You have established your philosophy camp. The next thing is to secure the perimeter. The primary boundary is that of the past of your tradition with its errors and insights, the secondary is that of the contiguous thought that may be confused with your own. Thus after a round-up of the main points of Sri Bhagavatpada (Sankara) Swami Sri Satchidanandendra Saraswati (hereafter Sri SSS) deals with the vedic tradition of enlightenment gained through the karma of sacrifice and ritual. Firmly he rejects this with a stern adherence to the doctrine that only knowledge can banish ignorance.
(Liberation is said figuratively to be the ‘result’ of knowledge, because metaphysical knowledge puts an end to the obstruction caused by Ignorance , while Ignorance cannot be destroyed by action.) Nor can one conceive of any other obstruction to liberation apart from ignorance of a kind that might be removed by action. For liberation is eternal, and is nothing other than the true nature of the seeker himself. (Bhr.Up. Bhasya XVIII. 67 intro)
In Chap.IV of The Method of the Vedanta Sri SSS deals with contiguous error namely the identity and difference (bhedaabheda) doctrine which he associates with Bhartrprapanca Sankara’s ‘contemporary’. I mark that term given that Sankara’s dates are disputed and that Bhartrprapanca is known only from references in various works including Sankara’s commentary on the Brhad.Up.
The difference in identity is often explicated by the use of a master analogy. Water which is one and identical is manifested in different forms such as waves, foam etc. We recognise this difference and identity simultaneously.
In the same way, the Absolute is both dualistic and non-dualistic. The sea consists of water, waves, foam, bubbles and so forth. And the waves, foam, bubbles and the rest, that arise from the water, are just as much the nature of the sea as the water is. True, they come and go; but they are perfectly real for all that. And all this world of duality is perfectly real too, comparable to the water and the waves in the illustration. The Absolute in its supreme form is comparable to the water of the sea.
Sankara uses the concept of material identity also in a different way in discoursing on ‘clay’ and vessels of ‘clay’ in his commentary on Ch. Up. Personally I do not find his ontology convincing but that is a separate issue. Here Sri SSS applies the principle of non-contradiction to Bhartrprapanca’s theory. A thing cannot both be and not be one with itself at the same time.
Duality and non-duality are contradictories. The theory would therefore be in danger of undermining the Vedic texts which speak of Consciousness as a single homogeneous mass. If the Absolute were of both dualistic and non-dualistic nature like the sea or the tree (branches, boughs etc), it would have parts, and so inevitably would be impermanent.
The austere monism of Sankara rejects any assimilation of the Real and the Un-real even to the suggestion of a gradual wearing away of maya by action (ritual).
Some hold that all ritual leads to the cessation of bondage. As one is liberated successively from each ‘death’, meaning from each new body, so one attains a new one, not for the sake of attaining it but for the sake of getting rid of it. Thus until duality is finally destroyed, all ( as the Upanishad says) is death. But when duality is finally destroyed, then one is truly released from the prospect of undergoing further death. Before that, one can only speak of liberation in a relative or secondary sense. (Brhad. Up. commentary III.ii.1, intro.)