The third chapter is the first to exclusively address core linguistic issues by comparison of the ancient Indian and modern Western traditions. It addresses rule interaction, an issue which has been a core topic of research in Pāṇinian linguistics, and which has also been a central issue in the development of modern phonological theory, in many respects driving theoretical developments over the last fifty years. A central focus is on the Elsewhere Principle, also known as 'Pāṇini's principle', and on the outworking of this fundamental principle in different phonological theories including Lexical Phonology, Declarative Phonology and Optimality Theory.

This co-authored chapter traces the development of generative and other formal approaches to phonology from 1960-2000. After discussing empiricism, positivism, and logical positivism, Prague Circle functional phonology (Jakobson, Trubetzkoy 1939) and American phonology (Harris 1950s), it turns to Generative Phonology, launched by Chomsky and Halle (Sound Pattern of English, SPE 1968), with its algorithmic mentalism: explicit formulation; formal simplicity used to choose between analyses; derivational rules (from underlying to surface form); no phonemic ‘contrast’; ‘abstract’ (non-occurring) segments can ‘trigger’ a rule.

From the 1960s to the end of the century, there were serious criticisms of SPE and debates about a series of new approaches: ‘concrete’ Natural Generative and Natural Phonology; Lexical Phonology; and, with the integration of the syllable, Autosegmental and Metrical Phonology. The late 1980s and 1990s brought (rule) ‘conspiracies’ and ‘harmonic phonology,’ which ultimately led to Optimality Theory (OT), in which an algorithm selects a surface representation that satisfies a set of ranked (universal) constraints. In 2000+, OT was the most popular formal approach.

Other approaches studied the relationship of phonetics and phonology, linked phonology and psychological experimentation, variation in phonology, and so forth.

Basic principles of generative phonology, as codified in SPE, and later developments within this framework, including metrical phonology, lexical phonology, autosegmental phonology, and underspecification theory. The role of cyclicity. The rise of Optimality Theory and the difficulties encountered in this framework in accounting for opaque relationships.

Principles of lexical phonology, properties of lexical strata, survey of English morphology, zero derivation, cyclicity and the strict-cycle condition. Summary of the cyclic rules of stratum 1.