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Knowledge That Cannot Be Contradicted - Advaita School Philosophy

Abadhita Jnana is the non-contradictable knowledge, a concept of knowledge preferred by the Advaita schools of philosophy.

In an error, for instance, in the rope mistaken for a snake, the snake-cognition is false because it is contradicted on closer scrutiny by the knowledge that it is a rope and not a snake as was believed at the first look.

To take another instance: in all the three experiences of waking, dream and deep sleep, the instruments of knowing change.

Hoysaleshwara Temple, Halebeedu - Karnataka

But the same consciousness witnessing all the three states remains the same, bearing testimony to all of them as, “I saw”, “I dreamt” and “I slept”. Hence it alone is real.
Abadhitatva (incontrovertibleness) at all times is the mark of the true proposition and real existence.

However, propositions can be entertained, as in the case of practical life in the world, provisionally as true till they are contradicted by another piece of evidence. Hence all empirical knowledge, according to Advaita, is empirical and corrigible.

However, knowledge worth the name must be true (abadhita) in all circumstances. It is only belief that can turn out to be true or false. Given normal conditions of knowing, all cognitions must be and are true.

If errors occur, it is because the natural process of knowing has been obstructed by extraneous factors like the physical and psychological conditions that prevail at the time.
Otherwise, all cognitions are intrinsically valid. Only their invalidation is extrinsic. In short, the same conditions that give rise to a cognition produce its truth also. Knowledge cannot be, and is not, validated.

Regarding memory, Advaita schools lay down the rule that it lacks novelty as it is only a reproduction of earlier perception. Therefore, it cannot be considered knowledge in the strict sense of the term, though it is un-contradicted.

Advaita considers “the world” mithya, a mere construct (in Shankara Advaita) because it is contradicted by the true knowledge of the Absolute (Brahman). Yet it is not unreal or non-entity; for example, a barren woman’s son, because it is given in some experience or another which would not be the case if it were a non-entity. Hence the world is neither real because of contradict-ability; nor unreal because of being given in experience. So it is a construct which is anirvachaniya (non-explicable).

Source - Encyclopedia of Hinduism - page 1 - Volume I - A - IHRF
Advaita Epistemology P. K Sundaram  (1984) University of Madras
Advaita and Neoplatonism J F Staal (1961) University of Madras
Revelation and Reason in Advaita Vedanta K Satchidananda Murty (1961) Asia Publishing House