In contrast with advaita (non-dualist), the most influential and widely followed philosophy expounded by Shankara, Madhva (who is also known as Madhvacharya) maintains that there is an eternal distinction between the individual self and the absolute. As explained by Gavin Flood:
Whereas the Advaita tradition emphasizes the non-difference (abheda) between the self and the absolute, Madhva insists on their complete distinction. Difference or bheda is a cornerstone of his theology and scriptural interpretation.
While each thing is unique, dvaita philosophy notes five categories of difference (bheda):
Despite these differences, there exists a clear and distinct relationship:
Vishnu is accorded supreme status and Lakshmi is his consort. Brahma and Vayu come the next level with both on the same level. Their wives (Saraswati and Bharati) occupy the next level. Garuda, Shesha, Shiva, Indra, Kama, Surya, Chandra, Varuna, Nala, Vignesh and others occupy the succeedingly lower hierarchy.
Madhvacharya taught that the life in the world can be divided into two groups Kshara and Akshara. Kshara refers to life with destructible bodies while Akshara have indestructible body. Lakshmi is Akshara while others from Brahma and so on are Ksharas or Jeevas. Vishnu doesn't have a body that is made up of Prakriti. So he is exempted from this classification.
The basic tenet of Madhavacharya's philosophy is the existence of two kinds of realities, the independent reality (svatantra tatva) and the dependent reality (asvatantra tatva).
The independent reality (svatantra tatva) refers to "God". Four generic names are applicable to or associated with God, as stated in the Bhagavata Purana. They are Paramatman, Brahman, Para Brahman, and Bhagavan.
In general, Madhvacharya's message is that every word and every sound in this entire universe refers to God which he equated with Vishnu.
According to Madhva, only Brahman is independent in every sense of the word.
The dependent reality (asvatantra tatva) refers to the plurality of jivas and prakriti. Both the jivas and nature are dependent on Brahman for their very existence. This dependence is expressed metaphorically as bimba-pratibimba (source-reflection) relation. The reflection is in every way dependent on the source.
Dvaita school belongs to the Realist school of Indian philosophy, in the same category as Samkhya, Nyaya, Vaisheshika and Purva mimamsa schools. They believe that the universe is a real creation of Brahman. The plurality of souls are bound by a "real" bondage due to beginning-less ignorance, and sadhana through Vishnu bhakti is the only way to be released from this bondage. Further, Madhva explains that Jnana or knowledge alone is not sufficient for the release from beginningless avidya or ignorance, since this bondage is sustained by the "Will" of Brahman and so needs Vishnu Prasadam, i.e., God's grace to ultimately break the bonds of Māyā.
The five are given by:
jiiveshvara bheda chaiva jadeshvara bheda tatha |
jiiva-bhedo mithashchaiva jaDa-jiiva-bheda tatha |
mithashcha jada-bhedo.ayam prapajncho bheda-panchakaH ||
"The difference between the jîva (soul) and Îshvara (Creator), and the difference between jaDa (insentient) and Îshvara; and the difference between various jîvas, and the difference between jaDa and jîva; and the difference between various jaDas, these five differences make up the universe."
From the Paramopanishad a.k.a. Parama-shruti, as quoted by Ananda Tîrtha in his 'VishNu-tattva-vinirNaya'.
Contrary to the Idealistic schools like Yogacara, Madhyamika buddhism or Advaita, Dvaita maintains that difference is in the very nature of a substance. This is the reason why some refer to the doctrine of Tattvavâda (the preferred name) as Dvaita. However, Dvaita is thought to be inadequately representative of the true grain of Tattvavâda.
The doctrine of Tattvavâda is considered to be eternal (in a flow-like sense, just as Creation is eternal); in historical times, it was revived by Ananda Tîrtha, who is also known as Madhvâchârya. Because of this, followers of Tattvavâda are called Mâdhvas, meaning followers of Madhva.
Additionally, Madhvacharya differed significantly from traditional Hindu beliefs in his concept of eternal damnation. For example, he divides souls into three classes, one class which qualify for liberation, Mukti-yogyas, another subject to eternal rebirth or eternally transmigrating due to samsara, Nitya-samsarins, and significantly, a class that is eventually condemned to eternal hell or Andhatamas, known as Tamo-yogyas.
Madhva followers cite authorities such as Bhagavad Gita, Chapter 17, verses 2 et seq. "There are three types of inclination, which are the self-same natures of the souls, these being satvika, rajasa, and tamasa," Chapter 16, verses 19-20, "These cruel haters, worst among men in the world, I hurl these evil-doers into the wombs of demons only. Entering into demoniacal wombs and deluded, birth after birth, not attaining me, they thus fall, Oh Arjuna, into a condition still lower than that," for their concept of eternal damnation. Madhvacharaya was the second after Ramanuja in the recent years who revived the timeless Vaishnava tradition. There were 21 different Bashayas (commenteries) before Madhvacharaya. He was the first to establish the facts of tri-patriate classification of souls. By contrast, most Hindus believe that souls will eventually obtain moksha, even after millions of rebirths.
Madhvacharaya during his time not only established dvaita philosophy, but also displayed extraordinary strength and skills to show that he is the third avatara of Vayu, who came down to earth to help people suffering from delusional philosophies and guide them in the right path. Madhvacharaya at the age of 79, year 1317, disappeared from the eyes of humans and continue to reside in Upper Badari in his continuning service to his eternal master Sri Vedavyasa.
Narayana Panditacharya captures Madhvacharaya's life in a beautiful poetic verses in his "Sumadhva Vijaya" which is in 16 Sarga (chapters), this book is an authentic work composed during his own time. This is a very rare work, there is no evidence of anyone composing works on any major philosopher like this before or after him from other disciplines. "Sumadhva Vijaya" is a composition which captures life history of MahdvAcharaya.
Madhvacharya's theology heavily influenced those of later scholars such as Nimbarka, Vallabha, and Chaitanya Mahaprabhu. B. N. K. Sharma notes that Nimbarka's theology is a loose re-write of Madhvacharya's in its most essential aspects. Vallabha even "borrowed without acknowledgement" a verse from Madhvacharya's `sarva-shAstrArtha-sangraha'. The followers of Chaitanya claim a link to Madhvacharya, though such a link is not historically tenable or theologically plausible.
Madhvacharya's singular contribution was to offer a new insight and analysis of the classical Vedantic texts -- the Vedas, Upanishads, Brahma Sutra, Mahabharata, Pancharatra, and Puranas -- and place uncompromising duality, which had been ravaged by attacks from Advaita, on a firm footing. Before Madhvacharya, Nondualism was rejected by others such as the Mimamsa tradition of Vedic exegesis, and by the Nyaya tradition of classical logic. However, it was only he who could build a cogent alternative system of Vedanta that could take on Advaita in full measure.