The Locality of Interpretation: The Case of Binding and Coordination

ion over that variable. (von Stechow was not concerned with answers to functional questions, but his remarks generalize directly to this case.) Under this view, the shift from the-mother-of'(x) to λx[the-mother'of'(x)] does not in fact involve extra machinery. Note, though, that this makes sense only under a Binders Out approach in general since it is only under such an approach that the rule in (10) is motivated. But that in itself requires extra machinery (and also, of course, crucially denies the hypothesis of local interpretation). Of course quantifier scope phenomena have long been taken to provide independent motivation for a Binders Out approach; but recent work in Categorial Grammar has shown that scope itself can be handled even when all quantified NPs are interpreted in situ (see, e.g., Hendriks, 1987). There are, then, perhaps some open questions as to whether or not the answers to functional questions require extra apparatus under the standard account whether or not it does depends on what other assumptions one makes. But in any case, we can note that under the approach here it is clear that nothing extra is needed: it follows immediately that his mother has the right kind of meaning to serve as answer to the functional question. The reason is, of course, that this is a function of type in particular, it denotes the-mother-of' function. Once again, the key centers on the locality property of the pronouns in the variable-free approach: the semantic effect of an (as-yet unbound) pronoun is "felt" in any constituent containing that pronoun thus his mother is not like an ordinary NP but is necessarily a function of type . Again, the conventional wisdom behind variables is that pronouns "pretend" to be like ordinary NPs until the point in the semantic composition where they are ready to be bound. The result of this is that his mother should denote an ordinary individual and not a function of the appropriate type. 4. Conjunction and Across-the-Board Binding We are now in a position to see why the interaction of conjunction (specifically, RNR constructions) and binding provides some rather striking evidence for this approach to binding and, in fact, for all three claims elucidated in Sec. 1. The exposition here will take place in several steps. This section will discuss the phenomenon of "Across the Board" (ATB) binding. I will show here that this phenomenon is quite similar to the case of functional questions under the variablefree semantics, this phenomenon comes "for free". It is, moreover, completely compatible with the analysis of RNR which maintains the hypothesis of local interpretation and direct model-theoretic interpretation (without a mediating level). In Secs. 5 and 6, I will show that under the standard view of variables, this phenomenon requires either a reconstruction analysis of RNR or one making use of functional traces (or an equivalent type-shift rule). However, it will be shown that both of these solutions suffer from a serious problem: both allow for binding out of just one conjunct which, in fact, is impossible. In Sec. 7 we will return to the variable-free account, to show that the problem does not arise here. The existence of ATB binding has been noted from time to time in the literature; see, e.g. Dahl (1981), Hohle (1990), von Stechow (1990): (17) a. Every mani loves but no manj wants to marry hisi/j mother. b. Every mani loves and no manj marries hisi/j mother. The first noteworthy point about (17) is that under the variable-free analysis discussed above (combined with the anlaysis of RNR discussed in Sec. 1), nothing more needs to be said the existence of the ATB reading is an automatic consequence of the analysis. Informally, the analysis of (17) proceeds in essentially the same way as does the anlaysis of (1) which was sketched in (3). The only difference is that here the subject function composes with z (loves') rather than with loves'. Thus the first conjunct every man loves denotes the set of functions f if type such that every man stands in the z -love relation to f. Similarly, no man hates denotes the set of functions g such that no man z -hates g. Hence the full conjoined expression every man loves and no man hates denotes the function characterizing the intersection of these two sets. Furthermore, his mother is of course of the right type to serve as argument of this function. Because it contains a pronoun it is of type , and denotes the-mother-of' function. The entire derivation is given in detail in (18): (18) every-man-loves' = every-man' o z (love') = every-man' o λf[λx[love'(f(x))(x)]] = λf[every-man'(λx[love'(f(x))(x)])] no-man-marries' (similarly) = λg[no-man'(λy[marries'(g(y))(y)])] every-man-loves-and-no-man-marries' = λf[every-man'(λx[love'(f(x))(x)])] λg[no-man'(λy[marries'(g(y))(y)])] = λf[every-man'(λx[love'(f(x))(x)]) no-man'(λy[marries'(f(y))(y)])] his-mother' = λx[the-mother-of'(x)] = the-mother-of' Again, the reasons that this proceeds so smoothly and works directly with the surface syntax is due to the locality of the binding effect and to the locality of the effect of pronoun meaning. To clarify this point, let us consider the implications of ATB binding for a standard theory with variables. Consider again how binding works for a simple case like (5) (Every mani loves hisi mother) in the standard view. As discussed in Sec. 2.1.2, binding under the standard view is the result of a type-shift rule which operates on the meaning of an expression containing a pronoun, and operates just before this expression combines with the binder. Thus it operates either on the meaning of the entire VP loves his mother or on the meaning of the entire S under a Binders Out approach. Since the latter requires an even bigger domain than the former, we will confine our remarks to the former approach. The problem posed by a sentence like (17) is obvious here there simply is no (apparent) surface VP to undergo the binding type-shift rule. But under the variable-free view there is no problem we do not need a full VP in order to accomplish the effect of binding. Rather, here binding is the effect of a very local type-shift rule which operates on the meanings of love and marry . Thus the fact that these expressions on the surface do not appear to be surrounded by additional material is no problem the locality of binding here means that we do not need to posit additional material surrounding these verbs in order to effect binding. (Moreover, the fact that his mother has the right meaning is also a consequence of the fact that pronouns always "make their effect known" in every local domain in which they occur; the relevant remarks here are exactly the same as those made in the previous section with respect to the analysis of the answers to functional questions.) Under the standard account, then, we are forced to do one of two things. One possibility is to give up the hypothesis of local interpretation, and posit a reconstruction level at which the "Right Node Raised" constituent (his mother) is in the position of each gap. The other would be to maintain local interpretation, but to assign a complex meaning to the gap in essence, to treat these analogously to the account of functional questions in Groenendijk and Stokhof (1983) and Engdahl (1986). We will turn to each of these alternatives below, and show that both have a serious defect. 5. ATB Binding Under Reconstruction A proponent of the standard view of binding might conclude that the existence of the ATB binding reading in (17) simply shows that the hypothesis of local interpretation is incorrect and that, rather, the interpretation of RNR sentences involves positing a "reconstruction" level at which copies of the Right Node Raised constituent is in the position of each gap. The basic idea, then, is that (17b), for example, is mapped into (or, derived from) a representation like (19) and that the binding effect takes place at this level. Here we have two full VPs, and so there is no problem with either the view of binding given in (9) or in (10): (19) Every man loves his mother and no man marries his mother. The basic idea here could be implemented in a variety of ways we will pick one for the sake of illustration (all varieties which I have been able to think of have the same basic problem). First, assume that LFs are derived from surface structures (rather than the other way around). Second, assume a theory where indexing conventions first apply to some level of representation, and the indexed representations are ultimately mapped into final LFs where indexed pronouns correspond to variables in the obvious ways. Finally, one can imagine reconstruction applying first and then indexing as in (20), or the processes could apply in the opposite order as in (21):: (20) a. Every man loves and no man marries his mother. ==> (reconstruction) b. Every man loves his mother and no man marries his mother. ==> (indexing) c. Every mani loves hisi mother and no manj marries hisj mother. (21) a. Every man loves and no man marries his mother. ==> (indexing) b. Every mani loves and no mani marries hisi mother. ==> (reconstruction) c. Every mani loves hisi mother and no mani marries hisi mother. I will consider only the second possibility here; the reader can verify that the problem(s) to be discussed below hold equally well for the first alternative. The problem which arises here is one which is noted (with respect to slightly different kinds of examples) in Hohle (1990) and von Stechow (1990). This is that there is no reading where the pronoun is understood as bound within the interpretation of one of the conjuncts but is understood as free in the interpretation of the other. In other words, (22a) does not have the reading shown in (22b). But this should be possible, as there is no obvious way to block the derivation shown in (23) (note that (23c) gives rise to the reading in (22b)): (22) a. Every man loves and no man marries his mother. ≠ b. Every mani loves hisi mother and no manj marries hisk mother. (23) a. Every man loves and no man marries his mother. ==> (indexing) b. Every mani loves and no manj marries hisi mother. ==> (reconstruction) c. Every mani loves hisi mother and no manj marries hisi mother. As an initial attempt at a solution, suppose we were to assume that free pronouns simply are indexed in some way which is entirely different from the indices for bound pronouns (this, in fact, is essentially the solution taken in von Stechow, 1990, although he was adopting a view like that explored in the next section). In the first place, though, this seems suspicious in view of the fact noted above that morphologically free and bound pronouns are identical (in English, at least). More seriously, however, is the fact that the problem here is much more general: one cannot have the "ATB pronoun" interpreted as being bound within the interpretation of one of the conjuncts but being bound from outside in the interpretation of the other. In other words, (24a) can't have the reading shown in (24b). Again this should be possible since there is no obvious way to block the derivation in (25). (24) a. Each boy believes that every man loves and (that) no man marries his mother. ≠ b. Each boyk believes that every mani loves hisi mother and (that) no manj marries hisk mother. (25) a. Each boy believes that every man loves and (that) no man marries his mother. ==> (indexing) b. Each boyi believes that every mani loves and (that) no manj marries hisi mother. ==> (reconstruction) c. Each boyi believes that every mani loves hisi mother and (that) no manj marries hisi mother. Note that (25c) gives rise to the reading shown in (24b) (given reasonable assumptions about what these indexed structures mean), because in the interpretation of the first conjunct his will be bound by every man as that is the closest c-commanding co-indexed NP, while in the second conjunct it is bound each boy. Note further that since both pronouns are bound here, the solution to (24) cannot rely on anything having to do with the treatment of free pronouns since here both pronouns are, in fact, bound. One could, or course, imagine various ways to try to rule out the derivation in (25). One obvious way which comes to mind is to rule out the LF in (25c) by a constraint against having the same index on two NPs if one c-commands the other (hence each boy and every man in (25c) cannot be coindexed). Although this works, it has two problems. First, while it would rule out (25c) it would be of no help for the case in (22) thus this would still have to be combined with an account which treats free pronouns differently from bound pronouns. Second, such a constraint on co-indexation is an added stipulation. One might counter this objection by claiming that it is a very "natural stipulation", but I would argue here that a "natural stipulation" simply means something which should follow without stipulation given a deeper understanding of the phenomenon in question. But as long as we are relying on indices and/or their corresponding translation into variables, the fact is that this stipulation does not follow from anything else. One final attempt at a solution for both (22) and (24) would account for both via some sort of "parallelism" constraint on the position of the binder vis-a-vis the reconstruction site. Again, though, any such solution that I can imagine will require an additional stipulation. Along these lines, note that the grammaticality of (26) cast some doubt on the existence of any kind of "parallelism" constraint; a final case that casts doubt on this is discussed in Sec. 8: (26) a. Every mani thinks that the world ought to love but indeed no manj is prepared to marry hisi/j mother. b. No mani actually loves although Mary thinks that every manj ought to love hisi/j mother. c. Every mani says that the whole world should love although Mary knows that in fact no manj (himself) actually loves the woman who brought himi/j into this world. Thus the fact that (22b) and (24b) are both impossible combined with the grammaticality of (26) suggests that the appropriate generalization is as follows: (27) Binding is not possible out of one conjunct unless there is binding out of both. (This is also discussed, although with a somewhat different class of cases, in Chierchia (1988).) This, of course, is reminiscent of Coordinate Structure Constraint on extraction, but it is interesting to note that the effect here is far more robust than run-of-the-mill Coordinate Structure Constraint effects on extraction. One might well argue as Lakoff (1986) and others have done that Coordinate Structure Constraint effects on extraction are actually pragmatically based. Here, however, no amount of "pragmatic tinkering" seems to improve sentences like (22b) and (24b). As evidence that the effect here indeed is not a pragmatic one, Maria Bittner (personal communication) has offered the following sort of sentence, whose pragmatics demand the reading of the type in (24b) but where this reading is nevertheless robustly impossible: (28) *Every mani thought that every other manj had already deposited and that the bursark still had hisj/i paycheck. 6. ATB Binding with functional gaps What we have seen so far, then, is that one way to maintain the standard theory of variables in view of the existence of ATB binding would be to posit a level derived by reconstruction. Such a solution, of course, abandons the hypothesis of local interpretation and, concomitantly, the hypothesis of direct model-theoretic interpretation. But this strategy provides no natural account of the generalization in (27). There is, however, another strategy which one might try here: this strategy remains compatible with the standard view of variables while also still maintaining the hypothesis of local interpretation. This involves a simple extension of the Groenendijk and Stokhof / Engdahl analysis of functional questions. In fact, just this analysis is explored in von Stechow (1990). Thus in (17), one could assume that each conjunct contains a trace in the position of the "gap", and that each of these traces is interpreted as f(x), exactly as in the Groenendijk and Stokhof / Engdahl analysis of questions. (Note once again that traces in the syntax are not really crucial here: one could have a type-shift rule shifting the meaning of love from love' into love'(f(x)) and similarly for marry. What is crucial, though, is the abandonment of the idea that the RNR "gap" is nothing more than a missing argument thus the functional gap analysis is not, for example, compatible with the Dowty/Steedman analysis of RNR.) Furthermore, each individual variable will be bound by the subject in just the way that variablebinding normally proceeds. As to the meaning of the Right Node Raised constituent itself, we will again need to assume that it translates as the-motherof'(x) and that x is then λ-abstracted over in such a way as to convert this into the function λx[the-mother-of'(x)] which is of course equivalent to the-mother-of' function. The detailed derivation is sketched in (29): (29) loves tf(tx); loves'(f(x)) --> (shift by binding rule in (9)) λx[loves'(f(x))(x)] every man loves tf(tx); every-man'(λx[loves'(f(x))(x)]) similarly for no man marries tf(tx); no-man'(λy[marries'(f(y))(y)]) every man loves tf(tx) and no man marries tf(tx); every-man'(λx[loves'(f(x))(x)]) ∧ no-man'(λy[marries'(f(y))(y)]) --> (λ-abstraction over the f variable, by presumably a general process which would apply in the case of RNR in general): λf[every-man'(λx[loves'(f(x))(x)]) ∧ no-man'(λy[marries'(f(y))(y)])] his mother; the-mother-of'(x) --> λx[the-mother-of'(x)] (this constituent can then serve as argument of the conjoined material) So far, this requires nothing new above and beyond what is needed for the case of functional questions and their answers under the Groenendijk and Stokhof / Engdahl analysis. Under this kind of analysis of questions, we in any case need traces which translate as f(x) (or a type-shift rule with the same effect), and we also need a way to type-shift constituents like his mother from "open individuals" to functions of type . But the interesting point to note about this approach is that it has exactly the same problem as the reconstruction analysis: it too does not account for the generalization in (27) without further stipulations. We will show this in detail momentarily, but in order to arrive at the intuition here one can note that the analysis of the two conjuncts under this approach is isomorphic to the postreconstruction representation of the two conjuncts under the reconstruction theory. The reconstruction theory posits a constituent such as hisi mother in each conjunct and the problem is that one occurrence of his can be bound within one conjunct while the other can be free within the second conjunct. Here each conjunct contains as part of its meaning the sequence f(x) and the same problem emerges: x can be bound within one conjunct and not within the other. (Note, then, that the f variable in this analysis is analogous to mother in the reconstruction analysis, while x is analogous to his.) To flesh this out in greater detail, consider first the case in (22b) where one variable is bound by one subject and the other is free. That is, there is no obvious way to block the derivation shown in (30) (this assumes the VP-level binding rule in (9); similar remarks would apply to the Binders Out approach shown in (10)): (30) loves tf(tx); loves'(f(x)) --> (binding rule in (9)) λx[loves'(f(x))(x)] every man loves tf(tx); every-man'(λx[loves'(f(x))(x)]) marries tf(tx); marries'(f(x)) no man marries tf(tx); no-man'(marries'(f(x))) every man loves tf(tx) and no man marries tf(tx); every-man'(λx[loves'(f(x))(x)]) ∧ no-man'(marries'(f(x))) The derivation will be completed by λ-abstraction over f and by application of the result to the argument λx[the-mother-of'(x)]. This yields the meaning in (22b) where the x variable within the first conjunct is bound by its subject, but where the x variable within the second conjunct remains free. Note again that it will not do to simply treat free pronouns in a different manner, since the same problem extends to the case of (24b) where both pronouns are bound, but where one is bound from higher up. To demonstrate this, we can note that there is obvious way to block the following derivation: (31) every man loves tf(tx) and no man marries tf(tx); every-man'(λx[loves'(f(x))(x)])∧ no-man'(marries'(f(x))) --> (λ-abstraction over f): λf[every-man'(λx[loves'(f(x))(x)])∧ no-man'(marries'(f(x)))] every man loves tf(tx) and no man marries tf(tx) his mother; λf[every-man'(λx[loves'(f(x))(x)])∧ no-man'(marries'(f(x)))]