Published online by Cambridge University Press: 12 March 2026
X-bar theory is widely regarded as a substantive theory of phrase structure properties in natural languages. In this paper we will demonstrate that a formalization of its content reveals very little substance in its claims. We state and discuss six conditions that encapsulate the claims of X-bar theory: Lexicality—each nonterminal is a projection of a preterminal; Succession—each Xn+1 dominates an Xn for all n ≥ 0; Uniformity—all maximal projections have the same bar-level; Maximality—all nonheads are maximal projections; Centrality—the start symbol is a maximal projection; and Optionality—all and only nonheads are optional. We then consider recent proposals to ‘eliminate’ base components from transformational grammars and to reinterpret X-bar theory as a set of universal constraints holding for all languages at D-structure, arguing that this strategy fails. We show that, as constraints on phrase-structure rule systems, the X-bar conditions have hardly any effect on the descriptive power of grammars, and that the principles with the most chance of making some descriptive difference are the least adhered to in practice. Finally, we reconstruct X-bar theory in a way that makes no reference to the notion of bar-level but instead makes the notion ‘head of the central one.
This paper supersedes two earlier papers, Kornai 1983 and Pullum 1985. We would like to thank the many people who contributed to our understanding of X-bar theory in various ways and gave us helpful comments on work that contributed either to our earlier work or the present paper. These people include: Erzsébet Csuhaj-Varjú, Janet Dean Fodor, Gerald Gazdar, László Kálmán, István Kenesei, Ferenc Kiefer, Katalin É. Kiss, András Komlósi, William A. Ladusaw, Steven G. Lapointe, P. Stanley Peters, Livia Polányi, Gábor Prószéky, John Richardson, Iván A. Ság, Stuart Shieber, Anna Szabolcsi, and Thomas Wasow. We also benefited greatly from the comments of several anonymous reviewers. None are to be blamed for errors that this paper might still contain. For partial support of their research, the authors are indebted to the Hungarian Academy of Sciences, the Center for the Study of Language and Information at Stanford University (funding by a gift from the System Development Foundation), and the Syntax Research Center at the University of California, Santa Cruz (funding by NSF grant no. BNS-85 19708).