Noncyclic Operations and the LCA in a Derivational Theory

In A Derivational Approach to Syntactic Relations (DASR), Epstein et al. (1998) present a derivational theory of syntax incorporating no levels of representation. The aim of DASR is to "advance the hypothesis that the structure building rules Merge and Move (Chomsky 1994) naturally express all syntactically significant relations" (DASR:3). Chapter 5 of DASR deduces the ill-formedness of noncyclic concatenation from assumptions needed independently to maintain such an approach to syntactic relations. However, another section of DASR (section 2.4) presents a derivational analysis of several binding phenomena that relies crucially on the noncyclic application of Merge. Thus, DASR appears to make contradictory assumptions. In section 1 I review DASR's deduction of the ill-formedness of noncyclic applications of concatenation, discussing the Merge/Move algorithm and Kayne's (1994) Linear Correspondence Axiom (LCA) in turn. In section 2 I examine some binding phenomena and the DASR account of them. In section 3 I clarify the incompatibility between the DASR account of the prohibition on noncyclic concatenation and the DASR account of the binding phenomena discussed in section 2.¹

1 The DASR Model: Concatenation and the LCA

Before we consider the DASR approach to excluding noncyclic operations, it is necessary to specify some general assumptions. DASR assumes that there are no levels of representation: a fortiori, that there are no levels of representation at which interpretation can take place. Rather, all relations necessary for interpretation are established by transformational operations applying iteratively within the derivation, whereas interpretation (semantic and phonological) is performed on the output of each transformational operation. More specifically, all syntactic relations (particularly c-command) derive from the application of concatenation, which is, informally, the minimal syntactic operation taking A and B and putting them together to form a constituent C. Binary concatenation is a property shared by both Merge and Move (see Kitahara 1995).

(1) Merge
Applied to two objects A and B, Merge forms the new object C by concatenating A and B.

(2) Move
Applied to the category C with K and α, Move forms the new object C′ by concatenating α and K. This operation, if noncyclic,² replaces K in C by L = {g, {α, K}}.

(DASR:61)

Given these definitions, the derivational definition of c-command is stated as in (3).

(3) C-command
X c-commands all and only the terms of the category Y with which X was concatenated by Merge or Move in the course of the derivation.

(4) Term
L is a term of K iff

1. a. L = K, or

2. b. L is a term of a category concatenated to form K.

(DASR:61-62)

Chapter 5 of DASR demonstrates how noncyclic operations are precluded, given that the output of noncyclic concatenation cannot (under a strict derivational interpretation of (4)) be reinserted into the object whose term entered into the operation. DASR's assumptions about noncyclic concatenation are best illustrated by (5).

(5) DASR's assumption about the output of noncyclic merger of X + A, yielding B: No reinsertion of B (orderirrelevant)

(DASR:146)

In (5) X and A concatenate noncyclically-that is, after X (X = {X{Q, R}}) and Z were concatenated to form Y. Under the analysis of Merge/Move presented in chapter 5 of DASR, the output of the operation (i.e., the projected term B) is not "reinserted" into the already created syntactic object (with B immediately dominated by Y, and immediately dominating A and X). Such reinsertion, which is standardly assumed (as in (2)), would destroy the immediate dominance relation between X and Y in (5) and replace it with a new one. This is contrary to the derivational method wherein the syntactic relations into which a term T enters are established only at the point at which T is introduced into a position P. Consequently, under the DASR analysis of (5), neither A (the category "added") nor B (the category projected) is a term (see (4)) of Y, and thus neither plays a role in computing Y's compositional structure. Given this, such outputs of noncyclic concatenation as (5) are excluded in DASR by appeal to...