Tree Maximization and the Generalized Extended Projection Principle

Since Chomsky’s (1981) addition of the requirement that every sentence have a subject to the Projection Principle, the apparent stipulative nature of this constraint has been a source of worry for generative grammarians. The empirical basis of the Extended Projection Principle (EPP) is well-established but the external motivations for why Universal Grammar should contain such a requirement are fairly mysterious. This lack of explanation has been compounded in more recent versions of the Minimalist Program, where the EPP has been generalized to all types of specifier positions (e.g., Chomsky 2001). At the same time, important work in the philosophical foundations of Minimalism has suggested that universal syntactic principles, in particular those governing the simple, mathematical computational system, should follow from general physical principles that govern the way biological systems emerge in the phenotype. For example, Uriagereka (1997) has claimed that linguistic structures exhibit the mathematical properties of the “Golden Mean” as exhibited, for example, in the Fibonacci Sequence (0, 1, 1, 2, 3, 5, 8, 13, etc). In this speculative squib, we observe that one particular Fibonacci-like sequence in tree structures which are maximized in terms of specifiers and complements might explain why languages aim towards filled specifiers as stipulated by the generalized EPP. This, in turn, we claim makes some interesting predictions about the binarity of the MERGE operation, the ambiguity of terminal complements and the nature of the labeling operation subsumed in MERGE.