Introduction to binding
In this section it will be assumed that the SSC and PIC are properly construed as principles of binding which hold for the relations of bound anaphora and disjoint reference. We will show that while anaphors and pronouns (in contrast to names) fall under these principles, wh-traces (like names) do not.
Considering for the moment just bound anaphora, one formulation of the PIC and SSC as binding principles could be (1).
(1)
We take (1) to be a filter at the level of LF (cf. Freidin (1978)). The domain of a category α is taken to be all the categories c-commanded by α. An anaphor is bound in a domain when there is a c-commanding NP with the same referential index in that domain. This formulation has advantages over previous formulations of the SSC and PIC—for example, the one in Chomsky (1980)—as will be discussed in section 3.
(1) accounts for the standard paradigm of bound anaphora, where the class of anaphors includes reflexive pronouns, reciprocals, and also NP-traces. Some of the relevant data are given in (2).
(2)
The anaphors in the (i)-examples are free in the domain of the complement subject and are therefore prohibited by the SSC (1a). The anaphors in the (ii)-examples are free in the domain of the complement tense and are therefore prohibited by the PIC (1b). In contrast, the anaphors in the (iii)-examples are in the domain of a subject and tense with respect to the matrix S, but not the complement S. In the matrix domain the anaphors are bound and thus not prohibited by (1). This formulation of the binding principles generalizes automatically to anaphors in simple sentences, as shown in (3).
(3)
The (i)-examples fall under the PIC (1b); the (ii)-examples, under the PIC and the SSC (1a). Previous formulations of the SSC and PIC, with the exception of Chomsky (1980), applied only to complex sentences. As a result, an account of (3) required additional stipulations (cf. Freidin (1978, (8))). Given (1), these are unnecessary.
Ordinary pronouns also should fall within the domain of the SSC and PIC, as discussed in Chomsky (1973; 1976). In the case of pronouns, however, the relevant property is obligatory disjoint reference (Lasnik (1976), Chomsky (1976)) rather than obligatory coreference as in the case of anaphors. Because of this, the filtering formulation of the SSC and PIC in (1) cannot be extended to account for the facts of disjoint reference. Therefore, the SSC and PIC as stated in (3) must be reformulated. A reformulation is given below. In the formalism for indexing of section 1, obligatory disjoint reference is expressed in terms of an anaphoric index. Under the procedure for constructing anaphoric indices stated above, the pronoun cases analogous to (2) will be assigned the indexed representations (4a–c).
(4)
The representations (4a) and (4b), in contrast to (4c), are incorrect because the pronouns him and he are not interpreted as obligatorily disjoint in reference from Harry in the corresponding sentences (5a) and (5b).
(5)
The pronouns in (5a,b) are free in reference with respect to Harry—that is, coreference is possible though not necessary.
In terms of indexing, a pronoun is free in reference with respect to an NP with referential index i when the anaphoric index of the pronoun does not contain the integer i. Given this, the correct representations for (5a,b) are (5′a,b), respectively.
In the framework of Chomsky (1980), (5′a,b) would be derived from (4a,b) by deleting the member 1 from the anaphoric index of each pronoun. In (4a), the member 1 is not bound (as defined for (3)) in the domain of a subject. In (4b), the member 1 is not bound in the domain of tense.5 Thus, the deletions occur when the member 1 fits the structural circumstance inherent in (1)—i.e., free (=not bound) in the domain of a subject or tense. (5′a,b) are derived from (4a,b) by reformulating the SSC and PIC as re indexing rules which carry out the required deletion under the stated structural circumstances. These rules can be formalized as follows:
(6)
A pronoun is free(i) in a domain when there is no c-commanding NP with referential index i in that domain.
This type of analysis can be extended to the anaphor cases, as Chomsky shows. For anaphors, the SSC and PIC affect referential indices. For example, the SSC and PIC as reindexing rules should map (2ai) onto (7a) and (2aii) onto (7b).
(7)
It must be assumed that an NP with a zero referential index is ill-formed—i.e., *NP(0). The appropriate reindexing rule can be formalized as follows:
(8)
The definition of free(i) with respect to pronouns extends without modification to anaphors. An anaphor is free(i) in a domain when there is no c-commanding NP with referential index i in that domain.
Given this system, we will now show that a wh-trace has an anaphoric index which is not subject to the reindexing rules, SSC and PIC. Thus, a wh-trace is distinct from an anaphor and also from a pronoun. The relevant evidence involves coreference possibilities between a wh-trace and a c-commanding pronoun. (9) gives the paradigm bearing on the SSC, and (10), the paradigm bearing on the PIC.
(9)
(10)
In the (b)-examples, the pronoun is free in reference with respect to the variable bound by who,6 whereas in the (a)-examples, the pronoun is construed as disjoint in reference from the variable bound by who. In the (a)-examples, the speaker must already know the referent of the pronoun; in the (b)-examples, he need not, but rather may be inviting the listener to provide a referent for the pronoun by answering the question. This difference is easily captured on the assumption that a wh-trace has an anaphoric index.
Under trace theory, the derivations of (9a) and (9b) involve the following partial mappings from S-structure to LF.
(12)
The S-structures (11a), (12a) are mapped onto (11b), (12b) by a rule which replaces a wh phrase with its meaning (see Chomsky (1976; 1977a) for discussion). The structures (11b), (12b) are mapped onto (11c), (12c) by a rule which assigns anaphoric indices. Further, (12c) will be mapped onto (13) by the SSC, thus accounting for the fact that him is free in reference with respect to the variable bound by who.
(13)
In contrast, the SSC should not apply to the anaphoric index of the variable in the complement of (13c); otherwise, we lose the relevant distinction between (9 a) and (9b). We conclude then that the anaphoric index of a wh-trace is not subject to the SSC.
The analysis given above is based on a discussion of (9) in Chomsky (1976). This analysis extends naturally to the PIC cases such as (10) which were not discussed there, and in Chomsky (1980) were assumed not to exist.
Parallel to (11) and (12), the derivations of (10a) and (10b) involve the following partial mappings in (14) and (15).
(14)
(15)
The PIC maps (15c) onto (16).
It does not apply to the variable in the complement of (14c), thereby preserving the distinction between (10a) and (10b). From this we conclude that the anaphoric index of a wh-trace is not subject to the PIC.
Thus far, we have established (a) that a wh-trace, which functions as a variable at LF, takes an anaphoric index, and (b) that this anaphoric index is not subject to either the SSC or the PIC. In this regard, a wh-trace patterns like a name (cf. Chomsky (1976, 335),
where the parallelism between variables and names was first discussed). Below we will consider the question of whether the referential index of a wh-trace might be subject to the reindexing rules.
The correct representations for the “crossover cases” (9a) and (10a) follow from the rule that assigns anaphoric indices and the assumption that the trace of wh is not subject to the SSC or the PIC. In addition, a rather natural account of violations of the COMP-to COMP condition on Wh Movement follows from this analysis without any further stipulations, as shown in May (1981).
COMP-to-COMP violations involve movements of a wh-phrase from a COMP to an NP position. In terms of binding, the condition prohibits the binding of a trace in COMP from an NP position in S. For the sake of exposition, we will assume that once a wh phrase is wh-moved, it must end up in a COMP position. Violations of the COMP-to COMP condition will result in structures in which a wh-phrase binds two different NP traces, one in a matrix S and the other in a complement S. There are two cases to consider: (i) where the complement NP-trace is in the predicate, and (ii) where the complement NP-trace is in subject position. An example of each case is given in (17).
(17)
The strings in (17) pair with the representations in (18).
(18)
The Roman numerals in (18) indicate the derivational history of the wh-phrase. In each example the second movement (II) violates the COMP-to-COMP condition.
The representations in (18) map onto those of (19) via Wh Interpretation and the rule which assigns anaphoric indices as discussed above for (11)–(12) and (14)–(15).
(19)
In each case the index of the variable in the complement is contradictory—in effect indicating that the intended referent of the variable must be disjoint in reference from itself. These contradictory indices are unaffected by the reindexing rules (i.e., the SSC and PIC). Therefore, we can now account for the COMP-to-COMP violations in terms of indexing—i.e., with a prohibition against contradictory indices of the form (i,{i}). (This observation is due to Robert May—see May (1981) for additional discussion.)
The indexing analysis of the COMP-to-COMP violations allows us to dispense with an ad hoc condition on derivations in favor of a natural condition on representations; namely, the prohibition against contradictory indices of the form (i,{i}). See Freidin (1978; 1979) for more detailed discussion of the issue concerning conditions on derivations vs. conditions on representations.
