Thanks for the summary Anon. From what i've seen it seems to match what you say about there being different approaches in Advaita. Some are more dialectic and emphasize inference where as other schools elect non-conceptual, direct-congntion as the real means of realization.
It seems that when Buddhists refute the positions of Advaita, we target the inconsistences found in Advaitan dialectic with the 'weapon' of the Catuṣkoṭi - the reasoning of the 4 extremes which Advaita doesn't adhere to...at least in theory. Both Dzogchen and Advaitia have non-cocneptual, valid-cognitions and I'm trying to understand how,where & why these cognitions differ in each system.
I've spoken to Advaitans who speak about Nirvikalpa samādhi. In Buddhsim there is also the closely related nirvikalpa-jñāna.
"Heinrich Zimmer in his book distinguishes Nirvikalpa Samadhi from other states as follows:"
Nirvikalpa samādhi, on the other hand, absorption without self-consciousness, is a mergence of the mental activity (cittavṛtti) in the Self, to such a degree, or in such a way, that the distinction (vikalpa) of knower, act of knowing, and object known becomes dissolved — as waves vanish in water, and as foam vanishes into the sea.
According to Swami Sivananda, it is also called Nirbija Samadhi:
"Without seeds or Samskaras [...] All the seeds or impressions are burnt by the fire of knowledge [...] all the Samskaras and Vasanas which bring on rebirths are totally freed up. All Vrittis or mental modifications that arise from the mind-lake come under restraint. The five afflictions, viz., Avidya (ignorance), Asmita (egoism), Raga-dvesha (love and hatred) and Abhinivesha (clinging to life) are destroyed and the bonds of Karma are annihilated [...] It gives Moksha (deliverance from the wheel of births and deaths). With the advent of the knowledge of the Self, ignorance vanishes. With the disappearance of the root-cause, viz., ignorance, egoism, etc., also disappear."
Edward Conze from 'Buddhist Thought In India' ellaborates on nirvikalpa-jñāna ,
'The "undiscriminate cognition" knows first the unreality of all objects, then realizes that without them also the knowledge itself falls to the ground, and finally directly intuits the supreme reality. Great efforts are made to maintain the paradoxical nature of this gnosis. Though without concepts, judgements and discrimination, it is nevertheless not just mere thoughtlessness. It is neither a cognition nor a non-cognition; its basis is neither thought nor non-thought.... There is here no duality of subject and object. The cognition is not different from that which is cognized, but completely identical with it'
I'm trying to understand the difference between these two states in terms of practice rather than the usual dialect of Brahman being taken as an absolute existent . The extinction of subject and object seems to be common to both traditions as does the burning away of Samskaras/vasanas and mental activity as a result of such samādhi/jñāna. So what is the experiential difference between the jñāna In Advaita that results in the extinguishing of karmic traces and conceptualization and the jñāna in Dzogchen that results in the karmic extinguishing of traces and conceptualization?
Is there still some subtle knowledge-obscuration [jneyavarana] that Advaita's Nirvikalpa Samadhi fails to make obsolete?
'When alone, watch your mind. When with others, watch your speech'- Old Kadampa saying.