority in India as a specific religion, the "Hindus" [Hans Küng, Christianity and the World Religions, pp.140-1].
Although sharing certain metaphysical opinions (karma, reincarnation, emanation, etc), these religions also developed a number of specific theologies. Some were dualistic and Theistic in the manner of the Judaeo-Christian outlook, as in Southern or Tamil Shaivism and in the Madhva-Chaitanya stream in Vaishnuism. But others were strongly emanationist, such as the Pancharatra cosmo-theology in Vaishnuism, and the Kashmir Shaivite philosophical system known as Trika or "Triadism" because it postulates three fundamental principles of manifestation: Shiva, Shakti, and the Soul. This latter cosmology was later incorporated into Shaktism (or Tantra), just as Shaivism adopted occult Shakta concepts such as the seven chakras or centres of consciousness aligned along the spine.
To lump together the diverse "orthodox" (Vedic-based) religions of Vishnu, Shiva, Shakti, Ganesha, etc, as "Hindu", just because they arose from a common cultural milieu and share certain doctrinal points in common, is like lumping together Judaism, Christianity, and Islam, as different sects of a single religion for the same reasons [Hans Küng, Christianity and the World Religions, p.143].
Even so, things are not so simple. While there have been disputes among both Vaishnavs and Saivism followers but even among them, their is not one who will not believe in Shiva or Vishnu. The bone of contention is basically who is greater, Shiva or Vishnu. But both believe in Them. You will not find anyone who claims to be Hindu but believes exclusively in either Shiva or Vishnu. (comment by Saurav posted the Kheper Forum; 22 07 05)
More on Hinduism
Hinduism - wikipedia article
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