For those who are new to Advaita Vedanta, might find these explanations helpful.
From various websites I've gathered information about the different theories of Advaita and I've explained them in simple English so that anyone interested can have a clear understanding of them.
If someone come across any error in my explanations then they are free to correct me.
1. Avachheda Vada
(The theory of limitation)
According to Avachheda Vada, the ONE indivisible Brahman 'appears' divided into many jivas because of various upadhis, just as the one great sky (Akasha) appears divided, by being contained in various pots (Ghatakasha).
This theory proposes that no real difference exists between the sky inside the pot and the sky outside. The distinction is only apparent. Once the pot is broken and the apparent distinction removed, the sky inside the pot and the sky outside are understood to be one and the same.
Similarly, the proponents of avachheda vada says, there is no difference between the jivaand Brahman.
The jiva's limiting adjunct (his subtle body) is actually a false covering, superimposed on Brahman, after Brahman comes into contact with Maya's avidya potency and it is this false covering alone that makes the jiva appear separate from Brahman.
Thus, when Brahman is limited by subtle bodies (Maya's avidya potency), it becomes the jivas.
But when Brahman is limited by Maya's vidya potency, it is called Personal God or Ishwara.
This theory of limitation is credited to Vachaspati Mishra, the founder of Bhamati school.
2. Pratibimba Vada
(The theory of reflection)
According to Pratibimba Vada, when the One true, formless, undivided Brahman is reflected in the various subtle bodies made of avidya, it (Brahman) appears to be many, just as the one sun reflected in various receptacles of water appears to be many.
In this analogy, the original sun remains unaffected by the agitation of the water in which it is reflected, even while the reflection is affected.
Similarly, Brahman is never affected by the changes, that its reflections (the jivas) undergo.
It is to be understood here that Brahman being formless can have no reflection. The reflection theory is just a metaphor. When we use terms like reflection or reflected consciousness, we simply mean the conditioned consciousness or the conditioned state of the jiva.
It is called conditioned consciousness because the pure original consciousness is experienced through the filter of mind and ego.
As mentioned above, Brahman (the pure original consciousness) is never affected by the changes that take place in its reflection (the jiva).
Changes like happiness, distress that the reflection/jiva undergoes are only illusions resulting from the conditioned state of the jiva. When the jivas free themselves from illusion upon attaining liberation, he goes back to his original Brahman consciousness.
This theory of reflection is credited to Padmapada, the founder of the Vivarna School.
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