Brahman according to S’a@nkara is “the cause from which (proceeds) the origin or subsistence and dissolution of this world which is extended in names and forms, which includes many
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agents and enjoyers, which contains the fruit of works specially determined according to space, time, and cause, a world which is formed after an arrangement inconceivable even by the (imagination of the) mind [Footnote ref 1].” The reasons that S’a@nkara adduces for the existence of Brahman may be considered to be threefold: (1) The world must have been produced as the modification of something, but in the Upani@sads all other things have been spoken of as having been originated from something other than Brahman, so Brahman is the cause from which the world has sprung into being, but we could not think that Brahman itself originated from something else, for then we should have a regressus ad infinitum (anavastha). (2) The world is so orderly that it could not have come forth from a non-intelligent source. The intelligent source then from which this world has come into being is Brahman. (3) This Brahman is the immediate consciousness (sak@si) which shines as the self, as well as through the objects of cognition which the self knows. It is thus the essence of us all, the self, and hence it remains undenied even when one tries to deny it, for even in the denial it shows itself forth. It is the self of us all and is hence ever present to us in all our cognitions.
Brahman according to S’a@nkara is the identity of pure intelligence, pure being, and pure blessedness. Brahman is the self of us all. So long as we are in our ordinary waking life, we are identifying the self with thousands of illusory things, with all that we call “I” or mine, but when in dreamless sleep we are absolutely without any touch of these phenomenal notions the nature of our true state as pure blessedness is partially realized. The individual self as it appears is but an appearance only, while the real truth is the true self which is one for all, as pure intelligence, pure blessedness, and pure being.