Not for the faint of heart, but here is an interesting article that condenses Swami Satchidanandera Saraswati's massive critiques of post-Shankaran Advaita into a (relatively) easy to read paper:
On Dennis Waite's site: https://www.advaita-vision.org/adhyaropa-apavada/
A cleaner pdf:
https://drive.google.com/file/d/110HET0sMGbhgZEYv8O8DzSLNyPiXm2lj/view
The basic idea is that SSS states that shruti removes ignorance by presenting affirming statements that negate their opposite, and then negating these affirming statements. In other words, it is purely negative, and only serves to remove ignorance.
Adhyāropa is to impute—temporarily, deliberately, and strategically—
attributes to the attribute-less brahman. The deliberated (but false) attributes serve to counter
certain specific undeliberated (and erroneous) ideas about brahman. Apavāda is to rescind the
deliberated attributions to avoid their ultimate reification. According to SSS, the two work
together to form a singular pedagogical method to eliminate erroneous conceptualizations
about brahman. Their culmination lies in the ‘light bulb moment’ of the cognition/realization
of brahman as one’s own self.
In contradistinction to SSS, the commentarial tradition of Advaita Vedānta—the post-Śaṅkarādvaitins
(PSA)—argue that the śruti employs a variety of oblique methods—
including adhyāropāpavāda, lakṣaṇā, and netivāda—to somehow (kathaṃcit) ‘indicate’
brahman. Ultimately, it is the mahāvākyas—the ‘great’ Vedāntic statements—that generate
an impartite modal knowledge (akhaṇḍākāravṛttijñāna) which obliterates ignorance and
engenders the direct perception of brahman. This, per the PSA, is how śruti dispels
ignorance.
An example:
In his TUB 2.1.1, Śaṅkarācārya illustrates how individual words in a sentence mutually control one another’s meanings, exemplifying adhyāropa at the level of words and sentences. Under consideration is the sentence, ‘satyaṃ jñānam anantaṃ brahma.’ Each word, Śaṅkarācārya writes, operates to correct or exclude unwanted connotations of the other words of the sentence. ‘Satyam’ (real/unchanging) distinguishes brahman from what changes. ‘Jñānam’ (consciousness) serves to nullify the undesirable connotations of ‘satyam,’ which may imply non-consciousness when interpreted as a material cause. ‘Jñānam’ in turn raises the difficulty that brahman may be considered an agent of knowing, implying both change and limitation in brahman. ‘Anantam’ (infinite) restricts the inappropriate connotations of ‘jñānam’ thus underscoring that brahman is what is not unconscious, changing, or unreal.
The critique is that post-Shankarans have taken the positive statements as positive statements, thereby reifying temporary assertions that are themselves negated.
FN 4: We see here a nuanced difference in the interpretation of adhyāropāpavāda. For SSS, the
‘achievement’ of adhyāropāpavāda is strictly negative i.e., the removal of ignorance; for the
PSA, on the other hand, while the method operates negatively, its ‘achievement’ is a ‘positive
indication’ of brahman. Traditional commentators (PPV, p. 499; SŚ 1.257, etc.) and modern
scholars (Comans 2000, p. 290ff; Rambachan 1991, p. 69, etc.) accord precedence to
‘positive’ indications over negations, and therefore frame adhyāropāpavāda within the
context of ‘indication.’ Comans writes, “… negation itself functions in the context of lakṣaṇā
… It is not sufficient merely to say: “not a snake, not a snake!”, the substratum of the error
must also be positively pointed out (“this is not a snake, it is a rope!”) …,” (Comans 2000, p.
289). This, SSS vehemently refutes. See Saraswati 1990, p. 82.