The Relationship between Hierarchy and Linear Order

similarities between languages. The two proposals are Kayne´s (1994) antisymmetry which focuses on word order, and Archangeli and Langendoen´s (1997) optimality theory which concentrates on different rankings of constraints. In spite of their differences, both antisymmetry and optimality aim at providing a more refined account of how differences among languages are to be explained; and how these differences are interrelated and explained in terms of UG. We will deal with each theory separately.

1.3. Antisymmetry

allowed. Evidently, this reduction in available mechanisms is a potentially important advancement because it represents a more restrictive syntactic theory.

As Kayne (1994) states, hierarchical relations have traditionally been encoded under the X´-schema in (39):

On the other hand, the order in which constituents appear has been considered to be a product of language-specific grammars, as reflected in (40a) and (40b) for English and Japanese, respectively:

(40) a. from Tokyo a’. Sandra hit Mary

b. Tokyo kara b’. Sandra-ga Mary-o but-ta

[Tokyo from] [Sandra-subject Mary-object hit-past]

Both in the case of phrases and sentences, word order was considered language- specific. Cases such as the ones in (40) were accounted for in terms of the directionality parameter or the head parameter (Travis 1989) which opposed languages such as English or Spanish to Japanese.

Given such variations, it has traditionally been assumed that the hierarchical arrangement between head and complement can have two symmetrical linear realizations; that is, the head may precede the complement, as in English (therefore,

XP Spec X’

head complement

(39)

a head-initial language), or it can follow the complement, as in Japanese (therefore, a head-final language):

Separate treatments of constituent order and hierarchical structure like this one have been a constant in generative linguistics, with the notions of universals and parameters of variation always in mind (Chomsky 1986).

According to Kayne (1994), this way of conceiving UG is too permissive.⁴⁵ He argues that, in spite of superficial appearances, the relationship between linear order and hierarchical structure is rigid. The only order in human language is the one where the specifier precedes the head, and the head precedes the complement, as in (39) repeated here as (42):

In that sense, asymmetric c-command always implies precedence, as opposed to subsequence.

This idea of precedence is key in the antisymmetry analysis. Kayne (1994) defends the existence of a mapping between hierarchical structure and the observed

XP Spec X’

head complement

(42)

XP Spec X’

head complement

(41)

Tokyo Mary from

hit

XP Spec X’

complement head Kara

but-ta Tokyo

Mary-o

linear order that is rigid. He refers to this mapping as the linear correspondence axiom (LCA), stated in (43):

(43) linear correspondence axiom (LCA): d (A) is a linear ordering of T⁴⁶

The function of this axiom is to map the different hierarchical relations established between specifier, head, and complement into the corresponding linear order.

Assuming that the universal order is Spec-head-complement, there is a redundancy between hierarchical relationships and linear order. Thus, there is a need to find a hierarchical relationship with similar properties of linear order. Such a relationship must be antisymmetrical, transitive and total.

As Ordóñez (1997) explains, the relationship between hierarchy and linearity is mediated by a trivial mapping from non terminal nodes (A), which are the ones relevant for hierarchical relations, to the corresponding terminal nodes (T), the relevant nodes for linearization. This mapping is called d (X). Kayne (1994) postulates that for any given non terminal node A which enters into asymmetric c- command with another non terminal node B, there will be a mapping into precedence of the terminals dominated by a non terminal node A with respect to the terminals dominated by the non terminal B.⁴⁷ The mapping must necessarily cover all the non terminal nodes in a given phrase marker.

Along the lines of Kayne (1994), Ordóñez (1997) analyzes the nature of specifiers and adjunctions within antisymmetry. Phrase structure only considers

45 See Ordóñez (1997) for the four different possibilities allowed.

46 Where T is a set of terminals and (A) are pairs of non-terminal nodes (Kayne, 1994).

47 This is only a partial answer as to why the order has to be Spec-head-complement. Nothing bars the possibility of the mapping from asymmetric c-command into subsequence, instead of precedence. This

heads (non-terminals immediately dominating a terminal), maximal categories (non- terminals dominating another non-terminal), and segments of maximal projections and heads. But since the status of intermediate category is eliminated, the formal differences between specifiers and adjuncts are also eliminated.⁴⁸

Before turning to the subject of adjunction, the other important dimension in the antisymmetry approach, let us illustrate briefly the consequences of this analysis up to now. According to this view, the different surface order we see between English and Japanese, for instance, is a product of movement. While in English the object remains in complement position, in Japanese it gets displaced to the left and becomes a specifier, as (44a) and (44b) reflect:

According to this hypothesis, these English and Japanese examples do not merely differ with respect to linear order; they also differ with respect to hierarchical

second option will yield the complement-head-Spec order. Kayne (1994) considers the first possibility to be the right one.

48 Ordóñez (1997) points out that Chomsky’s (1995) bare phrase structure system does not have these consequences. Chomsky dissociates the notions of maximal/minimal and projected/non projected as in Muysken (1982). For Chomsky, an intermediate X’ projection is not maximal and not minimal and is, therefore, invisible for the computational system. Thus, X’ is not able to c-command into its sister specifier. Since Chomsky’s system maintains the notion of intermediate projection and separate segments, adjuncts and specifiers are formally distinguished.

XP Spec X’

head complement

(44a)

from Tokyo

XP Spec X’

head complement

(44b)

Tokyo Kara

structure. This means that the object in Japanese is not only to the left of the preposition, but it is also more external in hierarchical terms.

A parallel case can be found when analyzing preverbal and postverbal subjects in Spanish. See the examples in (45) and (46):

(45) una canción canta Marta [a song sing-3^rdps Marta]

(46) Martai canta una canción proi

[Marta sing-3^rdps a song pro]

The OVS order in (45) is a product of V-movement, while the SVO order in (46) is the result of the adjunction of the subject and the chain relationship that is established between this and the resumptive pronoun in postverbal position (pro);

that is, a preverbal subject implies adjunction, not subject movement, the (postverbal) subject position being occupied by empty pro. Sentences with postverbal and preverbal subjects are, therefore, products of different numerations.

In this way, the traditional explanation that accounted for cases such as the ones in (45) in terms of being derived from the basic order in (46) has been totally abandoned.⁴⁹

Thus, one of the outcomes of this hypothesis is that every difference in linear order in the same language or across languages must reflect a difference in hierarchical structure.

49 See next chapter for a detailed analysis.