JOURNAL OF SEMANTICS Volume 24 Number 3
CONTENTS SIGRID BECK AND ARNIM VON STECHOW Pluractional Adverbials
215
MARTINA FALLER The Ingredients of Reciprocity in Cuzco Quechua
255
ROBERT VAN ROOIJ Strengthening Conditional Presuppositions
289
Please visit the journal’s web site at www.jos.oxfordjournals.org
Journal of Semantics 24: 215–254 doi:10.1093/jos/ffm003 Advance Access publication May 17, 2007
Pluractional Adverbials SIGRID BECK Universita¨t Tu¨bingen ARNIM VON STECHOW Universita¨t Tu¨bingen
This paper investigates the semantics of adverbials like ‘page by page’ and ‘stone upon stone’. An analysis is developed in which sentences containing such adverbials have a pluractional semantics; that is, pluralization affects simultaneously the event- and the individual-argument slot of a predicate. Sternefeld’s (1998) system of plural operators is used and extended for this purpose. The adverbial constrains the relation that is pluralized and makes visible a higher plural operator. In the case of ‘page by page’-type adverbials, this is a fairly standard operator that leads to a simple divisional interpretation. In the case of ‘stone upon stone’-type adverbials, the operator has a stronger semantics that leads to a sequence interpretation. The generality of our theory permits straightforward extension to data like ‘she ran and ran’ and ‘she climbed higher and higher’, among others. Finally we propose that inclusive alternative ordering reciprocals (Dalrymple et al. 1998) have a pluractional sequence interpretation as well.
1 INTRODUCTION The topic of this paper is the semantic analysis of the sentences in (1). Example (1a,b) contain the adverbial modifiers ‘one after the other’ and ‘dog after dog’, respectively, which add to the simple (1#) information on how the overall event of the dogs entering the room is to be divided into subevents based on a division of the group of dogs into individual dogs. We call these adverbials pluractional adverbials, following, for example, Lasersohn’s (1995) use of the term pluractionality for the division of larger eventualities into subeventualities. (1) a. These three dogs entered the room one after the other. b. They entered the room dog after dog. (1#) These three dogs entered the room. The type of situation described by (1a) [and also by (1b) if the referent of ‘they’ is the same as the referent of ‘the three dogs’] is depicted informally in (2). We will aim to derive this fact by associating with (1a,b) (roughly) the truth conditions in (3); that is, we will propose a The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email:
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Abstract
216 Pluractional Adverbials compositional semantics for (1a,b) that derives approximately the truth conditions in (3), and (3) serves to capture our intuitions about the situations in which (1a,b) would be considered true. (2) a. These three dogs entered the room one after the other. b. D3 / D2 / D1 #x / y# ¼ x enters the room after y (3) These three dogs entered the room, and the entering can be divided into a sequence of subevents in each of which one of the dogs enters, and the dogs can be divided into a sequence of individual dogs each of which entered in one of the subevents.
(4) a. This mystery offers puzzle within puzzle. b. She laid book upon book and built a staircase long enough to climb up and look over the wall. c. The Wall of Tears is a very big wall that was built, stone over stone by the prisoners when Isabela was a penal colony back in 1946. (5) a. Because life’s interaction is like a series of boxes one within the other, ecological studies are organized in hierarchical levels. b. In storing textiles, rugs, or other large-sized weavings, these should never be folded and piled one upon the other. c. My grandmother had on not just one skirt, but four, one over the other. There is a semantically simpler type of pluractional adverbial exemplified by (6) below. The analysis of the ‘piece by piece’ type of adverbial will be our basis for formulating the semantics for pseudoreciprocal ‘dog after dog’-type adverbials. (6) a. Sally ate the cake piece by piece. (6#) a. Sally ate the cake. (7) a. Cigar wrapper is harvested leaf by leaf. b. The traditional visual apple-by-apple inspection is labour intensive and prone to human error.
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While we largely concentrate on the particular examples in (1), the phenomenon as such is of course more general. Other examples of reduplicative adverbials like ‘dog after dog’ are given in (4), and other examples of the ‘one . . . the other’ type are provided in (5). These data were collected informally from the Web. All of these adverbials, we claim, have a semantics analogous to (1), which we call pseudoreciprocal.
Sigrid Beck and Arnim Von Stechow 217
We will introduce our background assumptions in section 2 and illustrate them with an analysis of ‘piece by piece’-type adverbials. Section 3 is devoted to the semantics of pseudo-reciprocals. In section 4, we address several issues closely related to our analysis, including a certain type of apparent reciprocal construction—inclusive alternative ordering (IAO) Reciprocals (Dalrymple et al. 1998)—as well as data like (8) below. We conclude the paper in section 5 with a summary, a discussion of related literature and some conclusions. (8) a. Sally ran and ran. b. Sally approached the horse step by step. c. Sally was sick and sick. d. The train arrived and arrived.
2 SIMPLE PLURACTIONALS
2.1 Background Besides individuals (type Æeæ), we use eventualities (type Ævæ). We assume that both De (the denotation domain of individuals—count and mass) and Dv (the denotation domain of eventualities) have a mereological structure. We assume a primitive (i.e. not formally defined) part of relation <, which must be antisymmetric, reflexive and transitive. It underlies the following definitions: (9) a. x and y overlap iff they have some common part: x o y iff dz[z < x & z < y] b. x and y are distinct iff they do not overlap (10) Let M be a subset of Dr, where r ¼ e or r ¼ v.
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c. The building was moved stone by stone to a site on campus. d. Many of the Open team drivers today actively buy, sell, and swap dogs with owners of the smaller kennels, and many of the limited class teams are dog for dog as fast as their open class counterparts. e. The procession was in the following order: 10 of His Majesty’s Horse-Grenadiers, advanced to clear the way. [. . .] Then followed on horseback a servant of the Office of Arms. Conductors with black staves, two and two. Kettle-drum, two trumpets. The standard born by a gentleman, supported by two others. Several servants of the nobility and gentry, two and two. [. . .]
218 Pluractional Adverbials +M is the fusion of the elements of M if it has all of them as parts and has no part that is distinct from each of them: +M ¼ that x 2 Dr.("y 2 M)[y < x & :(dz)[z < x & ("u 2 M)[z is distinct from u]] (11) If M is the finite set {x1, . . . , xn}, we write +M as x1 + . . . + xn.
(12) Cumulation operators n (Sternefeld 1998) Let R be an n-place relation. Then [n R] is the smallest relation R# such that the conditions in (a) and (b) are satisfied. (a) R# R (b) for all Æx1, . . ., xnæ and Æy1, . . ., ynæ: If Æx1, . . ., xnæ 2 R# and Æy1, . . ., ynæ 2 R#, then Æx1 + y1, . . ., xn + ynæ 2 R# The cumulation operators will provide the conceptual basis for the definition of our plural operators, which will be given in a moment. Simple instances of (12) are Link’s (1983) operator (1 in the schema) and Sternefeld’s own operator of type ÆÆe, Æe, tææ, Æe, Æe, tæææ. Below is a simple example for the application of the operator. An analysis in which the predicate ‘weigh 40 kg’ is pluralized, as in (13b) (Logical Form) and (13c) (our representation of the resulting truth conditions), predicts that (13a) can be true if the individual children weigh 40 kg. (13) a. The children weigh 40 kg. b. [[the children][ [1 [t1 weigh 40 kg]]]] c. C 2 [kx. x weigh 40 kg] The relevant case for our present purposes is an operator that pluralizes predicates of type Æe, Æv, tææ [cf. (14)]. The pluralized relation is true of all the things that the original relation was true of, plus all the part-whole structures that can be built from them. Alternative formulations of this operator have been proposed in the literature; for
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We assume that basic predicates can be pluralized in order to apply to groups (or generally entities with a part-whole structure). We call this plural predication (more accurate in our case would be, ‘mereological’ predication—we continue to use plural predication for simplicity and accordingly call the operators pluralization operators). For this purpose, we use a family of operators of various types, beginning with Link’s (1983) operator for the pluralization of Æe, tæ predicates, and moving on to operators pluralizing relations (compare in particular Sternefeld 1998, also Beck 2001). Example (12) below defines the general case:
Sigrid Beck and Arnim Von Stechow 219
our purposes, it will sometimes be useful to have in mind the version used in Beck & Sauerland (2000) given in (14#).
"x# < x: de# < e:R(x#)(e#) & "e# < e: dx# < x:R(x#)(e#). We further assume that all such pluralization is sensitive to a contextually given division of entities into sub-parts (Beck 2001). We concretely follow Schwarzschild (1996) who suggests that the context provides a cover of the universe of discourse (compare also Moltmann 1997). The covers relevant for our purposes will all be partitions [defined in (16a)]. (16b,c) defines two useful bits of notation: the constraint that the cover be a partition of an entity x in (16b), and in (16c) that subset of the cover whose fusion is the entity x. Note that for Schwarzschild (1996) (and for us), the cover variable always provides a cover of the entire universe of discourse. (15) Cover (mereological version): Cov is a cover of x iff Cov is a set such that +Cov ¼ x. (16) a. A cover Cov is a partition iff for any x, y 2 Cov: x and y don’t overlap. b. PART(Cov, x) d 1 iff Cov is a partition (and a cover) of x. c. Cov[x] ¼ {y: y 2 Cov & y < x} We use ‘Cov’ as a variable ranging over covers and write ‘Cov(x)’ for x 2 Cov (not to be confused with Cov[x]). The reanalysis of example (17a) is given in (17b,c). The cover variable is a free variable assigned a value by the context; this is the salient division of groups into subparts. The truth conditions predicted by this analysis say that the group denoted by ‘the children’ can be divided into salient parts that weigh 40kg. Suppose the salient parts are the individual children (the default cover); then (17c) says that each child weighs 40kg. This is the standard distributive interpretation of the example. (17) a. The children weigh 40 kg.
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(14) Cumulation operator Let R be a relation of type Æe, Æv, tææ. Then [R] is the smallest relation R# such that the conditions in (a) and (b) are satisfied. (a) R# R (b) for all Æx, eæ and Æy, e#æ: If Æx, eæ 2 R# and Æy, e#æ 2 R#, then Æx + y, e + e#æ 2 R# (14#) Let R be a relation of type Æe, Æv, tææ. Then for any x, e: [R](x)(e) ¼ 1 iff
220 Pluractional Adverbials b. [[the children][ [Cov [1 [t1 weigh 40 kg]]]]]1 c. C 2 [kx.Cov(x) & x weigh 40 kg] We implement this theory of plural predication through syntactic pluralization operations such as (18) for pluralization of type Æe, Æv, tææ predicates; (18) combines the operator with the requirement that the division into sub-parts be into the contextually relevant ones, plus the presupposition that the contextually provided cover be a partition of the entities considered. (18) ½½PL ¼ kCov.kRÆe, Æv,tææ.kx.ke: PART(Cov, e + x). [kx#.ke#.Cov(e#) & Cov(x#) & R(x#)(e#)](x)(e)
(19) a. b. c. d.
John ate the cake. [[the cake] [PLCov [Æe, Æv, tææ k1[John ate t1]]]] ke.Æe, Cæ 2 [kx.ke#.Cov(x) & Cov(e#) & J eat x in e#] "x[x < C & Cov(x) / de#[e# < e & Cov(e#) & J eat x in e#]] & "e#[e# < e & Cov(e#) / dx[x < C & Cov(x) & J eat x in e#]]
(20) a. g(Cov)[C + e] ¼ {c1, c2, e1, e2} with e ¼ e1 + e2 and C ¼ c1 + c2 b. ½½eat ¼ {Æ J, c1, e1æ, Æ J, c2, e2æ} Looking at these simple data, it is far from obvious that we need such an analysis in terms of Æe, Æv, tææ pluralization. Pluractional adverbials, however, show that it is indeed necessary. 1 The composition of Cov and the VP is intersective, that is, ‘Cov weigh 40 kg’ means kx.Cov(x) & x weigh 40 kg.
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The use of PL is illustrated in the example in (19). A predicate of type Æe, Æv, tææ is created through movement of the object NP. We assume that pluralization operators are inserted at the level of Logical Form (compare Beck & Sauerland (2000) and Beck (2001) for theoretical details). The PL operator together with its cover restriction is adjoined to the predicate created by QR. If the presupposition triggered by PL is met, the result will be the predicate of events in (19c). (19c) is true of an event e iff e and the cake can be divided into relevant parts x and e# that stand in the relation ‘John ate x in e#’. The cake and the big event e can be divided in this way just in case (19d) is true: each relevant part of the cake was eaten by John in a relevant subevent, and each relevant subevent has John eating a relevant part of the cake in it. Thus, (19a) is true of an event that can be divided into smaller events of eating parts of the cake; a sample situation would be (20).
Sigrid Beck and Arnim Von Stechow 221
2.2 ‘Piece by piece’ adverbials
(21) John ate the cake piece by piece. (21#) (21) is true of an event e iff the relevant division of the cake is into pieces, and each piece was eaten by John in a relevant subevent of e, and each relevant subevent of e is an eating of one of the pieces by John. (22) a. [[the cake][piece by pieceCov [Æe, Æv, tææ k2[John ate t2]]]]] b. ½½piece by piece ¼ kCov.kRÆe, Æv, tææ.ky.ke: PART(Cov, e + y). [ky#.ke#.Cov(y#) & Cov(e#) & y# is a piece & R(y#)(e#)](y)(e) c. ke.Æe, Cæ 2 [ky#.ke#.Cov(y#) & Cov(e#) & y# is a piece & John ate y# in e#] We can define an ‘N by N’ operator that takes the noun as a first argument. This is of course exactly PLCov with the restriction ‘P(x#)’ on the members of the cover of x added. Let’s call this version of the operator PLdiv (for division). (23) ‘N by N’ (preliminary analysis) ½½PLdiv ¼ kPÆe, tæ.kCov.kRÆe, Æv, tææ.kx.ke: PART(Cov, e + x). [kx#.ke#.Cov(e#) & Cov(x#) & P(x#) & R(x#)(e#)](x)(e) There are a few other examples of essentially this kind of pluractional adverbial, in both English and German. Some data are given below. References on such data include Moltmann (1997), Zimmermann (2002) and Oh (2005); see also section 5 for discussion.
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In (21), with the adverbial ‘piece by piece’, it is clear that the truth conditions of the sentence imply a division of the overall event of eating the cake into subevents depending on a division of the cake into pieces. This is reflected in the truth conditions described in (21#). The adverbial ‘piece by piece’ seems to be an instantiation of a version of the PL operator with a cover of the cake into pieces. We will not worry here too much about how to implement this idea; one possibility is given in (22). The resulting truth conditions (22c) correspond closely to the ones in (19c,d): (22c) is true of an event e iff e and the cake can be divided into relevant parts y# and e# such that y# is a piece and John ate y# in e#. That is, each piece of the cake was eaten by John in some relevant subevent, and each relevant subevent was John eating a piece of the cake.
222 Pluractional Adverbials
Our operator from (23) would, we think, be equally suitable for all these examples. The property P would end up being ‘piece’ or ‘apple’ in (24a,b), ‘page’ in (24c,d), numeral ‘two’ (i.e. being a two-membered group) in (24e). The reduplicative adverbials of this kind permit as middle particle (at least) fu¨r (‘for’), um (‘by’) and und (‘and’) in German, and by, for and and in English. It is also possible to have adverbs ‘N+ -weise/wise’, as in (24a) and (24e). All of the data in (24) have in common that they talk about multiple events. Example (24a) is distinguished from example (24a#), for instance, in that (24a#) can be true if Ede devoured all the pieces of the cake in one gulp. This does not provide the plurality of subevents that (24a) requires. Subevents can be individuated temporally [this is the plausible reading of (24a), spatially (this is possible in (24e)), e.g. if the children enter the schoolhouse simultaneously through different doors] or based on participants [plausibly involved in (7a) and (7b) through harvester and inspector]; compare Lasersohn (1995). No matter how they are individuated, our operator PL accounts for the ‘plurality of events’ requirement through explicit pluralization of the event-argument slot (see section 3 for more detailed discussion of this point). (24a#) Ede vertilgte die Stu¨cke des Kuchens. Ede devoured the pieces of the cake. Combining Sternefeld’s theory of a general pluralization mechanism for n-place relations with an event semantics, and a part/whole structure on the domain of events, leads one to expect that natural language has pluralization operators of the ÆÆe, Æv, tææ, Æe, Æv, tæææ type defined in (18) above. The ‘piece by piece’-type adverbials discussed in this section show that this prediction is borne out.
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(24) a. Ede vertilgte den Kuchen stu¨ckweise. Ede devoured the cake piecewise b. Die A¨pfel fielen Stu¨ck fu¨r Stu¨ck/Apfel fu¨r Apfel/einzeln vom Baum. the apples fell piece by piece/apple by apple/individually off the tree c. Irene bekritzelte die Bibel Seite fu¨r Seite. Irene scribbled on the bible page for page d. Sie durchforstete das Buch Seite um Seite. she went through the book page by page e. Die Kinder gingen zwei und zwei/paarweise ins Schulhaus. the children went two and two/pairwise into the school
Sigrid Beck and Arnim Von Stechow 223
3 PSEUDO-RECIPROCAL PLURACTIONAL ADVERBIALS We can now address the issue that interests us, repeated below. We approach it by first considering the ‘one . . . the other’ construction. We begin with more standard occurrences of the modifier ‘after NP’ and extend their analysis to ‘after the other’.
3.1 The modifier ‘after NP’ Our baseline will be the contribution of ‘after NP’ suggested in (25#) for (25). (25#a) says that Min’s entering must occur after the (relevant) entering by Katie. We express this as in (25#b). This leads to the semantics in (25$) for ‘after Katie’: it modifies a relation of type Æe, Æv, tææ and adds the information that the relation held between Katie and the immediately preceding event. We rely on the notion of the relevant predecessor of an event, which is the event whose running time is before the running time of the event considered. (25) Min entered the room after Katie. (25#) a. ke. Min enters the room in e & s(e) > s(ie#: Katie enters the room in e#) b. ke. Min enters the room in e & Katie enters the room in pred(e) pred(e): the relevant predecessor of e (25$) ½½after Katie ¼ kRÆe, Æv, tææ.kx.ke.R(x)(e) & R(Katie)(pred(e)) (26) pred(e) ¼ ie#: s(e#) < s(e) & "e$[s(e$) < s(e) / e$ ¼ e# or s(e$) < s(e#)] A generalized version of this idea is given in (27) and (28). There is an ordering relation on events based on temporal precedence. We can identify the predecessor according to that order. (27) ordering relation on events: e is before e#: e : e# iff s(e) < s(e#) (28) the immediate predecessor of e: pred(e) ¼ ie#: e# : e & "e$[e$ : e / e$ ¼ e# or e$ : e#]
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(2) These three dogs entered the room one after the other. D3 / D2 / D1 (3) These three dogs entered the room, and the entering can be divided into a sequence of subevents in each of which one of the dogs enters, and the dogs can be divided into a sequence of individual dogs each of which entered in one of the subevents.
224 Pluractional Adverbials
3.2 The ‘other’ dog The instance of the ‘after’-modifier that we are confronted with is ‘after the other’. The key to our analysis of pluractional ‘one after the other’ lies in our understanding of the meaning of ‘the other’ in this construction. We suggest that for each dog, the relevant other dog is always the immediately preceding one. That is, we propose that there is an ordering on the individuals that is derived from the ordering of events, as in (29). The predecessor of an individual can be defined on the basis of that derived order. (29) ordering relation on individuals: x : y iff de[x is in e and "e#[y is in e# / e : e#]] x is before y iff x occurs in a relevant event before y does (30) the immediate predecessor of x: pred(x) ¼ iy: y : x & "z [z : x / z ¼ y or z : y] Finding the predecessor for each dog requires that the dogs can successfully be ordered into a sequence. (31) defines the notion of sequence; the cover has to have this property so that its members can be ordered. In our example, we would have (32). (31) Cov[x] is a sequence iff Cov[x] ¼ {x1, . . ., xn} and for any xi, xi+1: xi : xi+1 (32) Cov[e] ¼ {e1, . . ., en} such that for any ei, ei+1: ei : ei+1 Cov[these 3 dogs] ¼ {x1, . . ., xn} such that for any xi, xi+1 xi : xi+1d {D1, D2, D3}
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Two remarks are in order. There might be a worry how we identify the relevant predecessor of an event in the general case. Even if we limit our attention to enterings by Katie, Katie may have entered the room many times. Example (25) talks about the contextually relevant entering; hence the immediate predecessor ought to be defined relative to a contextually given set of events. We will not concern ourselves with this here, since our pluractional data come with an obvious way of resolving this problem: we will only need to look for the predecessor within one overall plural event of entering, the parts of which are ordered. Secondly, when we talk about the immediate predecessor, this is to be understood in terms of events, not time. In ‘Min entered the room two minutes after Katie’, the running time of Min’s entering is two minutes later than the running time of the immediate predecessor event.
Sigrid Beck and Arnim Von Stechow 225
If the appropriate sequence is given, then the rest of the truth conditions of our example (1) can be stated as in (33) below. From (33a) we get (33b). The overall truth conditions we propose are paraphrased in (34).
(34) e can be divided into a sequence of subevents, and the three dogs can be divided into a sequence of individual dogs, such that each dog entered the room in a relevant subevent, and its predecessor entered in the preceding subevent, and each subevent was one of one of the dogs entering, and the preceding event was one of the predecessor of that dog entering. These truth conditions can be derived straightforwardly from the Logical Form in (35). The subject is raised, with the movement binding an anaphor contained in the NP ‘the other’; the relevant pluralization operator is attached to the modified relation (the predicate created by the movement). We propose a version of our PL operator (henceforth PLseq) that incorporates the constraint on the cover that the cover of the relevant entity and event be a sequence. And we suggest a semantics for the modifier ‘one after the other’ that is essentially a combination of what we found out about ‘after NP’ in (25$) and the idea that the NP here contributes, for each dog, the predecessor of that dog (the full semantic details of the composition of the modifier will be discussed in section 3.5). With this, (35) will give rise to the truth conditions in (34). seq
(35) these 3 dogs [PLCov kx [vt x
[evt entered the room] [(evt)(evt) one after the other x]]] j__________QR_________j anaphor
(36) ½½one after the other R(pred(g(x)))(pred(e))
xg
¼
kR.ky.ke.
R(y)(e)
&
(37) ½½PLseq ¼ kCov.kR.kz.ke. Cov[e] is a sequence and Cov[z] is a sequence & [kz#.ke#.Cov(z#) & Cov(e#) & R(z#)(e#)](z)(e)]
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(33) a. Æ3D, eæ 2 [kx.ke#.Cov(x) & Cov(e#) & x enters the room in e# & pred(x) enters the room in pred(e#)] b. "x[x < 3D & Cov(x) / de#[e# < e & Cov(e#) & x enters the room in e# & pred(x) enters the room in pred(e#)]] & "e#[e# < e & Cov(e#) / dx[x < 3D & Cov(x) & x enters the room in e# & pred(x) enters the room in pred(e#)]]
226 Pluractional Adverbials (35#) ½½(35)g ¼ seq ke.Æ3D, eæ 2 ½½PLCov ]] (kx.ke#. x enter t.r. in e# & pred(x) enter t.r. in pred(e#)]) ¼ ke.Cov[3D] is a sequence & Cov[e] is a sequence & Æ3D, eæ 2 [kx.ke#.Cov(x) & Cov(e#) & x enter t.r. in e# & pred(x) enter t.r. in pred(e#)]
3.3 The first dog The observant reader will no doubt have noticed that the truth conditions in (34) suffer from a problem: We require that for each dog, that dog enter after its predecessor. But the first dog in the sequence does not have a predecessor. So (34) as such could never be true. We propose to embrace this prediction—so our compositional semantics will derive these truth conditions. There must then be a pragmatic process that allows us to ignore the first dog, and thus makes it possible for (34) to be true. We suggest that essentially the same process is at work in (38) and (39) below. In (39) for instance, we must subtract Arnim from the domain of quantification and understand ‘everyone’ to mean here ‘everyone but Arnim’; else the sentence could never be true. Likewise, we subtract the first sentry in the row from the domain that ‘each’ quantifies over. (38) 20 Wachposten sind so in einer Reihe aufgestellt, dass jeder den vorherigen sehen kann. 20 sentries are standing in a row such that each can see the one before him. (39) Everyone has a faster computer than Arnim. Thus, we think that it is generally possible to reinterpret a quantificational statement that could not come out true by
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We rely on the context to provide an ordering relation which is used both to form a sequence of the relevant parts of the cover and to identify the relevant predecessor of an event; in the example, the preposition ‘after’ expresses this ordering relation. The predecessor of an event must then be the predecessor in the sequence. We will see in section 3.5 that the individual predecessor is found through the same ordering relation. Context (which specifically includes the linguistic context of the sentence itself ) furnishes an order and a division into relevant sub-parts of our pluralities. Plural predication makes use of this information through the plural operator PLseq. PLseq and the adverbial modifier are jointly responsible for the assertion we get, requiring a sequence of enterings by individual dogs.
Sigrid Beck and Arnim Von Stechow 227
subtracting the problematic individual from the domain of quantification. This process will also have to apply to our examples in (1). Let’s see how a pragmatic domain subtraction solution might work for (38) and (39). We assume with Westerstahl (1984), von Fintel (1994) and others that all natural language quantifiers come with their own domain restriction. The representation of (39) would be (39#). (39#) everyC one has a faster computer than Arnim every (C)(A)(B) ¼ 1 iff for every x such that C(x)&A(x):B(x)
(40) C ¼ {x: x is part of the situation talked about} C# ¼ C {Arnim} We refer to this as domain subtraction. The resource domain of a quantifier is determined by context, and we think that a pragmatic process applies after the usual interpretive mechanisms that could be described roughly as in (41). (41) Choose the value for the resource domain variable C in such a way that the sentence may come out true. We suggest that (38) is parallel. The first sentry does not have a predecessor, hence (38) could not be true as long as we consider the first sentry to be part of the domain of ‘every’. It is the presupposition triggered by the definite description ‘the one before him’ that is responsible for domain subtraction. This process has been discussed as presupposition accomodation (compare Kadmon (2001) and references therein). (38#) everyC one can see the one before him. C ¼ {x: x is part of the situation talked about} ¼ {x: x is a sentry} C# ¼ C {the 1st sentry} The parallel of (38) to our problem with the first dog is obvious. We would similarly want to exclude the individual for whom the predecessor does not exist from the quantification. It is not surprising that plural quantification is similar to other natural language quantification in this respect.
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The set C is the contextually determined resource domain for the quantifier. A normal value would be the set of individuals in the situation talked about with (39). While Arnim is clearly around, we must suppose that he is subtracted from C in order for (39) to receive reasonable truth conditions—that is, C is revised to C# to avoid necessary falsehood.
228 Pluractional Adverbials However, it must be acknowledged that plural quantification adds a small technical complication. The universal quantifier that needs to be affected by domain subtraction is not the quantifier that we find in the syntax. That is, domain subtraction cannot happen to PLseq itself, since we do not want to exclude the first dog once and for all (else the second dog would pose the same problem again, and so on!). We would like domain subtraction to apply at the level of cumulation, as shown below.
If the original value for C was the individuals in the context, the new value must be that set minus the first dog (and the first event) in the sequence. We propose to give the PL operator another parameter that is inherited by cumulation and serves as its domain restriction. Example (37#) gives the revised version of (37) and (14$) the revised version of the definition of cumulation (14#). We assume that C[z + e] 4 Cov[z + e] (i.e. nothing new suddenly becomes relevant); then (14$) results in (42). (37) Old definition of PL: ½½PLseq ¼ kCov.kR.kz.ke.Cov[z] is a sequence & Cov[e] is a sequence & [[kz#.ke#.Cov(z#) & Cov(e#) & R(z#)(e#)]](z)(e) (37#) New definition of PL: ½½PLseq ¼ kC.kCov.kR.kz.ke.Cov[z] is a sequence & Cov[e] is a sequence & [C[kz#.ke#.Cov(z#) & Cov(e#) & R(z#)(e#)]](z)(e) (14#) Old definition of of type Æe, Æv, tææ: Let R be a relation of type Æe, Æv, tææ. Then for any x, e: [R](x)(e) ¼ 1 iff "x# < x: de# < e:R(x#)(e#) & "e# < e: dx# < x:R(x#)(e#) (14$) New definition of of type Æe, Æv, tææ: Let R be a relation of type Æe, Æv, tææ. Then for any x, e: [C R](x)(e) ¼ 1 iff "x#[x# < x & C(x#) / de#[e# < e & C(e#) & R(x#)(e#)]]& "e#[e# < e & C(e#) / dx#[x# < x & C(x#) & R(x#)(e#)]]
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(42) "x[x < 3D & Cov(x) & C(x) / de#[e# < e & Cov(e#) & C(e#) & x enter in e# & pred(x) enter in pred(e#)]] & "e#[e# < e & Cov(e#) & C(e#) / dx[x < 3D & Cov(x) & C(x) & x enter in e# & pred(x) enter in pred(e#)]]
Sigrid Beck and Arnim Von Stechow 229
3.4 Similar cases: one above/upon/within the other In this subsection, we indicate how the analysis proposed for ‘one after the other’ extends to similar instances of pluractional adverbials with different prepositions. Some examples are given below. We will focus on (43a) with ‘above’. (43) a. These three children sleep one above/next to the other. b. She laid the books bundle beside/upon bundle on the porch. Our starting point is once more a regular occurrence of the modifier (44a). The semantics in (44b) leads to the meaning in (44c) for the modifier.2 Like our earlier example ‘after NP’, the PP modifies a relation. In this case, this is a relation between an individual and a place (not an event). It adds to the original relation the information
2
We leave out the event-argument slot in these data for convenience.
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Now, if R contains a presuppositional element, that element can be expected to trigger the same pragmatic effects in pluralization as it triggers in other quantification—in particular domain subtraction. This is how we propose to account for the first dog. We think that our Logical Forms and semantic representations already look complicated enough and will suppress the additional parameter C in what follows. The issue of the first dog, once resolved, does not seem to interact with the other topics we discuss below. Before we move on, let us use this opportunity to mention a different kind of exception to our sequence truth conditions. An anonymous referee points out to us that a sentence like ‘They shouted one man after the other’, could be considered true in a situation in which one individual, Boris (¼b), shouts twice, leading to the following sequence of shouting events (let a–d be the men and e1–e5 be the relevant events of shouting): Æa, e1æ, Æb, e2æ, Æc, e3æ, Æb, e4æ, Æd, e5æ. We concur that one might indeed use such a sentence in such a situation. We propose to view e4 as an exception in the sense of Brisson (1998). Brisson provides an analysis in terms of covers of the fact that a distributive plural predication may be used even though not all parts of a plurality contribute towards making the predication true. She proposes that in such cases one chooses an ‘ill-fitting’ cover of the plurality, which does not contain the exceptional part. See also Beck (2001) for more general use of covers to explain exceptions in plural predication.
230 Pluractional Adverbials that the relation also holds between the referent of the NP and the relevant preceding place, which is the place immediately below. (44) a. Hans sleeps above Fritz. b. kp. Hans sleeps at p & Fritz sleeps at bel(p) bel(p) ¼ the place immediately below p c. ½½above Fritz ¼ kR.kx.kp. R(x)(p) & R(Fritz)(bel(p)) Once more, then, we have an ordering relation, this time based on the meaning of the preposition ‘above’. A place is smaller than another one according to that ordering if it is below it. We then also have the notion of the immediately preceding place.
(47) ordering relation on individuals: x : y iff dp[x is in p and "p$[y is in p$ / p : p$]] x is below y iff x is in a place that is below any place that y is in. (48) the immediate predecessor of x bel(x) ¼ iy: y : x & "z [z : x / z ¼ y or z : y] The rest of the analysis is quite parallel to the analysis of the ‘after’ example. We must be able to divide both the place and the plural individual into a sequence. Given that, we propose the analysis in terms of the in (43#) which amounts to the truth conditional entailment in (43$). The resulting overall truth conditions are described roughly in (50). (49) Cov[p] ¼ {p1, . . ., pn} such that for any pi, pi+1: pi : pi+1 Cov[these 3 children] ¼ {x1, . . ., xn} such that for any xi, xi+1: xi : xi+1 (43#) Æ3C, pæ 2 [kx.kp#.Cov(x) & Cov(p#) & x sleeps in p# & bel(x) sleeps in bel(p#)] (43$) "x[ x < 3C & Cov(x) / dp#[p# < p & Cov(p#) & x sleeps in p# & bel(x) sleeps in bel(p#)]] &"p#[p# < p & Cov(p#) / dx[x < 3C & Cov(x) & x sleeps in p# & bel(x) sleeps in bel(p#)]] (50) The place p can be divided into a sequence of sub-places, and the three children can be divided into a sequence of individual
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(45) ordering relation on places: p : p# iff p is below p# (46) the immediate predecessor of p: bel(p) ¼ ip#: p# : p & "p$[p$ : p / p$ ¼ p# or p$ : p#] In order to find a denotation for the NP ‘the other’ in the pluractional adverbial ‘one above the other’, we again suppose that there is a derived ordering of individuals based on one of the places [as defined in (47)], which will permit us to define the predecessor of an individual according to the scale introduced by ‘above’ [cf. (48)].
Sigrid Beck and Arnim Von Stechow 231
children such that: each child sleeps above the one immediately below, and each place has a child sleeping in it (. . .). The compositonal derivation of these truth conditions is based on the Logical Form in (51) and uses the PL operator in (52)—the same one as before adapted to talk about places instead of events. seq kx [x [[sleep] [one above the other x]]] (51) these 3 children [PLCov seq ¼ kR.kz.kp.Cov[p] is a sequence and Cov[z] is (52) ½½PLCov a sequence & [kz#.kp#.Cov(z#) & Cov(p#) & R(z#)(p#)](z)(p)
3.5 Pseudo-reciprocal ‘one . . . the other’ The topic of this subsection is the composition inside the modifier. How do we derive the fact that the NP ‘the other’ contributes the relevant predecessor? The overt material in (53a) suggests an internal structure of the modifier as in (53b). We assume that in addition there is covert structure in the form of the anaphor x and a contextually given relation that will constrain us to the relevant other individual. A hidden anaphor in the expression ‘other’ has been suggested, for example, in Heim et al. (1991) on the basis of data like (54a): ‘another’ here means ‘a shirt different from this shirt’. The expression ‘another’ thus includes an anaphoric reference to ‘this shirt’. The difference between (54a) and our data (as well as the reciprocal pronouns investigated by Heim et al. 1991) is that the anaphor is bound in the latter case. More generally, hidden material in definites comparable to what we assume has been detected by Partee (1989) and Winter (2000) for examples like (54b) and underlies the analysis of E-type pronouns like (54c) spelt out in Heim & Kratzer (1998). (53) a. The dogs entered the room one after the other. b. [one [after [the [other]]]] c. [one [after [the [R other x]]]] (54) a. I don’t like this shirt, bring me another. another ¼ a shirt different from this shirt b. Every soldier hit the target. the target ¼ [the [target R x]] ¼ the target assigned to him
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Other prepositions occurring in the structure ‘one Preposition the other’ would give rise to different orderings, but be otherwise parallel to the examples discussed. Very roughly, all of these pluractional modifier constructions add to the relation modified that the members of the NP argument group can be ordered according to the preposition in the modifier.
232 Pluractional Adverbials c. Every host bought just one bottle of wine and served it with dessert. it ¼ the bottle of wine that he bought. In (55) we recall the desired semantics for ‘the other’, argued for in the previous section. We can achieve this result if the hidden relation variable is assigned by the context the value in (56a) (this must once more come from the preposition), and compositional interpretation proceeds as in (56b). We end up with the meaning ‘that y which is not x and immediately precedes x#—the predecessor of x according to the ’after’ relation.
(56) a. g(R) ¼ immediately precede b. ½½ [the [NP Æe,tæ [Æe,Æe,tææ R other] x]]] g ¼ iy: y 6¼ g(x) & g(R)(g(x))(y) ¼ pred(g(x)) The referential NP needs to combine with ‘after’ in the same way as the referential NP ‘Katie’ would in the simpler case, repeated in (57). The ‘after’ from (58b) is combined with the meaning of ‘the other’ in (59). The actual modifier we see also includes ‘one’. We propose that that provides an additional constraint on the individual argument of the relation, namely that that be a singular individual. The meaning of ‘one after the other’ is then as in (60). (57) a. Min entered the room after Katie. b. ke. Min enters the room in e & Katie enters the room in pred(e) (58) a. ½½after Katie ¼ kP.kx.ke.P(x)(e) & P(Katie)(pred(e)) b. ½½after ¼ kz.kP.kx.ke.P(x)(e) & P(z)(pred(e)) (59) ½½after the R other xg ¼ kP.ky.ke.P(y)(e) & P(pred(g(x)))(pred(e)) (60) ½½one after the R other xg ¼ kP.ky.ke.P(y)(e) & one(y) & P(pred(g(x)))(pred(e)) We believe that (61a,b) are equivalent. Hence, we suggest that the two modifiers make the same semantic contribution. One way to derive this would be to have an underlying form (62a) from which both are derived as different surface forms. (61) a. She washed them dog after dog.
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(55) ½½the R other xg ¼ pred(g(x)) ¼ iy: y immediately precedes g(x)
Sigrid Beck and Arnim Von Stechow 233
b. She washed them one (dog) after the other. (62) a. one dog after the other dog b. one dog after the other dog c. one dog after the other dog It is relatively obvious how to derive ‘one after the other’ from (62a), namely, through a process of N-deletion. This is not obligatory, at least not for the first N to be deleted, cf. (63). It is far less obvious how (62c) would be derived.3
The above considerations lead to a final revision for the internal semantics of the modifier which yields (64): we add the information that the relevant predecessor as well as the individual argument of the relation are Ns. (64) a. ½½ [the[[[R other]x]N]] g ¼ iy: y 6¼ g(x) & g(R)(g(x))(y) & ½½N (y) ¼ the dog immediately preceding g(x) pred(g(x)) b. ½½one N after [the R other x N] g ¼ kP.ky.ke.P(y)(e) & one(y) & ½½N (y) & P(pred(g(x)))(pred(e)) We call these modifiers pseudo-reciprocal. They are reminiscent of reciprocals formally in the use of ‘other’ and semantically in talking about a different member of the same group (in the example, the dogs). But they are not reciprocal pronouns formally—they are modifiers. Moreover, the NP in the modifier is a singular. By contrast, a reciprocal pronoun introduces a second plurality of individuals (Beck 2001).
3.6 Concluding remarks on Æe, Æv, tææ pluralization We have argued that ‘piece by piece’-type adverbials as well as ‘dog after dog’-type adverbials show us that natural language can pluralize relations of type Æe, Æv, tææ. The adverbial makes the pluralization visible by adding extra constraints on the simultaneous division into sub-parts (subevents and subindividuals) performed by the pluralization operation. In the case of ‘piece by piece’-type adverbials, this is the constraint 3
In view of data like (i), it may even be doubtful that one would want to make too close a connection between the two constructions. Thanks to David Pesetsky for pointing this out. (i)
I reviewed paper after paper after paper.
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(63) a. She put the books one bundle beside the other (bundle) on the porch. b. She examined the wine one bottle after the other (bottle).
234 Pluractional Adverbials that the division (the cover) of the plural entity in question be a partition into pieces. In the case of pseudo-reciprocal ‘dog after dog’ adverbials, the constraint is that the cover be a sequence of individual dogs. Now that we have an overview of the data, we think it makes sense to adopt a slightly more abstract analysis of ‘piece by piece’ and to subsume this kind of adverbial under plain Æe, Æv, tææ pluralization. The revised analysis is given in (66) and (67). The adverbial is just a modifier; the combination with the plain PL operator yields the same result as PLdiv earlier [repeated in (65)].
(66) plain Æe, Æv, tææ pluralization: ½½PL ¼ kCov.kRÆe,Æv,tææ.kx.ke: PART(Cov, e + x). [kx#. ke#. Cov(e#) & Cov(x#) & R(x#)(e#)](x)(e) (67) a. b. c. d.
John ate the cake piece by piece. [[the cake][PLCov [piece by piece [k2[John ate t2]]]]] ½½piece by piece ¼ kRÆe, Æv, tæækx.ke. x is a piece & R(x)(e) ke.Æe, the_cakeæ 2 [ky#.ke#.Cov(y#) & Cov(e#) & y# is a piece & John ate y# in e#]
We end up with just two pluralization operators: the plain PL operator and PLseq. This, as far as we can see, is irreducible. Sequence pluralization imposes a stronger requirement on the cover. (68) sequence Æe, Æv, tææ pluralization: ½½PLseq ¼ kCov.kR.kx.ke. Cov[e] is a sequence and Cov[x] is a sequence & [kx#. ke#. Cov(x#) & Cov(e#) & R(x#)(e#)] For both types of adverbials, the plural operator is not the adverbial itself. The adverbial is a modifier that merely seems to indicate the presence of the pluralization operator. This revision of the analysis raises a question. Pluractional adverbs like ‘piece by piece’ are predicates of singularities but come with a PL operator. There is nothing in the semantics of the pluractional adverb that triggers the semantic plural. Are these adverbs compatible with the singular, or do we need some mechanism that would force the adverbial to combine with a higher PL operator? (69) a. Ich habe die A¨pfel einzeln gekauft.
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(65) divisive Æe, Æv, tææ pluralization: ½½PLdiv ¼ kPÆe, tæ.kCov.kRÆe, Æv, tæækx.ke: PART(Cov, e + x). [kx#. ke#. Cov(e#) & Cov(x#) & P(x#) & R(x#)(e#)](x)(e)
Sigrid Beck and Arnim Von Stechow 235
(70) ½½piece by piece ¼ kCov.kRÆe,Æv,tææ.kx.ke: Cov(x) & Cov(e) & R(x)(e) & x is a piece In order to rule out the ‘singular’ interpretation of sentences like (69a), we need a syntactic principle that states that a cover variable is only licensed if it is the variable of a PL operator, or if it is co-indexed with a licensed cover variable (this licensing condition would amount to the ‘plural polarity item’ effect). It follows that the following LF is not possible for sentence (69a): (69a#) [vt the cake [evt piece by pieceCov [evt 2 John ate t2]]] (ill-formed) In contrast, the following LF is a good one and it has the ‘plural’ reading, provided the plural predicates are only defined for pluralities proper. (69a$) [vt the cake PLCov1 [evt piece by pieceCov1 [evt 2 John ate t2]]] Both options—the pragmatic and the plural polarity item one—would derive the fact that pluractional adverbials are fully acceptable only in
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I have the apples individually bought b. ?Ich habe den Apfel einzeln gekauft I have the apple individually bought It seems to us to be arguable that (69b) is pragmatically odd (it may serve as a sort of joke), but is semantically well formed. Under this view, there could be an implicature brought about by the pluractional adverb, to the effect that the argument of the relation the adverb modifies be a genuine plurality. The implicature could be generated by the notion that division into parts is only relevant when there is more than one part of the kind mentioned. At any rate, the suggestion would be that the pluralization requirement is a weak pragmatic one, one can then leave the compositional semantics as is. Alternatively, if one wanted to enforce that pluralization accompanies the adverbial, one could view the adverbial as a plural polarity item in the style of Oh (2005). Oh proposes that elements like Korean -ssik mark elements that need to occur in the scope of a distributivity operator. Analogously, our pluractional adverbials would have to occur in the scope of a cumulative operator of the appropriate type. Here is a way to spell out the connection in more detail: Cover variables come with plural operators. So there is connection between them and pluralization. Let us suppose that pluractional adverbs select a cover variable as well. The variable of an adverb must be anaphoric to the variable of the local plural operator. So the entry for ‘piece by piece’ would be this:
236 Pluractional Adverbials
4 There is an interesting type of example brought to our attention by an anonymous referee that we cannot completely analyse with the tools at our disposal. An instance is given in (i).
(i)
John glued the book together page by page.
The interesting aspect of (i) is that we are talking about the creation of a complex whole (the book does not exist in the beginning of the event, but it does by the end); our pluractional adverb tells us about how the event proceeds in terms of the parts of the whole (its pages). We think that the analysis will have to rely on the detailed semantics of the creation verb, but have found this too complicated to develop here. 5
Malte Zimmermann (personal communication) raises the question of a cardinality requirement accompanying pluractional adverbials. He suggests that ‘piece by piece’-type adverbials require that there be at least two pieces, while ‘one Preposition the other’ adverbials require there to be more, say at least three. A cardinality of at least two follows from the requirement that there be a genuine plurality. A stronger cardinality requirement would have to be spelt out separately (e.g. as in (i) below). However, we are not sure that we want to do that. Example (ii) seems to us to be fine. Perhaps, a larger cardinality is just an assumption one tends to make, rather than part of the semantics of such sentences. Malte Zimmermann also observes that reduplicative adverbials seem to require an even larger cardinality of the group they are anaphorically related to. Thus, (iii) is odd. (i) ½½PLseq ¼ kCov.kR.kx.ke. Cov[e] is a sequence and Cov[x] is a sequence & card(Cov[x]) > 2 & card(Cov[e]) > 2 & [kx#.ke#.Cov(x#) & Cov(e#) & R(x#)(e#)] (ii) The two women entered the room one after the other. (iii) The two women/they entered the room woman after woman. The idea brought forth in the text above that adverbials themselves have a cover variable allows us to capture such effects. We could for example use the semantics in (iv). We leave the details of this empirically delicate issue for future research. (iv) ½½one after the R other xg ¼ (kCov.kP.ky.ke: card(Cov[y]) is large.P(y)(e) & one(y) & P(pred(g(x)))(pred(e)) 6 In examples such as ‘She placed the books on the porch bundle next to bundle’, we have to assume that an ordering relation is derived from ‘next to’ that mounts to either ‘to the right of ’ or ‘to the left of ’. That is, more goes into the ordering relation than just the meaning of the preposition.
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the context of a corresponding pluralization operator. We will leave the choice between these two options open. Under both of them, notice, the term ‘pluractional adverbial’ becomes a descriptive notion. What brings about pluractionality in the analysis is the invisible PL operator which is triggered (pragmatically or at the syntax/semantics interface) and restricted by the presence of the adverbial. The adverbial itself is not a plural operator.4,5 We have two types of pluractional adverbs, the ‘piece by piece’-type and the pseudo-reciprocals. How do we know which is which? Pseudo-reciprocals require an ordering relation such as ‘after’, ‘above’, ‘within’. The relation is provided by the preposition and is the basis for the sequence restriction used by PLseq. The ‘piece by piece’ adverbs are built around particles such as ‘by’, ‘for’, ‘and’ which mean nothing by themselves; in particular, they do not express an ordering relation. Hence, they are unsuitable for combination with PLseq and use plain PL instead.6
Sigrid Beck and Arnim Von Stechow 237
4 RELATED ISSUES This section explores some issues related directly to the analysis developed in section 3. These concern IAO reciprocals, the scope of our PL operators, pluractionals in argument position, the event distributivity reduplications mentioned in the introduction and finally other ‘Noun Preposition Noun’ modifiers.
4.1 Apparent reciprocals
(71) a. b. (71a#)
The children sleep above each other. The three dogs came into the room after one another/ The three dogs followed each other into the room. IAO: Each child sleeps above or below some other child.
(72) a. b.
Schema of an elementary reciprocal sentence: A R each other. antecedent relation reciprocal pronoun IAO: "x[x < A / dy[y < A & xRy or yRx]]
We suggest instead that the data in (71) (and IAO reciprocals in general) have a pseudo-reciprocal semantics. That is, (71a) really amounts to (73a). The semantics we assign to (73a), and by assumption then also to (71a), entails (73b). (73) a. The children sleep one above the other. b. Each child sleeps above some other child (namely, her ‘predecessor’ relative to the ‘below’ relation). Why do we pursue this idea? There are three kinds of facts that motivate us. The first is that the IAO truth conditions are very weak indeed and intuitively too weak for example for (71b). The IAO truth conditions for (71b) are given in (74a). These truth conditions predict the sentence to be true in the situation depicted in (74b). This does not accord with intuitions. By contrast, our truth conditions will render
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In this subsection, we explore the possibility of extending our analysis of pseudo-reciprocals to certain apparent reciprocals, namely those that have an IAO interpretation. Some examples of such reciprocals are given in (71). The interpretation of (71a) according to Dalrymple et al. (1998) is paraphrased in (71a#). The general schema of an IAO interpretation is given in (72). The data in (71) are all taken to have such a weak semantics.
238 Pluractional Adverbials (71b) equivalent to (74c) and correctly predict that the sentence is false in a situation like (74b). (74) a. Each dog came into the room after or before some other dog. b. D3 + D2 / D1 c. The dogs entered the room one after the other.
(75) a. The plates are stacked on top of each other. b. The Smiths and the Johnsons outnumber each other. A third and final problem with IAO is noted in Beck (2001): IAO reciprocals are restricted to local reciprocal relations while other reciprocals are not. To illustrate what is meant by a non-local reciprocal relation, consider (76). The sentence is judged true if (76#a) is the case. This can be derived from the truth conditions in (76#b): the reciprocal relation ‘want to kill’ holds between non-identical members of the antecedent group ‘Tracy and Joe’. Example (76) is an example of a regular reciprocal interpretation, weak reciprocity. The reciprocal relation ‘want to kill’ is non-local in that it is not a relation that exists as the meaning of a surface constituent. (76) Tracy and Joe want to kill each other. (76#) a. Tracy wants to kill Joe and Joe wants to kill Tracy. b. ÆT&J, T&Jæ 2 [kxky: x 6¼ y. x wants to kill y] We should contrast (76) with (77). The sentence can be understood as in (78)—Tracy and Joe agree that they want to sleep above each other rather than, say, beside each other. It cannot be understood as in (79), which would be made true by the fact that Tracy wants to sleep above Joe. Example (79) would be a non-local IAO interpretation with the reciprocal relation ‘want to sleep above’. Clearly, this is not possible. Only a local reading inside the embedded clause in (78) is acceptable. (77) Tracy and Joe want to sleep above each other.
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A second problem for IAO reciprocals is the fact that an IAO interpretation is only possible with a restricted set of relations. See Langendoen (1978), Sauerland (1998), Beck (2001) and Schein (2003) for discussion. As an illustration, notice that (75a) with the relation ‘on top of ’ is acceptable under an IAO interpretation while (75b) with ‘outnumber’ is unacceptable and cannot have an IAO reading (which would be made true by the fact that the Smiths are more numerous than the Johnsons, for instance). If IAO were a regular interpretation for reciprocal sentences, why should it not be generally available?
Sigrid Beck and Arnim Von Stechow 239
(78) Tracy and Joe both have the following desire: we sleep above each other (i.e. one of us sleeps above the other). (79) For each x, x one of Tracy and Joe: either x wants to sleep above the other one of Tracy and Joe, or the other one of Tracy and Joe wants to sleep above x. The pair in (80) makes the same point: in (80a), a non-local interpretation is possible in which the different members of the antecedent group ‘these people’ were introduced by different linguists. A similar interpretation is not available in (80b); the same apprentice magician has to line up the glasses.
The two constraints on the availability of IAO interpretations (limited set of relations and local interpretation only) are quite unexpected as long as one thinks of IAO as a regularly available interpretation of reciprocal pronouns. This is additional motivation then, besides the problem mentioned above with inappropriately weak truth conditions, for looking for an alternative analysis of the phenomenon of IAO. We propose that IAO reciprocals only appear to be reciprocals, and are really pseudo-reciprocals: (81) above each other 0 (one) above the other That is, the example in (82a) should really be interpreted as (82b). (82) a. Tracy and Joe want to sleep above each other. b. Tracy and Joe want to sleep one above the other. The truth conditions we predict are the ones of pseudo-reciprocals, which seem right to us. As for the unexpected constraints on the relations that participate in an IAO interpretation, we have nothing concrete to offer. One may suppose that whatever process relates (82a) and (82b) is somehow restricted and cannot apply to every relation. For all we know, the connection may be lexical. But no concrete predictions arise regarding which relations can participate. We do have something to say about the fact that apparent IAO reciprocals—now reanalysed as pseudo-reciprocals—only receive a local interpretation. In (77) ¼ (82), for instance, the whole ‘(one) above the other’ is an adverbial that can only modify the embedded predicate ‘sleep’ (whishes cannot plausibly be above each other). And since there is no further potentially scope-bearing element in this modifier (‘the
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(80) a. These people were introduced to each other by a linguist. b. The glasses were lined up behind each other by an apprentice magician.
240 Pluractional Adverbials other’ being a singular), there is no process that could generate a nonlocal interpretation. A final comment: there are cases of IAO reciprocals for which our pseudo-reciprocal truth conditions might be thought too strong. Example (83b) is a case in point. Dalrymple et al. (1998) point out that such a sentence can be considered true in a situation with two bunk beds each of which sleeps two children. This is different from (83a), our pseudo-reciprocal. We speculate that (83b) permits a partition of the children into two groups of two, on which its interpretation with the bunk beds is based. This is excluded by the overt element ‘one’ in (83a) which tells us that the partition of the children is into singletons.
4.2 The scope of PL Our theory of pluralization is essentially syntactic in the sense that the PL operator applies in the syntax to an LF constituent. It is thus in line with Sternefeld (1998), Heim et al. (1991) or Beck & Sauerland (2000), but not compatible with pure lexical theories of pluralization such as Krifka (1989) or Winter (2000). The syntactic nature of the PL operator is obvious from the fact that pluractional adverbs are in the scope of the PL operator. Recall, for example, our analysis for (84): (84) These three dogs entered the room one after the other. The LF was (85). Sec kx [vt x (85) these 3 dogs [PLCov
j__________QR________j
[evt entered the room] [(evt)(evt) one after the other x]]] anaphor
The lexicalist has to explain the PL operator away, which seems difficult but is perhaps not impossible in this case (by using an appropriate distributor). But there are harder examples: (86) a. Die Ma¨dchen schenkten den Jungen eine Blume. the girls gave the boys a flower b. Die Ma¨dchen schenkten den Jungen eines nach dem anderen eine Blume. the girls gave the boys one (Nominative) after the other a flower c. Die Ma¨dchen schenkten den Jungen einem nach dem anderen eine Blume.
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(83) a. These four children sleep one above the other. b. These four children sleep above each other.
Sigrid Beck and Arnim Von Stechow 241
the girls gave the boys one (Dative) after the other a flower. The examples are knitted after the pattern of the examples brought forward in Beck and Sauerland (2000) against Winter (2000). They seem hard nuts for the lexicalist but fall out easily in our theory. The formalizations of (86b) and (86c) are these:
The examples illustrate that the object variable of ‘other’ does a useful job. It disambiguates the two readings: in (86b) the antecedent is ‘the girls’ and in (86c) the antecedent is ‘the boys’. Two possible scenarios satisfying the LFs are the following ones: (87) a. e ¼ e1 + e2, G ¼ g1 + g2, B ¼ b1 + b2, ½½ flower ¼ {f1, f2} b. e1: g1 give f1 to b1 + b2 e2: g2 give f2 to b1 + b2 c. e1: g1 + g2 give f1 to b1 e2: g1 + g2 give f2 to b2 The general conclusion is that the analysis proposed supports the syntactic plural theory developed and defended in previous papers by Beck and others. It is worth noting that pluractional operators can be iterated. Example (88) provides an example as well as the sketch of an analysis. Suppose that the boys are b1, b2 and the girls are g1, g2, and that the sequence of events was e11 < e12 < e21 <e22. The LF in (88#a) is then predicted to be true in the situation (88#c), as desired. (88) Die Jungen haben einer nach dem anderen die Ma¨dchen eines nach dem anderen geku¨sst. the boys have one after the other the girls one after the other kissed (88#) a. ÆB, eæ 2 PLCovseq (kx.ke#. ÆG, e#æ 2 PLCov#(e#)seq (ky. ke$. [x kisse$ y] o.a.t.oy) o.a.t.ox) b. Cov[B + e] ¼ {b1, b2, e1, e2} Cov#(e1)[G + e1] ¼ {g1, g2, e11, e12} Cov#(e2)[G + e2] ¼ {g1, g2, e21, e22}
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(86#) a. ÆG, eæ 2 seq (kx.ke#. x give B a flower in e# & pred(x) give B PLCov a flower in pred(e#)) b. ÆB, eæ 2 seq PLCov (ky.ke. G give y a flower in e# & G give pred(y) a flower in pred(e#))
242 Pluractional Adverbials c.
(89) She bounced a ball from wall to wall. Only one ball can be involved in this multiple action. Since our theory assumes that pluralization takes place in the syntax, ‘a ball’ might have narrow scope with respect to the PL operator and we predict the bouncing of possibly different balls. For ‘from wall to wall’, see the discussion in section 4.5. We consider an example with a more familiar adverbial, (90). The question is whether pluralization can take scope over the indefinite. This would correspond to Logical Forms like (90#a). (90) a. The boys kicked a wall one after the other. b. One after the other, the boys opened a drawer. (90#a) ÆB, eæ 2 PLCovseq (kx.ke#.x kick a wall in e# and pred(x) kick a wall in pred(e#)) Perhaps, it is easiest to assume that one wall is involved—we are not really sure about the facts. We concur, at any rate, that pluralization often has a tendency to take narrow scope. We do not have a general analysis of this effect. One restriction relevant in the present case could be the fact that event arguments like to be bound before they encounter an aspectual operator—say, just above VP (e.g. as in Diesing 1990; von Stechow 2002). This may limit the scope taking possibilties of our pluractional pluralization operations. Importantly, we think that the clear examples in which a plural operator does take non-trivial scope show that a syntactic analysis of pluralization is called for. That such an analysis must be constrained to limit scope possibilities, we would certainly agree to.
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Cov# is a variable for functions from events into Covers. The value of Cov# depends on the bound variable e#. The scenario (88#c) shows why this must be so: g1 is before g2 in the sequence of kissing that e1 consists of, but after g2 in the sequence of kissing that e2 consists of. Note that examples where covers must be parametrized functions are also given in Schwarzschild (1996). His examples involve modality. Angelika Kratzer (personal communication) mentions the following objection to syntactic pluralization to us:
Sigrid Beck and Arnim Von Stechow 243
Example (90b) has the pluractional adverbial topicalized. Such a structure is incompatible with our assumption that the adverbial contains a variable bound by the subject. We must assume that at Logical Form, the adverbial is reconstructed to its position within the VP.
4.3 Nominal pluractionals The data we have analysed all involve pluractional adverbials like (91). However, there are many cases where our pluractionals occur in argument position. The semantics we think (92a,a#) have is given in (92#). (92) a. She washed dog after dog. a#. She washed one dog after the other. b. She wrote paper after paper. b#. She wrote one paper after another. (92#) ke. dX [Cov[e] is a sequence and Cov[X] is a sequence & [kx.ke#.Cov(x) & Cov(e#) & dog(x) & she washed x in e# & she washed pred(x) in pred(e#)](X)(e)]] It is interesting that these expressions may alternatively play the role of adverbials or arguments syntactically. As regards semantics, we can assume that the meaning of ‘dog after dog’ is as before. We then shift the pluralization operation to existentially bind the individual argument: (93) Regular PLseq: kCov.kR.kz.ke. Cov[e] is a sequence and Cov[z] is a sequence & [kz#.ke#.Cov(z#) & Cov(e#) & R(z#)(e#)](z)(e) (93#) existentially shifted PLseq: ½½ PLd ¼ kCov.kR.ke. dz[Cov[e] is a sequence and Cov[z] is a sequence & [kz#.ke#.Cov(z#) & Cov(e#) & R(z#)(e#)](z)(e) The way from PLseq to PLd involves an existential type shift: (94) ÆCov, Æe, Æv, tææ, Æe, Æv, tæææ 0 ÆCov, Æe, Æv, tææ, Æv, tææ k .kCov.kR.ke.dz[ (Cov)(R)(z)(e)] (95) She washed dog after dog. dCov [[dog after dog][Æe, Æv,tææ kx. she washed x]] [PL ½½dog after dog ¼ kR.ky.ke. R(y)(e) & dog(y) & R(pred(g(x)))(pred(e))
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(91) She washed them dog after dog.
244 Pluractional Adverbials We need to move ‘dog after dog’ for type reasons. We can suppose that an existential shift is generally available (see, e.g. Partee 1987 for another version); it has to apply in this case in order for us to get a reasonable result. In case of a nominal pluractional in subject position (example below), we would assume reconstruction, just as we proposed in the previous subsection. (95#) Dog after dog entered the room.
4.4 Reduplicative event distribution
(97) a. Sally ran and ran. b. Sally was sick and sick. c. The train arrived and arrived. Example (97a) means that Sally ran a long time. It would seem then that ‘and’ simply means ‘a long time’ in this context. It is tempting do derive this reading from a pluractional meaning of ‘and’. (98) Sally ANDCov ran ke.e 2 [ke#.Cov(e#) & ran(Sally)(e#)] AND is a plain PL operator that is restricted to cumulative and non-divisive events. (99) ½½AND ¼ kCov.kPvt: P is cumulative & P is not divisive. ke.[ke#.Cov(e#) & P(e#)](e) A predicate is cumulative iff, whenever it is true of two arguments, it is also true of their sum. A predicate is divisive (or not atomic) iff whenever it is true of an argument, it is also true of a part of that argument (see, e.g. Krifka 1998). The two presuppositions account for the ungrammaticality of (97b) and (97c). The requirement that covers have to be non-divisive presumably follows from general assumptions for covers: if we want to
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We already mentioned data in the introduction that look parallel to our pluractionals and are semantically obviously related. Some examples are given below. (96) a. Wir warteten Stunde um Stunde. we waited hour for hour ‘We waited for hours.’ b. She surprised us time after time. c. Sie hat uns immer wieder ueberrascht. she has us always again surprised ‘She surprised us again and again.’
Sigrid Beck and Arnim Von Stechow 245
split a plurality into smaller units, we need some contextually relevant standard of individuation, that is, a measure that gives us smallest units. In this particular case, the verb gives us the principle of individuation by itself. Since states are divisive, they are excluded as principles of individuation. Achievements and accomplishments are excluded because they are not cumulative. Since these are conceptual requirements, it is perhaps not necessary to write them into the semantics of AND. A simpler version is (99#). The semantics for AND is very similar to the semantics given to durative adverbials in Kratzer (2003).7 (99#) ½½AND ¼ kCov.kPvt: ke.[ke#.Cov(e#) & P(e#)](e)
(100) a. Wir stiegen ho¨her und ho¨her. we climbed higher and higher b. Es wurde ka¨lter und ka¨lter. it became colder and colder c. Es wurde immer ka¨lter. it became always colder d. Sally approached the horse step by step. (100#) a. It ANDCov became colder b. ke.e 2 [ke#.Cov(e#) & become_colder(e#)] c. become_colder(e) ¼1 iff it is colder at the end of e than at the beginning of e (von Stechow 1996) Pluralization of Æv, tæ predicates (i.e. event distribution) is relevant in the analysis of a type of example brought to our attention by an anonymous referee. A representative is (101) below. (101) As the wheel turned, the flags hit the water one after the other.
7
(i)
Kratzer’s duratives: ½½for twenty minutes ¼ kP.ke.P(e) & fminute(e) ¼ 20 & e ¼ re#[e# < e & P(e#)]
The right conjunct in the definition is the contribution of our AND.
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It belongs to the pragmatics of AND that the selected cover must have a rather large cardinality (compare section 3.6). This entails that the running must be quite long. The following examples are degree achievements, that is, predicates which have the property that the result is attained to a higher degree at the end of the action than it had been attained at the beginning. They are cumulative and are analysed as before. ‘immer’ is presumably a PL operator with the same semantics as AND.
246 Pluractional Adverbials We propose that this example combines a sequence interpretation (the flags as ordered along the rim of the wheel) with an iteration of pluralization operations as observed in section 4.2, viz. Æv, tæ pluralization above PLseq. (101#) One sequence reading (the wheel turns once): ke.Cov[F] is a sequence & Cov[e] is a sequence & ÆF, eæ 2 [kz.ke#: z hits the water in e# & pre(z) hits the water in pred(e#)]
The data discussed in this subsection illustrate the generality of our theory of plural predication and pluractionality.
4.5 Other ‘noun preposition noun’ adverbials We have investigated the semantics of three kinds of modifiers of the form ‘Noun Preposition Noun’. They are exemplified by ‘piece by piece’, ‘dog after dog’ and ‘Stunde um Stunde’. These three types of modifiers do not have the same semantics, although their semantics is similar in that all three can be called pluractionals. We think that the form ‘Noun Preposition Noun’ may be used by other kinds of modifiers not all of which may be pluractional. To illustrate, consider the data in (101): (101) a. The houses stand side by side. b. The lovers walked hand in hand to the river. c. The squirrel jumped from tree to tree. The formal similarity to the data investigated in this paper may lead one to suppose that ‘side by side’, ‘hand in hand’ and perhaps also ‘from tree to tree’ should share the semantics of pluractionals like ‘piece by pice’ or ‘dog after dog’. But we do not think that this is the case. Consider the uses in (102): (102) a. Anna walked hand in hand with Lena. b. Haus A steht Seite an Seite mit/neben Haus B. House A is standing side by side with/next to House B We propose the semantics in (103) for example (102b).
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(101$) Iterative reading (the wheel continues to turn): ke$.e$ 2 ke: PART(Cov#, e). Cov[F] is a sequence & Cov[e] is a sequence & ÆF, eæ 2 [kz.ke#: z hits the water in e# & pre(z) hits the water in pred(e#)]
Sigrid Beck and Arnim Von Stechow 247
(103) ÆA, Bæ 2 [kx.ky. x is next to y and one side of x is adjacent to one side of y] The contribution of ‘side by side’ would be (104): (104) [kx.ky. one side of x is adjacent to one side of y] There is no evidence of a plural operation according to this analysis of (102b). The original examples (101) offer more justification of a connection to plural predication through the use of a plural subject. Their semantics could be as in (105):
(105#) ÆH, Hæ 2 [kx.ky: x 6¼ y. x is next to y and one side of x is adjacent to one side of y] That is, their semantics could plausibly be seen in terms of hidden reciprocity, the relevant reciprocal reading being weak reciprocity. Hence the appearance of a plural semantics in (101). But, we claim that this is not triggered by the ‘Noun Preposition Noun’ modifier—the modifier is equally happy without any plurality in the semantics of the sentence it occurs in. The plural semantics in (101) comes about through independent means (the plural subject plus covert reciprocity). We think that the semantics of (106a) is similarly weak (thanks to Cecile Meier for the example): (106) a. The squirrel jumped from tree to tree. b. The squirrel jumped from one tree to another tree. It seems clear that ‘from tree to tree’ does not involve a pseudoreciprocal semantics, that is, require a scenario in which the trees can be arranged in a sequence according to the jumping. The meaning of ‘from tree to tree’ seems to be something like ‘from one tree to another tree’. Ignoring possibly serious issues of compositionality, the prepositions generating the adverb mean perhaps the following: (107) ½½ from-to ¼ [kx.ky.kPevt.kz.ke.P(z)(e) & e starts at x & e ends at y] The meaning of sentence (106a) could then be analysed as (108) Æe, T, Tæ 2 ky.kx.ke#: x 6¼ y.Cov(x) & Cov(y) & Cov(e#) & the squirrel jumps in e# & e# starts at x & e# ends at y
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(105) a. Die Haeuser stehen Seite an Seite nebeneinander. The houses stand side by side next to each other b. The lovers walked hand in hand with each other.
248 Pluractional Adverbials The LF is generated by means of a three-place PL operator and means approximately: ‘The trees are divided in a way such that each tree is involved in a jumping to and from some other tree.’ If something along these lines is correct, weak reciprocity would be involved here as well. To be sure, this has to be worked out and might turn out to be wrong. For our purposes, the important point is that not all ‘Noun Preposition Noun’ sequences share the semantics of pluractional modifiers, and hence one should not take our proposals to extend to all data with a similar surface appearance without careful semantic consideration.
5.1 Summary To summarize, we subscribe to the view that all pluralization is sensitive to a division of pluralities into appropriate sub-parts. Pluractionals make this visible; in our cases with ‘piece by piece’ and ‘dog after dog’, they tell us which units are contained in the cover. They also show that natural language has pluralization of Æe, Æv, tææ predicates, that is, simultaneous pluralization of an event- and an individual-argument slot. We have integrated the two types of pluractional adverbials into a theory of pluralization which combines Sternefeld’s plural operators and one-place covers. As has been argued in Beck (1999), the partition of pluralities into parts is interdependent with the partition of events into parts. Pluractional adverbials restrict the partition induced by a cover by imposing restrictions on individuals: the adverbs say which criterion an individual must meet in order to be in a cover. Suppose we start from a plural fact R(e, x) and we know that a part y of x is in the relevant Cov, then that part e# for which R(e#,y) is true must be in Cov as well. So pluractional adverbs indirectly restrict covers of events. We have introduced two types of Æe, Æv, tææ PL operators, plain PL and PLseq. The former is plain pluralization and needed for ‘N by N’type adverbs. The second type is needed for pseudo-reciprocal adverbs. The two operators are very similar in structure but cannot be reduced to one operator in an obvious way. The PL operators apply in the syntax. Adverbials with ‘N Preposition the other’ are pluractionals that give rise to a sequence interpretation, which we have called pseudoreciprocal. Our theory of pseudo-reciprocals brings these together closely with reciprocals. The common core is the expression ‘other x’. In the case of reciprocals, it contributes towards ‘the others among
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5 CONCLUSIONS
Sigrid Beck and Arnim Von Stechow 249
5.2 Related literature There have of course been earlier approaches to these or related phenomena. Our goal in this paper has not so much been to develop a compositional semantics of pluractional adverbials, but rather to develop such an analysis in the framework of plural predication developed in Beck (2001). The other proposals do not have that aim. The point of our choice of framework is generality: we believe that embedding our semantic analysis in a general theoretical framework for the analysis of plural predication has allowed us to develop an analysis of pluractionality that is also very general, empirically and theoretically. Other approaches that, to our knowledge, our analysis still owes a significant theoretical debt to are the following: Lasersohn (1995) on pluralities of events; Moltmann (1997), who proposes an analysis of ‘one at a time’ adverbials and related data and some papers that add to our stock of pluractional phenomena, for example, Matthewson (2000) and Oh (2005). There are just a couple of works that propose an analysis of pseudo-reciprocals: Stockall (2001), who analyses ‘dog after dog’-type adverbials and Zimmermann (2002), who proposes a refinement of Stockall’s analysis. Also, Schein (2003) offers an analysis of reciprocals as adverbials. We will discuss the former literature first. Lasersohn (1995) introduces pluralities of events. The primary applications of this are analyses of ‘together’, verb conjunctions (plus
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them’. In the case of pseudo-reciprocals ‘the R other x# means ’the R-predecessor of x#, where R denotes an ordering. Pseudo-reciprocals are not reciprocals because they do not introduce a group. If apparent reciprocals with an IAO interpretation are reanalysed as pseudo-reciprocals (i.e. pluractional ‘one . . . the other’), this may explain some peculiarities that otherwise set apart IAO reciprocals from better behaved reciprocals. Pseudo-reciprocals are different from regular reciprocals in not introducing a plurality of type Æeæ. Rather, they are a modifier containing a singular ‘the other’ NP. Our truth conditions for IAO reciprocals are stronger than in the previous literature and empirically more adequate, we think. They give rise to the problem of the first dog viz. the problem of the bottom child. We solved these by assuming a pragmatic restriction for quantification. We have extended the analysis to event iteration as in ‘ran and ran’ and to occurrences of pluractionals in argument position. Finally, we have pointed out that not all ‘Noun Preposition Noun’ sequences share the semantics we propose.
250 Pluractional Adverbials
(109) John sold the apples one at a time. [112a] If we understand her correctly, the syntax she proposes in her definition [118] amounts to this: (110)
The node BIN-TIME is an ad hoc grammatical relation, whose interpretation is a semantic operation that makes sure that precisely the desired meaning of (109) is obtained when the value of BIN-TIME is applied first to ‘the apples’ and then to ‘John’. Something similar would have to happen in the case of ‘piece by piece’. By contrast, we suggest that natural language systematically makes available a family of pluralization operations for various types of predicates, all of which are restricted to contextually relevant part-whole structures (covers). Pluralization effects as such depend on those operators. Adverbials only add very particular information (for example, what goes in the cover). This amounts to a totally different architecture. Thus, we are indebted to Moltmann’s (1997) insights on simultaneous division of indivdual and event arguments of relations. We have a different theory on how this comes about in plural predication. There are several other works on adverbials like ‘one at a time’, including Matthewson (2000) on Salish and Oh (2005). Oh’s (2005)
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‘alternately’) and pluractional markers, which we need not go into here. His work is, we believe, the crucial reference for explicitly plural event predication. Moltmann (1997) includes an analysis of ‘one at a time’ (under the heading ‘binary distributive event quantifiers’ in section 6.6.4). The nature of that adverbial’s semantic contribution makes necessary a simultaneous division of individuals and events into sub-parts in the predication. This property emerges clearly from Moltmann’s analysis. It is shared by ‘piece by piece’ and ‘dog after dog’. She thus anticipates this aspect of our analysis. It is, however, embedded into a different architecture, in that her views of the syntax–semantics interface and pluralization operations in particular are incompatible with our own. We illustrate her proposal briefly by discussing her analysis of the pluractional adverb ‘one at a time’ in the following sentence:
Sigrid Beck and Arnim Von Stechow 251
work on Korean pluractional adverbials ought to be mentioned because her theoretical outlook is similar to ours, in attributing significant aspects of the semantics of the construction to standard plural operators, and only parts of it to the adverbial itself. The resulting semantics is similar to our ‘piece by piece’-type adverbials. In contrast to the authors mentioned above, Stockall and Zimmermann are concerned with the phenomenon whose analysis is the central purpose of the present paper. Stockall (2001) analyses the sentence in (111). She assumes the S-structure in (112). (111) Girl after girl arrived.
In this construction, ‘after’ has a complicated meaning. It applies to a pair of individuals and an intransitive verb, which is a relation between an individual and an event: (113) after#(x)(y)(arrive#) ¼ ke.de#,e$[e# < e & e$ < e & arrive(x)(e#) & arrive(y)(e$) & e# after e$] REDC is a reduplication operator, which applies to the common noun ‘girl’ and the two-place relation ky.kx.after(x)(y)(arrive). (114) REDC(girl)(ky.kx.after(x)(y)(arrive)) ¼ ke.C is a large subset of girls & "x,y[(C(x) & C(y) / x arrive after y in e or y arrive after x in e] The LF yielding the desired interpretation is the following: (115)
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(112) [IP[PPRED [after girl]] arrived]
252 Pluractional Adverbials The movement index of RED is 1 and that of girl is 2. So we have crossing k-abstraction. The structure gives us those events that are the arrival of a group of girls at different times. The approach gets this particular example right, but it does not generalize non-transitive prepositions such as in the following examples: (116) Sie schlug Nagel neben Nagel in die Wand. she hit nail next to nail into the wall
Acknowledgements We would like to thank audiences at Universita¨t Tu¨bingen, Sinn und Bedeutung 10 and MIT and moreover Philippe Schlenker, Malte Zimmermann and an anonymous reviewer for important comments.
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Zimmermann (2002: 287f.) criticizes Stockall’s (2001) proposal on syntactic grounds. He proposes a somewhat different syntax, which, however, yields the same truth conditions. Stockall/Zimmermann’s analysis of ‘dog after dog’ is also different from ours in theoretical outlook. Like Moltmann, they hold the adverbial itself and/or its composition within its local structure responsible for all of the specific semantics of the construction. Our analysis has been guided by the idea that we have a system of plural predication in place independently which includes plural operators of various types plus a restriction on relevant part-whole structures. Thus, the adverbial has a very slim semantics, with much of the burden to be carried by the pluralization operation. We believe that our approach offers a more general theoretical perspective. Finally, there is a connection between Schein (2003) and our paper in that Schein proposes that reciprocals are adverbial, just like we have suggested for IAO reciprocals above. The difference between Schein’s suggestions and ours is that he proposes this for reciprocals in general. That makes his suggestion unsuitable for the ground we want to cover in this paper: we want to analyse what distinguishes IAO reciprocals from other reciprocals. For this purpose, we attribute a pseudo-reciprocal (adverbial) semantics to IAO reciprocals (and derive their truth conditions and their scopal constrainedness). This cannot be extended to other reciprocals. There is a further connection in that Schein observes for IAO reciprocals the role of sequencing, which he attributes to temporal flow. We concur for the case of ‘after’, but use non-temporal sequencing for other cases like ‘above’, ‘within’, etc.
Sigrid Beck and Arnim Von Stechow 253 SIGRID BECK Englisches Seminar Universita¨t Tu¨bingen Wilhelmstrasse 50 72074 Tu¨bingen Germany
[email protected]
REFERENCES Krifka, Manfred (1989), Nominalreferenz und Zeitkonstitution: Studien zur Theoretischen Linguistik. Wilhelm Fink. Mu¨nchen. Krifka, Manfred (1998), ‘The origins of telicity’. In Susan Rothstein (ed.), Events and Grammar. Kluwer. Dordrecht. 197–235. Langendoen, D. Terence (1978), ‘The logic of reciprocity’. Linguistic Inquiry 9:177–97. Lasersohn, Peter (1995), Plurality, Conjunction and Events. Kluwer Academic Publishers. Boston. Lewis, David. (1991), Parts of Classes. Basil Blackwell. Oxford. Link, Godehart (1983), ‘The logical analysis of plurals and mass terms: a lattice-theoretical approach’. In R. Ba¨uerle, C. Schwarze, and A. v. Stechow (eds.), Meaning, Use, and Interpretation of Language. de Gruyter. Berlin. 302–23. Matthewson, Lisa (2000), ‘On distributivity and pluractionality’. In B. Jackson and T. Matthews, Proceedings of SALT X. CLC Publications. Ithaca, NY. Moltmann, Friederike (1997), Parts and Wholes in Semantics. Oxford University Press. Oxford. Oh, Sei-Rang (2005), Plurality Markers across Languages. Ph.D. thesis, University of Connecticut, Storrs. Partee, Barbara Hall (1987), ‘Noun phrase interpretation and type-shifting
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Beck, Sigrid 1999. ‘Plural predication and partitional discourses’. In Paul Decker (ed.), Proceedings of the 12th Amsterdam Colloquium. 67–72. Beck, Sigrid (2001), ‘Reciprocals are definites’. Natural Language Semantics 9:69–138. Beck, Sigrid, & Uli Sauerland (2000), ‘Cumulation is needed: a reply to Winter (2000)’. Natural Language Semantics 8:349–71. Brisson, Christine (1998), Distributivity, Maximality and Floating Quantfiers. Ph.D. thesis, Rutgers University, New Brunswick. Dalrymple, Mary, Makoto Kanazawa, Yookyung Kim, Sam Mchombo, & Stanley Peters (1998), ‘Reciprocal expressions and the concept of reciprocity’. Linguistics and Philosophy 21:159–210. Diesing, Molly (1990), The Syntactic Roots of Semantic Partition. Ph.D. thesis, University of Massachusetts, Amherst. Heim, Irene & Anglika Kratzer (1998), Semantics in Generative Grammar. Blackwell. Oxford. Heim, Irene, Lasnik, Howard, & May, Robert (1991), ‘Reciprocity and plurality’. Linguistic Inquiry 22:63–101. Kadmon, Nirit (2001), Formal Pragmatics. Blackwell. Oxford. Kratzer, Angelika (2003), The Event Argument. Chapter 4. Unpublished MS, University of Massachusetts, Amherst.
254 Pluractional Adverbials principles. In J. Groenendijk et al. (eds.), Studies in Discourse Representation Theory and the Theory of Generalized Quantifiers. Foris. Dordrecht. Partee, Barbara Hall (1989), ‘Binding implicit variables in quantified contexts. In CLS 25. Chicago Linguistic Society. Chicago. 342–65.
Schein, Barry (2003), ‘Adverbial, descriptive reciprocals’. In John Hawthorne (ed.), Language and Philosophical Linguistics, Philosophical Perspectives 17.1:333–67. Schwarzschild, Roger (1996), Pluralities: Studies in Linguistics and Philosophy. Kluwer. Dordrecht. Sternefeld, Wolfgang (1998), ‘Reciprocity and cumulative predication’. Natural Language Semantics 6:303–37. Stockall, Linnea (2001), ‘Pluractionality and prepositions in Germanic. The
First version received: 28.03.2006 Second version received: 30.10.2006 Accepted: 12.12.2006
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Sauerland, Uli (1998), ‘Plurals, derived predicates and reciprocals’. In Uli Sauerland and Orin Percus (eds.), The Interpretive Tract. MIT Working Papers in Linguistics, Vol. 25. 177–204.
syntax and semantics of [NP-P-NP]s’. In ConSole X. Leyden. von Fintel, Kai (1994), Restrictions on Quantifier Domains, Ph.D. thesis, University of Massachusetts, Amherst. von Stechow, Arnim (1996), ‘The different readings of Wieder ‘again’: a structural account. Journal of Semantics 13:87–138. von Stechow, Arnim (2002), ‘Temporal prepositional phrases with quantifiers. Some additions to Pratt & Francez (2001)’. Linguistics and Philosophy 25:1–40. Westerstahl, Dag (1984), ‘Some results on quantifiers’. Notre Dame Journal of Formal Logic 25:152–70. Winter, Yoad (2000), ‘Distributivity and dependency’. Natural Language Semantics 8:27–69. Zimmermann, Malte (2002), Boys Buying Two Sausages Each. On the Syntax and Semantics of Distance-Distributivity, Ph.D. thesis, Universiteit van Amsterdam, The Netherlands.
Journal of Semantics 24: 255–288 doi:10.1093/jos/ffm004
The Ingredients of Reciprocity in Cuzco Quechua MARTINA FALLER The University of Manchester
Abstract
1 INTRODUCTION This paper develops a compositional analysis of reciprocity in Cuzco Quechua (CQ) with the aim of elucidating the question of how languages may differ in the compositional derivation of this complex semantic notion. In a wider sense, it is a contribution to the growing literature on the possible space of cross-linguistic semantic variation. Consider the following Quechua reciprocal sentence and its English translation.1 (1) Hayt’a-na-ku-n-ku. kick-PA-REFL-3-PL ‘They kick each other’. 1
Where not indicated otherwise, examples are elicited, that is either translated from Spanish or constructed by the author and accepted/confirmed by native speaker consultants. The labels for morphemes used in the glosses are largely based on Cusihuaman’s (2001) study. The main exception is the label PA (‘pluractional’) for the suffix -na, which is based on my own analysis. Abbreviations used in glosses: 1O: first-person object, 1S2O: first-person subject second-person object, 1EXCL: firstperson exclusive, 1INCL: first-person inclusive, 3: third person, ABL: ablative, ACC: accusative, ADD: additive, BEN: benefactive, CAUS: causative, CIS: cislocative, COLL: collective, COM: comitative, CONT: continuative, DIM: diminutive, DIR: direct evidence, EMO: emotive, ILLA: illative, DIST: distributive, IMP: imperative, INC: inchoative, INT: intensifier, LIM: limitative, LOC: locative, NEG: negation, NMLZ: nominalizer, NMLZ.SS: same subject nominalizer, NX.PST: non-experienced past, PA: pluractional, PL: plural, PROG: progressive, PRTC: participle, PST: past, REFL: reflexive and TOP: topic. The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email:
[email protected]
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In Cuzco Quechua, reciprocity is marked by means of two verbal suffixes, one of which is a marker of reflexivity, the other of which is a marker of pluractionality. The paper develops an analysis that composes reciprocity from these more basic notions. Two further ingredients that are needed will be argued to derive from independent principles: universal quantification over parts of the reciprocal plural agent derives from plural predication, as has been argued by other researchers for English reciprocity, and distinctness of the participants in the reciprocal subevents derives from a semantic version of Condition B. This way of composing reciprocity is not universal, and other languages have dedicated reciprocal markers or make other reciprocal ingredients overt. The compositional derivation of reciprocity is therefore a clear candidate for cross-linguistic semantic variation.
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Both entail that there are at least two kicking events, that the agent and the theme of each kicking event are distinct but drawn from the same group consisting of at least two members (namely, the group denoted by they, which serves as the antecedent for the pronominal each other) and that each of the members of this group is an agent of at least one of these events and a theme of at least another one. In general, reciprocity is a complex concept that encompasses the more primitive notions of plurality, distinctness of co-arguments, reflexivity and universal quantification over parts of the reciprocal agent. While reciprocal sentences in the two languages share these semantic features, they are very different morphosyntactically: English employs the nominal bipartite anaphor each other, CQ employs two verbal suffixes: -na, which I will argue is a pluractional marker, and -ku, a reflexive. The main question for typological semantics that is raised by these observations is how the cross-linguistically uniform semantics is derived from the rather different morphosyntactic realizations, a question first raised in the formal literature by Dalrymple et al. (1994). The CQ data are interesting in this respect because the reciprocal construction in this language is not like other verbal reciprocals discussed in the literature (Mchombo 1993; Bruening 2006; Siloni forthcoming) in that it involves two morphemes rather than just one and thus raises the possibility that reciprocity is derived compositionally in this language. Dalrymple et al. (1994) studied the Chichew ˆ a monomorphemic verbal reciprocal and found that it shares the same cluster of semantic features as English reciprocal sentences; in addition to the features mentioned above, Chichew ˆ a and English reciprocals also have in common that they give rise to scope ambiguities when embedded. Dalrymple et al. (1994) concluded that the best way to deal with this semantic uniformity in the face of morphosyntactic diversity is to assume that any reciprocal construction is lexically specified as having reciprocal semantics. More precisely, they argued that reciprocal constructions denote RECIP, a polyadic quantifier, the semantics of which is such that it entails all the above features. The language-specific morphosyntactic realization of this quantifier is therefore largely semantically irrelevant. In particular, they argued that an account such as that of Heim et al. (1991) which composes reciprocity from a universal quantifier (each) and a so-called reciprocator (other) is not viable cross-linguistically as it cannot account for the fact that Chichew ˆ a reciprocal sentences have the same properties as their English counterparts despite not employing two morphemes that could
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2 In order to account for the morphosyntactic diversity of reciprocal constructions, Dalrymple et al. (1994: 157) hypothesize ‘that linguistic universals governing the interpretive relation between morphosyntax and meaning explain the naturalness of the quite different forms of expression English and Chichew ˆ a choose for reciprocal propositions’.
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be analysed as a universal quantifier and a reciprocator.2 While I agree with the conclusion that Heim et. al’s (1991) or any other compositional approach to the semantics of each other will not necessarily be applicable to reciprocals in other languages, not even other bipartite reciprocals, this does not necessitate an approach that associates reciprocal semantics directly with a morphosyntactically complex construction. In this paper, I will explore a different approach. It starts from the observation that the semantics of reciprocity is inherently complex. Even when one assigns a universal meaning such as RECIP to a reciprocal construction, one nevertheless has to require that this meaning has the components of plurality, universal quantification and distinctness of coarguments somehow bundled into it. It therefore should be equally possible to derive the universal features of reciprocity by composing two or more markers which have these more basic notions as their meaning. Thus, the observation that reciprocal constructions across languages share a number of features does not exclude the possibility that these features are derived compositionally in some languages. I will argue that CQ is such a language. Given languages like Chichew ˆ a with dedicated reciprocals, it follows that there is cross-linguistic variation in the way the complex semantic notion of reciprocity is composed (or not) from more basic building blocks. I will not enter the debate about what the best analysis of English each other is. But I will take my cue for developing an analysis of CQ reciprocal sentences from a third approach to English reciprocals, which neither tries to derive reciprocity compositionally from the meaning of each and other nor claims that each other directly denotes all features of reciprocity. Instead, this approach treats reciprocal sentences as special instances of relational plurals and argues that most semantic properties of reciprocal sentences follow from their plural properties (Langendoen 1978; Sternefeld 1998; Beck 2001). In particular, universal quantification over parts of the subject group is a direct consequence of plural predication and the definition of plural thematic roles. The overtly marked ingredients for reciprocity in CQ will be shown to be pluractionality (-na) and reflexivity (-ku). Most, if not all, previous accounts of reciprocity assume that the requirement that the arguments of the reciprocal subevents are distinct is encoded by the reciprocal construction itself. This paper departs from
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1.1 A note on reciprocal truth conditions Before proceeding with the main purpose of this paper, I should clarify that it is not my intention to contribute to the ongoing debate on how many truth-conditionally distinct reciprocal readings should be recognized. This question has still not been settled for English. For example, Langendoen (1978) considers six truth-conditionally distinct readings for elementary reciprocal sentences (ERS, those in which each other occupies the second argument position of a two-place relation R), but rejects five of these as generally adequate in favour of just one, Weak Reciprocity. An ERS with relation xRy and A as the denotation of the plural subject is true according to weak reciprocity if (2) holds: (2) Weak Reciprocity ("x 2 A)(dy, z 2 A)(x ¼ 6 y ^ x ¼ 6 z ^ xRy ^ zRx) (Langendoen 1978: 179) Under this reading, (1) is true if each member of the group denoted by ‘they’ kicks at least one other member of that group and is kicked by at least one other member. This is weaker than strong reciprocity which would require every pair of individuals in the subject group to be in the kicking relation, but this is in accordance with the intuitions of most speakers, who would not consider (1) false in a situation in which not every member kicks every other member, especially if the group is fairly large. Subsequently, other researchers have argued for distinguishing three (e.g. Bruening 2006), four (e.g. Beck 2001) or six readings (e.g. Dalrymple et al. 1998), and I refer the reader to these studies for the data and arguments on which these diverse counts of readings are based. All agree, however, that weak reciprocity is at least a possible
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this assumption and instead explores the possibility that the distinctness requirement corresponds to a general condition on semantic predicates requiring co-arguments to be distinct (Reinhart & Reuland 1993). The paper is organized as follows. Section 2 presents the CQ data to be accounted for and motivates an analysis of -na as a pluractional marker. Section 3 introduces the notion of cumulativity and how it has been used to account for reciprocity in English. Section 4 develops a formal account of simple reciprocal sentences in CQ based on the notions of pluractionality, reflexivity and cumulativity and suggests that the distinctness condition is a direct consequence of a semantic formulation of Condition B. Section 5 concludes and raises some issues to be investigated in the future.
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interpretation, and Bruening (2006) moreover argues that it is sufficient for most reciprocal sentences with eventive predicates.3 I will therefore only derive the weak reading for CQ reciprocal sentences. Future work will have to show whether it is empirically justified to recognize other readings in this language and how they can be derived compositionally. 2 THE CQ DATA
(3) a. Kunan-qa chay-lla-ta-raq tapu-na-yu-ku-nchik. now-TOP this-LIM-ACC-CONT ask-PA-INT-REFL-1INCL ‘For now we only ask each other this’. (‘Eso noma´s por ahora nos preguntaremos’.) (Vengoa Zu´n˜iga 1998: 15) b. Pay-kuna pura qu-na-ku-sha-n-ku. (s)he-PL amongst give-PA-REFL-PROG-3-PL ‘They are giving each other (things)’. (Description of video clip) c. Qusqu kay-man-qa ham-pu-ra-ni, chicu-cha-y-pa Cuzco this-ILLA-TOP come-DEF-PST-1 boy-DIM-1-GEN papa-n-wan t’aqa-na-ku-spa. father-3-COM separate-PA-REFL-NMLZ.SS ‘I came here to Cuzco after the father of my boy and I separated from each other’. (Conversation) The agent of the reciprocal event may be encoded by only the person suffixes on the verb (3a), by an overt plural subject NP (3b) or by 3 Following Fiengo & Lasnik (1972), Bruening (2006) claims that strong reciprocity is only required for stative predicates.
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CQ is an agglutinative language which employs a large number of derivational and inflectional verbal suffixes encoding a variety of semantic notions (see Cusihuaman 2001 for an overview). Some of the derivational suffixes are valence changing such as the causative suffix -chi, the benefactive -pu and the reflexive -ku. The basic word order in CQ is (S)(O)V, though this is quite variable. Person suffixes on the verb are sufficient for marking the grammatical relations of subject and object, that is independent pronouns can be, and often are omitted. In this section, I will provide the data to be accounted for and describe informally the meanings of the suffixes -na and -ku, which together derive reciprocity. The textual examples in (3) further illustrate the reciprocal construction.
260 The Ingredients of Reciprocity in Cuzco Quechua a (potentially dropped) singular or plural subject NP plus a comitative NP (3c).4 The reciprocal relation may hold between the agent and theme, (3a), or, with a ditransitive verb, between the agent and recipient, (3b).5 In the presence of derivational suffixes that introduce additional arguments such as the causative -chi the reciprocal relationship may also hold between the agent and this additional argument, as shown in (4).6
4 In CQ, using the comitative suffix -(pu)wan is a regular strategy of forming conjoined NPs, as shown in (i). (i) Tayta-y-wan mama-y-puwan-mi llaqta-ta-qa ri-n-ku. father-1-COM mother-1-COM-DIR town-ACC-TOP go-3-PL ‘My father and mother have gone to town’. (‘Al pueblo fueron mi papa´ y mi mama´’.) (Cusihuaman 2001: 140) In (i), the conjoined subject NP is plural as indicated by the plural agreement on the verb. In (3c), however, the use of the comitative NP does not result in a syntactically plural subject NP. The use of the same subject nominalizer -spa indicates that the subject of the subordinate clause is first-person singular, that is the comitative NP does not seem to form a single NP with the subject here. I thank an anonymous reviewer for pointing this out. The same reviewer suggests that there is a semantic implication of this construction that the singular subject assumes responsibility for the action, so that a more adequate translation might be ‘. . . after I separated from the father of my boy’. I will leave it to future research to determine the precise semantics of comitative NPs in reciprocal constructions. See Dimitriadis (2004) for a discussion of this strategy from a cross-linguistic perspective. 5 In CQ, it appears to be impossible to establish a reciprocal relation between the agent and theme of ditransitive verbs or between the theme and recipient. The former is the case for verbal reciprocals in other languages as well, and the latter appears to be impossible in any language (Bruening 2006). 6 Arguably, (i) and (ii) are examples in which the reciprocal relation holds between the agent and a beneficiary argument introduced by the benefactive suffix -pu. (i) Chay-pis waqa-pu-na-ku-n-ku. this-ADD cry-BEN-PA-REFL-3-PL ‘They cried with each other’. (‘Lloraron en los brazos el uno del otro’.) (Itier 1999: 196)
(ii)
Asi-pu-na-ku-n-ku pay-kuna pura laugh-BEN-PA-REFL-3-PL (s)he-PL amongst ‘They are laughing together/with each other’. (elicited description of a video clip in which two people are laughing) However, it is not clear whether -pu in these examples really is the benefactive suffix -pu. According to Cusihuaman (2001: 193), -puna in such examples is a single suffix which is used instead of -na with verbs that express that two things are put in contact with each other or that two people are looking at each other. An argument for considering -pu the benefactive in this construction is the fact that with intransitive verbs its presence appears to be necessary for introducing a second argument. While some speakers accept just -naku by itself with intransitive verbs (Faller 2005, 2007), fieldwork in 2006 has revealed that most do not, and those that do, strongly prefer the forms with -pu. More research is necessary to understand this construction properly.
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(4) Chay-pi tawa runa-kuna malli-chi-na-ku-sha-n-ku person-PL taste-CAUS-PA-REFL-PROG-3-PL this-LOC four imaymana-ta. whatever-ACC ‘There, four people make each other taste different things’. (Description of video clip)
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2.1 The meaning of -na The suffix -na has a variety of uses.8 This section discusses its use as a pluractional marker. As such, it is most productive within the reciprocal construction as illustrated above. When -na precedes the causative suffix -chi (5a), or when used in a passive participle (5b) (cf. van de Kerke 1996) it alone can convey reciprocity.9 (5) a. Hayt’a-na-chi-rqa-ni. kick-PA-CAUS-PST-1 ‘I made them kick each other’. b. Pin˜a-chi-na-sqa puri-ri-n-ku. anger-CAUS-PA-PRTC walk-INC-3-PL ‘They walk being in a state of anger with each other’. 7 See van de Kerke (1996) for a first analysis of the effect of the relevant suffixes in different Quechua varieties on argument structure, as well as Bruening (2006) for a cross-linguistic study of which arguments can be reciprocalised. 8 One is nominalizing -na which is used for different kinds of nominalizations, including not only the formation of nominalized clauses as, for example the second -na in (7a), but also the derivation of nouns from verbs such as pun˜u- ‘to sleep’ / pun˜una ‘bed’. Conversely, -na can verbalize certain types of nouns. With nouns denoting locations, it derives verbs meaning ‘to put in that location’, for example k’uchu ‘corner’ / k’uchuna- ‘to put in a corner’ (Cusihuaman 2001: 184). With nouns that denote sets of often small objects attached to a bigger one, for example feathers or seeds, the resulting verbs mean to separate the numerous smaller objects from the big one (Cusihuaman 2001: 185). For example, phuru ‘feather’ / phuruna- ‘to pluck’, ruru ‘seed’ / ruruna- ‘to deseed’. In Faller (2007) I had hypothesized that this use might be related to the suffix -na that occurs in the reciprocal construction, possibly providing a way of accounting for the distinctness of co-arguments, as these verbs tend to denote separating events, but I have in the mean time come to the conclusion that this cannot be the correct analysis. 9 In CQ the sequence -nakuchi is ungrammatical. However, in the Ancash and Huanca and possibly other varieties, this is the regular way of expressing the causation of a reciprocal event (Muysken 1981: 458; Cerro´n Palomino 1976).
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Further research is required to determine exactly which arguments can participate in reciprocity marked by -na-ku,7 and I will in the following only develop a formal analysis of reciprocity holding between the agent and theme of simple transitive verbs. While some grammar writers treat -naku as a single suffix, Muysken (1981) showed that it consists of the two suffixes -na and -ku. One argument for the bipartite analysis is the fact that -na and -ku can be split by intervening suffixes. For example, in (3a), they are separated by -yu. Furthermore, both -ku and -na can occur without the other: -ku on its own marks reflexivity and, as argued below, -na marks pluractionality. In the following two sections, the meaning of these two suffixes will be discussed informally.
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10 In the descriptive literature, pluractional markers are sometimes called distributive. This is somewhat misleading in comparison with the use of the term ‘distributive’ in the formal semantics literature, where distributivity is usually taken to entail universal quantification. That distributivity should not be identified with pluractionality has been argued, for example by Matthewson (2000), who has shown that an apparently distributive element in St’a´t’imcets is a pluractional marker precisely because it does not entail universal quantification. 11 Glosses are the current author’s. van de Kerke glosses -na as REC ‘reciprocal’.
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Besides showing that -na can occur on its own, the examples in (5) also raise the possibility that -na itself is a reciprocal marker. In fact, Muysken (1981) calls -na ‘the reciprocal’. However, he assumes that -ku is necessary to establish an anaphoric relationship with the subject, that is to ensure that the participants of the subevents are drawn from the plural individual denoted by the subject. Muysken’s ‘reciprocal’ does therefore not encode all essential components of reciprocity. If -na were a true reciprocal, we would expect it to be able to mark reciprocity on its own in any circumstance. But this is not the case, with the exception of the two environments just mentioned, reciprocity always requires both -na and -ku. -na can therefore not be analysed as a reciprocal marker. Most previous studies have focussed on the role of -na as part of the reciprocal construction. However, -na can also be used to mark plurality of events without implications of reciprocity. I will therefore analyse it as a pluractional marker, a term coined by Newman (1990) in order to distinguish plural agreement markers on verbs (well known from Indo-European languages) from verbal markers that express ‘a broad range of notions typically including action by more than one individual, temporally iterated action, and spatially scattered action (among others)’ (Lasersohn 1995: 238). The pluractional analysis of -na is weaker than the analysis presented in the predecessors of this article, Faller (2005, 2007), which had followed van de Kerke’s (1996) analysis of Bolivian Quechua -na as marking distributivity over participants, times or locations. Distributivity involves universal quantification, but pluractionality not necessarily.10 Since pluractionality subsumes distributivity as a special instance, the pluractional analysis of -na can account for the same set of data as the distributive analysis, and moreover predicts that -na should be possible in situations which do not involve universal quantification. van de Kerke presents the following two examples in support of analysing -na as marking distributivity and against analysing it as a reciprocal, both observed in naturally spoken Bolivian Quechua.11 Note that these also contain the reflexive -ku, demonstrating that this combination does not necessarily express reciprocity in this variety.
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(6) a. Pay-kuna runa-ta maqa-na-ku-n-ku. man-ACC hit-PA-REFL-3-PL (s)he-PL ‘They hit the man in turn’. (van de Kerke 1996: 149) b. Pay turril-is-man taqha-na-ku-sqa. (s)he vessel-PL-ILLA bump-PA-REFL-NX.PST ‘He bumped into the vessels’. (van de Kerke 1996: 150)
(7) a. . . .mana-n saru-na-wa-na-nchis-chu ka-sqa-nchis-wan. . . .not-DIR step.on-PA-1O-NMLZ-1INCL-NEG be-NMLZ-1INCL-COM ‘. . .(that) they must not discriminate against us (lit.: ‘trample on us’) for what we are’. (‘que no nos discriminen por lo que somos’.) (FARTAC 2002: 46) b. Maskha-na-ri-ku-spa puri-sha-n alqu. search-PA-INC-REFL-NMLZ.SS walk-PROG-3 dog ‘The dog walks, searching (for food) all over the place’. (spontaneous utterance in casual conversation)
12 In Faller (2005, 2007), I also presented the example in (i) as an illustration of the distributive use of -na: (i) Asnu-man chaqna-na-y kay kustal-kuna-ta. donkey-ILLA load-PA-IMP this sack-PL-ACC ‘Load all the sacks onto the donkeys’. This was judged acceptable by one of my consultants under the interpretation that each sack should be loaded onto the donkey. However, this same consultant does not accept this example anymore under this reading, and there is therefore some doubt that -na can be used to indicate distribution over objects. Another consultant accepts the example under a repeated action interpretation; her comment ‘amarrarlos a cada rato’, ‘to tie them up again and again’, reinforces the analysis of -na as a pluractional marker with temporal interpretations.
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The verbs of both these examples normally receive reciprocal interpretations, but in the contexts in which they were uttered, they are better translated in the indicated way. The beating in (6a) involved several men beating on another one with whips without that man reciprocating, and given that the vessels described in (6b) were stationary, a reciprocal interpretation could not have been intended. Instead, (6b) means that he bumped into each of the vessels or, perhaps weaker, that there were several events of bumping into vessels. van de Kerke notes that such purely distributive uses of -na are not very common, and I have not been able to get CQ versions of these examples accepted by my consultants. However, I, too, have been lucky to find some naturally occurring examples in which -na marks plurality of events. These are given in (7).12
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13 However, as pointed out by an anonymous reviewer, one could also analyse (7a) as involving distribution over the members of the plural object such that each of us is being stepped on (potentially only once). I have not been able to obtain clear judgments on whether this reading is to be preferred over the repeated stepping reading, though it seems to me that this example or any other use of saruna does not entail that each member of the object group is being stepped on. I have also not been able to obtain examples with this or other verbs containing -na that unequivocally involve distributivity over the object group (see also footnote 28). To really show that we are dealing with pluractionality, one would need an example with a singular object. Unfortunately, I have also not been able to obtain examples of this kind. However, the fact that consultants volunteered as a translation of saruna- into Spanish pisotear ‘to trample’ suggests to me a pluractional interpretation. Moreover, (7b) cannot be analysed as distribution over the object. 14 As an anonymous reviewer has pointed out, (7b) could out of context also mean that the dog is engaged in a mutual searching activity with other dogs (‘searching for each other’), and this would in fact be the more common interpretation. However, this example was uttered in a context in which there was only one dog and he was searching for food in every corner of the kitchen. In this context, no reciprocal interpretation could have been intended. 15 Given the relative unproductivity of -na as a purely pluractional marker, taking this meaning as basic and deriving reciprocity from it is a bit like ‘turning the world upside down’ in the words of an anonymous reviewer. This is true, but leads in my opinion to a simpler analysis than taking the reciprocal meaning as basic and trying to derive the non-reciprocal uses from it.
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Saru- means to step on something, and, according to the consultants who accept (7a), saruna- is best translated as pisotear ‘to trample’, that is an action that involves repeated stepping on something. (The Spanish translation as discriminar ‘to discriminate’, provided in the publication from which this example is taken, is a rather free translation.) Example (7a) is a relatively clear case in which -na marks plurality of events, but not necessarily distributivity. That is, there is no sense in which -na here introduces universal quantification over times.13 In contrast, (7b) is interpretable as distribution over locations, though it is also compatible with the weaker notion of plurality of events.14 Note that the contribution of -ku in this example is to indicate that the subject is a beneficiary of the described event. This use of -ku will be discussed in the next section. While such purely pluractional examples of -na occur, they are quite rare. There is also considerable variation between speakers and not everyone consulted accepts the examples in (7) as grammatical. Nevertheless, the existence of these examples indicates that marking plurality of events is at least one possible meaning of -na, and I will argue below that assuming this meaning for -na is sufficient for deriving reciprocity.15 The rarity of the examples calls for an explanation, of course, but it is not within the scope of this paper to fully investigate this. My hypothesis is that -na is restricted in its use because of the existence of other pluractional markers in the language. For example, the suffix -paya adds the meaning of repeated or repetitive action (wisq’a- ‘to close’, wisq’a-paya- ‘to close again and again’) (Cusihuaman 2001: 189), and the suffix -(y)kacha adds the meaning that the described action is scattered in
Martina Faller 265
space (apa- ‘to take’, apa-ykacha- ‘to take everywhere’) or repeated (kumpa-ku- ‘to fall’, kumpa-kacha-ku- ‘to fall again and again’) (Cusihuaman 2001: 188).16 In fact, the example in (7a) becomes acceptable to everyone if -na is replaced with -paya. There are other verbal suffixes (Cusihuaman 2001) which appear amenable to a pluractional analysis, and the study of the precise semantics of these markers will be an interesting topic for further investigation.
2.2 The meaning of -ku
(8) Asnu-n hayt’a-ku-n. donkey-DIR kick-REFL-3 ‘The donkey kicks itself ’. A related use of -ku is as a benefactive (cf. van de Kerke 1996: 144), requiring the beneficiary to be co-referential with the subject, as in (9). (9) Asnu-ta-n ranti-ku-rqa-ni. donkey-ACC-DIR buy-REFL-PST-1 ‘I bought myself a donkey’. Arguably, -ku is still reflexive in this use, indicating that the reflexive relation holds between a benefactive argument and the subject, and it can therefore be considered an extension of its basic reflexive use. In addition, as is typologically common, -ku also has uses as a middle and anticausative marker (van de Kerke 1996: 161). With the pluractional meaning for -na and the reflexive meaning of -ku having been given empirical support, we are now in a position to see how the reciprocal interpretation can arise when they are combined. Reciprocity involves plurality of events and this is marked 16 I would like to thank an anonymous reviewer for drawing my attention to the suffix -(y)kacha and its spatial meaning. 17 Note that this has to be understood as semantic reflexivity in the sense that the two arguments of a transitive verb are co-referential, but the resulting verb still can combine with a syntactic complement. This position can be occupied, for example by a body part noun, as shown in (i). (i) Juan uya-n-ta maqlli-ku-n. Juan face-3-ACC wash-REFL-3 ‘Juan washes his face’. The possessor of the body part noun is restricted to be the subject. van de Kerke (1996: 160) suggests that this is explained if one assumes that in Quechua ‘body parts are identified by means of the referential index of the subject possessor on the whole NP’. Thus, the body part noun is in fact coreferential with the sentence subject.
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The verbal suffix -ku has several functions, the one most relevant for current purposes is the marking of reflexivity illustrated in (8).17
266 The Ingredients of Reciprocity in Cuzco Quechua
3 CUMULATIVITY AND RECIPROCITY Langendoen (1978) observed that reciprocal sentences are interpreted in a similar fashion to relational plurals. A sentence like (10) is true if (i) each woman released some prisoner and (ii) each prisoner was released by some woman. This is captured by the semantic representation in (10), where A ¼ the set denoted by the women, B ¼ the set denoted by the prisoners and R ¼ the relation denotated by release. (10) The women released the prisoners. ð"x 2 AÞðdy 2 BÞðxRyÞ ^ ð"w 2 BÞðdz 2 AÞðzRwÞ (Langendoen 1978: 185) Compare this with the weak interpretation of the reciprocal sentence in (11) (an unpacked version of (2)). (11) The women released each other. ("x 2 A)(dy 2 A)(xRy ^ x 6¼ y) ^ ("w 2 A)(dz 2A)(zRw ^ w 6¼ z)
The two semantic representations differ only minimally. We can see that replacing the second plural NP with the reciprocal pronominal 18
Note that the analysis of pluractionality does not require events as ontological primitives, as is shown, for example by van Geenhoven’s (2004) successful analysis of pluractionality in West Greenlandic.
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by -na. The function of -ku is to identify the agent and the theme of the sum event, ensuring that the participants of the subevents are drawn from the same group. This alone does not constitute reciprocity yet, but if we can find the other ingredients, universal quantification and distinctness of the participants in the subevents, somewhere else, then the combination of -na and -ku provides a very good skeleton. In the following sections I argue that universal quantification comes for free with plural predication and the notion of plural agents and themes and that the distinctness condition is in fact a general condition on coarguments of a predicate. The account to be developed in the following sections is cast in a neo-Davidsonian event semantics. Having events in the representation language and as ontological primitives makes certain aspects in the analysis of reciprocity straightforward. For example, it is easy to distinguish the reciprocal sum event and the subevents of which it is constituted. Event semantics also is usually the framework of choice for work on pluractionality, as again, it captures straightforwardly the idea that a pluractional marker pluralizes events, not objects.18
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(12) For any set P, P is the smallest set such that a. P 4 P; and b. if a 2 P and b 2 P; then a4b 2 P For example, if dog# ¼ {Fido, Rover, Buddy}, then dog# ¼ {Fido, Rover, Buddy, Fido4Rover, Fido4Buddy, Rover4Buddy, Fido4Rover4Buddy}. Note that P contains atomic individuals, that is a starred predicate is true of single individuals as well. To derive a plural proper denotation, the atoms have to be subtracted from P: Rullmann & You (2003) argue that Mandarin Chinese unmodified nouns have ‘general number’, a term coined by Corbett (2000), that is they are P predicates. In this language, an optional plural marker PL, the semantics of which is given in (13), can be used to derive a properly plural interpretation. As will be shown below, CQ is like Mandarin in this respect. (13) PLðNÞ ¼ NAt 19
(Rullmann & You 2003)
I assume an ontology along the lines of Link (1998), where the domain of individuals De contains atomic/singular individuals as well as plural individuals. De is closed under the sum operation: if a and b are individuals in De, then a4b is an individual in De. Sums and their constituent parts form a join semi-lattice, structured by the ordering relation <. Thus, a < a4b. The ontology also contains events as primitive objects, and the domain of events Ds is structured in the same way as De.
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each other has the effect of identifying A and B and of adding the requirement that the arguments of R be distinct. This latter requirement is needed to ensure that the reciprocal sentence is not verified by a situation in which some women only release themselves. It is a plausible hypothesis then that the shared semantics should be accounted for in a parallel fashion. Such accounts have since been worked out in detail by Sternefeld (1998) and Beck (2001), both of whom have developed theories of plurality that treat reciprocal sentences as special instances of relational plurals. The interpretation of reciprocal and relational plural sentences is derived by cumulating the relevant relation; the reciprocal each other only contributes the nonidentity condition and the anaphoric link between the two NPs. In the first instance, cumulativity is a property of predicates P (Krikfa 1982; Link 1998).19 A predicate P is cumulative if it is closed under the sum operation. Plural nouns are cumulative. For example, if Fido and Buddy are dogs and Rover and Sam are dogs, then Fido, Buddy, Rover and Sam are dogs. Singular nouns are not cumulative: if Fido is a dog and Buddy is a dog, it does not follow that Fido and Buddy is a dog (they are dogs). Link’s definition of the plural ‘’ operator in (12) (as cited in Sternefeld 1998: 304) directly captures cumulativity.
268 The Ingredients of Reciprocity in Cuzco Quechua In Sternefeld’s and Beck’s theories, relational plural sentences involve cumulation of a relation, which is achieved by defining a twoplace operator ‘’ which pluralizes the arguments of a relation simultaneously. The definition in (14) is based on Sternefeld’s (1998: 304) definition of ‘’, differing from it only in adding an event argument. (14) For any R relating an event argument and two individual arguments, let R be the smallest relation such that a. R 4 R; and b. if Æa; b; e1 æ 2 R and Æc; d; e2 æ 2 R; then Æa4c; b4d; e1 4e2 æ 2 R
(15) a. kick# ¼ {Æa, b, e1æ, Æc, d, e2æ, Æf, g, e3æ} b. kick# ¼ {Æa; b; e1 æ; Æc; d; e2 æ; Æf ; g; e3 æ, Æa4c; b4d; e1 4e2 æ; Æc4f ; d4g; e2 4e3 æ; Æa4f ; b4g; e1 4e3 æ; Æa4c4f ; b4d4g; e1 4e2 4e3 æ} Thus, a sentence like (16a) is true iff an ordered triple consisting of the sum denoted by the donkeys, the sum denoted by the dogs and a sum of events, is in the denotation of kick#: This is equivalent to the truth conditions for relational plural sentences given in (11) (Sternefeld 1998; Beck 2001). Saying that such a triple is in the extension of kick# amounts to saying that the donkey sum individual is a plural agent AG in a plural event of kicking dogs, and that the dog sum individual is a plural theme TH in a plural event of being kicked by donkeys (see Landman 2000 for a detailed discussion of plural thematic roles). Being a plural agent AG in a plural event of kicking dogs requires every part of the donkey sum individual to be an agent in a subevent, that is every donkey has to kick some dog. Likewise, being a plural theme TH requires every part of the dog sum individual to be a theme in a subevent, that is every single dog has to be kicked by some donkey. Therefore, the equivalence in (16b) holds between the plural predicate kick# and its atomic counterpart kick# (a ¼ sum
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Example (15b) illustrates cumulation of the verb kick with the extension in (15a). Note that, for simplicity, I present the extensions of transitive verbs as triples, consisting of Æagent, theme, eventæ. In the semantic representations to be developed below, I will use neoDavidsonian thematic role functions on events. In such a framework the extension of a verb only contains events. The extensions in (15), and extensions of other verbs presented below, should therefore be considered a combination of the extension of the verb ({e1, e2, e3}) and the extensions of the thematic roles AGENT ({Æa, e1æ, Æc, e2æ, Æf, e3æ}) and THEME ({Æb, e1æ, Æd, e2æ, Æg, e3æ}).
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individual denoted by the donkeys, b ¼ sum individual denoted by the dogs).20 (16) a. The donkeys kicked the dogs. b. de:kick#ðeÞ ^ AGðeÞ ¼ a ^ THðeÞ ¼ b5 de½"x
(17) a. The donkeys kick each other. b. de:kick#ðeÞ ^ AGðeÞ ¼ a ^ THðeÞ ¼ a5 de½"x < AT a:dy < a:de# < e½kick#ðe#Þ ^ AGðe#Þ ¼ x ^ THðe#Þ ¼ y ^ x 6¼ y ^ "y
Read x
de:kick#ðeÞ ^ AGðeÞ ¼ a ^ THðeÞ ¼ b5 de½"x < a:dy < b:de# < e½kick#ðe#Þ ^ AGðe#Þ ¼ x ^ THðe#Þ ¼ y ^ "y < b:dx < a:de# < e½kick#ðe#Þ ^ AGðe#Þ ¼ x ^ THðe#Þ ¼ y
Since we are ultimately interested in how the atomic elements of a plural individual relate to the atomic subevents of a plural event, I prefer to state the equivalence as in (16). Note that the problems with collective action discussed for (16) in the following also hold for (i), as the reader can confirm for her-/himself. 21 Note that unstarred verbal predicates may contain plural individuals as agents or themes. For example, in (18a) the agent of e2 is i4p. However, they may not contain plural events, that is cumulation of verbal predicates in a neo-Davidsonian approach turns on events. This gives us an immediate handle on collective action. Any plural agent or theme of an atomic event is necessarily a collective agent or theme. In contrast, a plural participant of a plural event is not necessarily a collective participant. Thus, a4c in (15b) is not a collective agent because there is no triple in (15a) which has a4c as an agent (cf. Kratzer 2007).
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Thus, plural verbs inherently come with the "d quantifier sequence needed for weak reciprocity (Beck 2001). To derive the reciprocal interpretation of, for example (17a), we only have to add the distinctness condition and let a ¼ b, as in (17).
270 The Ingredients of Reciprocity in Cuzco Quechua b. carry# ¼ fÆi; b1 ; e1 æ; Æi4p; b2 ; e2 æ; Æi4p; b1 4b2 ; e1 4e2 æg In this situation the sentence in (19a) and its semantic representation in (19b) are true, because i4p is a plural agent and b14b2 a plural theme in the plural carrying event e14e2.
In addition to cumulative readings, English sentences with two plural or quantified NPs can also have readings in which one NP is distributed over the other. Take, for example the sentence in (21). (21) Five donkeys kicked ten dogs. In the reading in which five donkeys has wide scope, each donkey kicked 10 dogs, which are not necessarily the same 10 dogs for each donkey, that is there might be up to 50 dogs involved. When ten dogs has wide scope, the resulting reading is that each dog was kicked by five donkeys, which are again not necessarily the same five donkeys for each dog. That is, while the cumulative reading of (21) entails that there are a total of 5 donkeys and a total of 10 dogs, the two scoped distributive readings allow for more animals. It is often assumed that the scope mechanism is optional and freely available in the syntax without requiring overt expression, at least for 22 These intermediate individuals are comparable to the subsets of the cover of a plural individual. For covers, see, for example the work by Schwarzschild (1996), Landman (2000) or Beck (2001).
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(19) a. Isabel and Pablo carried the boxes upstairs. b. de.carry#(e) ^ AG(e) ¼ i4p ^ TH(e) ¼ b14b2 But it is not true that for every part x of i4p there is a part y of b14b2 such that x carried y upstairs, because p did not carry a box by himself. The equivalence in (16) is therefore too strong for the general case. For collective action all that is required is that every part of the plural agent (and theme) is part of a sum (minimally consisting of itself, maximally of the plural agent (theme) as a whole) which is an agent (theme) in a subevent. This is captured in the following reformulation of (16) for any relation R in terms of ‘possible intermediate individuals’ (x# and y# in (20); for simplicity, I continue to use the constants a and b for the agent and theme),22 a notion adopted from the reflexivity criterion of Langendoen & Magloire (2003) to be discussed in section 4.2. (20) de:RðeÞ ^ AGðeÞ ¼ a ^ THðeÞ ¼ b5 de½"x < AT a:dx# < a:dy < b:de# < e½x < x#^ Rðe#Þ ^ AGðe#Þ ¼ x# ^ THðe#Þ ¼ y^ "y
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4 COMPOSING RECIPROCITY IN CQ For CQ, the assumption that all predicates and relations are lexically cumulative makes immediate sense. Like Mandarin Chinese (Rullmann & You 2003), CQ nouns have general number. For example, the Spanish translation provided for (22a) translates uwiha as ovejas ‘sheep (pl.)’, but a singular interpretation would out of context also be possible. (22) a. Uwiha-q qhepa-n-ta urqo-ta ri-spa-n, . . . sheep-GEN behind-3-ACC mountain-ACC go-NMLZ.SS-DIR ‘Walking behind the sheep (pl.) to the mountains . . .’. (‘Yendo a los cerros tras las ovejas . . .’.) (Valderrama Fernandez & Escalante Gutierrez 1982: 26) 23 Unstarred predicates are nevertheless available in the semantic representation language, and I will use them in semantic representations to state entailments of starred predicates.
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English. Similarly, the plurality operators and are often assumed to be freely available syntactic operators (Sternefeld 1998; Beck 2001). This explains why a sentence like (21) without any further context is ambiguous between a cumulative and two distributive readings. An alternative view assumes that the denotations of lexical roots are cumulative from the start, that is their cumulativity is not derived from a non-cumulative version by applying silent star operators in the syntax. This view has recently been defended for English verbs by Kratzer (2007), following suggestions by Krifka (1992) and Landman (1996). The most obvious and immediate advantage of assuming that verbs have a cumulative denotation is that it provides an immediate account of ‘the effortless availability of a cumulative interpretation’ (Kratzer 2007) for sentences with two plural NPs without having to postulate phonologically silent and operators. I will adopt this lexical view of cumulativity for CQ predicates, both nouns and verbs. For example, kick translates as kick#; not just kick#.23 However, the assumption that predicates are lexically cumulative predicates cannot derive the two scoped distributive readings and Kratzer (2007) therefore assumes a second kind of cumulativity, phrasal cumulativity. In languages like English, the scoped distributive readings require the presence of plural DPs, and she therefore argues that phrasal cumulativity is the result of these DPs introducing -operators which may pluralize their sister Verb Phrases. Not all languages introduce phrasal cumulativity via nominal plural markers, however. Kratzer mentions Chinese, where the scopal distributive readings require an overt distributivity marker. This is also the case for CQ, as discussed in the next section, (24).
272 The Ingredients of Reciprocity in Cuzco Quechua
b. Chay-pi-ya Tashi tarpa-chi-ku-n. this-LOC-EMO Tashi catch-CAUS-REFL-3 ‘In this, Tashi let himself be caught’. Again, if verbs are lexically cumulative, this is immediately accounted for. While these data do not in and of themselves prove that lexical roots have cumulative denotations (the alternative being the silent application of pluralization operators), making this assumption leads to a simpler analysis. In contrast to English, the distributive readings which require the application of a scope mechanism are only available in CQ if an overt distributive marker is used. For example, (24a) can only mean that there is a total of 5 donkeys and a total of 10 dogs.24 As shown in (24b), 24
This claim is based on my own fieldwork. Fellow Quechua linguist Rachel Hastings, however, has obtained interpretations for similar sentences which involve the object NP being distributed over the subject NP. Nevertheless, she also observed that the use of -nka is strongly preferred to express distributive meanings (personal communication). In contrast to sentences with plural NPs, sentences with quantified NPs are expected to exhibit scope ambiguities. Since NPs with numerals appear to be non-scopal, I hypothesize that numerals are non-quantificational.
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b. Urqo-pi hina uwiha-cha-kuna michi-mu-sqa-y-man mountain-LOC like sheep-DIM-PL herd-CIS-NMLZ-1-ILLA hina . . . like ‘As I was herding the sheep in the mountains . . .’. (‘En lo que pasteaba a las ovejitas en los cerros . . .’.) (Valderrama Fernandez & Escalante Gutierrez 1982: 26) If nouns have a cumulative denotation to begin with, then the data in (22a) are expected; no zero derivation or the application of a freely available plural operator is necessary to account for the plural interpretation, as would be on an account in which nouns denote sets of atoms. There is an optional nominal plural suffix, -kuna, which enforces a plural interpretation of nouns, as for example in (22b), which only has an interpretation with two or more sheep. -kuna can therefore be analysed as instantiating the PL operator of Rullmann & You (2003) in (13). Verbs, too, can denote both singular and plural events without requiring any overt (agreement) morphology to indicate either. Thus, tarpachikun, which is morphologically unmarked for number, denotes several catching events in (23a), but only a single one in (23b). (23) a. Chay-pi-ya suwa-kuna tarpa-chi-ku-n. this-LOC-EMO thief-PL catch-CAUS-REFL-3 ‘In this, the thieves let themselves be caught’. (‘Es en eso pues que los ladrones se hacen atrapar’.) (Espinoza 1997: 82)
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a distributive interpretation requires overt marking, such as the suffix -nka which attaches to the distributive share (Faller 2001). (24) a. Pisqa asnu five donkey ‘Five donkeys b. Pisqa asnu five donkey ‘Five donkeys
chunka alqu-ta hayt’a-rqa-n. ten dog-ACC kick-PST-3 kicked ten dogs’. chunka alqu-nka-(ta) hayt’a-rqa-n. ten dog-DIST-ACC kick-PST-3 kicked ten dogs each’.
4.1 Pluractionality In the previous section we have seen that for nominal predicates in CQ there exists a plural morpheme which forces a plural interpretation of nouns which otherwise allow for both singular and plural reference. Under the assumption that the denotations of verbal predicates also contain both singular and plural events, pluractional markers have the same function, that is they apply to a verb and return only the set of plural events. But pluractional markers do more than pluralize the verb. They specify the way in which the atomic subevents of a plural event are distinguished from each other and may require ‘separate running spaces, running times, or participants’ (Lasersohn 1995: 251). To capture this, Lasersohn analyses pluractional markers as introducing the non-overlap condition :½f ðe#Þ+f ðe$Þ into the semantic representation, where e# and e$ are (atomic) subevents, and f is a function that may be instantiated in different ways by different markers. f may be the temporal trace function, resulting in a repetitive or repeated action interpretation, or f may be the spatial trace function, resulting in the interpretation that the action is scattered in space.25 f may also refer to the thematic roles of an event, for example if f is instantiated to THEME, 25 See, for example Krifka (1998) and Link (1998) on the notion of trace functions. Following Link (1998: 201), I assume that times and locations form semi-lattices, just like events. The temporal and spatial trace functions are partial functions from the domain of events to the domain of times and locations, respectively. Lasersohn (1995: 223) provides a set theoretic definition of the overlap relation. The lattice-theoretic counterpart is given in (i) for two elements s and t.
(i)
s+t4dx½x < s ^ x < t
ðLink 1998 : 156Þ
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The fact that the distributive, but not the cumulative readings require overt marking lends support to the hypothesis that cumulativity is built into lexical predicates, and this is what I will assume for CQ in the following. With this as background, we can now develop a formal semantic account of reciprocity.
274 The Ingredients of Reciprocity in Cuzco Quechua the resulting interpretation is that the action is performed on multiple themes. With atomic participants, the non-overlap requirement simply amounts to distinctness.26 A pluractional marker may also leave the nature of f unspecified. The semantics of a general pluractional marker can be represented as in (25).27
CQ -na denotes PA without setting f to a specific value.28 This means that depending on how f is chosen, distinct interpretations arise. When f is set to the temporal trace function, a repeated or repetitive 26 With non-atomic participants, non-overlap is more restrictive than distinctness. For example, the two sum individuals a 4 b and a 4 c are distinct, but they overlap. It is not clear to me at this point whether requiring non-overlap of participants may perhaps be too restrictive. But since nonoverlap is required for temporal and spatial f (Lasersohn 1995), I will continue to use + for f instantiated to thematic roles in order to maintain the generality of the definition. 27 The definition in (25) departs from Lasersohn’s (1995: 256) original definition given in (i) in three ways.
(i)
V-PAðXÞ5"e; e# 2 X½PðeÞ & :½ f ðeÞ+f ðe#Þ & cardðXÞ > n
(Lasersohn 1995: 256)
First, as pointed out to me by Philippe Schlenker (personal communication), the biconditional in (i) will never be true, because the non-overlap condition :½f ðeÞ+f ðe#Þ is false whenever e ¼ e#. The condition e# 6¼ e$ has therefore been added in (25). Second, for simplicity’s sake, (25) only requires e to be non-atomic, without requiring there to be a (pragmatically determined) number n of subevents. Third, Lasersohn’s definition contains the free variable P ranging over properties of the atomic subevents. P may be different from V to allow for subevents that do not fit the verb’s description. This is needed in particular for repetitive event types such as nibbling, where the constituent atomic events are not nibbling events but biting events. However, by making this allowance, we open the door wide for all kinds of subevents. For example, at some level of a kicking event, we find an event of a leg moving without that movement counting as a kicking. This event would, however, not involve a theme, and we would therefore have to allow subevents to differ from not only their superevent in P but also in their argument structure. Since these kinds of complications are not directly relevant to the purposes of this paper, I will simplify matters and restrict the type of subevents to which the non-overlap condition applies to those events which have the property denoted by the verb. To do this, I introduce the notation e#
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(25) PA ¼ PAvi _ PAvt PAvi : kP:kx:ke½:ATðeÞ ^ PðxÞðeÞ ^"e#; e$
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(26) a. hayt’a0kx:ky:ke½kick#ðeÞ ^ AGðeÞ ¼ x ^ THðeÞ ¼ y b. hayt’a-na 0 kx:ky:ke½:ATðeÞ ^ kick#ðeÞ ^ AGðeÞ ¼ x ^ THðeÞ ¼ y ^ "e#; e$
The overlap relation for pairs of elements may be defined as in (i). (i)
30
Æs; tæ+Æu; væ4dxdy½x < s ^ x < u ^ y < t ^ y < v
Note that the condition :[ÆAG(e#), TH(e#)æ + ÆAG(e$), TH(e$)æ] does not make reciprocal sentences false in situations in which an agent acts on a theme more than once. Consider the same situation with the additional event e5: a kicks b. In this situation, it is still true that there is a reciprocal sum event that fulfils the condition that the agent/theme pairs of all its subevents are distinct, namely, e14e24e34e4, that is the sentence A, b, and c are kicking each other comes out as true, e5 is simply irrelevant. It may, however, seem somewhat odd that according to this analysis the event e14e24e34e44e5 does not qualify as a reciprocal event. However, from a formal perspective, deeming e5 as irrelevant for determining the truth conditions is no different from deeming e#5 : a kisses b as irrelevant.
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action interpretation is derived as in (7a) with saru-na ‘to trample’, when it is set to the spatial trace function, a scattered in space interpretation is derived as in (7b) with maskha-na ‘to search all over’. For deriving the reciprocal interpretation, we have to require that the subevents have distinct agent/theme pairs, that is f ¼ ÆAG, THæ.29 To see why it is not enough to require just their agents or themes to be distinct, take the following situation involving the individuals a, b and c and four events—e1: a kicks b, e2: b kicks a, e3: a kicks c and e4: c kicks b. This situation satisfies weak reciprocity, but e1 and e3 have the same agent and e1 and e4 have the same theme. None of the events have the same agent/ theme pair, however. I assume that ÆAG, THæ(e) ¼ ÆAG(e), TH(e)æ.30 Together with the distinctness condition requiring the agent and theme of each subevent to be distinct, which will be discussed in section 4.3, this correctly captures weakly reciprocal situations. As an example, the semantic representation resulting from adding -na to the verb hayt’a ‘kick’ with f set to distinct agent/theme pairs is shown in (26).
276 The Ingredients of Reciprocity in Cuzco Quechua
4.2 Reflexivity
(28) a. Anna and Bob are in love with themselves. b. Anna is in love with herself and Bob is in love with himself. In contrast, the relation defend does not entail reflexivity on the atomic level: (29a) does not entail (29b), though this is certainly a possible interpretation. (29) a. Anna and Bob are defending themselves. b. Anna defended herself and Bob defended himself. But (29a) can also have the interpretation that Anna and Bob collectively defended themselves as a group. That is, reflexivity may only hold at the level of the plural individual. To capture this, Langendoen & Magloire (2003: 48) postulate the so-called reflexivity criterion, which I will adopt as the semantics for CQ -ku. Example (30) is a neo-Davidsonian event semantic reformulation of the criterion. (30)-ku0kR:kx:ke:"xi
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Reflexivisation through marking on the verb usually involves an operation on the verb’s argument structure (Reinhart & Reuland 1993), co-indexing two (or more) of its arguments.31 That reflexivisation is an operation on argument structure also in the case of the Quechua verbal reflexive marker -ku has been argued by van de Kerke (1996), and I will adopt this analysis in this general formulation here. In a recent paper, however, Langendoen & Magloire (2003) have argued that a more fine-grained formulation is needed of what it is that is being co-indexed. For some relations with a plural antecedent, reflexivity necessarily holds at the level of atomic individuals making up the plural individual, but for others this is not the case. An example of the former is the relation be in love with: (28a) entails (28b).
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however, required that for each atom there exists such an intermediate individual, that is indirectly, each atom is a participant in the reflexive relation. That intermediate individuals are needed can be seen by enlarging the group as in (31). (31) Anna and Bob and Cedric and Doris defended themselves.
(32) a. Hayt’a-ku-n-ku. kick-REFL-3-PL ‘They kick themselves.’ b. de:"xi
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This sentence is true in a situation in which Anna and Bob collectively defended themselves and Cedric and Doris collectively defended themselves. For the analysis of CQ reciprocity, the reflexivity criterion is necessary to capture the fact that reflexivity holds at the level of the plural individual denoted by the subject, but crucially not at the atomic level, where, as mentioned above, distinctness is required. Example (32) is the representation for the CQ equivalent of ‘They kick themselves’ using the semantics of -ku in (30).
278 The Ingredients of Reciprocity in Cuzco Quechua Therefore, (32) amounts to (34). (34) de:"xi < they#:dez < e½kick#ðez Þ ^ AGðez Þ ¼ xi ^ THðez Þ ¼ xi For reciprocal sentences, reflexivity at the atomic level cannot be permitted, but the components of reciprocity developed so far would allow this. The semantics for -na and -ku give us the representation in (35) for hayt’a-na-ku-n-ku ‘They are kicking each other’.
We can expand the second line in (35) to look at the individuals that make up the plural z and the subevents of e by applying the equivalence in (20) for -predicates. The resulting representation is given in (36). (36) hayt’a-na-ku-n-ku 0 de½"xi
4.3 The distinctness condition All accounts of reciprocity I am aware of make the distinctness condition part of the semantics of the reciprocal marker itself. For example, Langendoen’s definition of weak reciprocity repeated in (37) from (2) explicitly requires that the arguments of R be distinct: (37) Weak Reciprocity ð"x 2 AÞðdy; z 2 AÞðx 6¼ y ^ x 6¼ z ^ xRy ^ zRxÞ (Langendoen 1978: 179)
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(35) hayt’a-na-ku-n-ku 0 de½"xi < AT they#:dz < they#:dez < e½xi < z ^ :ATðez Þ ^ kick#ðez Þ ^ AGðez Þ ¼ z ^ THðez Þ ¼ z ^ "e#; e$
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(38) Condition B: If a predicate is reflexive it is reflexive-marked. From this it follows that any predicate that is not reflexive marked is not reflexive, that is its co-arguments have to be distinct.34 In CQ, where pronouns can be freely dropped, the co-arguments of a predicate are always interpreted as distinct, as shown in (39a). The only way to derive a reflexive interpretation is by adding the verbal suffix -ku as in (39b). (39) a. Hayt’a-n. kick-3 ‘(S)hei kicks him/herj’. (i 6¼ j). b. Hayt’a-ku-n. kick-REFL-3 ‘(S)hei kicks her-/himselfi ’. Returning to reciprocal verbs, the idea is that Condition B applies to the atomic predicates (kick#) in (36), resulting in (40). 34 Arguably, this condition is too strong (Philippe Schlenker, personal communication). Some speakers accept English sentences with a bound non-reflexive pronoun as in (i).
(i)
Everybody (including John/John himself) hates him (¼ John).
For (i) to be true, hate has to have Æjohn, john, eæ in its extension. Usually, such sentences are judged unacceptable, however, and it seems mainly due to the presence of the parenthetical that (i) is rescued. I therefore assume that Everybody hates him without any further overt material that explicitly includes John in the group of John-haters does not have an interpretation according to which John hates John. I furthermore assume for now that the parenthetical even without the reflexive pronoun constitutes a form of reflexive marking, but have nothing more concrete to say about how this comes about.
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Here, I will explore an alternative hypothesis for CQ reciprocal sentences, namely, that the distinctness condition is added to any relation, unless there is an explicit operator such as reflexive -ku requiring identity. This hypothesis is rooted in semantic reformulations of Principle B of the Binding Theory (‘a pronoun is free in its governing category’), in particular that of Reinhart & Reuland (1993) (see also Partee & Bach 1981; Sells 1991; Kiparsky 2002, and the pragmatic Disjoint Reference Presumption of Farmer & Harnish 1987 and Levinson 2000). Reinhart & Reuland define Condition B on semantically reflexive predicates, that is predicates the two (or possibly three) arguments of which are co-indexed. A predicate P is reflexive marked iff either P is lexically reflexive or one of P ’s arguments is a SELF anaphor (Reinhart & Reuland 1993). Given these definitions, they reformulate Condition B as (38) (also cf. Jacobson (2007)).
280 The Ingredients of Reciprocity in Cuzco Quechua (40) hayt’a-na-ku-n-ku 0 de½"xi
(41) hayt’a-na-ku-n-ku, z ¼ xi 0 de½"xi < AT they#:dei < e½:ATðei Þ ^ kick#ðei Þ ^ AGðei Þ ¼ xi ^ THðei Þ ¼ xi ^ "e#; e$
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For (40) to be a valid derivation it has to be shown that the atomic predicates are not reflexive marked despite -ku being present. As argued above, -ku marks the cumulative predicate kick# as reflexive, see example (35). What has to be shown therefore is that reflexivity at this level does not entail reflexivity at the atomic level in the case of the reciprocal interpretation of verbs marked with -na, even in cases in which this is entailed for the base predicate such as hayt’a. As we have seen above, only DN and DD predicates entail reflexivity at the atomic level. Thus, only if PA(R) predicates are DN or DD will the corresponding singular predicates also be necessarily reflexive. However, PA(R) predicates are neither DN or DD, even in cases in which the base predicate is. This can easily be seen by looking at the extension of PAðkick#Þ in (27), which does not contain any events with atomic agents or themes. While the plural individual a4b is an agent in PAðkick#Þ; a and b individually are not. Since (27) is a perfectly legitimate extension for a PA(R) predicate (though such a predicate may of course have atomic agents or themes), PA-predicates do not have the DN or DD entailments. Consequently, the atomic predicates in (36) are not reflexive marked and the distinctness condition is added as shown in (40). While reflexivity at the atomic level is not entailed for pluractional predicates, it is interesting to consider the case in which z equals atomic xi’s, that is the case in which the reference to intermediate individuals is eliminated. The representation for hayt’anakunku with this assumption is given in (41).
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4.4 Reciprocity with only -ku and with only -na The attentive reader will have spotted that the analysis developed so far predicts that a reciprocal interpretation should be possible with -ku alone for some predicates. For DN and DD predicates such as hayt’a-, this interpretation is excluded because they entail reflexivity for atoms preventing the distinctness condition from being added. However, for predicates such as defend, reflexivity at the level of atoms is not entailed. When the intermediate individual z equals x, the sum individual denoted by the subject NP, in the reflexivity criterion, there is nothing to prevent the distinctness condition from being added in the same way as discussed in the previous section for hayt’anaku-. Moreover, because I have assumed throughout that verbs are interpreted cumulatively, a verb marked only with -ku allows a plural event interpretation even without the condition introduced by -na that :AT(e). Likewise, there is nothing to prevent that the subevents are distinguished by having distinct agent/theme pairs. Thus, the sentence in (42) would not only come out true in a situation in which each defended him-/herself or in which subgroups of ‘they’ defended themselves but
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sentences containing -na and -ku should have a meaning in which each member of the subject group acts on her-/himself repeatedly (with f ¼ temporal trace function) or in different locations (with f ¼ spatial trace function). That is, (41) should have a meaning in which each member of they# kicks him-/herself repeatedly. However, consultants are extremely reluctant to accept (41) as an appropriate description of this situation. It can only mean that they are kicking each other. As mentioned in footnote 28, my hypothesis for why these predicted readings are not available empirically is that they are blocked by the existence of more specific pluractional suffixes such as the frequentive -paya. To summarize this subsection, the distinctness condition is added to any predicate unless there is an overt marker requiring identity of coarguments. It was shown that despite -ku marking the plural event denoted by a verb containing -na as reflexive, this does not entail reflexivity at the atomic subevent level. All the ingredients for deriving reciprocity are now in place: to derive the reciprocal interpretation of a verb form containing -na and -ku, pluractional -na requires plural events, the subevents of which are distinguished by having distinct agent/theme pairs, reflexive -ku identifies the co-arguments of the plural predicate, the distinctness condition is added at the level of atomic subevents and universal quantification over the atoms making up the group denoted by the subject is a direct consequence of plural predication.
282 The Ingredients of Reciprocity in Cuzco Quechua also in a situation in which they defended each other. This is not usually an interpretation that consultants agree to being available.35 (42) difiendi-ku-n-ku. defend-REFL-3-PL ‘They defend themselves’.
35
However, the almost identical examples in (i) and (ii) appear in a written text. (i) ayllu uhu-pi kuska-manta warmi qhari kamachi-ku-yku family/clan interior-LOC together-ABL woman man give.orders-REFL-1EXCL ‘Within the family, between wife and husband we give orders to each other’. (‘dentro del ayllu entre varo´n y mujer nos ordenamos mutuamente’.) (Espinoza 1997: 60) (ii)
warmi qhari uhu-pi-qa kuska-manta kamachi-ku-yku woman man interior-LOC-TOP together-ABL give.orders-REFL-1EXCL ‘Within the relationship of husband and wife we give each other orders’. (‘Al interior de la relacio´n entre marido y mujer nos damos o´rdenes mutuamente’.) (Espinoza 1997: 182) The Spanish translations and surrounding context of these sentences make clear that a reciprocal interpretation is intended. Of the three consultants I have presented (i) to, two outright rejected a reciprocal interpretation. However, a third consultant at first accepted (i) with a reciprocal interpretation. Only when explicitly asked to compare it to the same sentence with -na added did she retract her initial judgment of (i) as reciprocal. The example (ii) is followed almost immediately by roughly the same sentence, but this time with -na, without there being a detectable meaning difference between the two. It might be the case that the absence of -na in these examples is a transcription or speaker error, though this is perhaps made less likely by the fact that there are two instances. However, attempts to elicit other such examples have so far failed. It is therefore unclear whether or not some speakers allow -ku on its own to describe reciprocal situations. 36 This same pragmatic constraint may also explain why in most, if not all, cases an explicit distributive marker such as -nka is required to derive distributive interpretations of sentences such as (24). Making this a pragmatic rather than a semantic constraint would explain why some of Hastings’ consultants allow this reading for some examples without -nka (see footnote 24). In this context it is interesting that this constraint does not seem to hold for languages which use a reflexive pronoun also to express reciprocity such as the Romance languages. Thus, Spanish or French sentences with se can be disambiguated to the reciprocal interpretation by the addition of el uno al otro/l’un l’autre ‘the one the other’, but these are regularly omitted. This difference might have to do with the fact that the disambiguating elements are lexical expressions, whereas in CQ disambiguating -na is a bound suffix.
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That the combination of -na and -ku is practically always preferred for expressing reciprocity even with predicates that, according to the present analysis, should allow a reciprocal interpretation with only -ku is hypothesized to be due to the fact that -ku by itself does not entail plurality of events or distinct agent/theme pairs for the subevents, both essential ingredients of reciprocity. The conversational principle of maximizing informativeness (Grice 1989) within the grammatically possible space seems to be very strong for my consultants, that is it appears that they require a grammatical marker such as -na to be present if that marker disambiguates an otherwise ambiguous sentence.36 What I mean here by ‘grammatically possible space’ will
Martina Faller 283
37 For a possible explanation of why -ku is ungrammatical in these contexts, I refer to van de Kerke (1996). Briefly, van de Kerke analyses -ku as an operator on argument structure which coindexes an internal argument with the external argument (p. 159). Passive participles do not require an external argument and hence are incompatible with -ku. The causative -chi is incompatible with -ku under the assumption that causative formation is a lexical operation (in the Southern Quechua varieties only) which demotes the causee to an internal argument. 38 Philippe Schlenker (personal communication) points out that this condition might be too weak. In French, for example the verb sembler ‘seem’ cannot be reflexivised (i), but Condition B effects can nevertheless be observed (ii). (i) Jeani sei semble heureux. ‘Jean seems happy (to himself)’.
(ii)
Jeani luij/i semble heureux. ‘Jeani seems happy to himj (i 6¼ j)’. The difference between French ‘sembler’ and the issue just discussed for CQ is that ‘sembler’ appears to disallow reflexivity in any circumstance, whereas the CQ predicates allow reflexivity in principle. We might therefore want to limit Condition B to predicates that can be reflexive as well as nonreflexive. Let us introduce a feature [6refl] and assume that verbs like ‘sembler’ are lexically marked as [refl]. (iii) Condition B: a. A [refl] predicate is non-reflexive. b. If a [6refl] predicate is reflexive, it is reflexive marked, unless reflexive marking is ungrammatical for independent reasons.
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become clear in the following discussion of reciprocity in the absence of -ku. As mentioned in section 2, example (5), -na by itself can be interpreted reciprocally when it occurs preceding the causative suffix or when the verb is used as a passive participle. However, in the absence of -ku, the current formulation of Condition B would require the coarguments of the top-level plural verb to be non-identical as well, thus not permitting a reciprocal interpretation. In this context, it is relevant that -ku can in fact not occur before the causative suffix or in passive participles, that is the forms in (43) are ungrammatical (cf. van de Kerke 1996: 180).37 (43) a. hayt’a-ku-chi-n kick-REFL-CAUS-3 intended: ‘(s)he caused someone to kick her-/himself ’ b. hayt’a-ku-sqa kick-REFL-PRTC intended: ‘to be kicked by oneself ’ This suggests that -na can only convey reciprocity by itself when there are independent reasons preventing -ku from co-occurring with it. That is, we have to allow for identity of co-arguments just in case adding a reflexive marker is not possible for grammatical reasons, and I therefore propose the following reformulation of Condition B.38
284 The Ingredients of Reciprocity in Cuzco Quechua (44) Condition B: If a predicate is reflexive it is reflexive-marked, unless reflexive marking is ungrammatical for independent reasons.
5 CONCLUSION I have proposed an analysis of CQ reciprocal sentences which derives reciprocity from pluractionality and reflexivity, both overtly marked by verbal suffixes. Universal quantification over parts of the plural agent and the requirement that the arguments in the reciprocal subevents are distinct follow from assumptions independently made in the literature, namely, (i) plural predication and plural thematic roles (Sternefeld 1998; Landman 2000; Beck 2001) and (ii) a semantic formulation of Condition B (Reinhart & Reuland 1993). As should be clear from the comments I have made along the way, the main shortcoming of the particular analysis presented here for CQ is that it appears to overgenerate considerably. I say ‘appears’ because it is not yet entirely clear that those readings which are predicted to exist by the analysis but which I have not been able to confirm empirically are indeed impossible. Assuming that this is so, however, I hypothesize that the absence of these readings is due to constraints on language use. Thus, the fact that the marker -na is only rarely being used for expressing temporal pluractionality may be explained by appealing to the principle of maximizing informativeness: CQ has a dedicated morpheme, -paya, which expresses this notion and which therefore pre-empts the use of the less specific and less informative -na in most cases. Similarly, the fact that the reflexive marker -ku on its own cannot normally convey reciprocity may be explained this way. -na eliminates those readings available for -ku which only involve a single event, -na-ku is therefore more specific and informative than just -ku. An investigation of how exactly such pragmatic principles interact with the set of data discussed in this paper will be left for future research.
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With this revision of Condition B, -na by itself can give rise to a reciprocal interpretation just in case the addition of -ku is ungrammatical. In sum, the analysis predicts that some verb forms containing only -ku should be able to truthfully describe a reciprocal situation, in addition to purely reflexive situations. I hypothesize that this is impossible for most consultants because of a strong pragmatic requirement that a disambiguating marker, in this case -na, should be added whenever this is grammatically possible. In contrast, -na on its own can convey reciprocity, but only when the addition of the reflexive marker -ku would be impossible.
Martina Faller 285
Acknowledgements I am very grateful to my ever-patient consultants in and around Cuzco, Peru, Ine´s Callalli Villafuerte, Gloria Canal, Natalia Pumayalli Pumayalli and Edith Zevallos Apaza. I thank three anonymous reviewers and Philippe Schlenker for providing
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Other aspects of the semantics of reciprocity in CQ that the current paper has not touched on, but which are of interest for future investigation, are the question of how many truth-conditionally distinct readings can be identified for this language, whether or not the reciprocal construction gives rise to such scope ambiguities as discussed, for example by Dalrymple et al. (1998), and the different ways of encoding the reciprocal agents, that is either as a plural NP, example (3b), or as a subject NP together with a comitative NP, example (3c), which, as argued by Dimitriadis (2004) for other languages, may also lead to meaning differences. In addition to providing a formal analysis of reciprocity in CQ, the main contribution of the present paper is to cross-linguistic semantics, suggesting at least the following conclusions and hypotheses. First, reciprocity is indeed partly derivable from plurality more generally, as has been argued by Langendoen (1978), Sternefeld (1998) and Beck (2001) for English. In CQ, this involves not only nominal plurality but also verbal plurality. A plausible cross-linguistic hypothesis is that pluractionality may also play a role in the composition of reciprocity in other languages with verbal reciprocals. Second, we may hypothesize that the distinctness condition is also not encoded directly by reciprocal constructions in other languages but derivable from Condition B, in particular in languages which do not employ an element such as English ‘other’ which wears distinctness on its semantic sleeve. Third, while reciprocity involves the same semantic components crosslinguistically, languages can vary considerably in the way they compose this complex semantic concept. Some languages, for example Chichew ˆ a, employ a dedicated reciprocal marker, which does not in any obvious way express one or more of the ingredients of reciprocity, though in such languages it may also well be the case that universal quantification and distinctness derive from independent principles. Other languages employ markers which directly encode one of the reciprocal ingredients, for example reflexivity in CQ or the Romance languages. The compositional derivation of reciprocity is therefore a clear case for cross-linguistic semantic variation. An interesting research question for the future is to identify the possible semantic space of variation and its cross-linguistic morphosyntactic realizations.
286 The Ingredients of Reciprocity in Cuzco Quechua challenging comments on an earlier version of this paper which helped me to sharpen the analysis. Any remaining errors are mine. I also wish to thank the audiences at SULA 2005 and at the Workshop on Formal Semantics and Cross-linguistic Data held at ESSLLI 2005 for a stimulating discussion. Two preliminary versions of this paper have been published in the respective conference proceedings. The financial support of the British Academy for fieldwork during the summer of 2004 in Cuzco, Peru, and for travel to SULA 2005 is gratefully acknowledged. Some of the data were collected and confirmed during fieldwork in 2006 funded by a grant by the Faculty of Humanities, The University of Manchester. I also thank the Max Planck Institute for Psycholinguistics in Nijmegen for allowing me to use a set of video stimuli developed for eliciting reciprocal data within the joint project with the University of Melbourne, Reciprocals Across Languages.
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MARTINA FALLER School of Languages, Linguistics, and Cultures The University of Manchester Manchester M13 9PL United Kingdom e-mail: [email protected]
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First version received: 04.12.2006 Second version received: 28.02.2007 Accepted: 15.03.2007
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Journal of Semantics 24: 289–304 doi:10.1093/jos/ffm007 Advance Access publication July 2, 2007
Strengthening Conditional Presuppositions ROBERT VAN ROOIJ ILLC/University of Amsterdam
Abstract
1 INTRODUCTION The satisfaction theory of presupposition, as motivated by Karttunen (1974) and Stalnaker (1974) and implemented by Heim (1983) and others, is perhaps still the most popular theory of presuppositions on the market. Indeed, it has good selling points: the theory is simple and conceptually appealing. However, the theory has serious drawbacks as well: it is not always clear how to make it consistent with empirical facts. One of the most serious empirical problems is that it gives rise to presuppositions which seem too weak. In particular, it gives rise to the proviso problem: weak conditional presuppositions for conditional, conjunctive and disjunctive statements with a presupposition trigger occurring in the consequent, second conjunct or disjunct. Gazdar (1979) already argued convincingly that we infer more than just these weak presuppositions, and more recently, Geurts (1996) has given compelling arguments that simple repairs as suggested by Karttunen & Peters (1979) and others do not work. Partly on these grounds, Gazdar (1979), van der Sandt (1988, 1992) and Geurts (e.g. 1996) argue for alternative theories for which this proviso problem does not arise: Gazdar’s (1979) and van der Sandt’s (1988) theories that might be thought of as ‘Presupposition as default’-analyses and van der Sandt’s (1992) and Geurts’ (1996) so-called ‘Binding’ theory of presuppositions. However, in this paper I want to argue that theories that give rise The Author 2007. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
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In this paper it will be shown how conditional presuppositions can be strengthened to unconditional ones if we assume that the antecedent and consequent of a conditional presupposition are independent of one another. Our notion of independence is very weak, and based on Lewis’ (1988) notion of orthogonality of questions. It will be argued that our way of strengthening these presuppositions does not give rise to some wrong predictions Geurts (1996) argued other proposed strengthening accounts do.
290 Strengthening Conditional Presuppositions to weak conditional presuppositions1 are less inadequate than suggested by Gazdar, van der Sandt and Geurts because conditional presuppositions can be strengthened in a simple way after all, and this solution does not suffer from the problems discussed by Geurts. 2 THE STANDARD SATISFACTION ACCOUNT
[/v](r) ¼ {w 2 r j w(/) ¼ 1}, if [v](r) ¼ r, undefined otherwise, [:/](r) ¼ r [/](r) [/ ^ w](r) ¼ [w]([/](r)).
1 The standard satisfaction theory of presuppositions is not the only one to give rise to conditional presuppositions; the theory of Karttunen & Peters (1979) and a recent alternative due to Schlenker (2005) do so as well. My proposal can be used here too. 2 For generality, I will assume that all atomic sentences carry such a presupposition, but some presuppositions are empty, >. For readability, though, I make empty presuppositions invisible. 3 Let me immediately point out that I do not feel the resulting analysis of disjunctions is appropriate. For a more satisfying analysis, see van Rooij (2005).
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According to dynamic semantics (e.g. Heim 1982; Veltman 1996), the meaning of a sentence is its context change potential, where contexts are identified with information states that represent what is common ground in the conversation. The meaning of a sentence is modelled as an update function that takes a context in which it can be appropriately uttered as its argument and yields the updated context where the sentence is accepted as its value. Assuming that a sentence cannot be used appropriately in a context that does not entail, or satisfy, its triggered presupposition, this function will be partial. Although in dynamic semantics every full clause will be interpreted with respect to a context, it is crucial that not every embedded clause need be interpreted with respect to the context that figures as the context of interpretation of the embedding sentence. It is assumed, for instance, that the context of interpretation of the second conjunct of a conjunction or the consequent of an indicative conditional contains more information than the context with respect to which the whole sentence is interpreted. I limit myself here, and in the rest of this paper, to the propositional case, and represent a context, r, by a set of possible worlds. A possible world is a function from atomic formulae to the two classical truthvalues. I will represent an atomic sentence / with presupposition v as /v 2. We might treat disjunction and implication syncategorematically, by having ‘/ _ w’ and ‘//w’ stand for ‘:(:/ ^ :w)’ and ‘:(/ ^ :w)’, respectively.3 The update function is defined as follows (where r undefined ¼ undefined):
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3 CONDITIONAL PRESUPPOSITIONS The satisfaction theory of presuppositions is well known to be problematic, even for the simple fragment stated above. On the one hand, it is not completely clear how to account for presupposition accommodation; on the other hand, it seems to make wrong predictions. As far as the first problem is concerned, one might want to follow Beaver (1996) or Stalnaker (2002) and assume that hearers do not know what exactly is presupposed by the speaker. Accommodation is then an inference from a sentence to the set of contexts in which the sentence could be used appropriately. The second problem is perhaps more serious. It is well known that some examples involving presupposition triggers under a negation, in a disjunction, or in the antecedent of a conditional do not give rise to the predicted presuppositions.5 Although I believe that such examples can be accounted for on a more sophisticated version of the satisfaction theory (involving denial and modal subordination, cf. van Rooij 2005), I will ignore such examples in this paper. Instead, I will concentrate my attention only on a particular type of example involving conditional presuppositions. 4 5
w ^ /v, for instance, is predicted to be satisfied in any context if w~v: The well-known examples are the following:
(a) John doesn’t regret failing, because, in fact, he passed. (b) John either stopped or just started smoking. (Hausser 1976) (c) If I discover later that I have not told the truth, then I will confess it to everyone. (Karttunen 1971) I assume it is clear what counterintuitive predictions are made by the satisfaction theory.
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The appealing feature of this analysis of presuppositions within dynamic semantics is that it seems to solve the projection problem simply by means of rules of interpretation. Assuming that context r satisfies presupposition v iff [v](r) ¼ r, we can say that sentence / presupposes v iff for all contexts r, [/](r) is defined only if r satisfies v. As a result, it follows that sentences of the form :/v and /v ^ w presuppose v, but that w ^ /v need not do so.4 In fact, the theory makes exactly the same predictions as the more informal account of Karttunen (1974). Stalnaker (1974) explicitly rejects defining the notion of sentential presupposition in terms of the contexts in which the sentence is defined or used appropriately. He suggests that one can also say, for instance, that / presupposes v just in case from the utterance that / one can reasonably infer that the speaker presupposes v. It is this more general notion that will be crucial for our analysis.
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(1) a. If the bottle is empty, then [John]F drinks too. b. If the bottle is empty, there is someone other than John who drinks. c. There is someone other than John who drinks. (2) a. If I torture him, Boris regrets laughing at me. b. If I torture him, Boris has laughed at me. c. Boris has laughed at me. (3) a. If John has sprayed DDT, he knows that his stick insects are dead. b. If John has sprayed DDT, John’s stick insects are dead. c. John’s stick insects are dead. These observations are, no doubt, correct: we normally conclude the unconditional c-sentences from the conditional a-sentences. Gazdar (1979), van der Sandt (1988, 1992) and others have concluded from this that the satisfaction theory is wrong, because a conditional like (1a) should give rise to the unconditional presupposition (1c). Because their own theories do give rise to such unconditional presuppositions, the authors argue that they can handle conditional sentences better than proponents of the satisfaction theory can. But this reasoning is somewhat hasty, certainly if one follows Stalnaker’s suggestion 6
Like Geurts (1996), I will mostly concentrate on conditional sentences. Example (1a) was explicitly discussed by Karttunen and Peters (1979), (2a) is mentioned by Gazdar (1979), while (3a) is discussed by van der Sandt (1988). Gazdar (1979) finds the following conditional more convincing to make his point: ‘If gold is missing from Fort Knox, then the crooked accountants in the U.S. Treasury will be worried.’ Unfortunately, this example uses a definite description, and we seem to have independent reasons to assume that restrictors of quantifiers can take ‘wide scope’ (either via a two-dimensional actuality operator, or by means of two-sorted type theory) with respect to intensional operators (to account for ‘If every politician who is rich were poor instead, the world would be a better place’; with thanks to Philippe Schlenker). But on such a wide-scope analysis of quantifiers, Gazdar’s more favourable examples are compatible with the predictions made by the satisfaction theory. 7
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Note that the satisfaction theory predicts that sentences of the form //wv ; / ^ wv and :(/ ^ wv) can be asserted appropriately in context r, if the conditional //v is accepted in r, ½//vðrÞ ¼ r: But this means that such sentences are predicted to give rise to a conditional presupposition //v: Gazdar (1979) and van der Sandt (1988) claim that these predicted conditional presuppositions are too weak. They note that the satisfaction theory (like the theory of Karttunen and Peters [1979]) predicts that the following examples6 (1a), (2a) and (3a) give rise to the conditional presuppositions (1b), (2b) and (3b), respectively, while intuitively we conclude from these examples to the stronger unconditional sentences (1c), (2c), and (3c) (the presupposition triggers are in italics).7
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mentioned at the end of section 2. The fact that our intuitions are as expressed by Gazdar does by itself not mean that these examples show that a theory that states the minimal conditions under which a sentence is defined/appropriate makes the wrong predictions. If one does not identify the actual presupposition of an utterance with these minimal definedness conditions (neither Soames [1982] nor Beaver [1996] would do that), (1a)–(3a) only show that the satisfaction theory by itself is not enough to explain the inferences we actually make.8 8
van der Sandt (1992) and Geurts (1996) suggest that the appropriateness of the following dialogue is an extra argument for the unconditional presupposition:
The problem for the satisfaction theory here is that the antecedent entails the presupposition of the consequent. Consequently, the satisfaction theory predicts that (i-a) does not give rise to a (substantial) presupposition. Let me first note that some of my informants do not find the discourse (or the Dutch version of it) appropriate at all. But even if we agree with van der Sandt (1992) that the discourse (i-a)–(i-b) is appropriate, I do not think that this extra argument is very strong. First, as noticed by Geurts (1996), this anaphoric dependence can be accounted for by assuming that ‘the President of France’ was used referentially. Alternatively (cf. the previous footnote), we can assume that the descriptive content of the description is interpreted in the main context. Either way, this referent or descriptive material can be picked up by the (perhaps descriptive) pronoun in (i-b). But Geurts (1996) argues that sentences of the form //wv might imply v although / entails v even if the presupposition v is not induced by a definite descriptions. He argues that also (ii-a) has a reading in which it presupposes the presupposition of the consequent (ii-c), rather than the trivial conditional presupposition (ii-b): (ii) a. If all the boys failed the exam, then it wasn’t only Fred who did so. b. If all the boys failed the exam, Fred failed the exam. c. Fred failed the exam. I agree with Geurts that (ii-a) may be construed as implying that Fred failed the exam. But I wonder whether this implication is presuppositional in nature, and thus whether this is really problematic. Notice first that if it is commonly known that Fred is one of the boys, (ii-a) expresses a trivial proposition. This suggests that the conditional sentence is perhaps not used in the standard way. It is well known that conditionals can have a concessive reading: on this reading ‘If / then w’ means something like ‘Ok, I admit that /, but then you have to admit that w’. On such a concessive reading, the inference from (ii-a) to (ii-c) is completely unproblematic. Unfortunately, this type of inference is not only valid in concessive readings of conditionals. Another prominent reading of (ii-a) is one where it is intuitively an answer to the question ‘Did only Fred fail the exam?’. I guess most would claim that this question, in turn, presupposes that Fred failed the exam. But this means that if (ii-a) answers, and thus presupposes, the above question, the inference to (ii-c) can be explained. A reference to a presupposed question is also crucial, I believe, to account for Geurts’ following example: (iii) a. If all boys left at the same time, then the janitor will not have noticed that Fred left. b. Fred left. Also (iii-a) has a reading—perhaps the prominent one—where we infer (iii-b), a presupposition of the consequent. But then, I think this conditional is most natural with stress on at the same time, suggesting that it is an answer to a (perhaps implicit) question like ‘When did the boys leave?’. But such a question presupposes that the boys left, from which we can infer that Fred left (as well). To conclude, I am not convinced that examples of the form //wv where / entails v but where we still infer v show that the satisfaction theory is in trouble.
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(i) a. If all countries have presidents, then the president of France probably regards himself as their cultural leader. b. He is such a pompous person.
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(4) a. If all countries have presidents, then the president of France probably regards himself as their cultural leader. b. If all countries have presidents, then there is a president of France. c. There is a president of France. Perhaps better known are the following examples due to Beaver (1995) and Geurts (1996).9 Beaver claims that (5a) and (6a) suggest that the conditional sentences (5b) and (6b) are true, and not their unconditional counterparts. He would, no doubt, make the same claim with respect to (7a) and (7b): (5) a. If Jane takes a bath, Bill will be annoyed that there is no more hot water. b. If Jane takes a bath, there will be no more hot water. (6) a. It is unlikely that if Spaceman Spiff lands on Planet X, he’ll notice he weighs more than on earth. b. If Spaceman Spiff lands on Planet X, he’ll weighs more than on earth. (7) a. If Theo is a scuba diver, then he will bring his wet suit. b. If Theo is a scuba diver, he has a wet suit. These suggestions are then, of course, due to the claimed conditional presuppositions. Although perhaps not completely convinced by all 9 Examples (5a) and (6a) are due to Beaver, (7a) is mentioned in Geurts (1996) who attributes it to an anonymous reviewer.
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The main point I want to make in this paper is very weak: even if we accept the satisfaction theory and assume that conditionals like (1a), and other types of statements, give rise to conditional presuppositions, we can still account for the intuition that we infer the unconditional proposition (1c) without making the wrong predictions that Geurts (1996) has argued such a move would commit one to. A full defence of the satisfaction theory requires something more: an argument that establishes that conditional statements sometimes give rise to conditional presuppositions that (in some contexts) cannot be strengthened to unconditional ones. Soames (1982) and Beaver (1996) have provided some examples that—at least according to them—give rise to conditional presuppositions that are not, or need not be, strengthened to unconditional presuppositions. First, Soames (1982) argues that (4a) can be used appropriately in contexts that entail (4b) and that one does not automatically infer that (4c) is true.
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these above examples,10 I am sympathetic to the view Soames (1982) and Beaver (1995) argue for. However, in this paper I want to argue only for the weak claim that the strengthening of conditional presuppositions to unconditional ones is less problematic than Geurts (1996) has argued, not for the more controversial stronger claim that the examples discussed above in fact generate conditional presuppositions.11 4 STRENGTHENING DUE TO INDEPENDENCE
10 See the discussion of (5a) in the following section for why this doubt might depend on my (cultural) background. Merin (2003) contains a detailed discussion of some of these examples. 11 Thus, in this paper I am not arguing against theories, like van der Sandt’s (1992) DRT account of presuppositions, that do not predict conditional presuppositions.
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In this section I will propose that conditional presuppositions can be strengthened to unconditional ones if it is presupposed that the antecedent and consequent are independent of each other. On first thought, this might seem impossible. According to the standard notion of independence, / and w are independent of each other if (/ ^ w), (/ ^ :w), (:/ ^ w) and (:/ ^ :w) are all possible, that is each of )(/ ^ w), )(/ ^ :w), )(:/ ^ w) and )(:/ ^ :w) are true (where I say that )/ is true in r iff [/](r) 6¼ Ø). Unfortunately, however, if we assume that a speaker presupposes //w; he/she does not take it to be possible that / and :w are true at the same time, and thus that )(/ ^ :w) is false. This would contradict independence as standardly defined. In the following, we propose a weaker notion of independence of sentences/propositions based on Lewis’ (1988) notion of orthogonality of questions. It will be shown that for this weaker notion the above problem does not arise, and with this help conditional presuppositions can be strengthened to unconditional ones. David Lewis (1988) assumes that questions denote equivalence relations, QR (where the superscript R is mnemonic for Relation), meaning that two worlds are related, Æw, væ 2 QR, iff the same R complete answer is true in w and v. He defines QR 1 and Q2 to be orthogonal to one another iff for every two worlds w and u there is R R R a world v such that Æw; væ 2 QR 1 and Æv; uæ 2 Q2 : Take Q1 and Q2 to be the denotations of the questions whether John came and whether Mary came, respectively. If W ¼ {w, v, u, x}, ½½Came(j) ¼ {w, v} and ½½Came(m) ¼ {w, x}, the equivalence relations are QR 1 ¼ fÆw; wæ; ¼ fÆw; wæ; Æx; Æv; væ; Æw; væ; Æv; wæ; Æu; uæ; Æx; xæ; Æu; xæ; Æx; uæg and QR 2 xæ; Æw; xæ; Æx; wæ; Æv; væ; Æu; uæ; Æv; uæ; Æu; væg: Given an equivalence relation one can, of course, define a partition: QPi ¼ ffv 2 W j Æw; væ 2 R QR i g j w 2 Wg: Equivalence relation Q1 ; for example corresponds one
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From our definition of independence of / and w in context r, one can easily prove the following lemma:13 Lemma 4.3 (independence) Formulae / and w are independent of each other in context r iff the following four conditions are satisfied (where )/ means that [/](r) 6¼ Ø). (i) (ii) (iii) (iv)
If )/ and )w, then )(/ ^ w), if )/ and ):w, then )(/ ^ :w), if ):/ and )w, then )(:/ ^ w) and if ):/ and ):w, then )(:/ ^ :w).
Now assume that a conditional of the form ‘//w’ is interpreted as material implication and gives rise to the following appropriateness condition: the speaker knows (or believes) //w and all of /, :/, w and :w have to be compatible with the speaker’s belief and 12 This notion of independence is also discussed by Humberstone (2000). In terms of his terminology, my notion of independence (in r) requires that (with respect to r) w does not supervene on /, nor that / supervenes on w. 13 What is now derived as this lemma was proposed by Michael Franke (personal communication) to account for the strange way we analyse such so-called ‘biscuit conditionals’ as ‘If you are hungry, there are some biscuits in the refrigerator’. This proposal crucially influenced my analysis of strengthening conditional presuppositions presented in this paper.
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to one with the partition QP1 ¼ ffw; vg; fu; xgg ¼ f½½CameðjÞ; ½½:CameðjÞg; while QR 2 corresponds with {{w, x}, {u, v}}. Now we can define orthogonality in terms of partitions, which are somewhat easier to work with. Definition 4.1 (orthogonality of questions) Let QP1 and QP2 be two partitions, then we say that QP1 and QP2 are orthogonal with respect to each other iff "q1 2 QP1 : "q2 2 QP2 : q1 \ q2 6¼ Ø: Notice that if seen as partitions, the question whether John came is orthogonal to the question whether Mary came because both elements of QP1 are compatible with both elements of QP2 : More generally, one R P can easily prove that QR i and Qj are orthogonal to each other iff Qi P and Qj are. Let us now assume that the issue whether /, in context r, gives rise to the partition {/ \ r, :/ \ r}. Let us denote this question by ‘/?r’. Now we say that / and w are independent of each other in context r iff the questions /?r and w?r are orthogonal to each other.12 Definition 4.2 (independence of f and c in context s) Formulae / and w are independent of each other in context r iff /?r and w?r are orthogonal to each other.
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14 The assumption that conditionals are interpreted by material implication is not crucial. The same conclusion follows under a strict conditional account. 15 Of course, this method of strengthening conditional presuppositions can be applied to conditional presuppositions that are triggered by non-conditional statements as well. The standard satisfaction theory as stated in section 2 of this paper predicts that the presuppositions of / ^ wv, :(/ ^ wv) and :/ ^ wv are satisfied in any context that entails //v: By a similar reasoning, and on the same assumptions, these conditional presuppositions are also strengthened to v. For more complex sentences we have to make more independence assumptions. For a sentence of the form / ^ ðw/w#v Þ; for instance, to presuppose v, we have to assume that v is independent of / and w because it is satisfied in any context that entails ð/ ^ wÞ/v: Similarly, if we assume that embedded sentences of belief attributions should be interpreted with respect to what (it is presupposed that) the agent believes (as proposed by Stalnaker [1988] and Heim [1992]), a sentence of the form //Belða; wv Þ presupposes //Belða; vÞ; which can be strengthened to Bel(a, v). 16 The editor Philippe Schlenker rightly observed that in my reasoning here and in the rest of an earlier version of this paper I only make use of conditions (ii) and (iv) of Lemma 4.3. Perhaps this means that conditions (ii) and (iv) are all we need, but I find the (stronger) notion of independence I use more natural than just the combination of (ii) and (iv). Moreover, if the consequent or second conjunct of a complex sentence with / as antecedent or first conjunct gives rise to a negated presupposition :v (as in ‘After Ferdinant Magelhaes circumnavigated the earth, he knew that the earth isn’t flat’), we require the condition ‘If )/ and )v, then )(/ ^ v)’ anyway (even though it follows from condition (ii)).
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presupposition state (Gazdar’s [1979] clausal implicatures of indicative conditionals). Moreover, we will assume that the speaker’s assertion of / results in the update of the current presupposition state with /. Then it follows that ‘//w’ can never be appropriately asserted if the speaker presupposes that / and w are independent of each other. By assuming that after the assertion of //w the sentence is presupposed, it follows that in this new presupposition state it is not possible that / ^ :w. By Lemma 4.3 it follows that :)/ or :):w, meaning that the speaker’s assertion had the same effect as either his/her assertion of :/, or his/ her assertion of w. But the speaker could not have asserted any of those propositions because the appropriateness conditions of the use of the conditional require that the speaker did not believe either of them. From this we can conclude that the speaker does not presuppose that / and w are independent of each other.14 But now suppose that the assertion is //wv ; where v is the presupposition of w. The satisfaction theory then predicts the presupposition //v: Assume now that (i) the assertion is made appropriately with respect to the presupposition state r and (ii) that it is presupposed that / and v are independent of each other: that is / and v are independent of each other in presupposition state r. Then it follows that [/ ^ :v](r) ¼ Ø, that is )(/ ^ :v) is taken to be ‘false’ with respect to the presupposition state r. Given Lemma 4.3, this means that either :)/ or :):v must be the case. Given that ‘//wv ’ was made appropriately, it follows that )/ is the case, and thus that :):v [ hv holds. But this means that v is presupposed!15,16
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5 GEURTS’ EXAMPLES REVISITED We have seen above that our proposal of how to strengthen conditional presuppositions is highly reminiscent to especially the earlier suggestion of Karttuten & Peters (1979). Unfortunately, Geurts (1996) has raised problems with this approach which might carry over to our proposal as
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Perhaps one can see our above reasoning as a formalization of the account of Karttunen & Peters (1979) according to which a conditional presupposition can be strengthened in case the speaker has truthconditional grounds for presupposing the conditional presupposition: which means either presupposing :/ or presupposing v. On our analysis, the speaker is indeed predicted to have truth-conditional grounds for presupposing the conditional in case she presupposes antecedent and consequent to be independent of each other. Others (starting with Soames [1982], and worked out further by Beaver [1995]) suggested that a sentence of the form //wv can be satisfied in a context where just //v holds, or where the stronger v is already presupposed. If the latter context is more plausible than the former, the unconditional presupposition follows. This intuition can be accounted for in terms of independence as well. We either assume that / and v are independent, or not. If independence is more plausible, the unconditional presupposition follows. Consider now (5a), an example for which Beaver (1995) argued that strengthening should not go through. According to our reasoning this means that if we represent the sentence by //wv ; it has to be the case that / and v are not taken to be independent of each other. Because in the reasoning we would only make use of clause (ii) of Lemma 4.3, the following conditional would have to be false: ð)/ ^ ):vÞ/ )ð/ ^ :vÞ: Now take a presuppositional context in which )/ and ):v, that is it is possible that Jane takes a bath (at time t) and it is possible that there still is hot water (at time t + n). Depending on your (cultural) background it might be (for somebody from the Third World, or who is not used to geysers) natural to assume that in that same context it is not possible that Jane takes a bath (at time t) and that there still is hot water (at time t + n), that is :)(/ ^ :v). With such a (cultural) background, it is thus natural to assume that the independence assumption between / and v is not satisfied, and thus that the conditional presupposition (5b) cannot be strengthened to an unconditional one. In a country like the Netherlands, however, independence is perhaps more natural to assume, in which case we predict that (5a) gives rise to the unconditional presupposition.
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well. His first argument is that if strengthening requires independence, this might seem natural to assume for a conditional like (8a), but it seems less plausible for (8b), although here too the sentence gives rise to the unconditional presupposition that the problem was solved: (8) a. If the problem was difficult, then it wasn’t Morton who solved it. b. If the problem was easy, then it wasn’t Morton who solved it. c. If the problem was difficult/easy, then somebody solved the problem. d. Somebody solved the problem.
17 It is, in fact, controversial whether clefts give rise to such existential presuppositions. Kripke, for instance, suggests that perhaps clefts presuppose questions. But Geurts’ (1996) argument does not depend on this particular presupposition trigger, so we can just take over Geurts’ assumption for the sake of argument. 18 Merin (2003) suggested that although we might account for strengthening of conditional presuppositions to unconditional ones if we assume that antecedent and consequent of this presupposition are probabilistically independent, Geurts’ (1996) example (8b) shows that this reasoning is not good enough to account for our intuitions. Merin’s reasoning to strengthen conditional presuppositions goes as follows: We first have to assume that presupposition states should be modelled by probability functions. Now take an indicative conditional, //w; whose consequent presupposes v. This means that according to the satisfaction theory, the conditional as a whole presupposes //v: This means that the probability distribution P that models what is presupposed is such that Pð//vÞ ¼ 1: Let us assume that it is commonly assumed that v is probabilistically independent of /, that is P(vj/) ¼ P(v). Combining Pð//vÞ ¼ 1 and P(vj/) ¼ P(v), we would be able to conclude that P(v) ¼ 1, if the probability of the conditional presupposition //v; Pð//vÞ; is the same as the conditional probability of v given /, P(vj/). Although this equivalence does not hold in general, it holds in extreme cases: Pð//wÞ ¼ 1 iff P(wj/) ¼ 1, which is enough for our purposes. The notion of independence I use is not of the form P(vj/) ¼ P(v), but rather a set of conditions of the form ‘If P(/) > 0 and P(v) < 1, then P(vj/) < 1’, which is much weaker.
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To see whether this argument is problematic for us, let us assume with Geurts (1996) that clefts give rise to existential presuppositions.17 Then it is easy to see that Geurts’ objection to strengthening analyses based on independence is valid for strong notions of independence. In probability theory, for instance, v is said to be independent of / if the probability of v does not change if one learns that / is the case: P(vj/) ¼ P(v).18 This notion of independence is very strong: if learning / has any influence on the likelihood of v—however small—v and / are not counted as independent anymore. The notion of independence used here, however, is much weaker, and thus, the inference to the unconditional proposition much more robust. It only requires v and :v to be possible, whether or not / is true. For the inference from (8b) to (8d) to go through, this means that (ignoring the trivial case) it only has to be compatible with what is presupposed that somebody solved the problem, even though the problem was not easy. I think we can reasonably expect (8d) to be independent in this weak
300 Strengthening Conditional Presuppositions sense of the antecedent of (8b) and that is all we need for the inference to the unconditional proposition to go through. Geurts’ second objection to strengthening accounts is that if a speaker asserts a conditional, //wv ; he/she can take the antecedent of the conditional to be false. In that case the unconditional presupposition v is not predicted, against intuition: (9) If the problem was difficult, then it wasn’t Morton who solved it. But as a matter of fact the problem wasn’t difficult at all.
In this case [/](r) ¼ Ø, that is :)/, and so it seems that we cannot conclude hv anymore by independence. However, in this case we have to analyse the conditional sentence as a counterfactual, which means that we have to take worlds into account where the problem was, in fact, difficult. So, / is compatible with the context in which the antecedent of the counterfactual is evaluated. This context is now something like r [ r/ ;the context which is just like r except that acceptance of :/ is given up. In the theory of belief revision (Ga¨rdenfors 1988), r [ r/ is called the contraction of r with :/, and defined in terms of the revision of r with /, r/ :19 Obviously, for the conditional to be true, there can be no world in this context r [ r/ in 19
The easiest way to think of this revision, in turn, is to assume a context-dependent ordering
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What is wrong with this argument is that Geurts does not take the distinction between presupposition and assertion, or belief, seriously. The second sentence in (9) shows that the speaker believes that the problem was not difficult. Because what is presupposed is that which is commonly believed, this means that it cannot be presupposed that the problem was difficult. But it does not follow from this that it is presupposed that the problem was not difficult. In fact, for the second sentence to be appropriate, it must be the case that the problem being difficult must be compatible with what is presupposed, that is [/](r) 6¼ Ø, and this is all that is needed to guarantee that on the assumption of independence (9) gives rise to the unconditional presupposition that somebody solved the problem. But, or so Geurts could argue, we can change (9) into a counterfactual statement so as to make clear that the speaker actually presupposed that the problem was not difficult: (10) If the problem had been difficult, then it wouldn’t have been Morton who solved it. But as we all know, the problem wasn’t difficult at all.
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which / and :v are both true (on a strict conditional account).20 Assuming now that with respect to this context / and v are independent of each other, it means that v must be true in all worlds of this context via our familiar reasoning. But if v is true in all worlds in r [ r/ ; it obviously has to be true in all worlds in r, and it thus will be presupposed! Geurts’ third objection is closely related with his second objection. The objection is that whereas standard conversational implicatures can be cancelled, (11b), the unconditional presupposition cannot, (11c): If there are piranhas in the Rhine, then Theo’s wife should know about it. b. But of course, there are no piranhas in the Rhine. c. ? But of course, Theo isn’t married.
(11) a.
20 On a Lewis–Stalnaker account, the condition is somewhat different. Suppose that we interpret all conditionals in terms of similarity relations and that we represent such conditionals by / h/w: We can then assume that if w presupposes v, / h/w presupposes / h/v: Because / h/v is neither stronger nor weaker than v, Geurts (1996) argues that on this assumption the proviso problem becomes even worse: the inference to v cannot be due to some type of strengthening. Perhaps not, but the inference would still be the same. Suppose that <sw is the given Lewis–Stalnaker similarity relation between worlds, where s represents the accessible worlds potentially relevant for the interpretation of counterfactuals (what Lewis describes as the restricted field of the ordering <w). Let r denote the set of worlds consistent with what is presupposed in w, assuming that w 2 r. Then we can define the following similarity relation between worlds: u
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But again, this problem is due to the fact that Geurts does not make a distinction between what somebody presupposes and what somebody believes. What (11a)–(11b) illustrates is that somebody can assert a conditional sentence without believing that the antecedent is possible. This does not mean that one can assert a conditional appropriately in the indicative mood if the antecedent is incompatible with what is presupposed by the speaker and his/her conversational partners. Thus, (11b) does not cancel the appropriateness condition associated with (11a) with respect to the presupposition state at all. But this means that the ‘contrast’ between the appropriateness of (11b) and the
302 Strengthening Conditional Presuppositions inappropriateness of (11c) does not show what it is supposed to show. In fact, modulo independence (which is uncontroversial here), (11a) presupposes that Theo is married, which is inconsistent with (11c). Geurts’ fourth, and final, problem involves knowledge attributions: (12) Walter knows that if the problem was difficult, then somebody solved it.
21 This reasoning already explains why in contrast to (3a), the conditional (i) cannot give rise to the inference that John’s stick insects are dead (assuming with Karttunen and Peters [1979]) that managed has no truth-conditional impact, that is that ‘John managed to sit through a Chinese opera’ is true iff John sat through a Chinese opera).
(3a) If John has sprayed DDT, he knows that his stick insects are dead. (i) If John has sprayed DDT, he has managed to kill his stick insects. Thus, we can explain the falsity of van der Sandt’s (1988: 115) claim that if we can strengthen the conditional presupposition of (3-a) to the unconditional one via any Gricean reasoning, we are forced to accept that also (i) must suggest that John’s stick insects are dead.
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Everybody agrees that this sentence gives rise to a conditional presupposition that cannot be strengthened to an unconditional one. Geurts (1996) wonders why that could not be done via the same procedure Karttunen & Peters (1979) propose to strengthen other conditional presuppositions. We have seen in section 4 that the conditional ‘If the problem was difficult, then somebody solved it’, represented by //w; cannot be asserted appropriately, if the speaker presupposes that the antecedent and consequent are independent of each other. It follows that somebody who would assert a conditional sentence cannot presuppose that the antecedent and consequent are independent of each other (or presupposes that they are not independent of each other).21 Now we might argue similarly for Walter. If somebody truly makes the knowledge attribution (12), it is natural to assume that this speaker presupposes that it is not the case that Walter knows whether the embedded conditional is true for purely truth-conditional reasons. For otherwise the speaker would not have used the conditional embedded sentence. Thus, the speaker presupposes that Walter does not know that / and w are independent of each other, and he/she presupposes that Walter’s knowledge state is compatible with all of / ^ w, :/ ^ w and :/ ^ :w. Now, why would a speaker presuppose that Walter does not know (or knows that it is not the case) that / and w are independent of each other? Most naturally, because the speaker himself/herself does not presuppose that / and w are independent of each other (or presupposes that they are not independent of each other). To see why this is most natural, let us say that v denotes the proposition that / and w are
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independent of each other.22 Moreover, let us say that hv represents the proposition that the speaker presupposes v, and that K(w, v) represents the proposition that Walter knows v. A (most) natural default rule has it that if the speaker presupposes v, she also takes it to be compatible with what is presupposed (for the sake of conversation) that agents who are not participants of the discourse (including Walter) know that v: hv , )K(w, v). By modus tollens23 it follows that h:K(w, v) , :hv, which is exactly the assumption we used.24 But if the speaker does not presuppose / and w to be independent of each other, :hv, the strengthening from //w to w cannot be made and the conditional presupposition cannot be strengthened to an unconditional one.
In this paper I proposed a new condition under which two propositions are independent of each other and have shown how this notion can be used to strengthen conditional presuppositions to unconditional ones. I have argued that our method of strengthening these presuppositions does not suffer from the problems Geurts (1996) argued other accounts are. In fact, our reasoning also suggests under which circumstances conditional presuppositions //v are natural: in case it is presupposed that / and v are dependent on one another. Acknowledgements This paper was presented at the workshop in honour of Rob van der Sandt’s 60th birthday in Nijmegen in May 2006. I thank the workshop participants for discussion, and the organizers (especially Bart Geurts) for letting me give this talk. I would like to thank the anonymous reviewers and Philippe Schlenker for comments on an earlier version of this paper. I thank Tikitu de Jager for correcting my English.
ROBERT VAN ROOIJ ILLC/University of Amsterdam The Netherlands e-mail: [email protected] 22 To make sense of this, we have to assume that what is presupposed is a fact about a world (in a modal model). Although we have not assumed this in our simple framework stated in section 2, it is unproblematic to do so if we think of presuppositions in terms of accessibility relations (cf. Stalnaker [2002] and van Rooij [2005]). 23 Though valid (for simple examples) in Veltman’s (1996) system, it is, to be honest, not valid in most systems of non-monotonic reasoning. 24 Of course, if it is presupposed that Walter knows that / and w are not independent, hK(w, :v), the reasoning to the speaker’s belief or presupposition state follows already from what it means to know a proposition. If we do not make this assumption, however, we need the argument stated in the main text.
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6 CONCLUSION
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