Indexing and binding
Under the analysis presented above, the SSC and PIC are no longer interpreted as conditions on proper binding. Rather, they function as reindexing rules and therefore become part of the algorithms for assigning indices to representations in LF. Conditions on proper binding are given in terms of the conditions on well-formed indices in (1).
(1)
As demonstrated in the previous section, the SSC and PIC as reindexing rules apply to the referential index of an anaphor and the anaphoric index of a pronoun. They do not apply to the referential index of a pronoun, the anaphoric index of a wh-trace, or either index of a name. Whether they apply to the referential index of a wh-trace depends on the status of a wh-trace in LF—that is, is a wh-trace a special case of a name, or is it a fourth NP-type distinct from anaphors, pronouns, and names? In this section, we will show that the assumption that these rules do not apply to the referential index of a wh-trace leads to a simplification in their formulation, which in turn allows for a simplification of the algorithms for assigning indices proposed in Chomsky (1980).
In previous formulations of the SSC and PIC, rather than S was taken as the domain of proper binding for an anaphor. The ostensible reason for this choice was the assumption that a wh-trace had the same status as an NP-trace with respect to the conditions (cf. Chomsky (1973; 1976)). We know of no other reason for choosing over S.
In contrast, there are several reasons for choosing S over must be stipulated in the structural description of the reindexing rules, whereas S need not. It follows from the definition of in the domain of in conjunction with the phrase structure rule S→NP AUX VP that the domain of both the subject and the tensed element is S. In addition to allowing for a simplification of the reindexing rules, the choice of S provides an explanation for why non-wh-NPs in the domain of subject or a tensed element may not use COMP as an “escape hatch” (see Freidin (1978, 529) and the references cited there) with respect to the SSC and PIC—a possibility which was not explicitly discounted in previous formulations of these conditions.
Another reason for choosing S rather than is that the ungrammaticality of NPs like (2a) follows immediately from reindexing (specifically the PIC) and the filter (1a).
(2)
If S is the relevant domain of application for the reindexing rules, then the referential index of each other in the representation (2b) will be deleted. If, however, is chosen, then each other would not be subject to the reindexing rules since it is bound in Thus, another means of accounting for (2a) would be required.
An alternative method of accounting for (2a) would be to specify the algorithms for assigning referential indices in such a way that representations like (2b) would never be generated. One interpretation of the algorithms given in Chomsky (1980) has this effect. The algorithms and their ordering are given in (3).
(3)
(3a) is part of the syntax; (3b) and (3c) belong to LF, the latter constituting part of the construal rules. (3) will not generate the representation (2b) given the stipulation that whoi does not count as a c-commanding NP.
This alternative seems needlessly complicated. Coindexing applies in two different components, before and after contraindexing. Thus, the indexing operation must be given as two distinct suboperations, coindexing and contraindexing.
These complications can be eliminated by taking S to be the domain of application for the reindexing rules. Since the ill-formedness of (2b) will fall under (1a), it does not matter if the indexing rules generate such representations. Therefore, we might try to eliminate (3) in favor of the optimal rule of indexing (4).
(4) Index NP
Given (4), indexing applies freely, including as a subcase coindexing, at a single point in a derivation. There is no need to define the operation of contraindexing or to stipulate that it applies top-to-bottom as in (3b). Nor is there any need to stipulate that anaphoric NPs be coindexed with some c-commanding NP, excluding wh-phrase in COMP (3c). This follows automatically from the reindexing rules in conjunction with filter (1a).
Having established that the choice of S rather than several desirable consequences, let us now return to the question of whether the referential index of a wh-trace is subject to the reindexing rules. If a wh-trace’s referential index is subject to reindexing, then must be taken as the domain of application. Otherwise, the system of rules and filters would predict incorrectly that all wh-questions in English are ill-formed. To maintain this position without giving up the advantages of choosing S would require the implausible analysis in which the domain of application for the reindexing rules is generally S, but for the referential index of a wh-trace. In view of this, we conclude that neither index of a wh-trace is subject to the reindexing rules. Thus in LF, a wh-trace has the same status as a name.
We turn next to a formulation of the rule for assigning anaphoric indices. Following Chomsky (1980), let us take the anaphoric index of an NPi to be the set {a1,…,an}, where each aj is the referential index of an NP which c-commands NPi. Recall that only nonanaphors are assigned anaphoric indices. Note too that it must be assumed that a wh phrase in COMP or its trace in COMP is ignored by the algorithm which constructs anaphoric indices. Otherwise, the algorithm would produce representations like (5) which violate (1b).
(5)
Note also that anaphoric indices must be assigned after Wh Interpretation in order to account for disjoint reference in another crossover case (6a), in contrast to its noncrossed counterpart (6b).
(6)
In (6b), his is free in reference with respect to the variable bound by who. By Wh Interpretation, the trace theoretic representation of (6) is mapped onto (7) (see Chomsky (1977a)).
(7)
By the algorithm for constructing anaphoric indices, (7) is mapped onto (8).
(8)
Since his is interpreted as free in reference with respect to x1 in (8b), we assume that there is some principle operative which effects the deletion of the anaphoric index 1 on the pronoun.
Given that the reindexing rules follow the assignment of anaphoric indices, which in turn follows Wh Interpretation, wh-trace and NP-trace are distinct at the point in a derivation where the reindexing rules apply. At that point, a wh-trace is represented as a variable, whereas an NP-trace is represented as an empty category.
