The X-bar theory of phrase structure

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 X^{n + 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.