Advaita Vedānta

The non-dualists read sat and asat as limiting adjuncts (upādhis) of the one Imperishable, not as ultimate features of it. The 'real' (sat) is the existing, the manifest; the 'unreal' (asat) is that of which the notion 'it is not there' arises, the unmanifest. Krishna is figuratively called sat-asat because these two serve as the adjuncts through which the Imperishable appears. But in the highest truth the akṣara is beyond both the real and the unreal; that supreme thing, 'beyond the real and the unreal,' is what the knowers of the Veda speak of, and that is Krishna alone and no other. Some in this school read sat-asat instead as the existent grasped under the form 'it is' and the non-existent grasped under the form 'it is not,' or as manifest and unmanifest, but the conclusion is the same: the one Imperishable transcends the pair, and there is nothing apart from it.

Śaṅkarācārya · Śrī Ānandagiri · Madhusūdana Sarasvatī · Śrī Nīlakaṇṭha · Dhanapati Sūri

Viśiṣṭādvaita

These commentators give the terms precise metaphysical referents rather than treating them as mere adjuncts. The akṣara, 'that which does not perish,' is read as the principle of the individual self (jīva), since revealed texts such as 'the wise one is not born nor dies' establish that the self does not perish. 'Sat' and 'asat' name the matter-principle (prakṛti) in its two states: as effect it has the division of name and form and is called 'existent' (sat); as cause it lacks that division and is called 'non-existent' (asat). And 'that which is beyond' is the principle of the liberated self, higher than matter and than the self joined with matter. So the verse, on this reading, names three real ordered principles, the imperishable self, matter in its two phases, and the liberated self, and declares all of them to be Krishna's, since all are his body and depend on him. (Baladeva, a Bhakti commentator, reads the three principles in just this Vishishtadvaita-style ordering of self, matter, and liberated self.)

Rāmānujācārya · Vedānta Deśika · Śrīla Baladeva

Dvaita

The dualists ground the reading in the Mahābhārata rather than treating the terms abstractly. 'Mahātman' is explained as Krishna being both full (pūrṇa) and the Self, and the word 'ātman' is given its etymology from the Bhārata: He is called ātman because He pervades, takes up, eats the objects, and has continuous being. 'Sat-asat' and 'beyond' are read directly through the Bhārata line 'the world, which is both non-existent and existent, and that which is beyond the existent and the non-existent.' Crucially, the world made of the existent and the non-existent is said to be Krishna alone precisely because He is the giver of existence to it, not by identity; reading it otherwise would contradict the very next statement. So the schools that collapse the world into the Lord by sameness are blocked here, the dependence is causal and the Lord remains distinct as the bestower.

Madhvācārya · Śrī Jayatīrtha

Kashmir Shaivism

Abhinavagupta gives a cognition-centered reading of the pair. It is 'being' (sat) because it is a real thing; it is 'non-being' (asat) because it is no field for apprehension, that is, it cannot be made an object. He adds a further turn: even non-being, when in the mind it is joined to its own particular naming word and so takes on the form of knowledge, is not distinct from the being of the supreme Brahman, so apparent non-being is still within the one reality. And He is beyond both being and non-being, because His own form is apprehended precisely when the cognition of those two is veiled, that is, the Lord shines when the categories of object-being and object-non-being fall away.

Ācārya Abhinavagupta

Śuddhādvaita

The pure-non-dualists read the verse as fastening unsurpassable lordship (aiśvarya) onto the very one who, though He is the first agent, remains free of any taint from action. Vallabha takes the epithet 'sad-asat-param akṣaram' as the seal of this: the supreme sovereignty resting on every distinct attribute belongs to the eternal, imperishable one who does not perish and is not stained, and that one is Brahman, Krishna alone, with 'param' meaning the supreme cause. Purushottama names the 'beyond' explicitly as Puruṣottama, the Brahman-reality, and adds a devotional ground for the bowing: Krishna is the very own-form (svarūpa) of His devotees, so the perfected ones bow because they bow to their own innermost reality.

Vallabhācārya · Śrī Puruṣottama

Modern

The modern commentators keep the threefold structure and translate it for a present-day reader, with a notable shift in how sat and asat are defined. One reads sat as that which exists in all three periods of time (and so as Brahman) and asat as that which does not so exist (this world, this body), then notes that here sat and asat are used in the more usual Gita sense of manifest and unmanifest, the adjuncts of the akṣara that in reality transcends both. Another reads sat as 'immutable' and asat as 'mutable,' or perceptible and imperceptible (vyakta and avyakta), with the akṣara-brahman beyond both, cross-referencing other Gita verses where 'I am neither sat nor asat.' A third stays with the human meaning of the bowing: salutation is rightly offered to those from whom we receive light (teachers, gurus, elders) and to those from whom we are born (parents and our betters); since Krishna is the guru even of gurus and the originator even of Brahmā, the grandfather-creator, it is wholly fitting that the perfected ones bow to Him.

Swami Sivananda · Lokmanya Tilak · Swami Ramsukhdas