Relation-Based Explanation of the Nyāya–Vaiśeṣika Theory of Atomic Causation (Paramāṇu-kāraṇavāda).

Samavāya (inherence) in the Nyāya–Vaiśeṣika system is the eternal relation that connects two inseparable entities (ayutasiddha padārthas), such as part and whole, quality and substance, universal and particular, action and agent, and eternal substance and particularity. In each case, at least one relatum depends inseparably upon the other—for example, “cowness” exists only in an individual cow. Unlike conjunction (saṃyoga), which is non-eternal, inherence is accepted as eternal and irreducible. Nyāya maintains that inherence preserves real difference between relata. Advaita Vedānta, however, interprets such relations as ultimately non-dual (tādātmya), reducing difference to a conceptual level, while Pūrva-Mīmāṃsā accepts both difference and non-difference under svarūpa-sambandha. In the Brahma-sūtra, Adi Shankaracharya argues that inherence leads to infinite regress (anavasthā), since if it is distinct from its relata, it would require another relation to connect it to them. The Naiyāyikas respond that inherence is directly apprehended and intrinsically related to its relata, thus avoiding regress. This debate is central to the coherence of Nyāya–Vaiśeṣika atomism and its realist theory of relations.