Q: Does the world exist apart from a perceiver?
There are several very helpful ways to talk about this. And in none of these is the world ever truly independent.
(1) As Berkeley does. Then the answer is "No."
(2) As advaita vedAnta does. Then it would depend on the standpoint – sRRiShTi-dRRiShti-vAda, dRRiShTi-sRRiShTi-vAda, or ajAti-vAda. And for the last vAda at least, the answer is "No."
(3) Logically. The question mentions a perceiver and a world. Then the perceiver is either part of the world or not. If you say that the perceiver is not part of the world, then where would the perceiver be? Outside the world? This would entail that the perceiver exists but is outside the world. This makes no sense, and the world is missing something that is claimed to exist. If you say that the perceiver is part of the world, then what is it that is perceiving the perceiver? Rinse and repeat. The question, taken at face value, makes no sense. Independence need not be presumed.
Idealism is very effective in showing how the notion of material substance existing external to perception is an incoherent notion. But idealism leaves a subtle residue, which itself must be looked into.
Idealism (like Berkeley's) presumes the independence of the individual mind. Individuals' minds and God's mind. Idealism argues against a physical independent world, but bases these arguments on the assumption of a subtle independent world. The notion of independence has merely shifted. This is a helpful stage, but not final.
What does the advaitin make of the Berkeleyan idealist? They might say the idealist is like the student-son in the Taittiriya Upanishad who got stuck at Chapter III:v ("The Intellect as Brahman") instead of continuing to the end to Chapter III:x.6.
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