It seems that from this question that the Advaita Vedanta school of Adi Shankaracharya has two philosophical divisions within their Sampradaya- the Vivarana school of Prakasatman and the Bhamati school of Vachaspati Misra. What are the philosophical differences between these schools other than the nature of Avidya as described in that question?
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1The arguments are how they interpret the word knowledge. Whether it means 'Knowledge' - knowledge (realization of Brahman) or intellectual knowledge of scripture. The other argument as to the nature of Avidya is specious. As Swami Vivekananda says: "...nescience has no absolute reality. You can call nescience neither real nor unreal; 'Neither real, nor unreal, nor a mixture of both'. About a thing that is thus proved to be false, neither question nor answer is of any significance. Moreover, any question on such a thing is unreasonable."– Swami VishwanandaJan 2, 2019 at 9:02
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1btw, there are arguments in Sankaracharya for both views of knowledge and Avidya.– Swami VishwanandaJan 2, 2019 at 9:03
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1Wonder why questions like this don't get answered.– AmbiJan 29, 2019 at 8:14
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2 Answers
There are as many as six differences I could find and comprehend, between the Bhamati school of Vachaspati Mishra and Vivarana school of Prakasatman:
Karma
• The Bhamati school opines that the purpose of Karma is to inspire one to desire for knowledge. By performing one's duties efficiently without expectating its fruits and offering it to Ishwara, the desire for knowledge is arises in an individual.
• The Vivarana school opines that by performing one's duties efficiently without expecting it's fruits, knowledge automatically arises in an individual.
Detachment
• Bhamati school believes that, in order for an individual to develop detachment towards materialism, one must learn to discriminate between what is reality and what is unreality. It is not enough to know that world is not eternal since it does not produce detachment because they still generate happiness.
• Vivarana school believes that an individual can detach by simply knowing the non-eternality of the world.
Study of scriptures
• The Bhamati School stresses on the understanding of scriptures for all everyone, regardless of whether they want to practice Karma-Yoga or Jnana-Yoga.
• The Vivarana School opines that rote learning of scriptures is sufficient for people who wish to practice Jnana-Yoga as the understanding of the meaning of the scriptures is automatically attained through Guru's grace.
Avidya in all individuals
• Bhamati school believes that the Avidya in an individual differs from person to person.
• Vivarana school believes that Avidya is the same in all individuals.
Nididhyāsana and Shravana
• Bhamati school stresses on the importance of Nididhyāsana or profound meditation on the Upanishadic Mahavakyas.
• Vivarana school stresses on the importance of Shravana, the hearing of Vedantic secrets from one's Guru.
Cause of Brahmajnana
• Bhamati school believes that Manas is the main cause of Self-realization in an individual.
• Vivarana school believes that the Upanishadic Mahavakyas are the main cause of Self-realization in an individual.
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1@NaveenKick Bhamati school thinks that people who master Karma-Yoga, their thirst for knowledge arises and they as a result approach a Guru. Vivarana school believes people who mastered Karma-Yoga have already attained knowledge and they don't need to approach a Guru for it.– user9969Feb 5, 2019 at 7:28
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1Reason for your fourth point is that, Bhamati school puts the locus of avidhya in Jivatma and Vivatana puts the locus of Avidhya in Paramatma. Feb 7, 2019 at 16:11
After Shankara Advaita flowed in two directions Bhamati School & Vivaranam School. This is a picture of a scanned document.
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2Which book are you quoting from? See How to reference material written by others. Jun 14, 2020 at 20:05