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JOURNAL OF SEMANTICS Vol111me 14 Number
2
CONTENTS DIETER WuNDERLICH
Argument Extension by Lexical Adjunction E. OjEDA A Semantics for the Counting Numerals of Latin
95
ALMERINDO
143
ANDREA BoNOM1
The Progressive and the Structure of Events
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173
I
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Grammar and Meaning Essays in Honour of Sir John Lyons
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Lin guistic Semantics
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Linguistic Semantics: An Introduction is the successor to Sir John Lyons's important study
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Proceedings of the Thirteenth West Coast Conference on Formal Linguistics Edited By Susanne Preuss, Raul Aranovich, William Byrne and Martha Senturia
This volume presents the proceedings of the thirteenth West Coast Conference on Formal Linguistics at the University of California, San Diego. Two features have been added to this volume. The papers are grouped by subfields into rhe areas of phonology/morphology, syntax , and semantics, and two indexes (an author index and a subject index) have been added to increase the usefulness of the volume. £20.95
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1881526763
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Words and the Grammar of Context Paul Kay
The more or less currently accepted views of semantic compositionality, Gricean effects and indexicality are necessary, but not sufficient, to bridge the gap between the conventional significations of linguistic objects and the interpretations that sentences receive in contexts. Kay's radical contribution is his claim that the kind of theory of'indexicality' required by the facts must be able to avail itself of the recursive (in Chomsky's sense 'creative') aspect of language. £40.00 £15.95
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This new edition of The Study ofLanguage incorporates many changes that reflect developments in language study over the past decade. There is an entirely new chapter on pragmatics, with an expansion of the chapter on semantics. There are additional sections on speech recognition systems, sign languages, women's and men's language, input in language learning, and several other topics. The presentation retains the clear and lively style which made the first edition a hugely popular introduction to the study of language. £35.00 £12.95
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14= 95-142
Argument Extension by Lexical Adjunction DIETER WUNDERLICH
Heinrich Heine Universitiit, Diisseldorf Abstract' This paper proposes a unified account of the semantic and syntactic properties of certain particle and prefix verbs in German as well as of constructions involving resultative and
contrast to the traditional view, according to which the adjunct accommodates to the head. Section 1 motivates the theoretical possibility of the operation ARG within Categorial
Grammar, while section 2 briefly introduces the framework of Lexical Decomposition Grammar, in which the following analyses are situated. Section 3 shows that the operation ARG allows a satisfying analysis of prefixes and particles that introduce new arguments to the verb. This analysis will then be extended to resultative and depictive secondary predicates in sections 4 and s. and will be compared to some of the syntactically based alternatives that have been proposed in the literature.
I MODIFI CATION Some German prefixes and particles introduce arguments that are not selected by the base verb. For example, both the prefix ver- and the particle an turn intransitive verbs into transitive ones, that is, they introduce nonselected arguments, as is shown in (Ia-b)? Preftxes and particles are never heads of the complex verb, but they contribute an additional predicate to the verb in these instances.3 {I) a. Sie jubelte. 'She rejoiced' b. Sie schrie. 'She shouted'
=}
=}
Sie verjubelte die letzten Groschen. she away-rejoiced the last pennies 'She lavished her last pennies' Sie schrie den Kellner an. 'She shouted at the barman'
Secondary predicates in the resultative construction may likewise introduce nonselected arguments, as is shown in (2a). Depictive predicates, in contrast, occur only with arguments that are already selected by the base verb, as is shown in (2b). (2) a. Sie tanzte. 'She danced'
=?
Sie tanzte die Schuhe durch. 'She danced her shoes threadbare'
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depictive predicates. I will argue that the secondary predicates, considered to be adjuncts, are lexically integrated into the verb by an operation called Argument Extension (ARG), a general option of the modification rule which states that the head accommodates to the adjunct, in
96 Argument Extension by Lexical Adjunction
b. Sie aB den Fisch. 'She ate the fish'
=}
Sie aB den Fisch roh. 'She ate the fish raw'
All these constructions have been analyzed in terrns of a Small Clause (SC) by Hoekstra (rg88). The SCs that may be postulated here are summarized in (3), with the SC predicate being morphologically either bound or free. (3) a. b. c. d.
[die letzten Groschen ver-] [den Kellner an] [die Schuhe durch] [den Fisch roh]
'the 'the 'the 'the
last pennies away' barman at' shoes threadbare' fish raw'
(4) a. Die letzten Groschen wurden ve�ubelt. b. Der Kellner wurde angeschrien. c. Die Schuhe wurden durch getanzt. d. Der Fisch wurde roh gegessen.
'The last pennies were lavished' 'The barman was shouted at' 'The shoes were danced threadbare' 'The fish was eaten raw'
The SCs in (3a-c) add both a predicate and an argument to the base verb, while the SC in (3d) only adds a (depictive) predicate, with its argument being identified with one of the arguments of the base verb. The SC as a whole is neither the head of the resulting complex verb nor an argument of the base verb, and the same is true for the SC predicate taken in isolation. This suggests that the SC is an adjunct of the verb. The lexical analysis I will propose is a semantically based alternative to the SC analysis.4 I will assume that the verb, as the lexical head, may be extended by an additional predicate, which I will call 'lexical adjunct'. Those arguments of the adjunct that are not identified with arguments of the base verb are passed over to the resulting complex verb. Head extension is also at issue in (s), even though the adverbial adjuncts shown there do not add any arguments to the verb. In terms of the analysis proposed here, adverbial adjuncts differ from secondary predicates only in that they may be marked explicitly as functors on verbs, for instance, by the suffix -ly in English.
(s) a. Sie jubelte die ganze Nacht. b. Sie schrie eindringlich. c. Sie tanzte unaufhorlich. d. Sie aB japanisch.
'She 'She 'She 'She
rejoiced the whole night' shouted insistently' danced incessantly' ate in the Japanese style'
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In each case, the SC nominal (whether selected or not) is the direct object of the resulting verb. This is shown, for instance, by the fact that it can be subject in the passive.
Dieter Wunderlich 97
(6) a. Die Bar war laut. b. Da gab es eine laute Bar. c. Sie sang laut.
'The bar was noisy' type (e,t) 'There was a noisy bar' type ((e,t),(e,t)) 'She sang loudly' type ((e,(s,t)),(e,(s,t)))
A number of variants of a modification rule have been proposed to by-pass these problems (0-Identification: Higginbotham 1985, 0-role absorption: Bierwisch 1987: 98, functional unification: Wunderlich 1987). The common idea behind these proposals is that the modifier and the expression it modifies share one argument. Since the mechanism of argument sharing does not belong to the rules of Categorial Grammar {CG), it has to be introduced as an additional rule:6 {7) Argument A/B + >.x f(x) Head
Sharing: A/B >.y g{y) Adjunct
�
A/B >.x {f(x)
&
g(x)}
Argument Sharing itself is symmetrical because none of the two functors is designated semantically as the head. The distinction between head and modifier must be licensed by independent means, namely by the morphological or syntactic configuration in which the expressions occur. Argument Sharing may be regarded as a complex operation that consists of two steps: First, one of the involved elements adjusts its logical type, so that it becomes a functor with respect to the other element, and then
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Intuitively, attributes are NP adjuncts that occupy the position [NP_ NP] with NP as the head, whereas adverbs of the type illustrated in (s) are VP adjuncts that occupy the position [VP_ VP] with some VP level as the head. In contrast, lexical adjuncts occupy a position with Vas the head, either in the syntax (as resultative adjectives do) or in the morphology (as prefixes and particles do). As will be shown in sections 4 and s below, certain problems arise when lexical adjuncts are not adjacent to the verb, therefore the notion of lexical adjunct will be redefined in semantic terms. In the Montagovian and Cresswellian tradition, adjuncts are regarded as functors on the expressions they modify. This conception is confronted with two problems: first, modifiers, being functors, are the nonheads in the adjunct construction, even though all other functors are heads; modification thus destroys the homomorphism between semantic and syntactic struc tures. Second, many lexical items, such as adjectives that may be used predicatively, attributively and adverbially, must be given more than one lexical entry in terms of logical types.5 This leads to lexical inflation, which is undesired for general reasons. For instance, laut 'loud, noisy' belongs to the type (e,t), to the type ((e,t),(e,t)) and to the type ((e,(s,t)),(e,(s,t))), as is shown in (6a-c).
98 Argument Extension by Lexical Adjunction
Functional Application applies. The first step may be performed on either the adjunct or the head: either the category of the adjunct expression is extended; the adjunct then takes the head expression as its argument (an operation that leads to the Montagovian type of modifiers). Or the category of the head expression is extended; the head then takes an additional
(8)
X
a.
�
X
Head
b.
X
�
y
�X/X; MOD
Adjunct
�
X
XJY;ARG Head
y
Adjunct
(9) a. Modifier Extension (MODf ---* (A/B)/(A/B) A/B .Ag Ax {g(x) & f(x)} Ax f(x) b. Argument Extension (ARG) A/B ---* (A/B)/(A/B) .Ag Ax {f(x) & g(x)} Ax f(x) Although the results in (9a, b) are logically equivalent, they differ in the order of f(x) and g(x): the translation of the adjunct precedes that of the head in (9a), whereas it follows the translation of the head in (9b). In the framework I am going to discuss in the next section, the formulas with lambda abstractors are considered to be representations of Semantic Form (SF). Under the assumption that all SF structures are binary, coordination must be asymmetric. I adopt the convention that SFs are right-branching, corresponding to the syntactic structure of coordination. Under the perspective of what they imply conceptionally and of how they are related to syntactic structures, [g(x) [& f (x)]] and [f(x) [& g(x)]] represent different things.
Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
argument which is to be saturated by the adjunct expression. I will call the former operation Modifier Extension (MOD) and the latter Argument Extension (ARG). Semantically, these operations are equivalent, and they both allow Argument Sharing. However, MOD and ARG make different predictions about argument linking for adjuncts that have more than one argument slot (see section 3). Although we are used to regarding the head noun as a possible argument of the attribute rather than the other way around, there is in fact no principled reason for representing the relation between modifier and modified expression in only one way. For instance, the relation between a verbal head and a PP notoriously shifts between modifier and argument (Dowty 1994). MOD and ARG are schematically illustrated in ( 8) and defined more precisely in (9); f stands for the head predicate and g for the modifier predicate. I consider intersective readings only.
Dieter Wunderlich 99
The effects of MOD and ARG are shown with a rather simple example in (w). In more complex cases, the expression to be taken as argument by the respective functor has more than one argument slot; in this case, the additional arguments are inherited by the resulting expression through Functional Composition. (w) a.
red AY RED(y) � Hl.y{f(y)
&�
house
AX HOUSE(x)
AY {HOUSE(y) & RED(y)}; FA
house
red AY RED(y)
�
AX HOUSE(x) Ag Ax{HOUSE(x) & g(x)}; ARG
Ax{HOUSE(x) & RED(x)}; FA
The operation MOD is instantiated if an expression is morphologically marked for its modifying function. In German, for instance, the attributive use of adjectives is marked for agreement with the head noun, while the adverbial use is unmarked. In English, in contrast, the adverbial use is marked by the suffix -ly and the attributive use is unmarked. Some Western
Oceanic languages mark attributive adjectives like possessors (Ross 1997). However, if the noun that takes an attribute is marked (as in the Ezafe construction of Persian, Ortmann in prep.), the operation ARG is instantiated. If the modifying function is morphologically unmarked, either MOD or ARG could apply. They should then be understood as context-sensitive operations that apply only if the local combination of two predicates is licensed morphologically or syntactically but cannot be given a straight forward interpretation otherwise. Considering MOD as a context-sensitive operation allows us to avoid lexical inflation with adjectives of different logical types but otherwise identical meaning. Likewise, considering ARG as context-sensitive allows us to avoid lexical inflation with head categories. In section J, I will use the operation ARG to derive representations for the prefix and particle verbs shown in ( r ), and will show that ARG is the only operation that yields the correct argument structure for these verbs. I will then extend this analysis to resultative and depictive secondary predicates in sections 4 and s, and will show that it provides us with a unified account of all the phenomena in question. This makes it preferable over syntactically based alternatives. But let me first introduce the theoretical background on which this analysis is based.
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b.
roo Argument Extension by Lexical Adjunction
2 LEX IC A L DEC OMPOSIT ION GR A MMAR The analyses in this paper are situated in the framework of Lexical Decomposition Grammar (LDG), a theory that has been developed in a number of writings (Gamerschlag 1996, Joppen & Wunderlich 1995, Kaufmann 1995a, b, Stiebels 1996, Wunderlich 1992, 1996b, 1997). LDG tries to account for argument structure and argument structure alternations by assuming the following levels of representation:
Following proposals by Bierwisch ( 1983) and Bierwisch & Lang ( 1987), SF is assumed to be a partial semantic representation belonging to the computa tional system of grammar, while the more elaborated conceptual repre sentations of meaning belong to the general system of reasoning that may draw on any kind of mental operations. Lexical decomposition in terms of SF need not go beyond a certain degree of granularity. SF representations combine general template-forming predicates like BECOME, Pass and we, which determine the grammatical properties common to all members of a verb class, with idiosyncratic atomic predicates, which distinguish items within subclasses of the vocabulary. Structures of this kind, being part of grammar, must be finite and analytical, and they cannot be overridden by contingent knowledge. In contrast, a conceptual analysis of words, or the atomic predicates of which they are constituted, can be infinite and subject to any kind of contingent knowledge. This division of labour between SF and conceptual representations avoids the problem of infinite decomposi tion while at the same time providing sufficiently detailed analyses of meanmg. The notion of SF assumed here shares certain features with Logical Form (LF) and certain features with the VP shell structures of Larson ( 1988a, b) and the Cascade structures of Pesetsky (1995). Both LF and SF constitute interface levels that relate syntactic structures to a more articulated level of meaning. While LF was originally considered a level of syntax in which the scopal properties of unstructured lexical items are determined and now mainly serves as a level of feature checking, SF is considered a level of
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The Semantic Form (SF) of a lexical item captures its grammatically relevant properties by a decompositional structure formulated in Categorial Grammar with logical types. Clausal Phrase Structure (PS) is a syntactic representation that is projected from simple or complex lexical heads. Theta Structure (TS) is the interface of SF and PS in that it encodes the argument hierarchy in terms of abstract case features and thus allows matching with morphological case, agreement, and complement position.
Dieter Wunderlich 101
semantics that, in contrast to LF, takes into account the internal structure of lexical items. SF structures are right-branching in a way that resembles the structure of VP shells, their branching property being motivated by binding facts between the arguments of a verb. That is, SF differs from LF and VP shells not in terms of its structural properties but in its representational design: While LF and VP shells are represented in terms of syntactic categories, SF is represented in terms of logical types. All lexical items in the major categories are regarded as (possibly complex) predicates that belong to a particular logical type. This type determines both the number and the type of the predicate's arguments. For
(I I)
a. in den Keller treten/ gehen 'step/ go into the cellar' b. den Keller betreten 'enter the cellar'
The motion verbs treten and gehen in ( I I a) are analysed as verbs that (optionally) take a directional PP argument, while betreten in ( I I b) is analyzed as a verb that has incorporated the directional preposition. Both types of verbs have two constituents in SF, and this complex refers to just a single situation. This is reflected by the way in which s is separated from the 'propositional body' in ( 12). Even if each constituent might be related to some subsituation, this possibility is not reflected in SF representations, and neither do they reflect the way in which the subsituations may combine. That is, the existence of subsituations is left to conceptual inferences. ( 12b) can be paraphrased as follows: 's is a complex situation constituted by x's going and the transition to the state in which x is located in the interior of y.' Each predicate is assigned a logical type and, possibly, some ontological (conceptually available) sort, and its meaning can be grasped more finely by means of truth conditions. This is illustrated in
( I 3).
( 12) SF in conventional notation: {Go(x) & P(x)}(s) a. gehen 'go': b. betreten 'enter': {Go(x) & BECOME wc(x,rNT(y) )}(s)
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instance, the predicate POSS, expressing the possessive relation between two individual entities, is of type (e,(e,t)), with e for the type of individual terms and t for the type of truth-valued expressions. A special kind of entities are the situations to which verbs refer (called 'referential arguments'), where 'situation' covers all kinds of eventualities (processes, states, events). I will use the symbol 's' for both the situation variable and this particular sort of entities. For instance, the predicate SLEEP, expressed by the verb sleep, is of type (e,(s,t)) (a relation between an individual being and a process). The examples in ( I I ) indicate how SF representations are formed and mapped into syntax. Note that the VPs in ( I I ) are somewhat related to each other.8
102 Argument Extension by Lexical Adjunction
Since SF is assumed to have a binary structure, and all coordination structures to be right-branching, the ranking of arguments is uniquely determined. This ranking is most transparent in the Polish notation, according to which the predicate comes first, followed by the arguments in rising order. However, nothing hinges upon this choice, and in the remainder of this paper I will use the conventional notation.
(r4) SF in Polish notation: a. {& (P(x) )(Go(x) )}(s)
argument hierarchy:9
b. {& (BECOME(wc(INT(y) )(x) ))(Go(x) )}(s)
p <X< S
y <X< S
Theta Structure, the interface of SF and syntactic structure, is constituted by the sequence of A-abstractors formed from SF representations by abstract ing all and only those arguments that have to be mapped into syntax. Implicit arguments are ignored. A-categorial syntax itself does not restrict the order of abstraction, but for the particular use I want to make of it the following principle is observed (see Bierwisch 1989).
( rs) Hierarchy Principle. The order of Functional Application (FA) should mirror the order of arguments in SF. The Hierarchy Principle is motivated by the fact that the default word order reflects the ranking of arguments in SF: The lower the argument in SF, the closer it is to the verb in the clause. By observing this principle, the representations in ( 1 6) are yielded:
( r6) TS added to SF: a. gehen 'go': b. betreten 'enter':
AP Ax .As {Go(x) & P(x)}(s) AY Ax As {Go(x) & BECOME wc(x,rNT(y) )}(s)
The individual A-abstractors are the theta roles that serve as interface objects in this theory: They may be associated with categorial features, case
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(r3) GO is an active motion (process) predicate of type (e,(s,t)) P is a predicate variable of type (e,(s,t)) & is a functor of type (a,(a,a)) BECOME is a primitive transition predicate of type (t,(s,t)) BECOME(p)(s) is true iff there is, on the basis of a certain interval partition of s, a final subinterval s* C s, so that p is true in s*, while -.p is true in all preceding subintervals of s. [See Dowty 1979 for a more precise definition, and Naumann 1996 for a reconstruction in terms of Dynamic Semantics] wc is a primitive stative predicate of type (e,(e,t)) INT is a primitive functor of type (e,e) wc(x,INT(y) ) is true iff the place of x is contained in the interior of y.
Dieter Wunderlich 103
features and agreement features, as well as with additional sortal informa tion that restricts the possible semantic values of the variables (Wunderlich 1994). (17) illustrates this with just two kinds of features: [+dir] requires that the predicative argument role is saturated by a directional PP, and the abstract case feature [+hr] ('there is a higher role') indicates that this role is the direct object to be saturated by an accusative DP. [+dir] correlates with the fact that GO is a motion predicate, and [+hr] indicates that there is a higher individual role than Ay, namely Ax. ( 17)
annotated by syntactic features: a. gehen 'go': AP Ax As {Go(x) & P(x)}(s) +dir b. betreten 'enter': Ay Ax As {Go(x) & BECOME wc(x,1NT(y) )}(s) +hr
TS
(18)
a.
b.
VP
�
pp
[+dir]
v
VP
��
DP
[ace]
V
PP, DP, COMPP, etc. are syntactic categories that underlie the principles of syntax, whereas the elements in SF belong to logical types that underlie the principles of semantics. Categories in the sense of Categorial Grammar only reflect the argument structure of items characterized by SF, they do not reflect the internal composition of predicates in SF. Thus, gehen in ( 17a) simply belongs to a category ( (A/B)/C)/D, where D translates into a property expression of a certain sort, and B and C translate into individual expressions of different sorts. Arguments that are linked to subject, direct object or indirect object are the structural arguments of a verb. That is, they are subject to structural linking, which makes use of the abstract case features [± hr] 'there is a/no higher role' and [± lr] 'there is a/no lower role': Subjects are [- hr], direct objects are [+ hr, -lr], and indirect objects are [+ hr, + lr] (Kiparsky 1992, Wunderlich 1992, 1997,]oppen & Wunderlich 1995, and below). Structural linking does not apply to the referential arguments of verbs, arguments that are lexically marked as oblique (these must be realized by a semantic case or a particular preposition), arguments that are suppressed by a morphological operation such as passive, and (depending on the type of language) predicative and propositional arguments. There is a further VP,
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These entries license (or project) the VPs shown in (18). Both subject and referential argument come into play only in fmite verbs and dependent constructions, which is in line with general assumptions about the role of functional categories such as 1NFL and COMP.
104 Argument Extension by Lexical Adjunction
constraint on structural arguments, which will be discussed in the next section. The information contained in SFs like {I2) may also be represented by tree diagrams, whose nodes refer to logical types, as is shown in (I9). As any other semantic representations, SFs have a certain 'syntax' and are interpreted by models structured in conceptual-ontological terms. (I9) Tree diagrams a.
t
gehen 'go':
�s
<s,t>
------ ------
<<s,t><s,t>>
<s,t>
<s,t;.
&
��
p b. betreten 'enter':
X
t
�
s
<s,t>
----<<s,t><s,t>> � � <s,t>
GO
X
&
<s,t>
�
BECOME
t
�X
<e,t>
�e �y INT
LOC
Tree diagrams like these motivate the notion of L-command, a notion that is like c-command but is defined for SF.
(zo) In an SF representation, a node
a L-commands j3 iff a node 1 which either directly dominates a or dominates a via a chain of nodes type-identical with 1 also dominates (3.
According to this definition, the first occurrence of x in (I9a) asym metrically L-commands P, and both occurrences of x in (I9b) asym metrically L-command y. Put differently, subjects always asymmetrically L-command direct objects. In an SF structure of the form [A [& B] ], A asymmetrically L-commands B. In such a constellation, A mostly is the head and B the nonhead, which means that the head is associated with a particular phonological form, while the nonhead may characterize an extension that is visible only in the
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�
�X
GO
Dieter Wunderlich
105
argument structure of the complex. For instance, A may represent the core meaning of a verb, which can be combined with Bi, Bj, . . . , each representing a particular specific meaning. These Bs may or may not be associated with
(21) a. [ A [ & B [ & C ]] ] b. [ YP c [ YPB [ XA ]x ]x ]x A similar distinction has been proposed by Pesetsky (1995): his Cascade structures correspond to (21a), and his Layered structures to (21b). After this brief summary of the theoretical background, let us now turn to how it applies to the phenomena of secondary predication. 3
PRE F IX V ERBS AN D PAR T I CLE VERBS
The examples in (22) show that nonselected arguments occur productively in verbs with preftxes and particles (Stiebels & Wunderlich 1994, Stiebels 1996). The preftxes ver- and er-, as well as the particle an (with two different readings), may combine with both intransitive and transitive activity verbs. Further base verb candidates that participate in the alternation are listed below the examples. In (22a-b) only one additional argument is introduced, realized with accusative, while in (22c-d) a reflexive dative is introduced as well.10 (22) a. Sie fuhr 'She drove' (itt. jlieg en,
Sie verfuhr ihr letztes Benzin. she away-drove her last petrol 'With her driving she used up all the petrol' schwimmen, tanzen 'fly', 'swim', 'dance')
Er spielte Roulette
=>
=>
Er verspielte sein Geld mit/beim Roulette. he away-gambled his money at roulette
'He gambled away his money at roulette' 'He played roulette' (tr. rauchen, trinken, essen 'smoke', 'drink', 'eat')
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phonological information. For instance, BECOME wc(x,INT(y) ) in ( 12b) above is phonologically associated with the preftx be- in German, while it is fully integrated in the English verb enter. Recall that I consider preftxes like ver- in vetjubeln (ra) and particles like an in anschreien (1b) to be lexical adjuncts. In the following section, I will show that lexical adjuncts offer particular ways of instantiating a B meaning for a verb that itself instantiates an A meaning. An a4junct c-commands the expression it modifies in syntactic (as well as morphological) terms, while, at the same time, it is L-commanded by this expression in SF. Compare the SF representation in (21a), where B and C stand for modifters, with the syntactic representation in (21b), where YPc and YPB are adjuncts. XA is c-commanded by YPB and YPc. while B and C are L-commanded by A.
106
Argument Extension by Lexical Adjunction
b. Sie grinste.
=}
'She grinned' (itr. schreien,
liicheln,
Er sang Arien.
=}
Sie grinste den Lehrer an. she grinned the teacher at 'She grinned at the teacher' beten, blicken 'cry', 'smile', 'pray', 'look')
Er sang die Freundin mit Arien an. he sang the girlfriend with arias at 'He sang arias' 'He sang arias to his girlfriend' (tr. schreiben, sprechen 'write', 'speak')
c. Sie lief
Sie erlief sich die Goldmedaille. she er-ran ( ran and got) herself the gold medal 'She won the gold medal by running' lacheln, arbeiten 'swim', 'smile', 'work') =}
=
Er erschrieb sich sein Geld mit/durch Krimis. he er-wrote himself his money with detective stories 'He wrote detective 'He made his money writing detective stories' stories' (tr. spielen, kaufen 'gamble', 'buy')
d.
Er schrieb Krimis.
=}
Sie tanzte.
=}
'She danced' (itr. laufen, Er trank Bier.
turnen,
Sie tanzte sich einen Muskelkater an. she danced herself a muscle pain at 'she got muscle pain from dancing' schreien 'run', 'dance', 'cry')
Er trank. sich mit Bier einen dicken Bauch an. he drank himself with beer a fat belly at 'He got a fat belly drinking beer' 'write', 'eat')
=}
'He drank beer' (tr. schreiben, essen
The added argument becomes the direct object of the derived verb, while the original direct object of the base verb is suppressed and may only be realized by means of a preposition such as mit. The new direct object may be promoted to subject in passive and middle constructions, as shown by the examples in (23).
(23)
a. Das letzte Benzin {wurde verfahren/ verfahrt sich schnell} 'The last of the petrol {was used up/ is used up quickly} with driving' Das Geld {wurde verspielt/ verspielt sich leicht}. 'The money {was/ is easily} gambled away'
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'She ran' (itr. schwimmen,
Dieter Wunderlich 107
The argument extension triggered by a prefix or particle raises a number of questions that a theory of argument structure will have to answer, for example: Why are these argument extensions mainly restricted to activity (i.e. agentive process) verbs? Why cannot the direct object of transitive base verbs be expressed as a structural argument of the derived verb? And why is the added argument always structural, i.e. realized by accusative? Why do some extensions in addition require a (reflexive) dative? Note that a full dative DP is possible in some cases, as shown in (24a-b). Here, the bekommen-passive is marginally acceptable (24c-d), which shows that the dative argument is structural, too. (24) a. Sie erlachelte ihrem Mann einen neuen Job. she er-smiled her husband.DAT a new jobAcc 'Her smiling got her husband a new job' b. Der Ghostwriter erschrieb dem Kandidaten ganz neue Wahlerschichten. the ghostwriter er-schrieb the candidate.DAT totally new votersACC 'The ghostwriter's writing won the candidate new voters' c. Ihr Mann kriegte von ihr einen neuen Job erlachelt. her husband.NOM got by her a new job.Acc er-srniled 'Her husband got a new job through her smiling' d. Der Kandidat bekam ganz neue Wahlerschichten erschrieben. the candidate.NOM got totally new voters.Acc er-written 'The candidate got new voters through somebody's writing' Last but not least, how should the argument extension be represented? In approaching this latter question, I will assume that (25) represents the
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b. Der Lehrer wurde angegrinst. 'The teacher was grinned at' Die Freundin wurde angesungen. 'The girlfriend was sung to' c. Eine Medaille {wurde erlaufen/ erlauft sich nicht so schnell}. 'A medal {was won/ is not easily won} with running' Viel Geld {wurde erschrieben/ erschreibt sich nicht so Ieicht}. 'A lot of money {was made/ is not easily made} with writing' d. Ein Muskelkater tanzt sich schnell an. 'Muscle pain comes easily from dancing' Ein fetter Bauch ifit sich Ieicht an. 'A fat belly comes easily from eating'
roS Argument Extension by Lexical Adjunction
relevant information in minimal terms. Each base verb is characterized by an atomic predicate together with the respective number of argument variables. 's' represents the referential argument, which is affected by aspect, tense and mood, while 'u', 'x', 'y', 'z' represent arguments that may potentially be saturated by the verb's complements. The sequence of >.-abstractors corresponds to the hierarchy of arguments in SF in that the lowest argument occupies the first position and the highest argument the last position in the sequence. As can easily be seen, the referential argument is always represented as the highest argument (which it is by definition).
(25) a. Jahren:
b. grznsen: angrinsen: smgen: ansing en:
>.x >.s DRIVE(x)(s) {DRIVE(x)(s) & CONSUME(z)(s)} >.u >.x >.s PLAY(x,u)(s) AZ AU AX AS {PLAY(x,u)(s) & CONSUME(z)(s)} AZ AX AS
>.x >.s GRIN(x)(s) {GRIN(x)(s) & DIRECTED_TOWARDS(z)(s)} >.u >.x >.s SING(x,u)(s) AZ AU AX AS {SING(x,u)(s) & DIRECTED_TOWARDs(z)(s)} Az AX AS
>.x >.s RUN(x)(s) c. laujen: erlaufen: >.z >.y >.x >.s {RuN(x)(s) & BECOME(Poss(y,z) )(s)} schreiben: >.u >.x >.s WRITE(x,u)(s) erschreiben: >.z >.y >.u >.x >.s {WRITE(x,u)(s) & BECOME(Poss(y,z) )(s)} d. tanzen: antanzen: trinken: antrinken:
AX AS DANCE(x)(s) A z Ay AX AS {DANCE(x)(s) &
BECOME(Poss(y,z) )(s)} >.u >.x >.s DRINK(x,u)(s) >.z >.y >.u >.x >.s {nRINK(x,u)(s) & BECOME(Poss(y,z) )(s)}
The semantic contribution of the prefix or particle is represented as a second conjunct that is L-commanded by the first one. The second conjunct always shares the situation variable of the base verb and introduces one or two additional arguments (the nonselected arguments) to the base verb. This allows paraphrases such as the following: 'veifahren refers to a situation that is both a driving of x and a consuming of z.' DRIVE is here the head predicate and CONSUME the nonhead predicate, corresponding to the fact that Jahren is the morphological head and ver- a prefix to the head. Since the second conjunct is L-comrnanded by the first one, the additional arguments are always ranked lower than the arguments of the base verb itself, which is accounted for in the sequences of >.-abstractors shown in (2 5). The additional (nonhead) predicates are selected from a small list of putatively universal predicates. Their meaning may be grasped by the following truth conditions (see ( 13) for BECOME).
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verfahren: spielen: verspielen:
Dieter Wunderlich 109
(26) a. coNSUME(z)(s) is true iff the amount of z is steadily reduced to zero in the course of s. b. DIRECTED_TOWARos(z)(s) is true iff z is a nonaffected object to which an activity is oriented during the course of s. c. Poss(y,z) is true iff y has access to z. [There is in fact a family of Poss predicates which may be distinguished more finely on the basis of conceptual knowledge.]
(27) a. er-: AP Az Ay As {BECOME(Poss(y,z) )(s) & P(s)} Au Ax As WRITE(x,u)(s) b. schreiben: c. erschreiben: Au Ax Az Ay As {BECOME(Poss(y,z) )(s) & WRITE(x,u)(s)} (28) a. er-: AP Az Ay As {P(s) & BECOME(Poss(y,z) )(s)} Au Ax As WRITE(x,u)(s) b. schreiben: c. erschreiben: Au Ax Az Ay As {WRrTE(x,u)(s) & BECOME(Poss(y,z) )(s)} The crucial argument against these representations is that they violate general principles of lexical representations. (27c) violates the principle that in SF, the contribution of the morphological head must precede that of the nonhead (cf (2ra) ) and the theta structure in (28c) violates the Hierarchy Principle (cf (rs) ) : the sequence of abstractors does not conform to the hierarchy of arguments in the SF of (28c), which is z < y < u < x < s. Moreover, both representations would predict that the direct object of the base verb is preserved as the direct object of the derived verb, contrary to the facts. We might stipulate that argument swapping is possible, so as to overcome this problem, but this stipulation wou.ld no longer allow us to predict the facts of argument linking from the structure of SF representations and so would counteract the whole purpose of the enterprise. That is, argument swapping must be excluded with respect to lexical derivations. In terms of the present theory, argument swapping is only licensed if it is forced by syntactic environments that ,
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The question now is how the representations in (25) come about, and how the information they encode determines argument linking, i.e. the syntactic projection of the derived verbs. Representing the prefixes and particles as functors on the verb is not an option, since the arguments they add to the base verb rank below the arguments selected by the base verb itself (they become the direct objects of the resulting verb). Consider erschreiben, in which the predicate Poss is added to a transitive verb. If the prefix er- were a functor, either the head as in (27) or the nonhead as in (28), the arguments of Poss would rank above the selected arguments of schreiben, which are inherited by the resulting verb through Functional Composition. This would yield representations such as (27c) or (28c), which differ from that given in (2sc) in the order of theta roles.
I 10 Argument Extension by Lexical Adjunction
require the semantic composition of two adjacent expressions. A prominent example is Scrambling, which reorders the arguments syntactically.11 What the representations given in (25) clearly show is that the verb's SF is extended by a nonhead conjunct that is L-commanded by the head. I assume that in the given examples the preftxes and the particles are lexical adjuncts that contribute a 2-place or a 3-place predicate, and moreover that the verbal head and the preftx/particle share the situation argument (indicated by coindexation). In view of the given array of examples, four different constellations are possible:12 (29)
a.
A 2-place adjunct of an intransitive verb: grinsen AX ASi GRIN(x)(s) <e,<s,t>>
angrinsen AZ Ax AS {GRIN(x)(s) & DIR_TOW(z)(s)} <e, <e, <s,t>>> b. A 2-place adjunct of a transitive verb: an AZ ASi DIR_TOW(z)(s) <e,<s,t>>
singen AU Ax A.si SING(x,u)(s) <e,<s,t>>>
�
ansingen A.z AU Ax AS {SING(x,u)(s) & DIR_TOW(z)(s)} <e ,<e,<e,<s,t>>>>
(3o)
a. A 3-place adjunct of an intransitive verb: erA.z AY ASi BEC(POSS(y,z))(s) <e, <e,<s,t>>>
laufen AX Asi RUN(x)(s) <e,<s,t>>
-------
er/aufen AZ AY Ax AS {RUN(x)(s) & BEC(POSS(y,z))(s)} <e ,<e,<e,<s,t>>>> b. A 3-place adjunct of a transitive verb erAZ AY ASi BEC(POSS(y,z))(s) <e,<e,<s,t>>>
schreiben AU Ax ASi WRITE(x,u)(s) <e ,<e,<s,t>>>
------erschreiben
t..z AY AU Ax As {WRITE(x,u)(s) & BEC(POSS(y,z))(s)}
<e ,<e,<e,<e,<s,t>>>>>
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an A.z J... si DIR_TOW(z)(s) <e,<s,t>>
Dieter Wunderlich
III
(3r ) Possible instances of ARG � a. 01/S)/X Ax As f(x)(s) � b. ( 01/S)/X)/U Au Ax As f(u)(x)(s)
[itr.verbs] ( (V/S)/X)/(P/S) Ag Ax As {f(x)(s) & g(s)} ( ({V/S)/X)/U)/{P/S) [tr.verbs] Ag Au Ax As {f(u)(x)(s) & g(s)}
The additional (i.e. non-shared) arguments of the adjoined predicate are percolated to the result via Functional Composition (FC), which can be iterated for adjuncts with more than 2-places. (32) Functional Composition (FC) � V/Z V/P + P/Z Az (f(g(z) )) Ap f(p) Az g(z) By iteration: V/P + (P/Y)/Z � (V/Y)/Z Ap f(p) Az Ay g(z)(y) Az Ay (f(g(z)(y) ))
[2-place adjuncts] [3-place adjuncts]
The combination of ARG and FC explains why the order of A abstractors corresponds to the hierarchy of arguments in the derived SF. By ARG, the prefix or particle adjunct is integrated as a nonhead, and by FC, the nonselected arguments are projected to the lower end of the sequence of abstractors. This combination of operations appears to be the only way of not violating general principles of lexical representations. Let us now tum to the question of why the direct object of the base verb is suppressed in the derived verb and cannot be mapped onto a structural argument position in syntax. First, representations such as (33a) are rewritten as (33b).
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In these examples, the adjunct, the base verb, and the result are characterized by their respective logical types. In each case, the result may be obtained by Argument Sharing, defined in (7), under the assumption that the situation argument ('s') is shared. Since Argument Sharing itself says nothing about the way in which additional arguments in both components have to be accounted for, it should be decomposed according to the proposals in section r . This is shown explicitly in the following two paragraphs. Every process verb may be extended by a predicative argument that specifies or restricts the process. Argument Extension, defined in (r rb), may be regarded as a rule template to be instantiated for intransitive and transitive verbs as follows:
I I 2 Argument Extension by Lexical Adjunction
(33)
a. erschreiben: f...z AY AU Ax AS { WRITE(x,u)(s) & BECOME(POSS(y,z))(s)} b. erschreiben: AZ AY AU Ax AS { WRITE(x,u) & BECOME(POSS(y,z))} (s) propositional body
(34) erschreiben: t
�------
<s,t>
s
�
<s,t>
�
<e,<s,t>>
/"-....
WRITE
U
x
<<s,t>,<s,t>>
---------
&
<s,t>
/�
BECOME
t
�
<e,t>
�-Z POSS
y
Given the definition of L-command in (2o), one can verify that both x and y L-command z in (34), while u, highlighted in (34), does not. I assume that exactly this is the reason why u is suppressed from being mapped into syntax, or, in other words, why u is not a structural argument in the configuration shown in (34). More precisely, I assume the general constraint in (3s) . (3s) Restriction on structural arguments: an argument is structural only if it is either the lowest argument or (each of its occurrences) L-commands the lowest argument. (3s) states that the lowest argument is always structurally linked, and, in fact, it is linked to direct object. Likewise, since the highest argument always L-commands the lowest one, it must be structurally linked, too, and, in fact, it is linked to subject. However, arguments that are medial may be kept from being linked into syntax under certain conditions. These conditions are specified in (3s). The part given in parentheses accounts for multiple
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(33b) makes it transparent that the verb has a single referential argument and that the 'propositional body' of the verb predicates of it. Recall that it was crucial for the derivation of (33a) that the two conjuncts share one argument, thus, 's' in (33a) definitely does not relate to the partial situations to which the conjuncts may refer individually. These partial situations are not part of SF but have to be inferred. (34) illustrates the SF-structure (33b) in a tree diagram with type nodes.
Dieter Wunderlich I 1 3
(36) a. {pred(x,u) & b. {pred(x,u) &
pred(y,u)} (s) pred(u,z)} (s)
The constellation in (36a) can be illustrated with the rec1p1ent dative expressed in (37), and the constellation in (36b) with the locative alternation expressed in (38) below. (37) a. Sie schrieb dem Bischof einen Brief 'She wrote the bishop a letter' b. schreiben: Au >.y >.x As {WRITE(x,u) & BECOME{Poss(y,u) )}(s) The Pass-extension, which is not marked on the verb, is justified only if the base verb is transitive and the lower arguments are shared. Although the first occurrence of u is in a nonstructural position, u is structural here because it is lowest by virtue of the second conjunct. In contrast, the locative alternation exemplifies a case in which the lower argument of the base verb remains nonstructural even if it is shared by the second conjunct. The by now famous examples in (38) are represented as in (39).13 (38)
a. Sie spriihte Farbe an die Wand. 'She sprayed paint on the wall' b. Sie bespriihte die Wand mit Farbe. 'She sprayed the wall with paint'
(39)
a.
spruhen:
b. bespruhen:
).p
>.u >.x >.s {sPRAY(x,u) & P(u)}(s)
+dir >.z >.u >.x >.s {sPRAY(x,u) & BECOME(wc(u,A-r(z) )}(st
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occurrences of one argument variable, a constellation which will be illustrated in (36) below. According to (3s), x, y, and z can be structural in (34), and, since they are not marked as oblique by lexical means, they are structural, while u, representing the direct object of the base verb, cannot be structural. This argument can only be realized by means of a preposition, as shown in the examples in (13). (3s) thus explains why the direct object of the base verb may never be expressed by structural case in configurations like that in (34). Consequently, only verbs that allow optional direct objects may undergo derivations of this kind, since obligatory arguments cannot be suppressed. However, the direct object of the base verb is not always suppressed. (3s) claims that the argument u may be linked to structural case in a constellation like (36a), but it may not be linked so in a constellation like (36b). In the case shown in (36a), u is structural because it is the lowest argument, while in the case shown in (36b), u is nonstructural because one of its occurrences does not L-command the lowest argument. (Identical argument variables are highlighted in (36).)
1 1 4 Argument Extension by Lexical Adjunction
(4o) a. {pred(x,u) & pred(y,v) b. x and u, and y and v, I
I
& pred(w,z)} (s) and w and z. I
\
The most prominent intonational pattern produced in uttering a series like that in (4ob) has a rising contour on x and (possibly) on y and w, and a fmal falling contour on z (Wunderlich 1991) , that is, the first item of each group is rendered prominent, and also the last item of all. (4ob) is certainly not the way in which arguments of a verb are realized, but what possibilities are there to realize all the arguments of (4oa) in the syntax, given that the number of structural cases is restricted to two or three (depending on the type of language)? The constraint in (3s) tells us that the same choice is made as in the intonational pattern of uttering (4ob): the first argument of all must be made prominent (as the subject), then (possibly) the first argument of each predicate is made prominent (by structural case like dative), 15 and, finally, the last argument of all is made prominent (as the direct object). In all the examples considered so far, the first conjunct represents the head predicate (visible by the phonetic form of the base verb), while the nonhead predicate only survives if at least one of its arguments is mapped into syntax. An argument that is suppressed according to (3s) can mostly be inferred. For instance, from the sentence er erschrieb sich sein Einkommen 'he made his money with writing' one can infer that he got the money for the things he had written. Similarly, from the sentence er bespriihte die Wand 'he sprayed the wall' one can infer that the wall was covered with the substance he sprayed. The actual combination of predicates, as well as the possibility to identify
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The verb spriihen takes a directional PP, so that the goal comes in as the internal argument of P. In the b-variant, marked by the prefix be- in German, the meaning of the directional preposition is incorporated into the verb's SF, and, consequently, the internal argument of P becomes the lowest argument of the verb. The shared argument u is nonstructural in this configuration, according to the parenthesized part in (35), and, consequently, it cannot be linked to a structural case like dative, but only by means of the preposition mit 'with'. A conceptual motivation for the constraint expressed in (3s) runs as follows. Assume that the SF of a verb combines a number of predicates as shown in (4oa) and that someone wants to spell out all the involved arguments in the way shown in (4ob). Given that the number of ways of rendering elements prominent is restricted, a certain selection from the complex structure must be made.
Dieter Wunderlich
1 15
arguments as in (36) to (39), is subject to the following substantial constraints outlined by Kaufmann (1995a, b). (41) Constraints for possible verbs a. Connexion. A second member in a lexical SF conjunction specifies inferences about the first member. b. Coherence. An SF conjunction is contemporaneously or causally interpreted.
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Assume that verbs can be freely extended by additional predicates such as (BECOME) POSS, or by combination with prefixes or particles, there must be something to constrain the possible outcomes; for that reason Connexion and Coherence come into play. If one writes something, a possible inference is that there is an addressee: this (unmarked) inference can be specified by the Poss-extension in (37). Another possible inference is that the writer himself comes into the possession of something; this inference is marked but can be expressed by means of the prefix er. Even more marked is the inference that the writer causes someone else to possess something, but such an inference can still be expressed by er. The reader may realize that all the examples in (22), in combination with the representations in (25), comply with Connexion. In contrast, it is not possible to express in just one verb that by writing something one causes something else to be located somewhere. A particular way to connect the members of a conjunction is by identification of arguments. The morphologically unmarked Poss-extension of schreiben were not possible if, for instance, the possessor came in the possession of an emotional state rather than the written product. *Sie schrieb dem Bischof einen Wutanfall 'she wrote the bishop a fit of rage' is not possible.16 Recall that the examples in (22c, d) have a reflexive dative; here, the arguments are not identified in SF but rather one of the added arguments is syntactically bound to one of the head's arguments, that is, the Poss-extension expressed by er- or an is made more connected by identifying the added possessor with the subject of the base verb. Connexion also motivates why primarily nontelic activity verbs are subject to lexical argument extension. These verbs encode some process and thus invite inferences about the possible resources, direction or result of the process. For instance, the termination of a process can be expressed by a PP argument, by a PP adjunct or by means of a prefix or particle. The other constraint in (41), called Coherence, takes up the condition that the conjuncts forming the propositional body of a verb must be related to one single situation. If the two predicates are homogeneous in time, Coherence requires that they hold for the whole time span of the situation. An example is given by angrinsen, repeated in (42a). If, in contrast, the
1 1 6 Argument Extension by Lexical Adjunction
predicates are heterogeneous in time, they must be connected by a causal relation, that is, the first predicate must function as a causal factor of the second one. Since BECOME is restricted to a final subinterval (see ( 13) ), its occurrence in a second conjunct induces a causal reading of the verb. An example is given by erschreiben, repeated in (42b). (42) a. Contemporaneous reading: angrinsen: AZ AX AS {GRIN(x) & DIRECTED_TOWARDS(z)}(s) b. Causal reading:17 erschreiben: >.z >.y >.u >.x >.s {WRITE(x,u) & BECOME(Poss(y,z) )}(s)
(43) a. Sie grinste (stundenlang/*in einer Stunde) den Lehrer an. 'She grinned at the teacher (for hours/*in an hour)' b. Sie verfuhr (in einer Stunde/*stundenlang) ihr ganzes Benzin. 'With her driving she used up all the petrol (in one hour/*for hours)' c. Sie verfuhr (stundenlang/*in einer Stunde) Esso-Benzin. 'With her driving she used up Esso petrol (for hours/*in an hour)' d. Er erschrieb sich Qahrelang/*in einem Jahr) den Lebensunterhalt mit Krimis. 'He earned his living (for years/*in one year) by writing who dunits' e. Er erschrieb sich mit Krimis (in einem Monat/*monatelang) das Jahreseinkommen.
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Deviating from most other approaches (Dowty 1979, Jackendoff 1990, Pustejovsky 199 1, Levin & Rappaport Hovav 1995), the analysis proposed here allows us to derive the causal reading of a verb by means of Coherence, and so obviates the need to express it in the SF representation. SF representations are conceived of as minimal representations that should only encode what cannot be derived by general means (Wunderlich 1996b). While the argument structure of the derived verb is fully determined by the SF representation, the aspectual properties are only partially determined by SF and may be further specified by the DPs saturating the arguments. With the particle an (mRECTED_TOwARDs ), the process reading is always maintained, see (43a), while with ver- (coNSUME) a decremental predicate is added that induces an accomplishment reading with definite objects but maintains the process reading with indefinite objects, as shown by (43b) and (43c). The same is true with prefixes or particles that add BECOME, as shown by (43d) and (43e). All these aspectual properties are predicted, given the meaning of the predicates in (26) and the effects of definiteness vs. indefiniteness.
Dieter Wunderlich
r
17
'He made his money for this year (in one month/*for months) by writing whodunits'
(44) a. erschreiben: Az Ay Au +hr +hr * -lr +lr I
I
ace
dat
b. dative: accusative: nominative:
Ax As {wruTE(x,u) & BEe Poss(y,z)}(s) -hr +lr nom [+hr,+lr] [+hr] [ ]
The DPs specified in these terms can be linked to a theta role if the respective feature specifications can be unified, with the more specific linkers taking precedence over the less specific ones. This gives a unique result for all the examples in (22). The case distribution that results for erschreiben, representing the most articulate type of a 3-place adjunct combined with a transitive verb, is shown in the last line of (44). Thus, (44) correctly predicts that the syntactic reflexives occurring in (22c, d) must be dative reflexives. The fact that the suppressed argument may be expressed by means of prepositions such as mit 'with', durch 'through', or bei 'by' is a matter of the 'semantic' appropriateness of these prepositions, which I will not discuss here. PP arguments (that is, arguments that are licensed by a preposition) have to be adjacent to the verb, according to a general principle of German syntax, so the syntactic structure resulting from (44a) is that in (45), where the finite verb is characterized as an instance of I(nfl). (45) [IP [er] nom [ [sich] dar [ [sein Geld]acc [ [PP mit Krimis] [I erschrieb] ] ] ] ] he himself his money with detective stories er-wrote This section has shown that the lexical representations of the prefix and particle verbs given in (25) are adequate in so far as they conform to general
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I would finally like to show how the case distribution observed in the examples in (22) is derived from the SF representations given in (25). Recall from section 2 that structural arguments are mapped into syntax in virtue of their semantic ranking. The A-abstractors (or theta roles) related to these arguments are encoded in terms of the abstract case features [± hr] 'there is a/no higher role' and [± lr] 'there is a/no lower role', as shown in (44a). Theta roles corresponding to an argument in a non-structural position, such as u in (44a), are suppressed from structural linking, which is indicated by an asterisk. The morphological cases are encoded with the same features, as shown in (44b):
1 18
Argument Extension by Lexical Adjunction
constraints on possible verbs and allow us to predict how the aspectual properties of the base verb are shifted, whether the derived verb has a causal reading and how its arguments are linked into syntax. Furthermore, it has been shown that ARG must be applied to the base verb in order to perform all these tasks at the same time.
4 R E S UL T A T I V E C O N S T R U C T I O N S
(46) a. die Gaste tranken 'the guests drank' b. die Jogger liefen 'the joggers ran' c. es regnete 'it rained'
::::} ::::} ::::}
die Gaste tranken den Weinkeller leer 'the guests drank the wine cellar empty' die Jogger liefen den Rasen platt 'the joggers ran the lawn flat' es regnete die Stiihle naG 'it rained the chairs wet'
(47) Passive and Middle: a. Der W einkeller wurde leer getrunken/ trinkt sich schnell leer. 'The wine cellar was drunk empty/ drinks empty easily' b. Der Rasen wurde platt gelaufen/ lauft sich Ieicht platt. 'The lawn was run flat/ runs flat easily' c. Die Stiihle wurden naG geregnet/ regnen (* sich) leicht naG. 'The chairs were rained wet/ rain wet easily' Resultative constructions can also be analysed as the extension of a verbal head by a predicative argument. They differ from preftx and particle verbs in that the relevant predicate is usually delivered only in syntax instead of being expressed by a lexical adjunct. (Certain combinations of adjectival predicate and verb may be lexicalized as particle verbs, for example, plattlauftn 'run flat', leertrinken 'drink empty', nafiregnen 'rain wet'). Since a
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The analysis proposed will now be extended to resultative constructions. They are generally more acceptable with (directional) prepositional pre dicates than with adjectival predicates, so I will restrict myself to the latter, namely to the hard cases. Later on, I will argue that resultatives with prepositions have a different source from those with adjectives. The examples in (46) show that nonselected arguments also occur in resultative constructions. They may then become subjects in passive and middle constructions, and so must be structural arguments of the derived verb.18 Resultative constructions are possible for both transitive and intransitive verbs (including those with an expletive argument), provided these verbs describe activities or processes.
Dieter Wunderlich I I9
stative predicate is added, the adjective must be augmented her� with the predicate BECOME, not expressed overtly. (48) schemati�y shows the possible combinations; shared arguments are again coindexed. (48) Resultative extension of verbs: a.
with intransitive verbs: (example: platt
A.P A.z A.wi BEC P(z)(w) <<e,t>,<e,<s,t>>>
laufen) /aufen
A.x A.si RUN(x)(s)
<e,<s,t>>
laufen
b. with transitive verbs: (example: leer trinken)
A.P A.z A.wi BEC P(z)(w) <<e,t>,<e,<s,t>>>
trinken A.u AX A.si DRINK(x,u)(s) <e,<e,<s,t>>>
trinken
A.P A.z A.u Ax As { DRINK(x,u)(s) & BEC P(z)(s)} <<e,t>,<e,<e,<e,<s,t>>>>>
We can now generalize the analysis proposed in section 3 to the resultative construction. In particular, this yields the following results: The internal argument of transitive base verbs ('u' in (48b)) does not L-command the added argument ('z') and thus cannot be structural. The resulting case distribution follows from the structural linking mechanism. The causal interpretation of the SF conjunction follows from the addition of BECOME. Since the resultative extension of verbs is morphologically invisible, it has often motivated a syntactic analysis, in particular, in terms of Small Clauses (SC} or VP shells. A syntactic analysis is feasible in principle. However, in order to account for the full range of resultative constructions in a language like German it requires a number of assumptions about the organization of grammar that are not necessary for a lexical analysis like the one proposed here. Note first that in order to account for the interpretation of the adjective, the syntactic analysis must assume an invisible predicate BECOME, too, so as
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A.P A.z A.x A.s { RUN(x)(s) & BEC P(z)(s)} <<e,t>,<e,<e,<s,t>>>>
120 Argument Extension by Lexical Adjunction
to analyse den Rasen platt lauftn 'run the lawn flat' as den Rasen BECOME platt lauftn. Two syntactic analyses are possible for this construction: (49) a. [den Rasen [ [BECOME platt] lauftn]] b. [ [BECOME (den Rasen platt] ] laufen]
(so) BECOME: platt: BECOME platt: lauftn: ARG(lauftn): BECOME platt lauftn:
Ap AS1
BECOME(p)(s') .Az FLAT(z) AZ AS1 BECOME(FLAT(z) )(s') .Ax .As RUN(x)(s) .AP .Ax .As {RuN(x)(s) & P(s)} .Az .Ax .As {RuN(x)(s) & BECOME(FLAT(z) )(s)}
This analysis gives the same results as lexical adjunction, making use of the same devices: it allows the incorporation of invisible predicates in a syntactic structure, and ARG is assumed to be a possible rule in syntax, too. However, it is not generalizable to the surface form of English sentences (run the lawn BECOME flat), in which verb and adjective are not adjacent. In (49b), both BECOME and lauftn combine with the SC [den Rasen platt] by means of Functional Application (FA), given that lauftn itself is extended by ARG. This again yields the correct semantic results, as shown in (s I ).
(51 ) den Rasen platt:
FLAT(def_lawn) BECOME den Rasen platt: AS1 BECOME(FLAT(def_lawn) )(s') .AP .Ax .As {RuN(x)(s) & P(s)} ARG(lauftn): BECOME den Rasen platt .Ax .As {RUN(x)(s) & BECOME(FLAT(def_lawn) )(s)} lauftn:
From a purely semantic point of view, every analysis that takes the appropriate ingredients, such as an invisible BECOME and the right number of arguments and functors, is fme. It is other properties of the analyses that may discriminate between the alternatives, such as:
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(49a) represents an analysis that corresponds to the lexical analysis in terms of its compositional properties; (49b) represents an SC analysis (similar to what has been proposed by von Stechow 1996), an analysis that is mainly motivated by the fact that the object is selected by the adjective and not by the verb. Both analyses obtain the correct argument structure only by means of ARG as a modification rule, as I will argue in the following. Although syntacticians often do not offer explicit ways of how semantic composition works, they certainly assume that it is somehow possible. In terms of the semantic operations used here, a compositional interpretation of (49a) looks as follows: BECOME combines with platt by means of Functional Composition (FC), and then ARG(lauftn) combines with platt BECOME, again by means of FC, thus yielding the following:
Dieter Wunderlich 121
The number of steps in the semantic composition. The generalizability of a particular solution. The predictions for argument linking that follow from the analysis.
(52) a. [ [BECOME [den Weinkeller leer] ] trinken] b. >.y >.x >.s {oruNK{x,y)(s) & BECOME{EMPTY(def_wine_cellar) )(s)} Here, the internal argument of DRINK, y, cannot be linked into syntax because accusative is no longer available. But why is it suppressed in favour of the SC object? SC analyses do not answer this question; they have to stipulate that verbs like trinken 'drink' either select their own object or an sc.
Furthermore, the SC analysis cannot reasonably be generalized to prefixes and particles. For instance, sich sein Geld mit Krimis er-schreiben (see example (22c) ), would have to be analysed as in (53a). (5 3) a. [ [(sich) (sein Geld) er-] sc (Krimis) schreiben]VP ] VP b. [ [(Krimis) schreiben] VP (sich) (sein Geld) er-] VP ] VP If the verb is moved to the SC in order to combine with the prefix and assign case to the SC-objects, the trace of the verb remains ungoverned, thus violating the Empty Category Principle. No such violation occurs if the prefix is raised to the verb (provided that the SC is regarded as being in an argument position), but in this case it remains mysterious why Krimis cannot get case and is realized by means of mit 'with' instead, and moreover, it is not motivated why sich can receive dative in the SC.20 In contrast, the VP shell structure shown in (5 3b) allows the verb to raise to the prefix and to assign case in the higher position, but this is no longer an SC analysis, since the preftx would be the verbal head that allows another VP as one of its complements. The VP shell analysis is problematic in its own right, since it incorrectly predicts that the prefiX is the head of the prefiX verb, contrary to the morphological evidence.21 Comparing the resultatives in English with those in German, word order turns out to be the main syntactic difference. In English, the adjective
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Note first that the analysis shown in (5 r ) seems to imply that the accusative case on the object den Rasen is licensed by the adjective rather than the verb. Although proponents of SC analyses (e.g. Hoekstra 1988) correctly reject the idea that adjectives assign accusative, they have to stipulate that the verb can assign case to the SC object without being combined with the secondary predicate first.19 The SC analysis is even more problematic when it comes to explaining the resultative constructions with transitive base verbs. The SC structure for transitive verbs is shown in (52a), its corresponding interpretation in terms of the derivation in (51) is shown in (52b).
122
Argument Extension by Lexical Adjunction
(54) a. b. c.
[run [BECOME [the lawn flat] ]] [runi [the lawn [ti [BECOME flat]]]] [drinki [the wine cellar [ti [BECOME empty]]]]
To summarize, syntactic analyses of resultative constructions are able to deal with intransitive base verbs, but need additional stipulations for constructions in which a transitive base verb combines with a nonselected argument. The lexical analysis I have argued for is only possible by means of ARG and not by means of MOD. This has been shown in section 3 in the analysis of particle and prefix verbs, which include the resultative verbs without an overt marking as a special case. But even an SC analysis requires the operation ARG. For if the SC were considered a modifier of the verb rather than a complement, there would be no way to explain why the SC object may be case-governed by the verb. Nobody has ever proposed a modifier analysis for the case in which the SC introduces nonselected arguments. In this case, it has always been taken for granted that verbs may be optionally subcategorized for an SC, that is, in terms of the present analysis, they may take an SC by virtue of ARG, not MOD. Finally, the VP shell analysis treats nonselected arguments on a par with selected arguments, and thus implies the operation ARG as well. Let us now take a closer look at resultatives of transitive verbs that seem to preserve the selected argument. It is mostly examples of this type of resultatives that have been discussed in the literature. The examples in (ss) show that transitive verbs with optional arguments allow resultative extensions in which the object appears to be selected by the verb. (ss)
a. Er fuhr das Auto kaputt. b. Er biigelte die Hosen trocken.
'He drove the car to a wreck' 'He ironed the trousers dry'
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cannot be adjacent to the verb because a direct object intervenes, and so (49a) as a syntactic analysis cannot have a counterpart in English. The alternatives possible for English are the lexical analysis shown in (48), the SC analysis in (54a), which is problematic for the same reasons as the corresponding analysis in German, and the VP shell analysis in (s4b) (Larson 1 988b). Just like the lexical analysis, the VP shell analysis assumes that the verb underlyingly combines with the resultative predicate but must be moved in order to assign case. But again, it is unclear how this analysis handles resultatives with transitive base verbs that have nonselected arguments. One possible analysis is shown in (54c). Why is the object selected by empty rather than by drink? I will come back to the VP shell analysis in (82) below, after depictive predication has been considered.
Dieter Wunderlich 1 23
c. Er klebte die Briefmarken fest. 'He glued the stamps fast' d. Er hammerte das Blech flach. 'He hammered the metal flat' Recall that according to the analysis proposed here, resultative constructions involve the suppression of the internal argument of the base verb, so this argument must always be optional. For instance, (ssa) should have the reading that he demolished the car by driving something. In fact, this sentence need not specify the vehicle the man was driving-he may have driven the car that got demolished or some other vehicle by means of which he brought about the expressed result. Accordingly, sentences like those in (s6) are perfectly fine: Mit seinem Laster fuhr er das Auto des Nachbarn kaputt. 'With his truck he drove his neighbour's car to a wreck' b. Er biigelte die Hosen trocken, indem er die Hosen unter ein Tuch legte und dann das Tuch biigelte. 'He ironed the trousers dry by putting the trousers under a cloth and then ironing the a.
cloth' Thus, (ssb) can mean that he in fact irons some cloth when he irons the trousers dry. Similarly, all the other sentences in (ss) do not necessarily specify the object of the base verb. I conclude that this object itself need not be expressed, even though, in the default reading, it is identified with the affected object. The lexical analysis proposed in (48b) represents the object of the base verb and the affected object by different argument variables; they may be assigned identical values unless the context suggests otherwise, as in (s6). Note, however, that the English counterparts of the German examples seem to entail that the original object and the affected object are identical (Wilder 199 1), so that identical value assignment must somehow be forced (see below).22 Since obligatory objects cannot be suppressed, transitive verbs with an obligatory object should never allow adjectival resultatives.23 This holds indeed for German, but not for English, as is shown in (57).
(57)
a. b. c. d.
* Die Baren erschreckten die Wanderer sprachlos. The bears frightened the hikers speechless. * Sie beruhigte das Kind still. She calmed the child down.
To account for the English examples, several authors have proposed a ternary syntactic structure, which allows one argument to be selected by both the verb and the resultative predicate (Rothstein 1 985, Roberts 1 988, and Carrier & Randall 1992, among others). I object to such an analysis for principled reasons, since I assume that only a binary syntactic structure
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(s6)
124 Argument Extension by Lexical Adjunction
guarantees a unique semantic composition. Moreover, examples like
den Weinkeller leer trinken 'drink empty the wine cellar', where the object is not
selected by the verb, cannot be described by a ternary structure.
German and English also differ in that resultatives from 'unaccusative' verbs are for most German speakers not possible, but at least partially acceptable in English.
(s8)
a.
* Der Toast verbrannte schwarz.
b. The toast burned black. c. * Die Steine rollten glatt.
To account for the differences between English and German
I
adopt the
hypothesis that English allows identification of argument variables in cases where German does not. More precisely, the argument brought in by the resultative predicate may be identified with an argument of the base verb in English, but not in German (Kaufmann 1995a: 142). The argument extension of verbrennen 'bum', given in {59a), shows why the resulting verb is impossible. Connexion requires that the second conjunct must specify inferences about the first, that is, it must specify inferences about the state of x being burned, which is not possible if the two conjuncts have different arguments. But if they are identical, as in (59h), the resulting SF yields a possible verb.24 {59) a. German: *..\z ..\x ..\s {BECOME{BURNEn {x) ) b. English:
AX AS {BECOME {BURNED {x) )
Similarly, if the causative verb combination of ACT and
erschrecken {
&
&
{P {z) )}(s) {P(x) )}(s)
BECOME
BECOME
'frighten' is represented as a
)
BECOME FRIGHTENED ,
Connexion excludes the
extended version in (6oa), but not that in (6ob), since here, the two relevant arguments are identified. (6o) a. German: * ..\z ..\y ..\x ..\s {Acr(x) BECOME
b. English:
{P {z) )}(s)
..\y Ax AS {AcT(x) BECOME
{P {y) )}{s)
&
&
(
(y)) &
BECOME FRIGHTENEn
{
BECOME FRIGHTENED
{y) ) &
ACT represents some unspecified activity of an agent, and the resulting verb gets a causal reading by Coherence. A second conj unct with BECOME must specify the frrst, which is possible only if the arguments are identified. Note that transitive verbs with obligatory obj ects mostly have an achievement reading (represented with
)
BECOME ,
so they cannot undergo the resultative
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d. The stones rolled smooth. e. * Das ganze Eis schmolz fliissig. £ The ice melted completely liquid.
Dieter Wunderlich
125
(61) a. Die Vase zerbrach in Stucke/ zu Staub/ *staubig/ *kaputt ('broken'). b. The vase broke into pieces/ to dust/ *dusty. The directional PP is licensed by the SF in (62), which represents a more general extension of verbs than the SFs given in (6o) (see, for instance, (12a) in Section 2). The directional preposition expresses the transition to a result state in the syntax, while in combination with a stative AP the transition must be encoded lexically, that is, by means of BECOME in the SF of the verb itsel£ (62) AP Ax As {BECOME(BROKEN(x)) +dir
&
P(x)}(s)
Simpson (1983) observed that 'unaccusative' verbs do not allow reflexives in resultative constructions, while 'unergative' verbs require them, as shown in (63a, b). She explains this difference by assuming that unergatives have an external argument and so allow an internal reflexive, while unaccusatives already have an internal argument and so an internal reflexive is blocked. The behaviour of intransitive verbs under resultativization has been taken as a relevant diagnostic in the literature (Hoekstra 1988, Levin & Rappaport Hovav I 995).
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extension in German because two BECOME conjuncts cannot predicate of different arguments. According to the templates in (48), resultative extension is an instance of lexical adjunction, so only the situation argument is shared, identification of other argument variables being an additional device.25 It is not relevant here whether all or only a few English speakers use this device and opt for (59b, 6ob), and whether all or only a few German speakers do not. What is relevant is that argument identification suffices to explain why resultative constructions such as those in (57) and (58) are at all possible. Similarly, argument identification in SF explains why resultative predicates may predicate of the direct object of the base verb (see (ss) ), and more so in English than in German. To account for why an argument may be selected by two predicates, we thus do not have to assume a ternary syntactic structure or a special kind of case-assignment to SC objects. Clearly, argument identification that is not visible in syntax operates on SF, and not in syntax (where a reflexive should be expected), so if our hypothesis is right, it suggests a lexical treatment of resultatives. As I have noted earlier, resultative constructions with directional PPs are generally more acceptable than those with APs (see also Kaufmann 1995a: 146). This is exemplified in (61).
126 Argument Extension by Lexical Adjunction
(63)
The toast burned (*itself) black. b. She laughed *(herself) sick.
a.
(64) a. Az Ax As {LAuGH(x) & BECOME{P(z) )}(s) b. She laughed her neighbour sick. The analysis presented here implies that resultative predicates usually contribute arguments that are not selected by the base verb, just like the prefixes and particles considered in section 3· To improve the connection between the predicates, a language may introduce the lexical operation of argument identification, which is available in English but not in German. Furthermore, several implications of this analysis have been discussed. There is certainly more to be said about the cross-linguistic variation in resultative constructions, let alone elaborating the semantic constraints that require resultatives to specify information already implicit in the base verb (Kaufmann 1995a: 142, 160; Kaufmann in prep.). This is not the place to extend this discussion. In contrast to resultatives, constructions with a depictive predicate only allow arguments that are selected by the verb. So let us see how the present analysis accounts for this type of predication. s
D E P I CTIVE PRED I CAT I O N
The examples in (6s) show depictive predicates that modify the direct object of the verb. (6s)
(weil) sie den Fisch roh essen wollte. 'she wanted to eat the fish raw' b. (weil) er das Hemd ungebiigelt anziehen wollte. 'he wanted to put on the shirt unironed'
a.
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The present framework accounts for the different behaviour of intransi tive verbs without assuming that unaccusative verbs have an underlying internal argument.26 All undisputed candidates for unaccusative verbs have an inchoative meaning, represented by BECOME in their SF. As has been shown in (59), argument identification in SF is necessary to render grammatical the resultatives of inchoative verbs, so syntactic reflexivization Qicensed by an independent theta role) is excluded. Unergative verbs, in contrast, usually describe processes and lack a BECOME predicate. Hence, no argument identification is needed for these verbs, since process predicates allow one to express the termination of the process. Therefore, unergative verbs require a syntactic reflexive, as shown by the representation in (64a). The arguments may even remain distinct in this case, as shown by (64b).
Dieter Wunderlich
127
The depictive construction in (6sa) suggests that the fish is in a particular tempora ry state, it may be raw or cooked or fried, and that this state holds for the whole eating process. Thus, the depictive predicate must be a stage-level predicate that overlaps in its predication time with the situation referred to by the verb. A sentence such as (66a) with the intended meaning that she wants to eat long fishes, is not possible, and a sentence such as (66b), implying that the fish was raw only in the beginning of the cooking process, is deviant. (66)
n
b.
11
(weil) sie die Fische lang essen wollte. 'she wanted to eat the fishes long' (weil) sie den Fisch roh kochen wollte. 'she wanted to cook the fish raw'
According to the lexical analysis, depictive predication involves extending the verb by a predicative argument, which, due to semantic selection, shares its argument with the object of the verb. This extension can be described in two ways, depending on whether we assume that adjectives have a situation argument. If the adjective is assumed to have no such argument, it must be combined with the verb in sharing another argument, for instance, the verb's object, as shown by the derivation of roh essen in (67). But if it is assumed to have a situation argument, it is combined with the verb by situation sharing as described in the preceding sections, with subsequent argument identification in order to guarantee argument sharing with the verb's object, as shown in (68). Note that the results are identical. (67) a. roh: b. essen: c. ARG (essen): d. relativization to s: e. roh essen:
AZ RAw(z) Ay Ax As EAT{x,y)(s) AP Ay Ax As {EAT(x,y)(s) & P(y)} AP Ay Ax As {EAT{x,y) & P(y)}(s) Ay Ax >.s {EAT(x,y) & RAw(y)} (s)
(68) a. roh: b. essen: c. ARG (essen): d. roh essen: e. argument identification:
Az RAw(z)(s) Ay Ax As EAT(x,y)(s) AP Ay Ax As {EAT{x,y)(s) & P(s)} Az Ay Ax As {EAT(x,y)(s) & RAw(z)(s)} Ay Ax As {EAT{x,y)(s) & RAw(y)(s)} Ay Ax As {EAT(x,y) & RAw(y)} (s)
£
The crucial step in the derivation (67) is (67d). The verb should refer to a single situation, so that the added predicate is relativized to this situation. Thus, a contemporaneous reading with overlapping predication times results, according to Coherence. The adjective adopts a temporary reading when it is used in this construction. In contrast, (68) starts out with the
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a.
1 28
Argument Extension by Lexical Adjunction
adjective having a situation argument, and it is this argument that is shared if ARG has applied. Consequently, the argument sharing characteristic for the depictive construction can only be expressed after the adjective has been combined with the verb, that is, in the syntax. There are several reasons to reject the derivation in (68}. First, stative adjectives and prepositions lack an additional situation variable (Wunderlich 1 996a). The stage-level property of these predicates depends on contextual circumstances and so should not be represented in SF, in contrast to the referential arguments of verbs. This is already implied by the analysis of resultatives, according to which adj ectives yield a resultative reading by virtue of combining with the predicate
BECOME,
which introduces the
the SF of derived lexical items was described as a restricted option, which in general is not allowed in German; however, depictive predicates are quite common in German. Moreover, (68) requires argument identification in the syntax, and it would be mysterious why not, instead, syntactic reflexives apply. Any two arguments could be identified, so that this mechanism is too unrestricted and would not allow the restrictions on depictive predicates to be explained (see below). I therefore assume that the derivation in (67) is correct. However, it is still an open question how the operation ARG in (67c) is justified. In section r , (9), ARG was introduced as a possible option to express argument sharing in the combination of two one-place predicates, and in section 3, (3r), where this operation was used in the analysis of prefix and particle verbs, it was taken for granted that the situation argument is shared. But nothing prevents us from assuming that one of the other arguments of the base verb is shared with the additional predicate, depending on whether a contemporaneous or a result state reading obtains.27 In order to see which options of shared arguments are possible in general, consider the following cases: (69)
V a. b. c. d.
adjuncts
).p >.y >.x >.s * J.p >.z >.y >.x ).p ,\y >.x >.s 1 ).p >.y >.x >.s
>.s
{EAT(x,y)(s) {EAT(x,y)(s) {EAT(x,y)(s) {EAT(x,y)(s)
& P(s)} & P(z)} & P(y)} & P(x)}
(69a) holds for prefix and particle verbs as well as for resultative constructions: the shared argument is the situation argument, and addi tional arguments ofP are independent of the arguments of the verb. (69b) is excluded since no argument is shared: This representation could not be derived by means of ARG; moreover, it would be ruled out by the Connexion constraint. (69c) accounts for the depictive construction.
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temporal component. Secondly, in section 4 argument identification in
Dieter Wunderlich 129
Recall that the second occurrence of 'y' determines it to be the lowest argument, so that adding a depictive predicate preserves the linking conditions of the base verb. Therefore, depictive predicates related to the direct object should generally be possible, provided that they can express temporary properties. (69d) may be another possible option, but here the lowest argument is 'x', so that 'y' becomes nonstructural. This option can thus only be taken with an implicit object as in (7oa). Generally, a subject-related depictive predicate is generated as a VP adjunct rather than as a lexical adjunct, as shown in (7ob), from which the scrambled version in (7oc) can be derived. (7o)
(weil) sie schick angezogen essen wollte 'she wanted to eat fashionably-dressed' b. (weil) sie [schick angezogen [den Fisch essen wollte] ] 'she wanted to eat the fish fashionably-dressed' c. (weil) sie [den Fischi [schick angezogen [ti essen wollte] ]] 'she wanted to eat the fish fashionably-dressed' a.
(7r) a. b. * * c. d. * * e. £ * *
(weil) sie [den Fischi [schick angezogen [ti roh essen wollte] ] ] 'she wanted to eat the fish raw fashionably-dressed' (weil) sie den Fisch roh schick angezogen essen wollte. 'she wanted to eat the fish fashionably-dressed raw' (weil) sie [den Fischi [schnell [� roh essen wollte] ] ] 'she wanted to eat the fish raw fast' (weil) sie den Fisch roh schnell essen wollte 'she wanted to eat the fish fast raw' (weil) sie den Fisch roh auf/zuende essen wollte. 'she wanted to eat the fish up raw' (weil) sie den Fisch auf/zuende roh essen wollte. 'she wanted to eat the fish raw up'
Another question is how a VP adjunct is licenced. In the VP, the internal argument of the verb has already been given a certain value, which is here expressed by the constant 'a'. Assuming that ARG can be applied to VPs as well, this provides us with the following options:
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This analysis correctly predicts that the order of adjectives shown in {7ra) is possible, and that the order in (7rb) is ungrammatical. Situation-related adjuncts must precede the object-related depictive predicate as well, as shown in (7rc-d). In contrast, resultative predicates must follow the depictive predicate, as shown in {7re-�.28 This latter fact corresponds to the assumption that resultatives can introduce a new individual argument, while depictive adjectives predicate of an argument that is already there.
IJO Argument Extension by Lexical Adjunction
(72) VP adjuncts a. AP Ax As {EAT(x,a)(s) b. AP Ax As {EAT(x,a)(s)
& &
P(s)} P(x)}
(73) a. schenken: {noNATE(x,z) b. ARG (schenken): {noNATE(x,z)
& &
BECOME(Poss(y,z) )}(s) BECOME(Poss(y,z) ) & P(y)}(s)
Here, y, representing the recipient, should be linked to accusative, while z, representing the theme, should become nonstructural and therefore be suppressed. However, the theme can only be left implicit if the recipient is implicit too. The data in (74) show that a depictive predicate for the indirect object is in fact excluded, and the construction is only marginally acceptable if the adjective immediately follows the indirect object.29 (74) a. (weil) sie dem Jungeni eine Hose (*nackti) schenkte. b. (weil) sie dem Jungeni (*nackti) eine Hose schenkte. 'she gave the boyi trousers (*nudei)' c. (weil) er dem Hemdi einen Knopf (*ungebiigelti) annahen wollte. d. (weil) er dem Hemddat C?ungebiigelt) einen Knopfacc annahen wollte. 'he wanted to sew on a button to the shir� (*unironedi)' The lexical analysis in terms of ARG correctly predicts that depictive predicates are possible only with direct but not with indirect objects, that they must be able to express a temporary state reading, and that depictive and resultative predication are the only options lexically available. It furthermore predicts what kinds of argument structure can arise. In the remainder of this section, I will compare this analysis with syntactically based accounts, and I will argue that these accounts require too many additional assumptions or are too restricted. In the German examples the depictive predicate is adjacent to the verb
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(72a) allows to integrate situation-related adjuncts like schneil 'fast', while (72b) allows to integrate subject-related adjuncts like schick angezogen 'fashionably-dressed' in the above examples. Taken together, (69a), (69c), and (72a-b) exhaustively describe the options that are possible with ARG, and, in fact, no other type of verbal adjunct is known. The above analysis predicts that depictive predicates cannot be related either to indirect objects (dative NPs in German) nor to oblique arguments. Since the argument of the depictive predicate is lowest in the derived SF, it is structural according to (Js) and thus linked to accusative. Consider a 3-place verb such as schenken 'donate/give' and its hypothetical extension with a depictive predicate for the recipient, as shown in (73b).
Dieter Wunderlich
131
fmal position, which justifies a syntactic analysis with the structure in (7sa), parallel to the lexical analysis. Such a structure is not available in English because verb and adjective are not adjacent at the surface. Therefore, an SC analysis has been favoured for English, for example, by Stowell (1983), see (7sb). Stowell's analysis, however, raises the question of how PRO is licensed. Although solutions to this problem have been offered in subsequent papers (e.g. Hornstein & Lightfoot 1987), they are not fully convincing, and I will not discuss them here. (7sc) shows the structure proposed by Hoekstra (1988), which, again, is confronted with inherent problems.
[VP den Fisch [roh essen] ] [VP [eat the fish][sc PRO raw] [VP eat [sc the fish raw] ]
Hoekstra's SC analysis is problematic because of the number of necessary steps involved in the semantic composition of the proposed SC structure. Note first that [the fish raw] may not be reduced to the proposition RAw(def_fish), since it is the fish that is eaten and not a state of affairs denoted by a proposition. To make the analysis work, the SC must become an operator over the verb. This requires two steps: (i) the SC object must undergo Type Shift (TS) to range over the verb, (ii) the adjective must undergo MOD to become a modifier of the object. Moreover, the verb must rearrange its arguments by Argument Swapping (AS) in order to be properly affected by the SC. Since Argument Swapping (AS) destroys the correspondence between argument hierarchy and the ranking of >. abstractors, it is only allowed in syntactic composition. The derivation is shown in terms of logical types in (76), while the explicit steps are formulated in (77). 'eo' represents the individual referred to by the SC object.
a.
eat
[the fish
raw )
<e0,<e,<s,t>>>
eo
<eo ,t>
<e,<s,<e0,t>>>; AS
J
b.
d.
(77)
o .t>,<eo .t>>; MOD
<<e0,t>,t>; FC
e.
<e,<s,t>>; FC
a.
AS: >.v >.u >.s EA-r{u,v)(s) >.u TS: def_fish >.P P(def_fish)
b.
I �
<e0,t>,t>; TS
c.
�
�
c. MOD: >.x RAw(x)
�
>.v >.s EA-r{u,v)(s)
>. Q >.x {Q(x) & RAw(x)}
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(7s) a. b. c.
132
Argument Extension by Lexical Adjunction
d. FC: AQ [Ax {Q (x) & RAw(x)} (def_flsh)] A Q {Q(def_flsh) RAw(def_flsh)} e. FC: Au {[Av As EAT(u,v)(s) (def_flsh)] & RAw(def_flsh)} Au As {EAT(u,def_flsh)(s) & RAw(def_flsh)} =
&
=
(78) a. [w eat the fishi rawi] b. Mary [w met Johni [AP angry at himseif;"]i]. The binding facts, as well as other phenomena not mentioned here, can be dealt with in a binary syntax if one assumes a VP shell structure, as proposed by Larson (r 988b). His analysis is presented in (79). (79)
VP
------
NP
V'
-------
v
VP
-------
NP
V'
-----------
v I
Mary
e
John
met
AP
�----
anJiry at himself
The verb is combined with the depictive predicate in the lower position and is then moved into the upper position in S-structure. Here, John can properly function as the antecedent of himself Note that the resulting S-structure contains [John t angry at himself] as an SC. Larson's analysis is refined by Winkler (1994), who also gives a good survey of the development of the ideas on secondary predication. To account for the distribution of resultative and depictive predicates if they co-occur as in (8o), she proposes the general structure in (8r). (8o) Murphy hammers a coin from his grandfather's collection flat hot, drunk as a skunk.
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This derivation shows that a syntactic analysis based on (7sc) is quite expensive. Much less expensive is an analysis based on (7sb), since the shared-object property can be explicitly indicated by the control relation for PRO, so the verb may be extended by means of ARG, similarly to the lexical analysis shown in (52). There are alternative ways to indicate the shared-object property. For instance, Williams ( r 980) in his predication analysis proposed coindexing the depictive predicate with the object, as shown in (78a). However, given the binding facts in (78b) (Roberts 1988), this kind of analysis forces a ternary syntactic structure and so is undesirable.
Dieter Wunderlich 133
VP V P2
AP
----------- '
NP
V2
---------v2 VPJ � NPJ V' J � ' V1
AP
-----------
VJ
M.
e
the office the fish the coin a coin
�ft ate hammered hammers
/
flat flat
angry raw hot
drunk as a skunk
Here, the subject-related predicate functions as a VP modifier, while both the depictive and the resultative predicates related to the object form a predicate complex with the verb. This essentially is the claim of the lexical analysis too. But recall that the resultatives are analysed by the addition of BECOME through situation sharing, so that nonselected arguments arise. The fact that resultative predicates like flat are nearer to the verb than depictive predicates like raw is stipulated in (8r). In contrast, in the lexical analysis, the order of resultative and depictive predicates follows automatically, given that depictive predicates can predicate of arguments that are introduced by the resultative extension. (8r), where both V1 and AP theta-mark NPr> accounts for construc tions in which verb and adjective share an argument. If. however, the resultative AP predicates of an argument that is not selected by the base verb, as in the guests drank the wine cellar empty, one of the structures in (82) might be assumed: The verb drank theta-marks NP0, while the adjective empty theta-marks NP r . (82) a. (the guests) e [VP (NPr the wine cellar) e BECOME empty [VP drank NPo] ] b. (the guests) e [VP [sc (NPr the wine cellar) BECOME empty] [VP drank NPo] ] (82a) is a VP-shell analysis in which the verb moves in two steps, but it is unclear why BECOME empty is stranded in the second step. Moreover, one has to make the unintuitive assumption that BECOME empty is a verb that selects the lower VP with the verb drank. None of these problems arises with (82b). Here, the verb moves in one step to the upper position, and the
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John e John e John e
AP
134 Argument Extension by Lexical Adjunction
(83) a. VP shell analysis: (the guests) dranki (the wine cellar) BECOME empty [ti NPo] b. SF in the lexical analysis: (the guests) drank NPo and (the wine cellar) BECOME empty In the lexical analysis, the resultative predicate adds an individual argument that is linked to accusative because it is lowest in SF, while the VP shell analysis requires the added argument to be in an upper position in order to be assigned accusative. Thus, the relative positions of the original and the surface object of drink are just reversed in these two accounts. Hence, these accounts are not notational variants.30 It is hard to see how the VP shell analysis would make general predictions about the possible extensions of a verb. According to the present analysis, the only options available for adding a further predicate to the verb are given by the V adjuncts in (69a, c) and the VP adjuncts in (72a-b). In the case of lexical (or V) adjunction, the additional predicate is integrated via ARG and must share either the situational or the lowest argument with the verb. This additional predicate is delivered either in the morphology or in the syntax. Independent reasons lead to the syntactic differences in English and German. For the object to be linked, English requires positional adjacency, so the secondary predicate cannot be adjacent to the verb, while, in contrast, German allows this predicate to be adjacent to the verb.
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wine cellar BECOME empty constitutes an SC, functioning as an adjunct to the verb. However, in this case it is unclear how NPr can be assigned case. Thus, the VP shell analysis still has problems with instances of resultative constructions, even if it is successful in the case where individual arguments are shared. VP shell structures require the application of ARG rather than MOD in the semantic composition. In this respect, these structures are compatible with the main argument of this paper, that is, that ARG is the relevant operation to integrate secondary predicates. But the theoretical status of VP shells is still unclear. The VP shell analysis tries to account for several facts in one type of configuration simultaneously: for the binding facts, including those observed by Barss & Lasnik ( r 986), for theta role selection, and for structural case assignment. In contrast, the analysis in the LDG framework proposed in this paper deals with binding and theta role selection in SF, while it regards case assignment as resulting from the interaction of two kinds of features ( [hr] and [lr] ) rather than being directly expressed in the syntactic configuration. The difference between these two approaches becomes obvious when one compares them in terms of how the guests drank the wine cellar empty is represented.
Dieter Wunderlich
135
If the facts of binding are accounted for in SF, the reflexive-antecedent relationship need not be preserved in the syntax. Consider the above example in (78b), where angry at himself is predicated of John. The extended verb projects the syntactic structure in (84), where John does not c-command himself But the semantic composition in (8s) ensures that j {standing for John) will be the value for the argument that is linked to the reflexive pronoun. Note that himself, being an argument of ANGRY, requires that the argument variables u and z have identical value assignments. (84) Mary [VP [v met John] angry at himself)
angry: ..\u[at) ..\z A:NGRY(z,u) angry at himself ..\z ANGRv(z\u1) ARG(met): ..\P ..\y ..\x ..\s {MEE-r{x,y) & P{y)}(s) ..\P ..\x .Xs {MEE-r{xj) & PO)}(s) met John: met John angry at himself . Ax AS {MEET{xj) & Az ANGRY(z\u1)0)}(s) Ax AS {MEEr{xj) & ANGRYUj)}(s) .
The VP shell analysis is claimed to deal with the binding facts better than its predecessors. The analysis presented in this paper would suggest going a step further, that is, to assume an explicit semantic representation in terms of SF, and to regard this structure as the proper domain in which certain binding facts are explained.
6 C O NCLUS I O N I have argued in this paper that a unified analysis of lexical adjunction (by prefixes and particles) and secondary predication (by resultative and depictive predicates) can be achieved by assuming Argument Extension {ARG) as a general option of modification. Only certain classes of verbs may be extended by a predicative argument, which is in accordance with the fact that preftxes and particles as well as resultative and (object-related) depictive predicates are always restricted to particular verb classes. Since preftx verbs and particle verbs are morphological objects, ARG must be a rule available in morphology. The analysis given for these complex verbs was then extended to resultative and depictive constructions, which do not involve a morphological marking on the verb. Several variants of syntactic analyses have been considered and dismissed as too expensive, too limited in scope, or unable to explain the argument structure alternation, in particular, when resultatives like drink the wine cellar empty are involved.
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{8s) a. b. c. d. e.
I36 Argument Extension by Lexical Adjunction
DIETER WUNDERLICH
Received: 03.03.97 Final version received: 28.08.97
Heinrich Heine Universitiit Diisseldorf Seminar fur Allgemeine Sprachwissenschafi Universitiitsstr. 1 D-40225 Diisseldorf Germany e-mail:
[email protected]
NOTES I The ideas presented i n sections I and 3 originate from a course on Categorial
Grammar that I gave in summer I 993;
Semantics in Blaubeuren, October I994, and then prepublished as Wunderlich (I99S)· The final publication was delayed
they have then been developed in con
because another journal rejected publi
stant dialogue with Barbara Stiebels.
cation after a two years' reviewing
Section 4 on resultatives improves my analysis in Wunderlich (I992: 42ff); this
process. I would like to thank Ursula Brinkmann, Susan Dostert, Ray Fabri,
topic has been the subject of many discussions with Ingrid Kaufmann. I
Sandra Joppen, Uwe Monnich, Ralf Naumann, Barbara Partee, Manfred
am grateful to both, and I use the results that have been published in Kaufmann (I99Sa) and Stiebels (I996). A first ver
Pinkal, Tim Skellett, Amim von Stechow, Ede Zimmermann, and Ilse Zimmermann as well as four anony
sion of this paper was presented at the
mous reviewers for many valuable com
Conference on Recent Developments in the Theory of Natural Language
carried out in the SFB 282 'Theorie des
ments. The research reported here was
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The lexical analysis proposed in this paper is able to show why certain verbs can be extended and others cannot. It explains why unselected arguments become structural, even though the original object of the base verb may have to be suppressed. Furthermore, it shows why lexically triggered depictive predicates must be related to the direct object and why resultative extension precedes the addition of depictive predicates. One final remark is at place here. If verbal adjuncts of the kind considered here are analysed by means of ARG, it becomes immediately clear why those adjuncts may shift into 'true' arguments (see Dowty 1994). Predicative adjuncts as in etwas leer trinken· 'drink something empty' are potential arguments of a verbal host Qicensed by general inferences from the verb's lexical meaning), while 'true' predicative arguments as in consider him foolish belong to the meaning of the verb itself According to the analysis proposed here, the lexical adjuncts do not have to shift their logical type when they are incorporated into the verb's meaning in the course of lexicalization; what is shifted is the logical type of the verb when its SF representation is extended, thus specifying the verb's mearung more narrowly.
Dieter Wunderlich IJ7 7 This operation corresponds to the am operator in Hamann {I99I: 664), which goes back to Kamp {I975)· 8 Betreten is formed with the preftx be from treten; betreten and treten differ slightly in meaning, a difference that need not concern us here. 9 Only the higher occurrence of x is counted here. I o Sich is underspecifted in case, but that the reflexive is dative is shown by examples with ftrst or second person, for instance, ich tanzte mir einen Muske/kater an 'I got muscle pain from dancing'. I I In the default word order of German, the lowest argument combines ftrst with the verb, as is shown in (i), while in a scrambled structure like (ii) a higher argument combines ftrst. To combine the bracketed elements semantically, one has to assume argu ment swapping in the sequence of A abstractors. i. weil sie auch dem Bischof einen solchen Brief geschrieben hat. ii. weil sie einen solchen Brief [auch dem Bischof geschrieben] hat. 'because she wrote such a letter also to the bishop' Note that argument swapping also results in a syntactic analysis of scramb ling, in which the scrambled element leaves a trace that is interpreted as a bound variable. The scrambled structure iii. weil sie einen solchen Brie� [auch dem Bischof t; geschrieben] hat. corresponds to a transformation of Az Ay Ax VBRB(x,y,z) to Az Ay Au Ax VBRB(x,y,z)(u), which reduces to Ay Au Ax VBRB(x,y,u). 12 Recall from note 3 that the morphological structure is [P•max V]v in the parricle verbs in (29), but P•min V]v in the preftx verbs in (3o) (see also Stiebels & Wunderlich I 994). An interesting variant of this view is held by Zeller(I997). who assumes for particle verbs that the lexical entry (Prt + V]v is
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Lexikons' and supported by the German Science Foundation (DFG). 2 The predicates expressed by ver- and an will be analysed in section J; it is not possible to gloss them adequately here. The additional argument receives accusative case in both {Ia) and {Ib). Note that both prefixes and particles can occur in other functions than those considered here; see Stiebels {I996). Prefixes and particles cannot be heads because it is the base verb from which the complex verb inherits its inflectional properties. More arguments against a head analysis of prefixes and particles are given in Stiebels & Wunderlich {I994) and in Stiebels (I996, I997). Prefixes and particles behave very simi lar semantically, although they differ in a morphological feature: prefixes are morphologically minimal (and thus must be affixed), whereas particles are morphologically maximal (and thus must remain visible in syntax). 4 As will be shown below, this analysis captures certain features of the ana lyses proposed by Larson (I988b) and Winkler {I994= r r7). There are a few adjectives that can only be used attributively by virtue of their lexical meaning, for example, recent, former, alleged. These items are always functors on nouns. 6 Throughout this paper, I use the slash notation of CG in the undirected vari ant, so A/B does not entail any state ment of whether B has to be found at the right or at the left. I use the expressions of CG as a convenient way to briefly represent functor-argument relations. Each rule in a CG format is accompanied by a translation in tertns of lambda formulas. As will become clear in section 2, I do not assume that CG itself describes morphological or syntactic structures of natural languages, in my view, it rather describes the 'syntax' of semantic representations.
IJ8 Argument Extension by Lexical Adjunction 'superimposed' on a syntactically derived
+ Vo]v<> at LF. Compare this with betreten 'enter' repre
head structure [P
0
IJ
sented as Ay Ax As {GO(x) & BEe Loc(x,rn-r(y))}(s) in ( I 7b). I4 wc(u.AT(z)) is true iff u is contained in a region that surfaces
z.
I s If there are more than one structural cases linked to dative, either double dative is used or some selection has to be made (Wunderlich I 997)· I6 Note that
Sie schrieb den Bischof in
construction with a PP (see below). I7 One reviewer raised the question of how the ambiguity of {i) versus non ambiguity of (ii) {von Stechow I 996) can be explained in our theory. 1.
wei! er sich ihre Gunst wieder
{restitutive or repetitive)
erschrieb because he himself her favour again er-wrote ii. wei! er sich wieder
(repetitive)
ihre Gunst erschrieb because he himself again her favour er-wrote Let us assume that an adverb with narrow scope like in (i) can either modify the whole situation referred to by the verb or some subsituation of it. The representation in (42b) allows us to infer two subsituations: a trarlSition characterized by
BECOME,
and a pos
terior state specified by poss. The latter gives rise to the restitutive read ing: by his writing he got her favor again. If one derives the possible read ings in terms of structural positions, the real question is why there
can
be only
two and not three readings. It is maybe
Wunderlich (I 997: 28) I argued that a scopal analysis alone cannot explain how many and exactly which readings can arise with adverbs. I8 Carrier & Randall {I992) argue that the direct object in English resultatives is only an argument if it is selected by the base verb. They test argumenthood of the direct object by middle formation, adjectival passive and nominalization.
As Goldberg {I99S) points out, these tests are not reliable, since some resul tatives of transitive verbs also fail to pass
them. Thus, one can only conclude that the direct object is an argument when the construction passes the test, but not that it is not an argument if it fails. Note that all resu!tatives in German pass the tests (Wunderlich I 992: 44, Kaufmann I99sa: I 4J). The difference between English and German may be due to semantic restrictions that hold in English middles, adjectival pas sives, and nominalizations, but not in German. I 9 The verb is an ordinary intransmve rather than an ECM verb. Even in the case of ECM verbs a lexical analysis would dispense with the notion of exceptional case marking and instead assume a more differentiated lexical entry: hiiren 'hear' in (i) is represented by (ii) but hiiren in (iii) by (iv), where the propositional variable is split off into a predicate variable and an individual variable (Wunderlich I 989). 1. als ich horte, dal.\ er kam 11. Ap Ax As HEAR(x,p)(s) iii. als ich ihn kommen hone
'when I heard that he came' 'when I heard him come'
1v. AP Ay Ax As HEAR(x,P(y) )(s)
Coherence that forbids the reading with
Note that the representation in (iv) is
again(sEcoME)
subject to ordinary case linking, with
because this would sug
gest that one and the same causal factor
accusative
can induce several transitions (see also
argument.
for
the
lower
structural
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'she wrote the bishop in a rage' is possible, but this is a resultative
Wut
Apppendix 2 in von Stechow I 996). In
Dieter Wunderlich I39 20 If
mit Krimis
is regarded as an adjunct
one needs some mechanism of coin
no accusative can be assigned to the argument 'z'. By the same reasoning
dexation between adjunct and the sup pressed argument of schreiben. Recall
since here
that in the analysis given in section J, Krimis is an argument that is realized by 'lexical case', that is, by means of the preposition mit. Two reviewers found my argumentation concerning an SC analysis not conclusive. I am not sure whether more elaborate assumptions, for instance, the assumption of [Spec,
one can explain why (s9b) is possible, no
additional
argument
shows up. Still, the problem remains for von Stechow to explain why English allows the option in (s9b), whereas German does not. 25 More precisely, ARG adds Q(s) to the verb, and Q is saturated by the resulta
tive extension predicate .\P .\z .\s BEC P(z)(s), thereby leaving ),z to the result. z must thus differ from any argument
tion, could make things better. Since my
variable of the base verb. One would have to state another, more complex
approach captures the semantic moti vation for an SC analysis and, simul taneously, avoids the inherent problems such an analysis is confronted with, why not adopt the analysis that works? 2 I Mulder (I992) and Den Dikken (I 992) propose SC analyses for some preftx and particle verbs in Dutch. They assume that these elements are SC heads that themselves are subcategorized for an SC, but it is unclear how they would account for the interpretation of these verbs more explicitly and to what extent their analyses could be generalized. 22 One reviewer offered an English example to me which shows the same indeterminacy as German. He tied the
bag shut: the knot he ties can be either in the bag itself or in a string around the
ARG operation to ensure that more than one argument is shared. 26 A semantic-conceptual explanation of the differences between unaccusative and unergative verbs has been proposed by Kaufmann (I995c). 27 Consider the following examples: i. Sie biigelte das Hemd nai\. 'She ironed the shirt wet' ii. Sie sah ihn krank. 'She saw him sick' iii. Sie lachte ihn krank. 'She laughed him sick' It is unlikely that shirts become wet by being ironed, and, similarly, that someone becomes sick by being seen. Therefore, the object of the base verb must be the shared argument. In con trast,
opening of the bag.
lachen
'laugh' is basically intransi
23 Generally, resultatives formed with directional prepositions are more toler
tive, so that (iii) can only mean that the respective person becomes sick, a read
able, for instance, (i) is possible, as pointed out to me by one of the
ing that is licensed by situation sharing. 28 The accepted order in English is just reversed to that in German because
reviewers. 1.
Der Bar erschreckte die Maus zu Tode.
The
bear
frightened
the
mouse to death' I will return to this difference below.
the verb is VP-initial in English but VP-ftnal in German.
29 The word order in (74d) cannot
be
generated by scrambling. The adjective could only function as an apposition
24 Von Stechow (I 996: I o8) explains the
here, meaning 'when it was unironed'.
Case theory. He assumes that unaccu
acceptable in all grammatical positions,
satives do not have voice, hence, AgrO, selecting voice, cannot be projected and
for instance, with prepositional objects as in the following example:
ungrammaticaliry of (59a) by means of
Similar
constructions are
marginally
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AgrO] as a structural accusative posi
I40 Argument Extension by Lexical Adjunction i.
(weil) er auf dem Hemd ungebii gelt/gerade gebiigelt nicht sitzen wollte.
'he did not want to sit on the shin unironed/just ironed'
30 Although Hale & Keyser (I 992) rein terpret Larson's syntactic structures as lexical relational structures, these structures crucially differ from SF structures.
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Folia Linguistica, 29,
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12, 377-427.
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Kiparsky, Paul ( I992), 'Structural case', MS, Berlin, Institute for Advanced Studies.
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Levin, Beth & Hovav, Malka Rappaport (I 995). Unaccusativity. At the Syntax-Lexical
Semantics Interface, MIT Press, Cambridge, MA Mulder, Rene (I 992), "The Aspectual Nature of Syntactic Complementation', doctoral dissertation, University ofLeiden. Naumann, Ralf ( I996), Aspectual Composition
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Linguistic Inquiry,
19, 703- IO.
Ross, Malcolm ( I997), 'Possessive-like attrib
ute constructions in the Oceanic languages of western Melanesia', paper delivered at the I 3th International Congress of Histori cal Linguists, Diisseldor£; August I 997.
M Rappaport, & A Zaenen (eds), Papers in Lecical-Functional Grammar, Indiana Uni
versity Linguistics Club, Bloomington, Indiana, I 43-57. Stechow, Amim von (I996), "The different readings of wieder "again": a structural account', journal ofSemantics, 13, 87- I38. Stiebels, Barbara (I 996), Lexikolische Argu
mente und Adjunkte. Zum semantischen Beitrag von verba/en Priif.xen und Partikeln, Akadernie-Verlag, Berlin. Stiebels, Barbara {I 997). 'Complex denomi
nal verbs', in Geert Booij & Jaap van
Made (eds), Yearbook of Morphology 1997 (in print). Stiebels, Barbara & Wunderlich, Dieter (1 994), 'Morphology feeds syntax: the case of particle verbs', Linguistics, 32, 9 I 3-68. Stowell, T. (1 983), 'Subjects across categories',
Linguistic Review, 2, 285- 3 1 2. Wilder, Chris (I 99 I), 'Small clauses and related objects',
Groninger Arbeiten zur Germanistischen Linguistik, 34, 2 I s -36.
Williams,
Edwin
Linguistic Inquiry,
(1980),
11, 203-38.
'Predication',
Winkler, Susanne (I 994), 'Secondary predi cation in English: a syntactic and focus theoretical approach', doctoral disserta tion, University of Tiibingen (working
papers of the SFB 340 'Sprachtheoretische Grundlagen fur die Computerlinguistik', 64, IBM Deutschland Heidelberg).
Wunderlich, Dieter (1 987), 'An investiga tion of lexical composition: the case of German
be-
verbs',
Linguistics,
25,
283-33 1 .
Wunderlich, Dieter (I989), 'Amim von Ste chow, das Nichts und die Lexikalisten',
I 22, 32 I -29. Wunderlich, Dieter (I99I), 'Intonation and
Linguistische Berichte,
contrast', journal ofSemantics, 8, 239 - 5 1 .
Wunderlich, Dieter (1992), 'CAUSE and the structure of verbs',
Working Papers of the
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of Predication', doctoral dissertation, MIT (distributed by Indiana University
1 42 Argument Extension by Lexical Adjunction SFB
282 'Theorie des Lexikons', 36, University ofDiisseldorf Wunderlich, Dieter {1994), Towards a lexicon-based theory of agreement', Theoretical Linguistics, 20, 1 -35. Wunderlich, Dieter (1995), 'Argument extension by lexical adjunction', in Fritz Hamm, Joachim Kolb, & Arnim von Stechow (eds), The Blaubeuren Papers, SfS-Report-09-95, UniversitatTiibingen, 435-73· Wunderlich, Dieter (1996a), 'Lexical Cate gories', Theoretical Linguistics, 22, 1 -48.
Wunderlich, Dieter ( 1996b), 'Models oflexi cal decomposition', in Edda Weigand & Franz Hundsnurscher {eds), Lexical Structure and Language Use, Niemeyer, Tiibingen, 169-83. Wunderlich, Dieter (1997), 'Cause and the structure of verbs', Linguistic Inquiry, 28, 27-68. Zeller, Jochen (1997), 'Against overt par ticle incorporation', Penn Working Papers in Linguistics, 4, 1997 (Proceedings of the 21st Annual Penn Linguistics Colloquium). Downloaded from jos.oxfordjournals.org by guest on January 1, 2011
jounltll of&mantics
14' 143- 171
© Oxford Univenity Press
1997
A Semantics for the Counting Numerals of Latin ALMERINDO E. OJEDA University of California at Davis Abstract
I
I NTROD U C T I O N
Latin had two formally distinct series of counting numerals: the series of cardinals and the series of collectives. The purpose of this paper is to provide a precise semantics for these two series of numerals. Crucial to this semantics will be mereologies-a family of algebraic structures which was originally conceived by Lesniewski (1916) in his attempt to avoid the paradoxes of set theory, and was later applied to the formalization of nmninalistic philosophy (Eberle 1970V The use of mereologies in the semantic study of grammatical number is not new. It was pioneered by Massey (1976) and Wald (1977), and has now become commonplace after the work of Link ( 1983)- see for example Krifka (1989 and 1990), Landman (1989 and 1991), Barker (1992), Eschenbach ( 1993), and Ojeda (1993a). Readers who are not familiar with mereologies are invited to tum to the Appendix to this paper, where the fundamental concepts of mereological theory are defmed. The body of this paper is organized as follows. First we will present the uses of the counting numerals of Latin that have been traditionally recognized in the literature {§2). Then we will endow these numerals with a precise semantics (§3), and show that this semantics can account for the rather diverse uses the counting numerals of Latin can be put to (§4).
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In this paper we present a precise semantics for the two series of counting numerals of Latin: the cardinals and the collectives. Couched in the framework of mereological model theoretic semantics, the proposal is that while a cardinal denotes a set of equinumerous combinations of elements of an individuation of the model, a collective denotes a set of equinumerous combinations of elements of a panition of the model. Crucial to the success of this simple proposal will be a number of nontrivial assumptions concerning the narure of groups and kinds in linguistic discourse, the semantics of pluralia tantum, and a distinction between specific and collective plurality. The paper also contains a preliminary discussion of the semantics of cardinals and collectives in the Germanic, Baltic, Slavic, and Indic branches of Indoeuropean and, beyond Indoeuropean, in Finnish, Mongolian, and Greenlandic. An appendix presents the fundamental concepts of Mereological Theory.
144 A Semantics
for the Counting Numerals of Latin
2
U S E S O F CARD I NALS AND C OLLE C T I V E S
Latin had several formally distinct series of numerals (Leumann et al. I963, §§206-8). Two of these series were used for counting: the series of cardinals and the series of collectives. The morphological differences between these two series of numerals may be gathered from (I), which contains the declensions of the first five terms of each of these series (Allen & Greenough I 904: § §94£)
(I) CARDINAL: iinus, �a, � um, � ius, �i, �am, �o, �a. COLLECTIVE: uni, �ae, �a, �arum, �is, �as, �as. CARDINAL: duo, �ae, �arum, �arum, �obus, �abus, �os, �as. coLLECTIVE: bini, �ae, �a, �arum, �arum, �is, �as, �as, �us, �um, �am, CARDINAL: tres, � ia, � ium, � ibus, � is. coLLECTIVE: trini, �ae, �a, �arum, �arum, �is, �os, �as, �us, �um, �am, CARDINAL: quattuor (indeclinable). coLLECTIVE: quaterni (quadrini ) , �ae, �a, �orum, �arum, � is, �as, �as, � us, � um, �am, �o, �a.
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We conclude (§s) by presenting the uses of cardinal and collective numerals found in languages other than Latin. These uses suggest that the analysis of the counting numerals of Latin proposed in this paper applies more generally, and may perhaps be a semantics for counting numerals in general. Essentially, our proposal will be a simple one. It will be that the cardinal numerals of Latin denote equinumerous combinations of indivi dual entities, whereas their collective counterparts denote equinumerous combinations of discrete entities. Crucial to the success of this simple proposal, however, will be a number of nontrivial assumptions concerning the nature of groups and kinds of linguistic discourse, the semantics of pluralia tantum, and the distinction between specific and collective plurality. To be more specific, we will assume that both groups and kinds are combinations of individuals, that count nouns are either specific (in which case they involve combinations of individuals) or collective (in which case they involve combinations of groups), and that the groups denote by typical pluralia tantum are not individuals (so that pairs of scissors, trousers, or goggles correspond not to individuals, but rather to pairs of individuals).
Almerindo E. Ojeda
1 45
CARDINAL: quinque (indeclinable). coLLECTIVE: quini, � ae, �a, ,.., (]rum, �arum, � is, �os, �as, � us, � um, �am, �o, ,.., a.
(2) a. singuli, �ae, �a, �arum, �arum, � is, �os, �as. b. terni, �ae, �a, �arum, �arum, � is, �os, �iis. Collectives and distributives are best analyzed, therefore, not as two variants of the same series of numerals, but rather as two distinct series of numerals (but see below).2 Intuitively, cardinals were used to count individuals. Examples of this perfectly unsurprising use of numerals are given in (3). (3) uno ictu (Pl. Bac. 968) 'one blow' I duo Julmina (Verg. Aen. 6.842) 'two thunderbolts' I tres Gratiae (Sen. Ben r.p) 'three Graces' I quattuor aras (Verg. Eel. s.6s) 'four altars' I earum quinque stellarum (Cic. Rep. r.22) 'of those five stars' I sex dies (Suet. Nero 38.2) 'six days' I septem noctes (Pl. Poen. 274) 'seven nights' I annos octo (Cic. Clu. 7) 'eight years' I nouem libros (Gel. 1.19.2) 'nine books' I decem talenta (Ter. An. 95 1) 'ten talents (of weight)'. Collective numerals had, on the other hand, quite a variety of uses. For one thing, they could be used 'occasionally in poetry with the meaning of the corresponding cardinal' (Hale & Buck 1903: §247.3), i.e. simply to count individuals, as centenas is in (4): (4) .iEgaeon qualis centum cui bracchia dicunt centenasque manus (Aen. 10, 566) '.tEgeon, hundred-armed, they say, and hundred-handed' I optet nunc bracchio centum centenasque in bella manus (Stat. Th. 10, 294) 'now would he have a hundred arms, a hundred hands to fight with' I centenasque pater det Phoebus Jundere voces (Sil. 4, s28) 'and if Father Phoebus granted me to speak with a hundred tongues'.3 But collectives also contrasted with cardinals in a number of ways.
•
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Collectives have been sometimes regarded as variants of distributives, the numerals used in the enumeration of entities apportioned apiece, as in sepfena iugera 'seven jugera each', quingenos denarios 'five hundred dinars to each' (Allen & Greenough I904: §95a, Ernout and Thomas 1964: §2o4a). In fact, they have been occasionally construed as two uses of the same series of numerals. To do so, however, is to disregard the fact that collectives and distributives differ from each other not only in meaning, but also in form. Thus, instead of the collective forms of uni and trini listed in (I), the distributive series contained, respectively, the forms of singuli and terni listed in (2).
1 46
A
Semantics for the Counting Numerals of Latin
According to Brugmann (I907: 4of£) and LOfstedt (I 9S8: §4), for example, the collective numerals of Latin could be used in up to four different ways. First, they could be used to count a number of individuals belonging to the same group or kind. Thus, according to LOfstedt (I9S8: §4, I}, 'they designate a collection (eine Zusammenfassu ng), an integrated whole (eine Zusammen
gehorigkeit), a grouping (eine Gruppierung)'. Examples of this use can be found in (s).
a group of seven reeds)'.5
·
Brugmann and LOfstedt also include here cases in which the singular form of a collective numeral combines with a noun in the singular to count the parts or 'folds' of single objects. According to LOfstedt (I 9S8: § §48f£), the sense of these constructions is that of 'double, triple, and so on- that is [the sense of being] composed of two, three, etc. parts which are integrated into a whole'. Examples of this use follow. (6)
duplici natura et corpore bino (Lucr. s. 879) 'twynatured and of body twain'6 I pectore bino (Anthologia Latina I, 2, 79I , 25) 'double breast' I latratu trino (Sen. Thy. 67sf) 'triple barking' I trina ustione (Plin. nat. 36, I SS) 'triple calcination' I trina ratio vivendi (Chalc. comm. 24S) 'threefold reason to live' I trina foce (Avien. Arat. 903) 'triple face' I septeno murmure (V. Fl. 7, 464) 'sevenfold muttering' I centenaque arbore jluctum verberat {Verg. Aen. IO, 207) 'he strikes the waters with a hundred-fold oar (lit. tree)'.7
Second, they could be used to count the groups or kinds themselves. As LOfstedt (I 9S8: §4, 2) put it, 'by means of collectives units are counted each of which is a multiplicity (ein Mehrfaches)'. This use is illustrated in (7)-
(7) Quo modo oletum agri iugera CCXL instruere oporteat [. . .] boves trinos, asinos ornatos clitellarios tris [. . .] (Cato agr. 1 0. I ) 'This is the proper
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(s) binos scyphos (Cic. Verr. II, 4, I4, 32) 'two matched goblets; pair of goblets belonging to a set' I boves bini (Plaut. Pers. 3 I 7) 'pair of yoke of oxen' I bina hastilia (Virg. Aen. I, 3 I3) 'two spear shafts in a set' I aratro binae aures (Virg. Aen. I, I 72) 'two moldboards (lit. 'ears') of a plough' I bina frenae (Virg. Aen. 8, I 68) 'pair of bridles' I boves trinos (Varro r.r. I, I9, I} 'triad of oxen, eine Dreiheit von Ochsen'4 I numina trina (Ov. Fast. S·I 46) 'triad of divinities' I trina capita Cerberi (Sen. Here. Fur. 7, 83) 'head triad of Cerberus' I epistulas quaternas (Plin. Nat. 7.9 I) 'set of four letters �it. epistles)' I quaterni quinique exercitus (Liv. 9. I9.3) 'group of four or five armies' I seni (praetores} (Veil. 2.1 6.3) 'succession of six leaders' I septenis fistula cannis (Ov. Met. 2, 682) 'seven-reed (shepherd's) pipe �it. pipe with
Almerindo E. Ojeda
1 47
This use of collectives was observed already by Marins Victorious, a Latin grammarian from the fourth century of our era, who pointed out {Art. Gram. 1, 4) that 'tria and trina are not the same: tria are indeed singularities, while trina are multiplicities. Thus we say trinos calceos and trina vestimenta, not tria' (c£ Keil 196 1: VI, 22, 22f£). As LOfstedt (1958: §36) remarked, 'it would seem obvious that Marins Victorious uses trinos calceos in the sense of "three pairs of shoes". For, otherwise the example would be hardly appropriate as an illustration of the use of trina as multiplicia'. Invariably included among the groups counted by collectives are the groups contributed by pluralia tantum which referred to a number of entities in a way that 'regard [was] had to the compound [units]' which the entities made up {c£ Madvig 1 851: §76c, Brugmann 1907: 49; Kiihner 1912: §121.5). The vast majority of the pluralia tantum of Latin were of this kind. A small sample of these plurals is given in (8).
(8) aedes 'house' I arma 'weapons' I auxiliae 'aids' I bonae 'goods' I carceres 'barriers (of a race course)' I castra 'camp' I codicilii 'tablets' I comitia 'elections (town meeting') I copiae 'troops' lfores 'double doors' lfortunae 'possessions' I gratiae 'thanks' I scalae 'stairs' I valvae 'folding doors' I horti
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equipment for an oliveyard of 240 jugera: [ . . . ] three yoke of oxen, three asses bearing a pack-saddle, . . .'8 I mow asinarias unas et trusatilis unas Hispaniensis unas (Cato agr. 10.4) 'one pair of donkey mills (lit. mill stones), one pair of hand mills (lit. millstones), one pair of Spanish mills (millstones)' I qui (sc. labor) [. . .] omnis manibu.s nunc pendet ab unis (Val. Flac. po) 'all of which work is dependent on one pair of hands [i.e. those of Tiphys]' I prius de trinis copulis discernendum [. . .): primum de copulis naturae et usuis [. . .], secundum de copulis multitudinis ac finis [. . .), tertium de copulis personarum (Varro ling. 9, 4} 'first there must be a clear distinction of three sets of relations, first the distinction of the relations of nature and use, second the distinction of the relations of extension and limitation, third the distinction in the relations of the speaking persons.' I ad hunc quadruplicem Jontem ordines deriguntur bini, uni transversi, alteri derecti [. . .] transversi sunt qui [. . .] derecti sunt qui [. . .] (Varro ling. 1 0, 22) 'to this fourfold source two sets of lines are drawn up, the ones crosswise and the other vertical [ . . . ] crosswise are those which [ . . . ] vertical are those which [ . . . ]' I habetis interim bina animalia, deos ab hominibus plurimum difforentis (Apul. Socr. 4} 'you have in the meantime two kinds of creatures-gods very different from men.' I salsamina denique, quae sunt una commixtio quadrinis copulata de frugibu.s (Arnob. nat. 7, 24) 'sauces which are a mixture combined from four kinds of fruit'.9
1 48
A
Semantics for the Counting Numerals of Latin
'pleasure grounds' I impedimenta 'baggage' I litterae 'letter(s) of corre spondence' I loci 'topics' I ludi 'public games' I natales 'descent' I nuptiae 'nuptials' I operae 'day laborers, hands' I tabellae 'documents, records' I viscera 'entrails'.
(9) ( 10)
(I I)
a. b. a. b. a. b.
duae aedes 'two temples' binae aedes 'two houses' tria castra 'three forts' trina castra 'three camps' quinque litterae 'five letters of the alphabet' quinae litterae 'five letters of correspondence'
The pluralia tantum in (8) must be distinguished from the few pluralia tantum which referred to a number of personal entities in a way that 'regard [was) had to the individuals which [made) up the number' of personal entities (Madvig I 8SI: §SI). Some of these pluralia tantum are listed in {I2). 'children' I maiores 'ancestors' I proceres, primores 'social leaders, nobles' I penates 'household gods' I manes 'spirits of the departed' I superi 'inhabitants of the upper world' I inferi 'inhabitants of the lower world' (c£ Kuhner I9I2: §12r.s).11
(12) liberi
Interestingly, these pluralia tantum combined with cardinals (c£ tres liberi 'three children', and sex liberi 'six children', cited by Madvig r8s i : §76.c and Kuhner 1 9I2: I2r.s). In a handful of documented cases, the groups or kinds counted by a collective differed from each other, even to the point of being in direct opposition. In the words of LOfstedt (1 958: §4, 3), 'they designate different or opposing parts of a whole'. These cases represent the third use of collectives recognized by Brugmann and LOfstedt, and are listed in {IJ).
( r3) naturasque rerum binas esse
(Apul. Plat. r , 9) 'the nature of things is ipsius quoque terrae binas partes contrarias inter se diversaque constituit, orientem scilicet occidentemque (Lact. inst 2, 9, s) 'of the earth twofold' I
itself he has established two parts [=kinds of parts?) contrary and different &om each other, that is east and west'
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Some of the nouns in (8) may be used either as pluralia tantum or as ordinary, contrastive, plurals. Interestingly, when used as pluralia tantum they called for collectives; when they were used as ordinary plurals they called for cardinals. This can be seen from the contrasts in (9)-(u). When these nouns combine with collectives, the senses consigned in (8) emerge, but when used with cardinals, the senses associated with the ordinary uses of these plurals arise (c£ the singular nouns aedes 'temple', castrum 'fort', littera 'letter of the alphabet'1�.
Almerindo E. Ojeda
1 49
3 T H E I N TE RPRETAT I O N O F N U M E RALS A model for the interpretation of the counting numerals of Latin is an atomistic mereology (M, � ) in which M is the combinatorial closure of the set of individuals we may talk about on some particular occasion, 12 � is a relation of inclusion, and the atoms of the mereology are the individuals we may talk about on the occasion in question. Let vii be a model for the interpretation of the counting numerals of Latin. The interpretation of these numerals relative to vii is as shown in
(r4). (r4)
A semantics for the counting numerals of Latin a. The denotation of the nth cardinal numeral of Latin relative to vii is the set of combinations of n elements of an individuation of vii . b. The denotation of the nth collective numeral of Latin relative to vii is the set of combinations of n elements of a partition of vii .
The notions of individuation and partition involved in
(r4)
are defmed as
follows. 13 The individuation of a model is a subset of the model which contains all and only the atoms of the model. A partition of a model is a subset of the model which contains elements which are mutually exclusive and jointly exhaustive in the model. The elements of a subset of a model are mutually exclusive if and only if no two elements of the subset are such
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But notice that the groups and kinds counted by means of the second use of collectives were not required to be similar in any way (consider in this regard the next to last example in (7) above). It follows that the cases in (r3) should be regarded as particular cases of the second use of collectives illustrated in (7). This we shall do from now on. The fourth and final use of collective numerals according to Brugmann and LOfstedt was distributive (LOfstedt 1958: §4, 4). In other words, they were used to count the number of entities distributed to any one of several beneficiaries. The allegedly distributive use of collectives will be ignored in the sequel, as it is the proper use of the distributive series of numerals, which has been argued to be separate from the collective series of numerals. In short, then, while the cardinal series of Latin numerals was used to count individuals, the collective series of Latin numerals had three rather different uses, namely (i) to count groups or kinds proper, including the groups contributed by pluralia tantum of the appropriate kind, (ii) to count individuals, and (iii) to count individuals belonging to the same group or kind, including the parts of a single object.
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A Semantics for the Counting Numerals of Latin
{I S)
abcdef
�
abcde abcdf abcef abdef acdef bcdef
a
b
c
d e
f
The individuation of the model diagramed in { I S) is
{a, b, c, d, e,J } . Hence
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that there is some element of the model which they both include. The elements of a subset of a model are jointly exhaustive if and only if their combination is equal to the combination of all the elements of the model (or, equivalently, of the atoms of the model). Notice that the individuation of a model for the interpretation of numerals is a subset of the model whose elements are all mutually exclusive (no two individuals may include a common part). Notice also that these elements are jointly exhaustive (the combination of all the elements of the model is a combination of all the individuals therein). Every individuation is, therefore, a partition. But, as we shall see below, not every partition is an individuation. The notion of partition thus arises as a proper generalization of the notion of individuation-and a natural one at that. It will be noticed that our interpretation of the cardinal numerals of Latin is similar to a number of proposals in the formal literature-see for example the interpretations of numerals proposed in Bartsch { I973). Hurford ( I987), Link (I987), Eschenbach {I993). and Ojeda ( I 993a), all of which are in tum indebted to the definitions of number in Mill {I 84J: 111, xxiv, §s), Frege { I 884). and Russell (I903: xi). It should be pointed out, however, that no similar tradition exists for the interpretation of collective numerals, be they the collective numerals of Latin or the collective numerals of any other language that has them (see below). In fact, collective numerals have remained hitherto uninterpreted in the formal literature-let alone unrelated to the interpretation of their cardinal counterparts. To illustrate the interpretations in {I4), let us assume that the model for the interpretation of the counting numerals of Latin is an atomistic mereology diagramed in { I s).
Almerindo E. Ojeda 151 the denotation of the first six cardinal numerals of Latin relative to model will be as indicated in (I6).
this
{a, b, c, d, e,J } [duo] { ab, ac, ad, ae, af, be, bd, be, bf, cd, ce, cf, de, df, ef } tres] {abc, abd, abe, abJ, acd, ace, acf, ade, adf, aef, bed, . . . , def } quattuor] {abed, abee, abcf, abde, abdJ, abef, acde, acdJ, . . . , cdef} quinqueK { abcde, abcdJ, acdef, abdef, bcdef } [sex] { abcdef}
(I6) [unus]
=
=
I
=
=
=
=
{ab, cd, ef } {abed, abef, cdef } { abcdef} As to cardinals over sex and collectives over trini, they will all have one and (I7) [uni]
=
[bini] [trini]
=
=
the same denotation relative to (Is), namely the empty set. It should be plain, however, that this is not a shortcmning of the interpretations in (I4), but rather a consequence of the poverty of the model we used in our illustration. To assign distinct interpretations to the cardinals of Latin all we need is a model which has as many atoms as Latin has cardinals, and this is something one can always have. Similar considerations apply to the collectives of Latin and a partition which has as many elements as there are collectives in Latin.
4 A C C O U N T I N G F O R T H E USES O F CARD I NALS AND C OLLE C T IV E S The interpretation o f numerals we have proposed i n (I4) accounts straightforwardly for the uses of cardinals illustrated in (J). To illustrate, let us assume that (IS) represents a model in which there are exactly four oxen a, b, c, d. If pluralization amounts to combinatorial closure (as argued by Link I 98J, Barker I992, Ojeda I99Ja, and others), then the denotation of the plural boves 'oxen' relative to this model will be as indicated in (I8). (r8)
[boves]
=
{a, b, c, d, ab, ac, ad, be, bd, cd, abc, abd, acd, bed, abed}
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With collectives, things are a bit more involved. For one thing, partitions are seldom unique. In fact, in this case, the model in (Is) has exactly two hundred three partitions.14 One of these partitions is { ab, cd, ef}. It is the partition of the model into three pairs ab, cd, ef. The denotations of the first three collective numerals relative to this model and this partition would therefore be as shown in (I7).
1 52 A
Semantics for the Counting Numerals of Latin
Moreover, if we assume that the denotations of nouns and numerals combine by default via set-theoretical intersection, then the denotation of boves duo 'two= oxen' relative to ( I S) would proceed as follows:
[boves duo] = [boves] n [duo] = t a, b, c, d, ab, ac, ad, be, bd, cd, abc, abd, acd, bed, abed } n {ab, ac, ad, ae, af, be, bd, be, bf, cd, ce, cJ, de, df, eJ } = {ab, ac, ad, be, bd, cd } In other words, if (I 4) is taken in conjunction with a number of independently motivated assumptions, then boves duo is correctly interpreted as the set of
( I 9)
of the appropriate kind, (ii) to count individuals, and (iii) to count individuals belonging to the same group or kind, including the parts of a single object. Let us tum first to (i), the use of collectives to count groups or kinds. This use was exemplified in (7) and ( IJ). As we see it, the interpretation of these cases proceeds entirely like (I9), except that it would involve collectives rather than cardinals. Consider for example the inter pretation of boves bini 'twocou oxen' relative to (15) and the partition
{ab, cd, ej }: (2o) [boves bini] = Wboves] n [bini] = t a, b, c, d, ab, ac, ad, be, bd, cd, abc, abd, acd, bed, abed} n {abed, abef, cdef } = {abed} So ( 14) and independently motivated considerations are able to interpret boves bini correctly as the set of elements of the model which are two pairs (possibly yokes) of oxen each.
It should not escape the reader that our account of this use of collective numerals depends on the view that groups and kinds are simply combina tions of individuals- at least in extension. The reason for this is simple. The only entities models contain (and hence the only entities numerals may count) are either individuals or else combinations of individuals. Extended arguments for such a view of groups and kinds were advanced in Ojeda ( I 993a). Naturally, other pairs (or indeed units other than pairs) would have been counted in (2o) if the interpretation had proceeded relative to partitions other than { ab, cd, ef}. All such enumerations are allowed by our account and rightly so, as I do not take it to be the task of semantics to account for the choice of partition in any particular occasion of use. The choice of a particular partition in a particular occasion should be as external to
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elements of the model which are each two oxen. As to collectives, they had, we recall, three uses. They were (i) to count groups or kinds proper, including the groups contributed by pluralia tantum
Almerindo E. Ojeda 153
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semantics as the choice of a particular model in a particular occasion. As we see it, semantics proper begins only once we are given a particular model (and in this case a partition of a model as well). Needless to say, claiming that the choice of partition is external to semantics, is not the same thing as claiming that this choice is either arbitrary or inconsequential. Each choice of partition is a choice of the set of minimal units, be they individuals, groups, or kinds, of the totality formed by all the entities one may enumerate on some particular occasion-a fundamental choice every user of collective numerals must make. Arguably, this choice is not made at random, but is instead governed by factors such as spatial proximity, concerted action, and similarity in shape. The identification and ranking of such factors remains wide open to further research. In any event, the interpretations in (I4) also accommodate the use of collective numerals with pluralia tantum illustrated in (9b), (10b), and (ub) at least if we adopt the view that these plurals have the ordinary semantics of a plural noun and denote the combinatorial closure of a set of simple rather than compound objects.15 To see what this entails, let us assume that the plural noun litterae denotes the combinatorial closure of the set of letters of the alphabet in the model, not the combinatorial closure of the set of letters of correspondence of the model. It follows that if litterae combined with a cardinal numeral, then the set of combinations of a fixed number of letters of the alphabet would be denoted, and that if litterae combined with a collective numeral, then the set of combinations of a fixed number of groups or kinds of letters of the alphabet would be denoted (possibly the groups of letters of the alphabet in a letter of correspondence). To be more specific, if litterae combined with the fifth cardinal numeral (as it does in (ua)), then the set of combinations of five letters of the alphabet would be denoted. If, on the other hand, litterae combined with the fifth collective numeral (as it does in (nb)), then the set of combinations of five letters of correspondence would be denoted. These, of course are the desired denotations. We can therefore explain the contrast between (1 1a) and (1 1b) if we take the interpretations in (I4) in conjunction with the interpretation of pluralia tantum sketched above. Notice that it is essential for this account to succeed that if litterae denotes the combinatorial closure of a set of individuals of a model, then these individuals are letters of the alphabet, not letters of corre spondence. For if litterae denoted the closure of a set of individual letters of correspondence, then this noun should be able to combine with cardinal numerals (to denote combinations of a ftxed number of letters of correspondence), and it should not be able to combine with collectives (unless combinations of groups of letters of correspondence are denoted). This, of course, is in direct opposition to the facts in ( I I ). Litterae calls for
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A Semantics for the Counting Numerals of Latin
(21 ) duae litterae (Serv. Aen. 8, 1 68) 'two letters of correspondence' I duabus quadrigis (Liv. I, 28, 10) 'two four-horse chariots' I castra duo (Ammianus r 8, 7, Io) 'two camps'. Independent evidence of the new status of litterae and similar nouns is provided by the ulterior development of Latin litterae in Romance (c£ French lettre(s) 'letter(s) of correspondence') and by the existence of singular attestations litterae, quadrigae, and castra already in the Latin corpus (I..Ofstedt
I9s8: §3I). Naturally, what we have said about litterae and ( I I ) can be said for aedes and (9) and for castra and (Io). In fact, it can be said for all the pluralia tantum in (8) and all the pluralia tantum like them. While this includes most of the pluralia tantum of Latin, it does not include all of them. As we have seen above, the pluralia tantum in ( 12) call for cardinals rather than collectives. This is so because these plurals do not involve natural groups of objects in
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collective numerals, not for cardinal numerals, in order to refer to combinations of letters of correspondence. The plurale tantum litterae thus differs from the ordinary plural epistulae 'letters of correspondence', which does call for cardinal numerals.16 Furthermore, notice that we do not need to claim that litterae is polysemous ('letters of the alphabet' vs. 'letters of correspondence'). We just need the sense 'letters of the alphabet' -surely prior to the sense 'letters of correspondence', both logically and historically. It is the interpretation of the numerals set forth in ( 1 4) and pragmatic considerations concerning what the natural partitions of the letters of the alphabet are what will determine whether an expression containing the noun litterae will refer to letters of the alphabet or to letters of correspondence, not the stipulation of a lexical ambiguity for litterae. As far as I can see, the view that pluralia tantum denote combinatorial closures of compound objects is committed to the stipulation of such an ambiguity in the lexicon. It is interesting to note that Latin litterae did eventually become ambiguous, as a new noun litterae developed which denoted the combina torial closure of the letters of correspondence of the model. Crucially, however, the new noun ceased to be a plurale tantum (= it contrasted with a singular) and cardinal numerals could be used with it. Interestingly, this development was already in progress in Ciceronian Latin, as it has been recorded that Cicero once admonished his son for using duae litterae instead of binae litterae (Servius Aen. 8, 168, cited in the Thesaurus Lingvae Latinae s( 1 ): 2246) . This and other documented examples of cardinals with erstwhile pluralia tantum are collected in (21 ) and, according to LOfstedt ( 1 958: §3 1), it is not unlikely that analogous examples will be found in late and vulgar Latin texts.
Almerindo E. Ojeda
I SS
(22) [ u n i,MPROPEa] = [anus] = {a, b, c, d, e,J } [bini,MPaoPEa] = [duo] = { ab, ac, ad, ae, af, be, bd, be, bf, cd, ce, cf, de,
df, ef}
Thus, when improper collectives combine with plurals they have the same effect as cardinals illustrated in (3), (9a), (10a), (ua), and (21). Collectives may therefore combine with plurals to count individuals, and the uses in (ii) are accounted for without any assumption over and above the interpretation in (14). It should be acknowledged that terms 'proper collective' and 'improper collective' are somewhat misleading, as we are not dealing here with two series of collective numerals, but rather with two uses of one and the same series. The denotation of collective numerals is simply broad enough to encompass two possibilities-one based on greatest partitions and the other
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the way most pluralia tantum do. Hence there is no need to combine them with numerals dedicated to counting just such groups. It should be pointed out that the interpretation ofpluralia tantum adopted above runs counter to a generalized-albeit mostly implicit-view of these plurals, one which holds that the individual scissors, the individual pants, and the individual goggles are the pairs of blades, the pairs of pant legs, and the pair of lenses. What contrasts like those in (9)-(u) suggest, however, is that the individual scissors, the individual pants and the individual goggles are instead the individual blades of a pair of scissors, the individual pant legs of a pair of pants, and the individual lenses of a pair of goggles, respectively. The fact that these individuals are seldom referred to is a consequence of the circumstance that they are of little practical importance for most speakers. I suspect, however, that if we shift our attention to speakers for whom such individuals are important (say the makers of scissors, pants, or goggles), reference to those individuals will rise significantly. Consider next (ii), the use of collectives to count individuals. This was the use illustrated in (4). To accommodate this case we should recall that every individuation is a partition in its own right. In fact, every individuation of a model is the greatest partition thereof (i.e. the one with the most elements). For now, since collectives denote combinations of elements from any partition, they will be able to denote combinations of elements of greatest partitions, namely individua tions, as well. To ease exposition, let us say that a collective numeral is improper when it denotes combinations of an individuation and proper when it denotes combinations of other partitions. We thus have that, relative to the model in (15),
156 A Semantics for the Counting Numerals of Latin not. In other words, collectives are vague rather than ambiguous with respect to the proper/improper distinction. Now, it might be objected that if improper collectives can be used to count individuals, and if cardinals are dedicated to the enumeration of individuals, then pragmatic principles of cooperation would require that,
count as two - say, when they must contribute two of the arguments of the preposition tra 'between' (24) (c£ Rocchetti 1 968). (23)
Era un grasso uomo [ . . . ] che [ . . . ] muoveva le mani su una carta topografica aperta sulle ginocchia (Calvina, I Racconti, 49).
'He was a fat man moving his hands on a map opened on his knees' (24) [ . . ] il soldato ( . . . ] rannicchiato con la testa tra i ginocchi (Calvina, I Racconti, 63). ' . . . the soldier crouching with his head between his knees' .
To account for the difference between these plurals, Ojeda (1 995) argues,
essentially, that a plural in -i denotes the combinatorial closure of a set of individuals of a model while the corresponding plural in -a denotes the
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everything else being the same, cardinals should be used in (4). True, but not everything is the same in this case. Recall that the cases in (4) were used 'occasionally in poetry' (Hale & Buck 1 903: §247.3; see also Lane 1 903: §2422, where it is said that 'the plural [of the collective numeral] is sometimes used in verse for the cardinal'). In such contexts, collectives may serve a number of nonreferential functions -notably providing synonyms with an alternative meter. Improper collective numerals are furthermore motivated by (iii), the use of collectives to count individuals belonging to the same group or kind, including the parts of a single object. This use was illustrated in (5) and (6) above. To accommodate this use we need to adopt a view of plurality which is more general than the one normally encounted in the literature. To introduce this view, notice that all the plurals we have seen so far denote the combinatorial closure of a set of individuals of a model. Let us call these plurals specific. As we are about to see, plurals may be found which denote the combinatorial closure of other sets of discrete elements. We will call these plurals collective. Italian, a direct descendent of Latin, has a number of nouns which admit two plurals. One of these plurals is masculine and ends in -i; the other is feminine and ends in -a. Semantically, many of the plurals in -a are said to have a 'collective' force, while plurals in -i are instead said to be 'distributive' (Meyer-Liibke 1905: §98) or 'singulative' (Regula & Jernej 1965: 87). Thus, ginocchio 'knee' admits both a masculine plural ginocchi and a feminine plural ginocchia. The feminine plural is used when the knees count as one-say, as a lap (23). The masculine plural is used when the knees must
Almerindo E. Ojeda
1 57
combinatorial closure of a discrete set of combinations of individuals of a model. Thus, if ( 16) represented a model in which there were exactly four knees a, b, c, d, and if a, b represented the knees of some person while c, d the
knees of another, then the denotation of ginocchi 'kneesSPEc' and 'kneescou.' could be as shown in (25).
(25)
a.
b.
ginocchia
lfginocchi] = {a, b, c, d, ab, ac, ad, be, bd, cd, abc, abd, acd, bed, abed } lfginocehia] = { ab, cd, abed}
Overt differences between specific and collective plurals are found in another descendant of Latin, namely Rhaeto-Romance (Haiman & Beninci 1992: §2.2.1 .2). Outside Romance, a distinction between collective and
( 1983: 281 ). Now, it is true that Latin does not have an overt distinction between specific and collective plurality. It is conceivable, however, that this distinction is still made, albeit covertly, in Latin-if not in every language
with an inflectional plural. If so, let us consider a plural like boves 'oxen'. Taken specifically it would denote the combinatorial closure of the set of oxen in the model. Taken collectively it would denote the combinatorial closure of a set of groups of oxen in the model- say, the combinatorial closure of the set of pairs (or yokes) of oxen. If
which there are four oxen a,
(15)
represents a model in
b, d, and if a is paired (or yoked) with b, and if e is paired with d, then the two senses of boves 'oxen' would be as indicated in
(26), which
(26)
a.
b.
c,
should be compared with
(25).
[bovesSPEc] = {a, b, c, d, ab, ae, ad, be, bd, cd, abc, abd, aed, bed, abed } [ bovescou.] = { ab, ed, abed}
We are fmally in a position to account for the uses of (iii) illustrated in (s). They arise simply when an improper collective numeral is combined with a collective plural noun. The semantics of this combination is illustrated in (27).
[bin iiMPROPER] = �b0Ve5COLL] n [duo] = {ab, ed, abed } n {ab, ac, ad, ae, af, be, bd, be, bf, ed, ee, cJ, de, dj, ef} = {ab, ed }
(27) [boVeSCOU. b in iiMPROPER] = [ bo VeSCoLL]
As can
be readily seen,
(14)
n
and independently motivated assumptions are
able to interpret boves bini 'two,MPaoPEa oxencou.' as the set of elements of the model which are a pair of oxen each. Once again, the success of this account
depends on viewing groups and kinds (in this case the pairs of oxen) as combinations of individuals.
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'distributive' plurality has been claimed for South Slavic by Stankiewicz
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Semantics for the Counting Numerals of Latin
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Naturally, there is nothing to prevent cardinals from combining with collective nouns to count individuals in a group or kind. And that may in fact be what happens in some of the cases in (3), (9a), (10a), (ua), and (21). One good candidate is the example tres Gratiae 'three Graces' given in (3). Since the three Graces of Classical Antiquity formed an obvious group, Latin Gratiae can be arguably analyzed as a collective noun which refers to the singleton of the group formed by the three Graces. Notice that this is a legitimate denotation for a plural noun since every singleton is its own combinatorial closure. Notice also that the fact that this noun is a proper name may be accounted for by the claim that it denotes a singleton. But, if this is so, then it might again be objected that, since Latin had a special series of cardinals dedicated to the enumeration of individuals, then pragmatic considerations should require them to appear, ceteris paribus, in the examples in (5). Interestingly, however, grammarians tend to mention the uses in (s) in connection with cultivated speech, where collectives could be performing stylistic as well as referential functions-so, once again, everything is not the same. Thus, Allen & Greenough (1904: §95d) point out that collectives 'are used by the poets instead of cardinal numbers, particularly where pairs or sets are spoken of'. The only example he gives of such use is bina hastilia (Virg. Aen. 1, JIJ), which they gloss as 'two shafts (two in a set)'. This, of course, is one of the examples in (5). Along the same lines, Gildersleeve and Lodge (1895: §295) say that 'poets and later prose writers often use the distributive [i.e. the collective] when the cardinal would be the rule; thus bini is not unfrequently used of a pair, even in Cicero'. Their sole example is binos scyphos (Cic. Verr. II, 4, 14, 32) 'two matched goblets', also in (5) above. Perhaps more accurately, LOfstedt (1958: §43) points out that even though the use in question is frequent with the poets, many examples from prose can still be found (see (5)). Yet he acknowledges later (§47) that one probably has to reckon here with the influence of poetic speech on the writers of cultivated prose. To this he adds the intriguing suggestion that the development of the improper sense of collective numerals-what he calls the 'weakening' of these collectives- is a natural tendency which could also appear occasionally in colloquial speech. In any event, given collective plural nouns and improper collective numerals, an account of the uses of (iii) illustrated in (6) above now becomes available. Consider first what the singular of a collective plural might be. If a collective plural is the combinatorial closure of a set of groups, then the singular of such a plural would have to be the set of groups in question. Collective singulars are motivated independently of the issues at hand. Consider for example the sentences in (28).
Almerindo R Ojeda I 59
(28)
a.
b. c. d. e.
John was hit on the arm. Claire skinned her knee. Susan pinched her finger. Bill broke the headlight on his car. Ann had to pick her son up at the airport.
(29)
[corporeCOLL b lnOJMPROPBR]
= = = =
[corporeCOLL] n [hlnOJMPROPBR] [corporeCoLL] n [duo] { ab, c, d } n { ab, ac, ad, ae, af, be, bd, be, bJ, cd, ce, cJ, de, dJ, ej } {ab}
More generally, the combination of an improper collective with a collective noun in the singular will denote a set of entities which are simple (in light of the enumerated noun) but yet multiple (in light of the numeral). In other words, we would have the desired paradoxical senses of 'double breast' (= a breast which is two breasts), threefold reason (= a reason which is three reasons), and so forth, found in (6). The paradox is not, of course, a contradiction. A group is an entity which is simple from one point of view but multiple from another.17 It should again be noticed that the semantic effect of an improper collective numeral with a singular noun illustrated in (6) could be attained by a cardinal numeral and a collective noun. It is therefore interesting to point out that the uses in question have been justified on stylistic grounds. According to Emout & Thomas ( 1 964: §205), 'the poets found in the distributive [= collective] an easy metrical substitute [ . . . ] they used it due to stylistic refmement [ . . ] notably in the collective singular [sic], by an abusive extension of the latter'. Their example here is centenaque arbore .
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Definite descriptions are generally believed to carry with them presupposi tions of uniqueness. But if this is so, then how can the sentences in (28) be true when John has two arms, Claire has two knees, Susan has ten fmgers, and so on? The solution to this puzzle offered in Ojeda (1993b) is that arm, knee, finger, and so on, are collective nouns in the singular. Each denotes a subset of a partition respectively containing John's unique group of arms, Claire's unique set of knees, and so on. It is these unique objects that the definite descriptions in (28) refer to. Now, if we can avail ourselves of collective singulars, then we may assume that the singular nouns in (6) are all collective. The intersection of improper collectives with such singulars would now proceed as follows for corpore bino (Lucr. s. 879) 'of body twain'. Let ( 1 6) be a model in which there are exactly four bodies a, b, c, d, and that a, b are (the only) two bodies that are somehow blended into one. Now,
160
A
Semantics for the Counting Numerals of Latin
(30) [boveSCOLL bini]
= = =
[boveSCOLL] n [bini] {ab, cd, abcd } n {abcd, abeJ, cdef } {abed }
In other words, boves bini 'two pairs (yokes) of oxen' would denote the set of elements of the model which are each two pairs (possibly yokes) of oxen. This, of course, is as desired. Similar interpretations are available for all cases in (7), (9b), (wb), (ub), and (13)-if and when they involve collective nouns. It follows that there are two ways to assign the same interpretation to cases like (7), (9b), (10b), (ub), and (13) -one if the nouns in question are collective and the other if they are specific (compare for example (3o) and (2o) above). Since the interpretation assigned in both cases is the desired one, constructions like the ones in (7), (9b), (10b), (ub), and (13) can be correctly interpreted regardless of whether they involve specific or collective nouns. It should be pointed out, however, that for interpretations like (3o) to be sound, the collective numeral and the collective noun in question should involve one and the same partition, and nothing we have said so far will ensure this. In short, if we assume (a) that a model for the interpretation of the counting numerals of Latin is an atomistic mereology formed by the combinatorial closure of the set of individuals we may talk about on some particular occasion and a relation of inclusion, (b) that the interpretations of these numerals relative to such a model is as given in (14), (c) that both groups and kinds are combinations of individuals, and (d) that the individuals typical pluralia tantum denote are simple rather than com pound, then the data in this paper can be analyzed as indicated in Table (3r).18 Table (31) brings to light two gaps in our data: the use of proper
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Jluctum (Verg. Aen. 10, 207) 'he strikes the waters with a hundredfold oar Qit. tree)', which is one of the examples in (6). These grammarians also add that 'the prose writers of the Imperial Era sometimes imitated them'. A similar point is made in Lane (1903: §2422), who points out that 'poets sometimes use the singular of distributives', and adds the example from Lucretius interpreted in (29). So far we have considered the cases in which improperly collective numerals combine with collective nouns. But nothing prevents properly collective numerals from combining with collective nouns. If they do, then the numerals in question would have the effect of counting groups or kinds drawn from the denotation of the noun. This should be as desired. Consider by way of example the case in which bini denotes as indicated in (17) and boves denotes as shown in (26). The interpretation of boves bini 'two pairs (yokes) of oxen' would be as follows:
Almerindo E. Ojeda
I6I
collectives with specific nouns in the singular, and the use of proper collectives with collective nouns in the singular (see the question marks in (31)). Nothing in this paper precludes such uses. In fact, if the noun is specific, then the proposals advanced above predict that the collective numeral would have to be a form of unus, and hence that reference will be made to groups or kinds with one member or instance each. In other words, reference would be made to individual entities which are isolated or sui generis. Thus, an expression like uno ictu would have, in addition to the sense 'one blow' mentioned in (3), the sense of 'one isolated blow' or 'one unique blow'. No discussion of such senses is provided in the literature, and hence the first gap in our data.
CARDINALS
COLLECTIVES PROPER
SINGULAR SPECIFIC PLURAL
IMPROPER (4sG)
(3sG) (3PL), (9a- I I a), (2 1) (7), (9b- I I b), (I 3)
(4PL)
NoUNs SINGULAR
(6)
PLURAL
(s)
(6)
CoLLECTIVE (7), (9b- I I b), (I 3)
(s)
The second gap in our data pertains to the use of proper collectives with collective nouns in the singular. Here our prediction is that reference would be made to n-fold kinds or groups of individuals. Thus uno ictu would have, in addition to the senses mentioned in the preceding paragraph, that of 'one kind of blow'. Along the same lines, corpore bino would allow the reading 'twofold kind of body'; latratu trino would be able to mean 'triple kind of barking', and so on for all the examples in {6). Again, I have not come across any acknowledgement of such senses in the literature.
s
COUNTING NUMERALS I N OTHER LANGUAGES
Latin is not the only language where numerals for counting individuals are distinguished from numerals for counting groups or kinds. Outside Italic, a cardinal/collective distinction can be found in the Germanic, Baltic, Slavic, and Indic branches of Indoeuropean (Brugmann 1907) and, beyond
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NuMERALS
r 62
A
Semantics for the Counting Numerals of Latin
Indoeuropean, it has been described in Finnish (Hurford, forthcoming), Mongolian (Bosson 1964: §r r.6), and Greenlandic (Kleinschmidt r87r). 19 Although justice cannot be made here to the wealth of these Eurasian data, a sample of the facts may still be useful. The first four cardinals of Icelandic have collective counterparts?0 The citation forms of these numerals are given in (32). (32) CARDINALS: einn, tveir, j:Jrir,fjorir. COLLECI'IVES: einir, tvennir, prennir, Jernir. Cardinals are used to count individuals (33) while collectives are used to count groups of individuals (34). (34) a. einir vettlingar 'one pair of mittens' b. tvennir sokkar 'two pairs of socks' c. prennir skor 'three pairs of shoes' d. Jernir eyrnalokkar 'four pairs of earrings'
Icelandic collectives are also used with pluralia tantum (Js).
(Js) einar dyrr 'one door' I eina Ptiska 'one easter' I tvennar buxur 'two pairs of trousers' I tvenn gleraugu 'two pairs of glasses' I prennir tonleikar 'three concerts' I Pren ]61 'three Christmasses' I fern gleraugu 'four pairs of eyeglasses'
Collective numerals were used for counting groups already in Old Icelandic. 21 Thus, the author of the SkiOarima refers to one and the same pair of shoes either as (36a) or as (36b). (36)
tvennir skor (Str. r 93) twocou. shoes 'two pairs of shoes' b. sk6na fjora (Str. 38) fourcARD shoes 'the four individual shoes' a.
Collective numerals are also used with nouns of quantity like niund 'group of nine' and tylft 'group of twelve'. These and other examples of Old Icelandic collective numerals used as group or kind counters are gathered in (37)· (37) tvennir skOr (Ski
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(33) a. einn vettlingur 'one mitten' b. tveir sokkar 'two socks' c. prir skor 'three shoes' d. fjorir eyrnalokkar 'four earrings'
Almerindo E. Ojeda
163
meyja (Helgakv. Hjorv. 28, r) 'three groups of nine maidens' I frrennar tylftir exa (Olafss. helga 234, 8) 'three groups of twelve axes' I vm pessa omaga frrenna (Gr:ig. St. 31 c. 21) 'of these three (previously enumerated] categories of needed supplies' I par voro tvennar hallir [. . .] voru a/Jrar yfir olJrum, ok hetu pat hin efri hU5 (Fornmannasoger VI, 1 47) 'they were two series or groups of halls situated one on top of the other; that was called "the upper houses" ' I femer imbrodagar merkia boporp IIII. gupspilla. prir imbrodagar
IIJI•m sinnom haldner merkia prenningar trv pa er (>SS er synd i IIJI•m gupspiollom (Stock. Hom. 35, 26f£) 'the four groups of ember days
Particularly revealing in (37) is the contrast between Jerner imbrodagar 'four groups of ember days' and prir imbrodagar 'three individual ember days'. Collective numerals contrast with cardinals also in the Baltic and Slavic branches of Indoeuropean. Thus, while Balta-Slavic cardinals are used to count individuals, collectives may be used 'in the sense "n-fold" or "n kinds of"; in place of the ordinary cardinals when referring to groups of people (especially if of mixed sex), and with pluralia tantum' (Comrie 1992: 8o8). These facts are displayed by sixteenth-century Russian (Unbegaun 1935: 439f£), which had the cardinals in (38a) and the (plural) collectives in (38b). (38) a. odin", dva, tri, cetyre, pjat', sest', sem', (v)osm', devjat', desjat' b. *, dvoi, troi, cetvery, pjatery, sestery, semery, (v)osmery, devjatery, desjatery The collectives in (38b) were used with names of things which come in pairs (39), with pluralia tantum (4o) or-albeit more rarely-to count the groups or kinds named by other nouns (4r). (39) vezonki 'knitted gloves' I golovy 'uppers (of shoes)' I iernovy 'millstones' I podosvy 'soles' I rukavicy 'gloves' I sapogi 'boots' I ser'gi 'earrings' I tebenki 'pieces of leather on both sides of a Russian saddle' I kolesa 'wheels (mounted on an axle)' I ielezo, ral'nik", sosnik", soska (=nouns naming paired parts of an old Russian plough). (4o) vorota 'door' I dveri 'door' I drovni '(kind of) sled' I kleili 'pliers' I porty 'trousers' I poxvi 'crupper' I sani 'sled' I cetki 'rosary' I knigi 'burrow'. (4r) v" Rimu e v" Rimskom" uezde mnogo monastyrej, a lem'cy troi,-odni xodjat" v" belom" plat'e, a �rugie v" cernom", a tret'i v" serom" 'In Rome and the Roman district there are many monasteries but three kinds
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[each of which groups comprises three days] represent the precepts of the four Gospels. The three individual ember days, which are obligatory four times a year, represent the faith in the Trinity, which is revealed to us in the four Gospels' I PingmQnnum, Jarm(>nnum, bruiim(>nnom, g9ngum(>nnum: peim mqnnum femum [ . . . ] {Gr:ig. St. 31 c. 2 r) '[ . . . ] of these four kinds of people'.
164
A Semantics
for the Counting Numerals of Latin
of monks; some go in white dress, others in black, and still others in gray' I na berezu o dvoi rubci 'two kinds /series of notches on a birch tree' I vosm' iem luikov" da dvoi kamyiki jaxonty 'eight pearls and two sets/varieties of hyacinth stones' I kupi/11 pjatery plely v" ul]ax" 'he bought 6ve swarms of bees in hives' I a ne v" poru kupiti, dvoi dengi dati 'if you do not buy it in time, then you must pay twice �it. double moneys)'.
(42) a. dvoji opanci 'two pairs of sandals' b. troja vrata 'three doors' c. troji svatovi 'three wedding processions ('trois corteges de noce')' Consider also the contrasts in (43)-(44), taken from (Brugmann 1907: 51). (43) a. b. (44) a. b.
letiri crevlje 'four shoes' letvore crevlje 'four pairs of shoes' pet rukavica 'five gloves' petere rukavice 'five pairs of gloves'
Along the same lines, Finnish is said to have both singular and plUFal numerals. While singular numerals are used to count individuals, plural numerals are used in a variety of ways. First, they could be used with pluralia tantum (cf yhdet sakset 'one pair of scissors', kahdet haat 'two nuptials').22 Second, they could be used to count groups of individuals. See for example the contrasts in (45)-(48), taken from Hurford (forthcoming). (45) a. yksi hammas one.NOM.SG tooth.NOM.SG 'one tooth' b. yhdet hampaat one. NOM/ACC.PL tooth.NOM/ACC.PL 'one set of teeth; one denture' (46) a. kaksi kiita 'two.NOM/ ACC.SG hand.PART.SG 'two hands' b. kahdet kadet twO.NOM/ACC.PL hand.NOM/ACC.PL 'two pairs of hands'
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Although these uses are no longer present in Modem Russian, they are still found in Modem Serbo-Croatian according to Unbegaun (1935: 442n. 444£), as here we have collectives with names of things corning in pairs (42a), pluralia tantum (42b), and to count groups or kinds (42c).
Almerindo E. Ojeda 165 (47)
a.
kolme saapasta three.NOM/ACC.SG boot.PART.SG 'three boots'
b. kolmet saappaat three.NOM/ACC.PL boot.NOM/ACC.PL 'three pairs of boots' (48)
a.
neljii kuppia
four.NOM/ ACC.SG cup.PART.SG 'four cups'
Third, they could be used to count grouped individuals. Thus, Hurford (forthcoming: 26) observes that, when asked to specify the exact meanings of phrases containing plural numerals, speakers hesitate between readings 'where an exact number of groups of things is specified (e.g. "four groups of apples"}' and readings 'with an inexact number of groups, each of some exact cardinality (e.g. "groups of four apples"}', adding that 'almost always, informants settled on the former type of reading, sometimes after a little thought'. Alternatively, speakers varied with respect to the readings of such phrases. Thus, according to one informant, (49) could mean 'papers in quintuplicate for a meeting' (and hence groups of five copies each), while according to another, it could refer to 'the set of each participant gets for the meeting' (and hence to five groups of copies). (49) viidet paperit 'five.PL papers.PL'
Another example of the same variation is given in (so). (so) oppilaat saivat kolmet kirjat pupils got three.PL books.PL According to one informant, (so) describes a situation in which there are copies of three different books and each pupil got one copy of each. According to another informant, (so) calls to mind a situation in which 'a teacher has three variously sized groups of pupils and gives each group of pupils one pile of books; we don't know how many books are in each pile, but there are exactly three piles' (Hurford forthcoming: 27). In other words, for the first informant, (so) involves sets with three different books each (and hence reference is made to three grouped individuals) while for the second informant it involves three piles of books (and hence reference is made to three groups of individuals).
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b. neljat kupit four.NOM/ACC.PL cup.NOM/ACC.PL 'four cup sets (typically, four cup-and-saucer sets)'
1 66 A
Semantics for the Counting Numerals of Latin
(s I) a. oqaatsit marluk 'two words' b. oqaatsit marluit 'two languages' We conclude that the obvious similarities between the Latin data and the facts from Icelandic, Russian, Finnish, Mongolian and Greenlandic call for a unified explanation. Perhaps the semantics for the counting numerals of Latin provided in this paper can serve as the basis of such an account. Furthermore, even though we have explicitly excluded distributive numerals from consideration in this paper, it must be acknowledged that remarkable similarities exist, at least in Latin, between collective and distributive numerals?3 Recall first that the distributive and collective numerals of Latin overlapped in form to a large extent, their forms being in fact indistinguishable except for the cases of 'one' and 'three'. But distributives and collectives also overlapped to a large extent in terms of content. For, recall once again that distributive numerals were used in Latin to count entities apportioned apiece; they were used to answer the question 'how many each?'. But if entities are to be apportioned equitably, then they must be placed into pairwise-disjoint groups and counted as entities in a group. As we have seen, one of the uses of collective numerals is, precisely, to count grouped entities. It is hoped that the affinities which obtain, in both form and content, between the collectives and the distributives of Latin, can be accounted for on the basis of the semantics of the latter provided in this paper. Acknowledgements
I am grateful to Joseph Greenberg for talking collective numerals with me, to Peter Schaeffer and David Traill for help with Latin, to Asta Svavarsdottir for help with Icelandic, to James Gallant for help with Russian, to James Hurford, Tapio Honkanen, and
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The uses of cardinal and collective numerals has not been extensively documented for either Mongolian or Eskimo. Yet, the evidence there is agrees with what has been presented so far. In Mongolian, for example, collective numerals with meanings of the form 'in a group of n' or 'n together' or 'all n' are derived from cardinals by regular morphological processes (Bosson I964: § I 1.6; Poppe I964: §I99; Gnmbech & Krueger I976: §46.c). In Greenlandic, Kleinschmidt (I 87 I) gives contrasts for numerals from two through five, and glosses them as 'two, each consisting of many', 'five groups', and so on (see under mardluk, pingasut, sisamat, tatdlimat; see also Fortescue I984: 308). Greenlandic collectives may also count the groups denoted by pluralia tantum. Thus when oqaatisit combines as a regular plural with a cardinal, words are counted, while when it combines as a plurale tantum with a collective, languages are counted instead:
Almerindo E. Ojeda 167 Siiroinen for help with Finnish, to Jerrold Sadock for help with Greenlandic, to Steven Lapointe for his comments on earlier versions of this paper, and to all the participants of the First Conference on Nonlexical Semantics {Universite de Paris Vll, 2o22 June 1996), where this paper was presented.
Mari
Received: o8.1 1.96 Final version received: 24-09.97
ALMERINDO E. OJEDA Linguistics Program University of California at Davis Davis, California 95616-8685 USA e-mail:
[email protected]
Fundamental notions of mereological theory
First, some order-theoretic definitions. Let M be a set and let :s; be a binary relation on M. Some m E N is an upper bound for some N � M if and only if n :s; m holds for all n E N. Some m E M is a least upper bound for some N � M (or, equivalently, a sum of all the elements of some N � M) if and only if m is an upper bound for N and, for all m' E M, if m' is an upper bound for N, then m :s; m'. Now, let x and y be arbitrary elements of M. x and y are disjoint if and only if there is no z E M such that z :s; x and z :s; y (some N � M is pairwise-disjoint if and only if, for all n, n' E N, n and n' are disjoint if they are distinct). Finally, let < be a binary relation on M defined as follows. For all x, y E M, x < y if and only if x :s; y and it is not the case that y :s; x. Now let x < y. Some z E M is a difference between y and x if and only if x and z are disjoint and y is a sum of x and z. We are now in a position to define mereologies. A mereology is a pair (M, :s; ) such that Ml -M5 hold. MI. For all x E M: x :s; x M2. For all x, y E M: x :s; y and y :s; x jointly imply x y. M3. For all x, y, z E M: x:s;y and y:s;z jointly imply that x:s;z. M4. For all N � M: if N is a nonempty subset of M, then there is one and only one element of M which is a sum of all the elements of N. MS. For all x, y E M: if x < y, then there is one and only one element of M which is a difference between x and y. A mereology is, therefore, a partially ordered set in which two partial operations are defined-one for positive addition and one for positive subtraction. Alternatively, a mereology can be defined as (the canonical partial order of) a complete Boolean algebra whose null element has been removed (Tarski 1956: 33£) Let (M, :s; ) be a mereology. Some x E M is an atom of (M, :s; ) if and only if there is no y E M such that y < x. (M, :s; ) is atomistic if and only if every element of M is a sum of atoms of (M, :s; ). To illustrate, let M be the set containing the least common multiples of the first n prime numbers and let :s; be a binary relation on M such that for all x, y E M, x:s;y if and only if x divides y evenly. The pair (M, :s; ) is an atomistic mereology. To be more specific, let M { 2, 3, s, 6, 10, 15, 30} and let :s; be the binary relation of even divisibility on M. The pair formed by this set and this relation is an atomistic mereology =
=
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APPEND IX
I68
A Semantics for the Counting Numerals of Latin
whose atoms are the first three prime numbers 2, 3, S· We may diagram this mereology follows.
as
30
�
6
10
15
2
3
5
[>()<]
NOTES I See Simons (I 987) for a comprehensive study of mereologies. 2 Latin would not be the only language where collectives and distributives were assigned to distinct series of numerals. A systematic morphological difference between collective and distributive numerals is attested in Modem Mongolian (Bosson I 964: 98). 3 These examples were Kuhner (I9I 2: § Iso.3).
taken
from
=
s These examples were taken from Madvig (185 I : §76d), Allen & Greenough (1904: §9sd), Brugmann (I907: 42), Kuhner (19 I 2: §m.s.c). LOfstedt (I958: §44£), and the Oxford Latin Dictionary (OW). See these references for more examples. 6 Lane { I 903= §2422).
OW for
LOfstedt (I 958: § §34-6) and the IO Here and henceforth, letter(s) alphabet should be taken to
OW. of the mean
of the alphabet.
1 I These plurals are reminiscent of English nominalized adjectives found in the rich, thefamous, the homeless; both are personal and lack singular counterparts. I 2 By the combinatorial closure of a given set I mean the set containing the elements of the given set, their combinations, and nothing else. 13 Following a widespread abuse of ter
§22), Kuhner
(19 I 2: § Iso.2), LOfstedt (I958: the
9 These examples have been drawn from
token(s) of letters
4 Brugmann (I 907: 40). Kuhner { I 9 I 2: §1 so.2) adds 'bino duplici'.
7 See Brugmann (I907:
8 To support his standard gloss of boves trinos as 'three pairs of oxen', Lofstedt points out that the same text recom mends below (c£ 10.2-3) three yokes and six harnesses to go with the oxen in question.
more examples.
VI),
and
minology,
I will
henceforth speak of
mereologies (M, :::; ) and their sets M as if they were the same thing.
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More generally, a directed graph is a diagram of a mereology (M, � ) if and only if the graph contains, for all x, y E M, an upward path from a node x to a node y if and only if x < y. Furthermore, if some graph is the diagram of a mereology, then the atoms (if any) of the mereology are the nodes at the bottom of the diagram. It should be borne in mind that not every mereology is atomistic. A mereology (M, � ) is, in particular, atomless if and only if no element of M is a sum of atoms of (M, � ) or, equivalently, if and only if no x E M is an atom of (M, � ). The pair formed by the set of solids of three dimensional Euclidean space and the relation of solid inclusion is an atornless mereology.
Almerindo E. Ojeda I 69 (combinations of a higher cardinal and a singular noun would be presumably ruled out on syntactic grounds). In such cases, individuals would be counted as expected (c£ uno ictu 'one blow' in (3) above). I8 Here '(3sG)' stands for the singular examples in (3), '(3PL)' represents the plural examples in (3)-and so on. As indicated above, nouns are specific if they denote combinatorial closures of individual entities and collective if they denote combinatorial closures of other discrete entities; collective numerals are improper if they are based on indivi duations and proper if they are based on other partitions. I9 I am indebted to James Hurford and Jerrold Sadock for bringing to my atten tion the Finnish and the Greenlandic facts, respectively. 20 Thanks to Asta Svavarsdottir for most of the Modern Icelandic data. See also Einarsson (I 94s: 67). Cleasby & Vigfusson (I9S7). and Kress (I982: §245). 2I The Old Icelandic data come from Eduard Sievers (see Brugmann I907: 7I -6). 22 See Hakulinen (I96o: 2I5). 23 Furthermore, the distributive numerals of Latin derived historically from col lective numerals of Proto-Indoeuropean (Lofstedt I 958: §4).
REFERENCES Allen, Joseph & Greenough, James (I904), Latin Grammar, Ginn & Company, Boston. Barker, Chris (I992), 'Group terms in English: representing groups as atoms', Journal of Semantics, 9, 69-93. Bartsch, Renate (I97J), 'The semantics and syntax of number and numbers', in John Kimball (ed.), Syntax and Semantics z, Seminar Press, New York. Bosson, James (I964), Modern Mongolian Uralic and Altaic Series, 38, Indiana
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I4 The number of partitions of a model with n atoms is the nth Bell number. See Ojeda (I 993a: I 88ff.). IS This seems to be the simplest inter pretation of pluralia tantum that will do justice to their selection of collective numerals. More complex interpretations are also possible. Pluralia tantum could for example denote collective plurals see the discussion of (3o) below. But potential evidence for the more com plex interpretation of pluralia tantum as collective plurals comes from the fact that not all nouns referring to groups of individuals called for collective numer als in Latin. Thus, neither nouns refer ring to walls (which are groups of bricks) nor nouns referring to libraries (which are collections of books) called, for example, for collective numerals. The difference between litterae 'letter(s) of correspondence' and murus 'wall' would thus be accounted for by the fact that only the former, not the latter, is a collective plural I6 Thus we read in Servius' commentary to the Aeneid 8, I 68 that 'epistolas binas non dicimus, sed duas' 'we do not say epistolas binas but rather [epistolas] duas' (cited in Thesaurus Lingvae Latinae S(I): 2246). I7 Note that any time a cardinal numeral combines with a singular noun, then the cardinal would have to be unus
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A Semantics for the Counting Numerals of Latin
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Translated by D.I. Barnett as 'Founda
tions of the general theory of sets, 1', in Stanislaw Surma et al. {eds) (1992)
Stanislaw LeSniewski: Collected Works (Nijhoff International Philosophy Series,
44),
Kluwer
Academic
Publishers,
Dordrecht, I29- I?J. Leumann, Manu et al.
{I963), Lateinische Grammatik, erster Band (Handbuch der Altertumswissenschaft, Il.z.I), C.H. Beck'sche
Verlagsbuchhandlung, Munich. Link, Godehard { 1 983), The logical analysis
of plurals and mass terms', in R. Bauerle
et al. (eds), Meaning, Use, and Interpretation of language, Walter de Gruyter, Berlin. Link, Godehard (1987), 'Generalized quan
tifiers and plurals', in Peter Gardenfors
Generalized Quantifiers (Studies in Linguistics and Philosophy, JI), Reidel, Dordrecht, r s i -So. LOfstedt, Bengt (1958), 'Zum Gebrauch der (ed.),
lateinischen distributiven Zahlworter',
Eranos,
56,
?I - I 17, 1 88-223.
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{I964), Syntaxe Latine (Nouvelle Collection a /'Usage des Classes, 38), Klincksieck, Paris. Eschenbach, Carola (I 993), 'Semantics of number', Jou ma l of Semantics, 10, 1 -31. Fortescue, Michael (I 984}. West Greenlandic, Arithmetik,
Bartsch et al. (eds), Semantics and Con textual Expression (Groningen-Amsterdam Studies in Semantics, II), Foris, Dordrecht. Krifka, Manfred (1990), 'Four thousand
Almerindo E. Ojeda 171
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Grammatica Italiana Descrittiva, Francke McCawley, James (1968), Review of Cur Verlag. Bern. rent Trends in Linguistics J, Language, 44, Rocchetti, A. (1968), 'Les pluriels doubles de 556-93. Madvig, Johan (1851), Latin Grammar, trans l'italien: une interference de Ia seman lated from the German by the Rev. tique et de Ia morphologie du nom', Les George Woods, J. H. Parker, Oxford. Langues Modernes, 62, 351 -9. Massey, Gerald (1976), 'Tom, Dick, and Russell, Bertrand (1903), The Principles of Harry, and all the king's men', American Mathematics, George Allen & Unwin Philosophical Quarterly, 13, 89- 1 07. Ltd., London. Meyer-Liibke, Wilhelm (1905), Grammatik Simons, Peter (1987), Parts: A Study in der italienischen Sprache, second edition, Ontology, Clarendon Press, Oxford. Trubner, Strasbourg. Stankiewicz, Edward (1983), 'The collective Mill, John Stuart (1843), A System of Logic, and the counted plurals of the Slavic J. W. Parker, London. nouns', American Contributions to the Ojeda, Almerindo (1993a), Linguistic Indi Ninth International Congress of Slavists, viduals (aU Lecture Notes, 31), Stanford, Slavica, Columbus. Center for the Study of Language and Tarski, Alfred (1956), 'On the foundations Information, Stanford University. of Boolean algebra', in Logic, Semantics, Ojeda, Almerindo (1993b), 'New evidence Metamathematics, Papers from 1923 to for a more general theory of singularity', 1938 by Alfred Tarski, translated by in Andreas Kathol & Michael Bernstein J.H. Woodger, second edition, edited (eds), Proceedings of the Tenth Eastern and introduced by John Corcoran, States Conference in Linguistics, Ithaca, 1983. Hackett Publishing Company, Department of Modern Languages and Indianapolis, 320-41. Linguistics, Cornell University. Unbegaun, Boris (1935). La Langue Russe au Ojeda, Almerindo (1995), 'The semantics of XVIe Siecle (1500-155o), I. (Bibliotheque the Italian double plural', journal of Russe de l'Institut d'Etudes Slaves, XVI), Semantics, 12, 213-37. Institut d'Etudes Slaves de l'Universite Poppe, Nicholas (1964}, Grammar of Written de Paris, Paris. Mongolian (Porta Linguarum Orientalium, Wald,Jan (1977), 'Stuff and words: a seman Neue Serie, I), Otto Harrassowitz, tic and linguistic analysis of nonsingular Wiesbaden. reference', Ph.D. dissertation, Brandeis Regula, Moritz & Jernej, Josip (1965), University.
Journal ofSnnantia
14: 173-205
© Oxford University Pres.
1997
The Progressive and the Structure of Events ANDREA B O N O M I University of Milan Abstract
semantics for the progressive in which a 'mereological' analysis of eventualities (based on the pan-of relation) is combined with a contextualist approach.
r
INTRODU CTI ON
In logic and philosophy of language there have been lively discussions on the truth-theoretical status of the future tense. One of the main problems is that, whilst the truth of sentences in the past tense depends on facts that have already occurred, the truth of sentences in the future tense involves facts that have not yet occurred. As stated in Prior (1957: 87), 'it is not now a fact that x will ¢, nor is it now a fact that x will not ¢; that is, the statement that x will ¢ is not now true, nor is it now false.' A consequence of Prior's philosophical analysis was his idea that the Future is not the simple 'mirror' image of the Past and that it deserves a different kind of semantic treatment. Contrary to Prior's expectations, natural language semantics makes no distinction, in principle, between sentences in the future tense and sentences in the past tense, since they are arguably associated with the same kind of truth-conditions: it will be the case that P is true at a time t iff
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In the analysis of the progressive proposed in the paper, two notions play a crucial role. On the one hand, since the same event can be 'embedded' into several possible developments that are relevant to the truth-conditions of the progressive, a first task of the analysis is to account for the part-of relation which connects an event with its possible continuations. On the other hand, this kind of connection is largely dependent on contextual factors, and a second task of the paper is to analyze this notion of context both in terms of events in the world (the 'concomitant facts' selected as relevant) and in terms of the situation of the discourse (the conversational background that makes those facts relevant). After presenting, in section 2, the so-called imperfective paradox, in section 3, I address a problem of ambiguity engendered by the underdetermination of the data, whilst a related issue is discussed in section 4· The new examples analyzed in this section are an interesting illustration of the intensional character of the progressive. In section s. I discuss the role of mereological relations in the semantics of the progressive, whilst in section 6, I take into consideration the use of this aspectual form in connection with improbable courses of events. In the final sections, all these problems are considered from the point of view of a
1 74 The Progressive and the Structure of Events
progressive which will be presented here. The idea is that our perception of an event involves a bunch of possible developments of that event. My going to the blackboard and taking a piece of chalk can be considered as part of a number of alternative events, as putting the room in order, writing some instructions, proving a theorem,
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there is a time t ' later than t at which it is true that P, exactly as it was the case that P is true at t iff there is a time t' earlier than t at which it is true that P. The implicit j ustification for such a solution, which represents a departure from Prior's approach, is the assumption that the task of truth theoretical semantics is to account for the conditions on which a sentence is true, independently of the cognitive tools we have to verify it: if I say at a time t that a certain event will occur, my statement is true if and only if this event occurs at a time later than t, no matter how I can justify this statement. A similar problem arises in the case of sentences in the progressive form, whose truth can depend on events not yet realised. If I say that Leo is proving a theorem, this statement entails that the proof at issue is an event whose completion lies in the future. Therefore, one might hope that the same semantic realism adopted to deal with the future tense will work nicely with the progressive as well, and that the same kind of plain truth conditions can be associated with this aspectual form. Unfortunately, the progressive raises further problems. If I say that Leo will prove a theorem, this statement makes no essential reference to any current event: what is relevant for its truth is only what happens in the future, not at the present time. If an event of Leo's proving a theorem occurs n days after the present time, the statement is true, and that's all. But consider a progressive sentence such as Leo is proving a theorem. This time, the simple reference to a future event of Leo's proving a theorem is not enough, because the truth of the sentence entails that a part of that event has already occurred. Unlike the future tense, the progressive aspect makes an essential reference to a current state of affairs, by connecting events occurring at the present time (as Leo's writing some formulae on the blackboard) with an event (if any) occurring in the future (as Leo's completing the proof). So, the straightforward approach characterizing the �emantic treatment of the future tense wo�ld not be justified here, for we have to account for a more complicated situation, in which some current event is seen as part of a more extended event {if any) whose temporal extension stretches over the future. The difficulty is that a progressive sentence involves both the present and the future, and that this double reference is determined by the idea that if an event is in progress, then part of it has already been realized. That is why the part-of relation between eventualities (or some other equivalent relation) plays an important role in the semantics of the
Andrea Bonomi 1 75
2
THE I MP E R F E C T I VE PARA D O X
The so-called imperfective paradox is based on the following remark, made first in Kenny ( 1963). When activity predicates are involved, from sentences in the progressive form such as:
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and so on. This is a central issue of the progressive, because we have just remarked that what is peculiar to this aspectual form is the connection that it establishes between something occurring at the present time and something occurring in the future. It is in this sense that my writing a formula on the blackboard can be seen as part of my proving a theorem and can justify the statement that I am proving a theorem. Since the same event e can be 'embedded' into several possible continuations, the context is a determining factor in selecting the relevant ones. If e is considered in connection with a given set of concomitant facts, then its possible extensions are events of a certain type. But if another set of concomitant facts is selected as the relevant background, then the type of the global event which is considered in progress will be different. This is why, as shown in section 3, the same situation can be described by alternative progressive sentences. As in some classical examples discussed by Gestalt-oriented theories of perception, different backgrounds can lead us to see the same entity as part of different configurations. One of the tasks of the paper is to account for this notion of context both in terms of events in the world (the 'concomitant facts' we have just mentioned) and in terms of the situation of the discourse (the conversational background that makes a particular set of facts relevant). The articulation of the paper is essentially based on the discussion of five problems. In section 2 I present the so-called impeifective paradox and its solution in the possible world semantics, as developed in Landman ( 1992). This theoretical framework leaves two questions open: in section 3 I address a problem of ambiguity engendered by the underdetermination of the data, whilst a related issue (what I call the multiple-choice paradox) is discussed in section 4· The new examples presented in this section are an interesting illustration of the intensional character of the progressive. Questions of a different kind are presented in connection with a contextualist approach. The first issue has to do with the role of mereological relations in the semantics of the progressive (section s). The second is represented by the use of this aspectual form in connection with improbable courses ofevents (section 6). In the final sections all these problems are considered from the point of view of a semantics for the progressive in which a 'mereological' analysis of eventualities (based on the part-of relation) is combined with a contextualist approach.
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The Progressive and the Structure of Events
( 1) (2)
Leo is pushing the cart Leo is writing
it is often possible to infer the corresponding sentences in the perfect tense: (3) Leo has pushed the cart (4) Leo has written. The idea is that if the time interval taken into consideration is representa tive enough, the sequence of events that justifies the statement that an activity is in progress can already be seen as an instantiation of that activity. But this is not true of accomplishment predicates, as shown by the fact that the inference from: Leo is proving the theorem
to:
(6)
Leo has proved the theorem
is not sound. Therefore, a first problem is to find an explanation for these different behaviours. The main feature of the approach to the progressive in possible world semantics is the following idea: presenting an event e as an event in progress in the actual world (at a given time) means that, if nothing anomalous happens, e is expected to be fully realized (at a later time). This intuition is captured in the truth-conditions proposed by Dowty (1979):
(7) Mary is building a house is true in a world w at an interval i iff in every
inertia world w' for w at i this interval i is a subinterval of a larger interval where Mary build a house is true.
Here, an inertia world w' for w at i is a world which is identical to w up to i and where, from there on, no unexpected events occur. So, the notion of normality is crucial here, as is explicit in this reformulation of Dowty's truth-conditions suggested by Landman (1992):
(7') Mary is building a house
is true at an interval iff under normal circumstances there would be a larger interval where Mary build a house is true.
It is easy to see how the imperfective paradox is solved in such a theoretical framework: a sentence as (s) is true only if in every inertia world the event of Leo's proving the completeness theorem is fully realized. But this condition can be satisfied even if the event at issue is not realized in the actual world, as required by (6). So, (s) does not entail (6). The problem, with this kind of analysis, is that it makes the following
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(s)
Andrea Bonomi
I 77
prediction: the progressive cannot be applied to events whose completion is presented as inherently unrealizable, for these events can be realized in no state of affairs which represents a reasonable alternative to the actual one. Yet it is not so unusual to ftnd sentences in the progressive form which do refer to events whose realization is presented as already impossible at the utterance time. Consider the following example: (8) Leo is making the Christmas cake. When he ftnds out that the stove has just broken down, he will give up.
(9) PROG(e, V) is true in a world w iff in some world in the continuation branch of e in w some event realizes the event type V. A continuation branch for an event e in w is a set of pairs of events and worlds. The intuitive idea is that we have to follow the development (if any) of e in our world w. If e stops in w, then we follow it in the closest world w' where it does not stop, provided that w' is a reasonable option2 for e in w. According to the truth conditions stated in (9), Mary is building a house is true in the world w iff an event J of the type Build-a-house (Mary) occurs in some world, a stage3 of which occurs in w, where this stage is an event e which develops into f on the continuation branch for e. As for sentences such as (8), in Landman's semantics they are simply true
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Suppose that this sentence is uttered on Christmas eve in some remote cottage and that, for several reasons, there is no way to ft.x the stove in time or to ftnd any other stove in the vicinity. Well, in these conditions the event at issue turns out to be unrealizable, even if the progressive sounds natural here. What characterizes the ongoing process in (8) is not only its failure in the actual state of affairs (which is not problematic in Dowty's treatment of the progressive), but its necessary failure in any 'normal' course of events which shares with the actual one all the past occurrences.1 As a consequence, since there is no 'inertia' world where Leo succeeds in making the Christmas cake, in Dowty's semantics (8) turns out to be false, against our intuition. To solve such a problem Landman (r992) presents a more sophisticated theory, where the idea of normality still has a crucial role, even though in a different way. The essential idea is that in determining what is a 'normal' continuation of a given stage 'we have to abstract away from facts about the world that are external to that stage. Thus . . . we are interested in its chance of continuing solely on the basis of what is internal, inherent to that stage' (p. 25). The formal tools Landman resorts to in order to implement this idea are taken from both event semantics and possible world semantics. In his treatment, the progressive is seen as a relation between an event e and an event type V, such that:
1 78
The Progressive and the Structure of Events
(as desired), because the fact that the stove has broken down is an 'external' accident that can be ignored, and in every world in which everything works normally Leo succeeds in making the cake. Let '.ls now consider two problems that this theoretical approach leaves open.
3 THE U ND E RDETERMI NATI O N O F THE D ATA
( 10) Leo is going to Metz and imagine you must evaluate it at this exact moment, i.e. at a quarter to three p.m. In Dowty's semantics for the progressive, (10) turns out to be false because the condition that in every 'inertia' world there is an interval, temporally including the evaluation time, where Leo go to Metz is true is not satisfied (recall that there is no way, at this moment, to discriminate between the different alternatives: they really are on the same level; so there are inertia worlds in which Leo does not go to Metz). The problem, here, is that, for the same reasons, the following sentences are also false at the given moment:
(I I )
Leo is going to Paris. ( 12) Leo is going to Besan�ron. So (ro)-(12) are all false with respect to the local evaluation time. In particular, the following holds in Dowty's framework: (r3) The sentence
Leo is going to Besanfon turns out to be false on 14 July, at
a quarter to three p.m. At first sight, everything is in order. But suppose that at last Leo decides to go to Besan�ron, where he arrives two hours later. Well, the day after someone asks Teo: what was Leo doing yesterday, at a quarter to three p.m.? Teo's answer is simple and effective:
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Suppose Leo has just begun a journey in France. As a Hrst stage, he drives from Milan to Dijon, where he arrives on I4 July, at a quarter to three p.m. He does not stop there because he has planned to spend his first night in France in one of the following cities: Besan�ron, Metz, Paris. Actually, he must make a decision, since three different routes correspond to these alternatives. But at a quarter to three p.m., while driving round the Dijon ring road, he has not yet decided where to go: he is thinking it over because, for several reasons, all these cities attract him exactly in the same way. Take the sentence:
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( r 4) Yesterday, at a quarter to three p.m., Leo was going to Besan�on. Is Teo a liar? I do not think so or, at least, I believe that there are many circumstances in which ( 1 4) is a reasonable answer. But, in this case, how to make the truth of ( 1 4) on 1 5 July compatible with (13), which describes a situation predicted by Dowty's theory? Such a problem does not arise in Landman's analysis. What holds, in the circumstances we have just described, is not (r3), but its negation, that is: ( r s) The sentences Leo three p.m.
is going to Besan�on is true on
1 4 July, at a quarter to
(16) The sentence p.m.
Leo is going to Metz is
true on 14 July, at ten past three
Nobody, I suppose, will question (r 6). So, let us follow the fmal developments of the story. Leo is not a lucky man. At twenty past three
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As a consequence, the truth of ( 1 4), the day after, is no problem any longer. Let us examine the reasons why, under these circumstances, ( 1 5) holds in Landman's semantics for the progressive. The point is that, before turning to the possible developments of an event e in other worlds, we have to follow its evolution in the actual world itself So, if in this world the stage of Leo's journey we are considering (at a quarter to three) develops at last into an event of Leo's going to Besan�on, then it is true at a quarter to three that Leo is going to Besan�on, as stated in (1 5). If one should object that at this moment the situation is not determinate enough to justify such a statement (because where Leo is going is still an open issue), one might reply that it is not the first time that semantics refers to idealized situations, where all the necessary data are assumed to be available, although they actually are out of the reach of situated speakers. This is the case of sentences in the future tense, which in most model-theoretic treatments (contrary to the analyses developed by Peirce and Prior) tum out to be true now if the event at issue occurs at an interval later than the present one, in spite of its inaccessibility to the present speakers. So far, so good. Yet, with respect to the case of the future, there is something peculiar to the progressive which is sacrificed here. Consider the following more detailed description of the facts. The journey goes on without interruptions. At three o'clock, Leo decides to go to Metz and, ten minutes later, he has already taken the freeway leading from Dijon to that city. He reckons on being there in a couple of hours and this is a reasonable hypothesis: his intention is now completely definite, he is not tired, he is on the right freeway, etc. Under these circumstances, the following statement sounds quite natural:
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The Progressive and the Structure of Events
he runs into a road block. He does not stop, but he follows the suggested detour and, half an hour later, at ten to four, he finds out that Besan�on is now much nearer than Metz. Without stopping, he takes the &eeway to Besan�on, where he arrives one hour and a half later. And that is the end of this tormenting story. Exactly as ( 1 6), this other statement sounds very natural in the scenario we have just described: (17) The sentence Leo
is going to Besanfon
is true on 14 July, at five to four
p.m.
As
( 1 8) The sentence Leo p.m.
is going to Besanfon is true on 1 4 July, at ten past three
So, the problem, in Landman's theoretical framework, is to make the truth of Leo is going to Metz, at ten past three, consistent with the truth of Leo is going to Besanfon, at the same time. To overcome an analogous difficulty, in the appendix of his paper Landman hints at the notion of perspective, illustrated by the following example. Suppose I was on a plane to Boston which got hijacked and landed in Bismarck, North Dakota. What was going on before the plane was hijacked? One thing I can say is: 'I was flying to Boston when the plane was hijacked.' This is reasonable. But another thing I could say is: 'I was flying to Boston. Well, in fact, I wasn't, I was flying to Bismarck, but I didn't know that at the time.' And this is also reasonable . . . What we carve out as an event and what we decide to regard as stages of that event depends on our perspective in a certain context.
Yet, it is not clear how to incorporate this vague notion of perspective in Landman's theory and how to avoid a floating or arbitrary ontology where
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desired, this statement holds in Landman's theory. In fact, suppose e is the stage of Leo's journey up to five to four p.m. As imposed by the corresponding definition, e has a unique continuation branch in the actual world w, and in this branch we havefirst to follow the evolution (if any) of e in w. Since in w the final result of this evolution is an event J of the type Go-to-Besanfon (Leo), the pair (f w) belongs to the continuation branch for e in w, and as a consequence ( 1 7) holds. But, against our intuition, for the same reasons (16) cannot hold in this reconstruction: the stage of Leo's journey up to ten past three develops without interruptions into the eventJ of Leo's going to Besan�on in w itself, so that, according to Landman's definition of continuation branch, we have to take into account no other development in alternative worlds. Do not forget that it was exactly this peculiarity that allowed Landman's semantics to evaluate ( 1 5) as true and, as a consequence, to justify the truth of ( 1 4) as well. That (16) cannot hold in Landman's theory is shown by its inconsistency, in this theory, with the following statement, which does hold:
Andrea Bonomi
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one can 'carve out' events as much as one pleases. So, I shall stick to the original, explicit version of Landman's theory, where it is quite problematic to account for the validity of { r6).
4
THE M U L T I P LE - C H O I C E PARAD O X
cities. Unfortunately, a few minutes later, before Leo makes a decision about his final destination, his journey is definitively interrupted because the engine breaks down. Now imagine that Metz, Besan�on, and Paris are the only cities, in France, where today there is a concert of Baroque music. Take this sentence, uttered by a well-informed observer shortly before the engine's breakdown:
(r9)
Leo is going to a French city where today there is a concert of Baroque mustc.
There surely is a sense in which, in this situation, (r9) is true. In fact, although it is false (or simply not-true) that Leo is going to Metz, or that he is going to Besan�on, or that he is going to Paris (because none of these cities can be selected as the destination at issue, given the present stage of the journey and its future developments), it is anyway true that he is going to a city with such and such characteristics, i.e. the characteristics satisfied only by the three cities we have just mentioned. According to this weak interpretation of the sentence, (19) is true even if there is no particular city with a concert of Baroque music where Leo is going. But (r9) can also be interpreted in a different way. On this stronger reading, a necessary condition for the truth of (r9) is that there is a particular city (i.e. Metz, Besan�on, or Paris) where Leo is going. But such a condition, as we have just remarked, is not satisfied in the given situation. So, on this reading, which is equivalent to: (2o) There is a French city x where today there is a concert of Baroque music, such that Leo is going to x. our sentence
(r9) is false.
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Before presenting a theoretical framework i n which this kind of difficulty can be overcome, let me address the following problem:4 does the progressive create an intensional context? To answer this question, consider this variation of our basic example. Suppose that, as before, Leo has decided to spend the night in one of the following cities: Besan�on, Metz, or Paris. At three o'clock he has already left Dijon and is travelling on a freeway that has Besan�on, Paris, and Metz as possible destinations. At this moment, thanks to his cellular phone, he makes a hotel reservation in each of those
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The Progressive and the Structure of Events
In other terms, (r9) is ambiguous, and this ambiguity between a 'specific' and a 'non-specific' reading is due to the presence of a particular intensional context determined by the progressive. This peculiarity of the progressive can be stressed by considering the different behaviour of the future (as predicted by our remarks on this topic in the introductory section). In fact, the future counterpart of (r9): (2 r) Leo will go to a French city where today there is a concert of Baroque muslC has
only one
reading, which is equivalent to the future counterpart of (2o):
This means that, in the given situation, (2 r) cannot be true unless it is true of Besan�on (or Paris, or Metz) that Leo will go there. Unlike the progressive, in the same circumstances the future allows no 'weak' reading. As I suggested in the introduction, the reason why (r9) can be ambiguous in this sense, whilst (2r ) cannot, is that the characteristics of the present state of affairs can be relevant to the evaluation of the progressive, whilst the evaluation of a sentence in the future tense is independent of them. For (r9) to be true on its stronger reading, there must be, at the evaluation time (the utterance time, in this case), an ongoing event determinate enough to be described as an event of Leo's going to Besan�on, or as an event of Leo's going to Metz, or as an event of Leo's going to Paris. But the requirements that the weaker interpretation of ( r 9) imposes on the present situation are less restrictive, and the characteristics that the ongoing event must have do not entail the reference to a particular city as a possible, final destination. This is why (r9) can be considered as true or false, with respect to the same situation, according to the intended reading. On the other hand, such a reference to the present situation has no role to play in the truth conditions for the sentence in the future tense: what counts is only what happens at some time t later than the evaluation time, and no ambiguity5 of the kind illustrated before is allowed. One might object that the source of this peculiar kind of intensionality, in the example we have just discussed, is not the progressive, but the intentional character of the event, due to the presence of a human agent with his beliefs, desires, etc. But it is easy to see that the same 'paradox' arises in situations where the subject is no human agent. Consider, for instance, the case of an avalanche which normally descends a gorge A and then, because of the conformation of the ground, can continue its run only in two distinct, alternative ways: it falls either into a first valley B or into a second valley C. Statistically, both alternatives are equally probable. But
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(22) There is a French city x where today there is a concert of Baroque music, such that Leo will go to x.
Andrea Bonomi
183
suppose that, on a particular occasion, since both valleys were temporarily populated by chamois, the avalanche was destroyed at place D by a special cannon shortly before taking either path: A
O D
B
�
c
(23) The avalanche was descending to a valley populated by chamois when it was destroyed by a special cannon is true, on its 'non-specific' reading, even if it is false (or simply not true) both that the avalanche was descending to valley B and that it was descending to valley C. But the sentence is false on its 'specific' reading, which entails the existence of a particular valley x (populated by chamois), such that the avalanche was descending to x. So, the same problem of ambiguity we have detected in Leo's example arises in this case, where the subject is no human agent. To conclude these remarks, it should be noted that such examples are problematic for Landman's theory, which easily accounts for the stronger reading of (19) (or (23)), but not for the weaker one. In our example, Leo's journey stops when the engine breaks down. Let e be the event corre sponding to this part of Leo's journey. Since e stops in our world, we must follow its developments in other possible worlds (in the continuation branch of e) until we find a world w and an eventf in w such that e is a stage off and f is an event of Leo's going to Paris, or an event of Leo's going to Metz, or an event of Leo's going to Besan�on. Only one continuation branch of e is admitted, and only one of these alternatives is realized in this continuation branch. So, suppose thatf is an event of Leo's going to Paris. In Landman's theory, this means that it is true that Leo is going to Paris: it follows that there is a city x, where today there is a concert of Baroque music, such that Leo is going to x. The problem is that, in Landman's theory, such a conclusion represents a necessary condition for the truth of (19). But we have just seen that this prediction is not correct when the weaker reading of (19) is considered. Therefore, besides the so-called imperfective paradox, another apparent paradox must be accounted for by any adequate theory of the progressive. The difficulty, this time, has to do with disjunction and existential
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In this situation, the sentence
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quantification for, if our analysis is correct, it can be true that a is going to b or c although it is not true that a is going to b and it is not true that a is going to c; and, for the same reasons, it can be true that a is going to a place with such and such characteristics although it is not true that there is a particular place x. with such and such characteristics, such that a is going to x. Let us call this predicament the multiple-choice paradox.
s EVENTS, PARTS , AND CAUSES
(24) Prog(¢)(s) is true [in a world w and with respect to a context c] just in case there is a perspective 7r such that in all the worlds in which s is normal with respect to the property attributed to s in 7r, there is an event e cotemporaneous or later than s such that ¢>(er (Here ¢ is a property of events, and 'Prog' an operator that takes an event-predicate ¢> and returns a state-predicate Prog(¢).) Since different perspectives can apply to the situation described in section 3, in this theoretical framework it is possible to account for the truth of both (16) and (18): i.e. it is possible to solve the problem of the underdeterrnination of the data. And the same holds for the multiple choice paradox. A first problem with this characterization of the truth conditions for the
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We have just seen that one of the merits of Landman's theory is the recognition of the role that the mereological structure of eventualities must have in the semantics of the progressive. But we have also seen that what is left unexplained is the way different perspectives on the same data can be relevant to individuating different types of events in progress. An explicitly contextualist approach like Asher's6 is more adequate from this point of view. I will not go into the technical details of Asher's theory, where the notion of perspective has a crucial role. In a nutshell, a perspective is a function from worlds, contexts and states to propositions (i.e. sets of worlds): the idea is that, given a context c and a state s in the world of evaluation w, a perspective 1r selects a set of worlds that verify some relevant characteristics of s in w. In intuitive terms, perspectives are different ways of considering the state s associated with the progressive form by singling out, each time, some particular properties of s and by selecting the set of worlds p in which these properties are attributed to s. Finally, given p and the world of evaluation w, it is possible to fix the set N of the 'normal' p-world from the point of view of w. The truth conditions for the progressive can be paraphrased as follows:
Andrea Bonomi 185
progressive is that, as it stands, the lack of an appropriate relation (as, for instance, the part-of relation) between the relevant eventualities leads to false predictions. In fact, consider an event of Leo's going up the stairs from the first floor to the third floor of his house. Everything is perfectly in order and, in fact, he reaches the third floor without any problem. Now take a moment t during his going up the stairs from the fust to the second floor. In the given circumstances, what is true at t is not only the statement that Leo is going up the stairs from the first floor to the second floor, but also the following statement: (25) Leo is going up the stairs from the first floor to the third floor.
(26) Leo is going up the stairs from the second floor to the third floor.
But this is absurd. One might think that this difficulty is caused by the lack of causal relation between the current eventuality (i.e. Leo's going up the stairs from the first to the second floor) and the eventuality of Leo's going up the stairs from the second floor to the third floor and that requiring the existence of such a relation between the state s and the event e in the truth conditions (24) might solve the problem:8 But this is not correct. Suppose that the water of a brook which has just been diverted is approaching a little meadow and that, at the moment t �ong before it reaches the meadow), I utter this true statement: (27) The water is descending to that meadow.
As before, there must be a state s and a perspective 7r which selects some particular characteristics of s such that in all the possible worlds which are 'normal' with respect to these characteristics there is a (complete) event e, later than s, of the water's descending to the meadow. For obvious reasons, in all these worlds there must also be an eventf, later than s, of the water's
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If for example someone asks me, at t, what Leo is doing, (25) is a perfectly appropriate answer. So, according the above truth conditions, there must be a perspective 1r which selects some particular characteristics of Leo's current state s such that in all the possible worlds which are 'normal' with respect to 1r there is a (complete) event e, later than s, of Leo's going up the stairs from the first to the third floor. Since this is so, in all these worlds there must also be an event f, later than s, of Leo's going up the stairs from the second floor to the third floor (in fact, reaching the second floor first is a necessary condition for reaching the third floor). As a consequence, in this situation, according to the truth conditions stated in (24) the truth of (25) entails the truth, at t, of the following statement.
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wetting the meadow (for, if the water reaches the meadow, it wets it). As a consequence, in virtue of (24), the truth at t of (27) entails the truth at t of:
(28) The water is wetting that meadow.
6 UNEXPE CTED EVENTS
What is essential, in this theoretical framework, is the fact that the notion of normality is characterized by the following axiom schema:
(29) 'v's [Prog(¢) (s) > :3 e [s � e 1\ ¢(e) ] ] which states that, unless we are told otherwise, the truth of the non progressive (or perfective) form follows from the truth of the progressive form. In (29) ' > ' stands for a conditional which supports non monotonically valid inferences as, for instance, defeasible modus ponens. To go back to a previous example, (29) is the formal counterpart of 'default' statements as the following: (3o) When you are making a cake, you typically make a cake eventually. So, all you have to check, for the truth of the progressive, is whether the characteristics of Leo's actions justify the reference to such default assumptions, independently of the fact that the event at issue is already presented as one whose realization is not possible. But making the notion of 'normality' more flexible by connecting it to default and generic statements may not be sufficient, as shown by the following example. Suppose that an international sailing association
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But this entailment, predicted by the truth conditions in (24), is not acceptable. Even if there is a causal connection between the state of the water at t (i.e. its being in the process of descending to the meadow) and the event of the water's wetting the meadow, in the given situation (27) is true at t, whilst (28) is simply false.9 This problem is even more dramatic in the case of non-telic event-types. In this connection, Asher introduces an interesting idea, which I will take up in the last section: 'for non-telic event types, all the information needed to decide upon the occurrence of the culminating event is already present with the state characterised by the progressive. The only relevant perspective for evaluating the truth of Prog(¢) at a world w where ¢> describes a non-telic event-type is the singleton of w itself' (Asher, 1 992: 481 ). But, given the truth-conditions in (24), it turns out that any state s (in the real world), if it is simply followed by a complete event of a non-telic type ¢, satisfies Prog(¢).10
Andrea Bonomi 187
organizes a competition whose goal is the circumnavigation of the globe. Mter a very thorough selection, a hundred boats are admitted and they sail at the scheduled date. Some days later, during a public presentation of the competition, the spokesman of the association says: (3 I) A hundred boats are circumnavigating the globe. Most of them will fail.
(32) For every boat x (in the competition) which is circumnavigating the globe, x typically circumnavigates the globe eventually. Yet (32) is simply false, although the progressive form sounds quite natural in (3 I ). More in general, the problem is that in some cases the use of this aspectual form does not conform to the idea that the state denoted by the progressive 'must have some characteristics that would lead to a completion (of the event at issue]'.11 A different problem12 is raised by those situations in which the completion of the event at issue is quite improbable, almost impossible, but in the end this completion is realized. Suppose that an observer A. who sees Leo write some formulas on the blackboard, asks another observer B what Leo is doing. Since the answer is: (33)
Leo is proving Goldbach's conjecture
A objects: 'You are lying! It is awfully difficult, perhaps impossible, to prove that conjecture.' So, the problem is: which of the observers is right? There is a temptation to say that A's reaction is justified because it is highly improbable that Leo will manage to prove Goldbach's conjecture, and B has no serious reason for justifying the plausibility of (33). But suppose that, some hours later, he completes the proof (perhaps because the solution is suggested by a dream he has during a break). Well, at this moment we may agree with B who says: 'Do you see? It was true that Leo was proving Goldbach's conjecture!' What is interesting, in this final comment, is B's implicit reference to what happens in the actual course of events, although it was out of the reach of common-sense assumptions at the utterance time. Why is this reference
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In the given circumstances, the statement is not only consistent, but also true (since the spokesman's assertion is based on experience, and as a matter of fact only fifteen boats will manage to circumnavigate the globe). But in Asher's theory, (29) is an axiom schema of the logic of the progressive, so that, since {J I ) attributes to every boat x (in the competition) the progressive 'state' of circumnavigating the globe, the truth of the following default (or generic) statement is a necessary condition for the truth of the progressive sentence (3 I ):
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so important? Because, once realized, this course of events provides the schema of a consequential chain of eventualities where the original event
at t itself, of B's statement. No requirement of this kind is entailed by the corresponding statement in the future tense.
7
T H E R O L E O F C O NTEXT
From the above discussion we can draw the following temporary con elusion: both an account of the 'mereological' structure of eventualities (based on the notion of part-of or something equivalent} and a contextualist
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observed by A and B is associated with other concomitant eventualities leading to an event of proving Goldbach's conjecture. The moral is that if common -sense assumptions fail to identify the characteristics that a set of events must have to be qualified as a process of proving Goldbach's conjecture, reality can provide the necessary information. The theoretical reasons that justify B's attitude might be condensed by the maxim: wait and see! This possibility of referring to the actual course of events as an approximate source of information for the truth of the progressive will be discussed in the last section, in connection with the existence of 'totally realistic' frames. One might obj ect that, since the reference to what will really happen (independently of its plausibility at the utterance time t} is crucial here, then, at least in such situations, the difference in truth-conditions between the progressive and the future is not as dramatic as suggested in the introduction. At the moment t at which B says that Leo is proving Goldbach's conj ecture there is no 'generic' or default statement which makes the completion of the event plausible and the possibility of him succeeding turns out to be highly improbable: so, it might seem that what makes B's assertion true at t is the mere fact that Leo proves the conj ecture at some subsequent moment (which is a necessary and sufficient condition for the truth of the corresponding statement in the future tense). To see that such a conclusion is not correct, suppose that, a few moments after B's utterance, Leo gives up and that he succeeds in proving Goldbach's conjecture in different circumstances (e.g. two months later, after realizing that what he was doing at t was completely wrong). In this case, B's statement would be false at t because there is no way, at t or later than t, of connecting the event of Leo's proving Goldbach's conjecture with his actions in the context of the events occurring at t. As I have just emphasized, the reasons that j ustify such a connection may be available only at a time t' later than t, but in any case they are a necessary condition for the truth,
Andrea Bonomi 189
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approach are necessary ingredients of the semantics of the progressive. To see how these two aspects can be integrated into a unitary framework, let us go back to our original example. We have seen that, since the event of Leo's driving &om Milan to Dijon has different, but equipollent, possible continuations in the future, considering a statement in the present progressive as true or false with respect to a local evaluation time (14 July at a quarter to three p.m., in our example) might be problematic. We have also remarked that if an analogous statement (but in the past progressive) is uttered at a later time (the day after, in the same example), treating it as plainly true can be quite natural (at least in many contexts). A plausible reason for this dissymmetry might be the following. On 14 July, at a quarter to three p.m., how Leo's journey will evolve is still an indeterminate issue, since the first stage of the journey.(from Milan to Dijon) can develop into several, distinct events (going to Metz, or to Paris, or to Besan�on), all of which are on the same level. At this moment, the context is not determinate enough to reduce this set of alternative event types and if we refer to this context all the developments just mentioned are still relevant. A little more exactly, we might say that, given an event e (as, for instance, Leo's driving &om Milan to Dijon), it is possible to associate with e, at a given interval t and on the basis of the relevant context of facts, a set D of courses of events, where every course of events in D contains events with which e is in the part-of relation, i.e. possible developments of e. Let us call this structure the embedding setfor e at the interval t in the context c. The intuitive idea is that an event e in the world is surrounded by a bunch of possible developments in different scenarios, some of which become actual, whilst others are discarded as time goes by. The point of view that we can take on e by selecting some properties of e acts as a constraint on the class of developments that can be associated with e, depending on other relevant circumstances. For example, suppose (against the above assumptions) that it is already certain that Leo will not go to Paris because he cannot to afford to live in such an expensive city. Well, in this case the embedding set at issue will turn out to be more restricted than the one described above, because all the courses of events containing an event of Leo's going to Paris will be discarded. The interesting thing is that by assuming different points of view it is possible to attribute different embedding sets to the same eventuality. Going back to our example, the set of developments contextually associated with the event of Leo's driving from Milan to Dijon contains heterogeneous courses of events on 14 July, at a quarter to three p.m.: what characterizes the evolution of the ongoing event is its indeterminacy. (Notice that this is not simply due to a cognitive failure: it is a real fact that at the given time Leo has made no decision yet, is deliberately following a route which leaves
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all the relevant alternatives open, is not too tired and can continue his journey, etc. So, it is this particular state of affairs, not our state of ignorance, that allows for such a proliferation of relevant options.) But the day after, most of these options are no longer relevant, since Leo's decisions and actions related to the continuation of his journey after getting to Dijon are now in the past. As a consequence, the present point of view can now assign to the same event e of Leo's driving from Milan to Dijon a reduced set of open developments (at the given time). In connection with examples (16) and (18), we shall later discuss the case in which different perspectives on a given eventuality are relevant at the same time. It should be clear why the conversational background has a crucial role in determining when an event can be considered as a stage of another event of a given type. Consider, for instance, a situation where the professor of logic goes t
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then H will contain an eventf of type V, such that e is part off. Therefore, to account for the difference in truth-value between the two sentences at issue, we can say that the different contexts in which the same actions take place justify the reference to the intended stereotype in the former case but not in the latter.
8 FRAMES
•
•
•
. . . Metz
D H,
g
H2 e 6E:t-------44-
. . . . Paris
. . . Besancron
(The circles, in the different courses of events H10
• • •
, Hn,
. . . •.
are events with which e is
in the part-of relation. f. g, and h are respectively events of Leo's going to Metz, to Paris, and to Besan�on.)
When is it reasonable, in such a picture, to say for instance that Leo is going to Metz? My idea is that this statement is true when the relevant information provided by the context is sufficient to force every ideal development of the event at issue to satisfy the given event type. In other terms, we must fmd an event of Leo's going to Metz in every course of events in D', the set of developments that can be associated with e in the given context. This means that the characteristics of the ongoing event
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Let us try to make these ideas more precise by sketching a ftrst, tentative version of the truth-conditions for the progressive. We can reason as follows. As we have seen on 1 4 July, at a quarter to three p.m., the event e of Leo's driving from Milan to Dijon can be seen as part of other events; these events belong to different types, or sets, of events, even though the context puts drastic restrictions on the range of alternatives. For example, e can be seen as a part of a journey to Auxonne, which is part of a journey to Dole, which is part of . . . , which is part of a journey to Besan�on. But e can also be seen as part of a journey to . . . , and then to . . . , and ftnally to Metz. And the same can be said about Paris. Formally speaking, all these events can be seen as elements of potential courses of events H1 , , Hn which can be associated with e in the context c. In the situation we are discussing, the set D of these courses of events can be represented as shown in D.
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and of the concomitant eventualities are definite enough to force the embedding of that event in an event of type Go-to-Metz (Leo), i.e. to qualify every course of events Hn as a situation leading to an event of Leo's going to Metz. D'
f
. .. Metz
HI H2
e
. . . . Metz
. . . Metz
(Here, f, g and h are all events ofLeo's going to Metz. So, there is an event of Leo's going to Metz in every course of events in D'. Recall that there can be different events of the type Go-to-Metz (Leo), for there are several ways to go to Metz from Dijon.)
These remarks are mirrored in the truth-conditions I am going to propose, where the contextual approach illustrated above is suitably refined by referring to the notion of conversational background.14 A course of events is a structure H = (E, C), where E is a set of eventualities and C, the part-of relation, is a partial order on E. Given a course of events H, a context CH is a set of eventualities included in H. A stereotyp ical conversational background (or a frame) is a function F from eventualities and contexts such that F(e, CH) is the set of courses of events (containing e and the eventualities in CH) in which the event e, in view of the concomitant facts in CH, follows its natural course. More exactly, any course of events H1 in F(e, CH) satisfies stereotypical constraints of the following kind:
If (I) H 1 contains an eventuality e of type A;, (II) for every type Au . . . , An, H contains an eventuality of that type; 1
then (III) H 1 contains an eventuality f of type V such that e C f.
The idea is that if an eventuality e has the characteristics denoted by the predicate A, and if other concomitant eventualities, whose character istics are respectively Au . . , An, are realized, then e is part of an event of the intended type V in all the stereotypical developments of e. Au . . . , An are the types of the concomitant facts in the context CH (the 'background', in the sense of Gestalt-oriented theories I will discuss below) that are .
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HJ
g
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Given a course of events H and a time interval t, it is true in H at the time t that e is an eventuality of type V in progress if and only if there is a context of concomitant facts CH and a stereotypical frame such that, in all the courses of events selected by this frame with respect to this context, there is an event J such that the time of evaluation is included 15 in the temporal extension ofJ, J is of type V and e is part off. For example, Leo is going to Metz is true in a course of events H (at a time t) of an eventuality e iff there is a point of view on e, with respect to a context of concomitant facts, such that in all the courses of events compatible with this point of view there is an event J of the type Go-to-Metz (Leo) such that e is part off. Intuitively speaking, this means that Leo is going to Metz is true iff there is an event whose characteristics, with respect to the some features of the world and a given stereotypical constraint, force the perception of e as part of a process of Leo's going to Metz, whatever developments may originate from e. (Notice that, as desired, this is compatible with the existence of various ways of achieving the task: for example, although the situation is at this point
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necessary to force the perception of e as part of an event of type V. So, a stereotype F can be seen as a particular way of considering the possible developments of the event e in view of the relevant facts in CH. For example, suppose that e is an event of Leo's writing some formulas on the blackboard and that the concomitant eventualities in CH are the following: Leo is a professor of logic; proving the completeness theorem is included in the program of his course; he has already explained all the necessary notions, etc. What the stereotypical frame tells us, in this situation, is that e must be considered as a stage of an event of Leo's proving the completeness theorem, in the sense that all its ideal developments lead to a complete event of Leo's proving the theorem. There are at least two senses in which the notion of context turns out to be fundamental in this reconstruction. First of all, what is crucial here is not only the characteristics of the event as such, but also the set of concomitant facts CH (i.e. a context provided by the world) by which the event is surrounded. Secondly, which characteristics of the event and which concomitant facts are relevant depends on the existence of a suitable frame or conversational background (where the appropriate constraint ftxes the type A of the event e and the types An . . . , An of the concomitant facts), and this is a context or background provided by the situation of the discourse. These two main ingredients determine the following truth-conditions for the progressive (where T is a function which assigns temporal extensions to eventualities): {34) I Prog {e , V) I H, t = 1 iff 3F3CH[v'H ' [H ' E F{e , CH) ---+ 3j[t C T (j) 1\ f E H ' 1\ V ( f ) 1\ e C j]]J.
1 94 The Progressive and the Structure of Events
completely definite because Leo has decided to go to Metz, has all the necessary means to do that, etc., there can still be different chains of events leading to an event of Leo's getting to Metz. He might take a toll road or a freeway, stop at X rather than Y, and so on. This is why we have to refer to a plurality of courses of events, even though the type of the event which is going on is already definite. At the given time i there can be lots of different events of the type Go-to-Metz (Leo) which are extensions of the given event of type Go-to-Dijon (Leo)).
To see how the truth-conditions in (34) work in more interesting situations, let us go back to the example of Leo's journey. Consider the following sentences: (3s) Yesterday, at ten past three p.m., Leo was going to Metz (36) Yesterday, at ten past three p.m., Leo was going to Besan�on. As we saw, there are contexts in which (35) is perfectly natural; but there are also contexts where (36) is a suitable description of the facts (a posteriori). It is tempting to say that in a sense (3s) is true de dicto and (36) de facto. The problem, here, is that on the one hand we would like to make the truth of both sentences possible, but on the other hand we do not want the truth of (3s) and (36) to entail the truth of (37)
? Yesterday, at ten past three p.m., Leo was going to Metz and (was going to) Besan�on.
In fact, the truth of this sentence would be quite counterintuitive in the given situation, since there is no moment, in the story, at which it is plausible to think that Leo is going to both cities (they are alternative destinations). Before considering how the present framework is equipped to deal with such an issue, notice that this other sentence is not problematic: (38) Certainly, yesterday, at ten past three p.m., Leo was going to Metz. But, in a different respect, it is also true that he was going to Besan�on. What is the reason for this difference between (37) and (38)? First of all, let us explain why the simultaneous truth of (3s) and (36) is no problem. The intuitive idea is that the contextual considerations implicitly assumed as relevant to justifying (3s) concern for instance Leo's intention to go to Metz, his taking the freeway to this city, his position at ten past three, and so on.
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9 P O I NTS OF VIEW
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The relevant stereotypical constraint, here, is that if an event e such as Leo's journey up to this moment is realized at t, and if other concomitant eventualities are realised at t (as, in this situation, Leo's taking the freeway to Metz, his position at t, etc.), then in all the courses of events compatible with this constraint (where the road block does not occur), the event e develops into an event of Leo's reaching Metz. So,
(3s) is true with respect to
a frame with this stereotypical constraint and to this set of concomitant facts. for the justification of (36), other concomitant facts and another
As
constraint are relevant, so that
(36)
can be true with respect to a different
frame, i.e. a different point of view. (It should be stressed that having different 'perspectives' on a given event is possible not only when this event present interval. For instance, we can imagine a situation in which two observers, referring to different sources of information, are both justified, at ten past three p.m., in asserting respectively that Leo is going to Metz and that Leo is going to Besan�on. In other terms, time can be important in licensing different perspectives, but it is not the only factor involved.) What is crucial, here, is the fact that the same event (e.g. Leo's going from Milan to Dijon) can be seen as part of different events with respect to different contexts. Such a situation is quite familiar in the domain of cognitive phenomena, where the context or background has an essential role in selecting the entities in which a given entity can be 'embedded' as a recognizable part. Take; for instance, the case of perception. In the following figure, discussed by Kohler ( 1940)
,
a
b
line a is naturally seen as part of a group of two lines which includes
b. But
in this other figure
a
b
the same line a, in a different context, is naturally seen as part of a different group of two lines.
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is in the past-as in the case we are discussing-but also if it is located in the
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The Progressive and the Structure of Events
There is a further sense in which the context (i.e. a set of concomitant facts) is relevant to selecting the appropriate mereological structure of events both in cognitive phenomena such as perception and in the semantics of the progressive.
As
a matter of fact in both situations it
the context that allows for the reference to
virtual entities, i.e.
are not realized in the actual world. We have j ust seen that
entities that
if we consider
Leo's journey up to a given moment (that is Leo's going to Dijon)
respect to some given focts (his intentions,
is
with
his current position, etc.) then this
appropriate mereological relations is quite similar to the role it has in perception. The segments in the following ftgure are simply seen as parts of a discontinuous line.
/
/
/
/
But the same segments can be seen as parts of a continuous line in a different context, where the completion of the line behind the stripes is a 'virtual' event determined by the appropriate mereological constraints.
A similar dependency upon the relevant context (i.e. the 'concomitant facts' in CH mentioned in the truth-conditions case of the progressive. Coming back to
(Js)
(34)) can be observed in the (36), the idea is that two
and
different contexts are to be selected, so that two different frames are relevant:
(Js)
is true with respect to a given context of concomitant
eventualities and a given frame (where Leo's journey up to ten past three is seen as part of a journey to Metz), whilst
(36)
is true with respect to a
different context of eventualities and a different frame (where Leo's journey up to ten past three
is
seen as part of a journey to Besan�on). The oddity of
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event is seen as an event of going to Metz even if this second event does not occur in the real world: it is simply a possible (but not actual) event. But we have also seen that, with respect to a different context (i.e. with respect to other relevant facts) the event of Leo's going to Dijon is not seen as part of an event of going to Metz. Here, the role of context in ftxing the
Andrea Bonomi 197
(37)
is due to the fact (stressed by K.amp and Partee ( 1 995) in connection
with a different problem) that the default case, for direct conjunction, is the reference to the same context. This is the origin of the inconsistency detectable in (37). But this inconsistency can be removed by associating the Hrst conjunct to a given context (and the corresponding frame) and the second to another. This is exactly the move suggested in the case of (38), which is quite acceptable: distinct sentences, in the development of the discourse, can be supported by different &ames. The truth-conditions stated in (34) enable us to account for the different types of reasons that make a progressive sentence false. For instance, consider a sentence such as:
The reason why (39) is false is simply that there is no frame F, in the background assumptions, which selects courses of events leading to the realization of an event of Leo's emptying the Ocean with a bucket. But take this other sentence: (4o) Leo is emptying the bathtub with a bucket and imagine a situation in which Leo correctly moves the bucket, but the bucket has a large hole on the bottom. In this case we have the frame F, the relevant event e, but what is missing is a concomitant fact in Au . . , An. i.e. .
the fact that the bucket has no hole. Since not all the requirements in Au . . , An are satisfied, there is no guarantee that in every course of events associated with the intended frame the event of Leo's emptying the bathtub .
is realised, so that (4o) turns out to be false. It should be noticed that this conclusion is possible because we have not considered the state of the bucket as one of the eventualities that can be ignored in order to determine the set of ideal courses of events. But in a different situation this option would be available, so that (4o) would tum out to be true. It may depend on the size of the hole, on the time at which the bucket broke, on Leo's awareness of the situation, and so on. A continuum of contiguous but slightly different cases is imaginable here, and it is not difficult to refer to situations in which our intuitions about the truth of a progressive sentence such as (4o) waver. In general, the theory does not predict whether an eventuality e must be considered as an inherently missing condition of type Au . . , An or as an 'external' mishap that can be ignored. But leaving some parameters indeterminate is probably an essential feature of any analysis of the progressive, in order to mirror the flexibility of its use in different .
circumstances.
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(39) Leo is emptying the Atlantic Ocean with a bucket.
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r o C O NCLU S I O N S AND OPEN P R O B LE M S I n the analysis o f the progressive proposed in the paper two notions play a crucial role. On the one hand, since the same event can be 'embedded' into several possible developments that are relevant to the truth-conditions of the progressive, a first task of the analysis was to account for the part-of relation which connects an event with its possible continuations. On the other hand, this kind of connection is largely dependent on contextual factors, and a second task of the paper was to analyse this notion of context both in terms of events in the world (the 'concomitant facts' selected as
(r6)
The sentence p.m.
Leo is going to Metz is true on 14 July,
at ten past three
and ( r8) The sentence Leo p.m.
is going to Besanfon is true on 1 4 July, at ten past three
can be true. The idea is that (r6) refers to a frame or point of view which selects some facts in the world as the relevant ones, whilst other facts are relevant in the case of (r8). 3· An easy solution can also be found in the case of the multiple-choice paradox. As you will remember, the ongoing event d and the context of concomitant facts are determinate enough to individuate a restricted set
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relevant) and in terms of the situation of the discourse (the conversational background that makes those facts relevant). Combining a 'mereological' analysis of eventualities with a contextualist approach allows for a better comprehension of problems discussed in the paper. Let us see why. r. As for the imperfective paradox, suppose that it is true that Leo is proving the completeness theorem. In the semantics of the progressive presented here, this means that there is an event e (e.g. the event of Leo's proving that every Hintikka set is satisfiable) which develops into an event of Leo's proving the completeness theorem in all the courses of events selected by the relevant frame F, i.e. in all the courses of events which belong to the set F(e, CH)· But the actual course of events H may not belong to this set and, as a consequence, the event of proving the completeness theorem may abort in H. This means that the truth of the sentence Leo is proving the completeness theorem does not entail that Leo has actually proved, or will have proved, that theorem. 2. As for the second question, connected with the underdetermination of the data, we have just seen how in the present framework it is possible to account for the fact that both:
Andrea Bonomi
199
of possible destinations (ie. the set whose elements are Paris, Besan�on, and Metz: the cities where today there will be a concert of Baroque music), but not to select a particular city, in this set, as the intended destination. In the semantics presented here, this means that there is a frame F such that in all the courses of events selected by F, i.e. in all the courses of events in F(e, CH), there is an event/ such that d is part off andf is an event of l...eo's going to Paris, or an event of Leo's going to Metz, or an event of Leo's going to Besan�on. That is, in the given situation, in all these courses of events there is an event f such that d is part ofJ and f is event of Leo's going to a city where there is a concert of Baroque music. Therefore, on its weaker reading, the sentence Leo is going to a French city where today there is a concert ofBaroque mustc
turns out to be true. But since there is no city x such that, in all courses of events in F(e, CH), there is an event J such that d is part of J and J is an event of Leo's going to x, (19) turns out to be false on its stronger reading. 4· Let us consider again the fourth problem. As we saw, in the given situation (27) The water is descending to that meadow. is true, whilst (28) The water is wetting that meadow is obviously false. In the framework under discussion the truth of (27) is due to the existence of an event e (e.g. the water's reaching a certain position in its descent towards the meadow) which is seen as part of an event of descending to the meadow. But e is not part of an event of the water's submerging the meadow (in fact, at the evaluation time there is no event that is part of an event of the water's submerging the meadow), and since this is a necessary condition for the truth of (28), this sentence turns out to be false. S· The problem raised by sentences such as:
(3 I)
A hundred boats are circumnavigating the globe. Most of them will fail
was that the default assumption, for each boat, is not that the circum navigation will be completed, but that it will abort, although (3 I ) turns out to be intuitively true in the given circumstances. But the truth conditions stated in (34) do not entail the existence of such default assumptions. For {3I)
to be true it is not necessary that most boats are supposed to complete the circumnavigation. What is sufficient is that there is a frame or point of
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(I9)
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The Progressive and the Structure of Events
view according to which, since the boats have particular characteristics, have been officially selected by an authoritative sailing association, etc., what these boats are doing can be seen as part of an event of circumnavigating the globe, even though most of the boats will fail and the completion of the event is not entailed by any kind of generic or default statement. As I have already remarked, a stereotype does not entail that the realisation of the event at issue must be probable or 'plausible' (in the sense of default inferences).
(33) Leo is proving Goldbach's conj ecture he says something true? We remarked that the only j ustification for the (intuitive) truth of this sentence at the utterance time is that the event at issue will occur in the actual course of events H. The theoretical attitude we can associate with B's statement is: wait and see! Ideally, we are asked to look only at H (independently of what might happen in other, more reasonable worlds) in order to check whether the event of proving Goldbach's conjecture is realised in H. In the present framework such a situation is nicely accounted for by referring to a totally realistic frame, that is a frame in which the set of the relevant courses of event is the singleton of the actual course of events H. This means that the only course of events to be taken into consideration is H itself, which is exactly what happens in the case of (33). In a sense, this is the case in which the truth conditions of the progressive (condensed by the maxim: wait and see!) are very close to the truth conditions of the plain future. But, as predicted by the informal remarks developed in the introduction, an important difference remains: unlike the future, the progressive requires that part of the event has already been realised at the evaluation time. This requirement is correctly accounted for by the truth conditions stated in (34). At this point, we might ask ourselves whether there is a systematic connection between types of eventualities and types of frames. Since the former classification (in the sense of Kenny-Vendler tradition) is not the topic of the present paper, I will content myself with some informal and tentative remarks. Take the case of accomplishments, as for instance the type of events of proving a theorem. Referring, in general, to a plurality of courses of events accounts for the idea that we have to look not only at the evolution of the current situation in the actual course of events H, but also in other, alternative courses of events. This is essential when (in contrast with the example we have just discussed) the event at issue is not fully
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In the same section we also considered a different but related problem: the case of events whose completion is highly improbable, even prodigious, although it occurs in the actual world. How to account for the fact that when, in the circumstances described above, B utters the sentence:
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(41) e C J 1\ V(J)
�
V(e).
IfJ is an eventuality satisfying the activity predicate V and e is a (relevant) part ofJ, then e itself satisfies that predicate.17 According to (34), a necessary condition for the truth of a sentence such as Leo is running is that the eventuality e we are considering is part of an event ofLeo's running: but what (41) tells us is that if e is part of an event of Leo's running, then (under some conditions) e is itself an event of this type! (Notice that such a situation cannot hold in the case of accomplishments.) So, in order to check whether an event of Leo's running is in progress there is no need to look at the future, possible developments of e. All we need is already available at the present moment, in the actual course of events. The relevance of the mereological structure of eventualities for the semantics of the progressive can be seen from another point of view. Take, for instance, the activity of a water-scooping machine whose engine is designed to draw up water for twenty minutes and then to make a cooling pause for five minutes before starting again. Suppose that this machine worked from two to nine o'clock. So, the following statement is not problematic:
(42) The water-scooping machine drew up water from two o'clock to nine o'clock. But imagine that, between four and five past four the machine stopped to cool down, because the engine is designed to do so at regular intervals. In this situation, there surely is a sense in which the following statement is true:
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realised in the actual world. That is why, in general, a non-totally realistic frame is appropriate in the case of accomplishments. What happens in the plurality of alternative courses of events selected by the frame is relevant in this case. What about activities?16 An exact answer to this question presupposes a more adequate account of the relation between the time of evaluation t and the temporal extension of the event at issue which is not in the scope of the present paper. Roughly speaking, the idea is that, in the case of an activity predicate such as running, in general what is relevant is exactly the totally realistic frame, because there is no need to look at the future developments of the present situation and, as a consequence, no need to look at alternative courses of events in order to evaluate the progressive statement. Referring to the actual course of events is sufficient. Let us see why. An activity predicate V (unlike accomplishment predicates) is character ized by the property of 'Divisivity':
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The Progressive and the Structure of Events
(43) Between four and five past four the water-scooping machine was not drawing up water. On the other hand, there are contexts in which we are justified in saying:
(44) Between four and five past four the water-scooping machine was drawing up water.
(45) What's he doing? Even if it is quite clear that at the moment the professor is idly walking around and not working, a perfectly natural answer might be the following: (46) He is proving the completeness theorem where the intended meaning is that, at the present stage of the course in logic, the professor has already started that proof and he will go on in the next few lectures. This is possible because proving a theorem can be a discontinuous activity, with lots of dead times, and such kind of information is surely part of the conversational background. So, there is a relevant constraint that makes (46) true, although the last lecture took place three weeks ago, before the Christmas holidays. On the contrary, even if the professor has just left his cycle in the courtyard and both students know that he is resuming his cycle riding in a few moments, such as answer would be quite odd: (47) ? He is pedalling. Although the interruption at issue is very short, an activity such as pedalling has a 'dense' characterization which (as in the case of the water-scooping machine) calls for an adequate analysis of the internal structure of eventualities.
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To account for the fact that both sentences can be true although they seem to contradict each other, we have only to remark that, in the theoretical framework under discussion, it is possible to refer to different frames, i.e. different points of view on the same situation. What is crucial here is the fact that the five-minute pause is considered as part of the global event of the machine's drawing up water in the case of (44), but not in the case of (43). Such flexibility of the progressive is one of the reasons of the 'productivity' of this aspectual form, which can be properly used in different situations. Suppose that, while walking in the courtyard of our department, two students see the professor of logic and that one of them, pointing at that teacher, asks the other:
Andrea Bonomi
203
Acknowledgements I would like to
thank P. Casalegno, G. Chierchia, S. Zucchi, and three anonymous referees
for many helpful comments on previous drafts l)f the paper.
ANDREA BONOMI
Received: Final version received:
Universitti degli studi di Milano Dipartimento di Filosofia Via Festa del Perdono 7 I-20122 Milano Italy
1 5.04.97 18.1 1.97
N OT E S What is peculiar to this situation is that an event of a given type is presented as an event in progress even if the cause that makes it unrealizable is already an accomplished fact. Whilst in other similar examples, but in the past tense (like Mary was crossing the street when a truck hit her), the event is presented as going on
up to
the occurrence of the
obstructing causes, here it is presented as going on after that occurrence. This means that the event is unrealizable not only in the actual world, but in every world coinciding with the actual one up
2
to the present moment. According to Landman's characteriza tion, v is a reasonable option for e in w iff 'there is a reasonable chance on the basis of what is internal to e in w that e continues in w as far as it does in v' (p. 25). Intuitively speaking, the problem is that if we resort to a possible world v where an event e is more developed than it is in w, there must be some specific reasons, in this world v, for such an increment, and since these reasons are not present in w, there is no reason able chance that the event has the same extension in both worlds. Actually, the concept of 'reasonable option' should be taken as a primitive notion in Landman's theory. Both
the
part-of relation
(between
eventualities) and the stage-of relation are required in Landman's theory. But
whilst the former notion is quite clear, the latter is intuitively more compli cated. The idea is that 'not every part of e at an interval is a stage of e; to be a stage, a part has to be big enough and share enough with e so that we can call it a less developed version of e . . . We cannot say that when an event stops in a world, there is no bigger event of which it is part in that world, but we can say that, when it stops, there is no bigger event in the world of which it is a (Landman, 1992: 23). But consider the publication of the Hrst volume of
stage'
Proust's Recherche. On the one hand, there surely is an event e of publishing this volume which stops at a given date ( 1 4 November 1913). On the other hand, since the publication of this
volume is a stage of the event of
publishing the whole Recherche, we must also have an event J which (as a stage of the bigger event) does not stop. So, in this theory, there must be two distinct entities: the event e which stops at the given date and the event J,
which does not stop. (The same can be said of my proving lemma A as a stage of my proving theorem B. As an event
of its own, the event of proving lemma A stops at a given moment, but as a stage of the event of proving theorem B, it cannot stop, and we must have a distinct event.) In the framework adopted in the present paper, where
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1
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The Progressive and the Structure of Events
only the part-of relation is relevant, such a duplication is not necessary.
4 This
problem is explicitly discussed in Landman (1992), where some argu
shortly before the event of the water's wetting the meadow.
10
ments are developed against the thesis, argued for in Parsons ( 1990), that the progressive creates no intensional context.
Since the set of worlds circumscribed by this perspective is simply the singleton of the real world w, according to (24) all we have to do, in order to check whether s is of type Prog(¢), is simply
Needless to say, other kinds of ambi guity can be caused by the future tense. For example, in the sentence 'Leo will go to a French city run by
tense is replaced by the past tense.) This means that on both interpretations some kind of existential generalization is allowed. On the other hand, we have just seen that, on its weak reading, (19) allows no inference about the existence (at the evaluation time, or in the future) of the city at issue.
6 7 8
is missing is an account of the mereo logical relations that must exist between the state s and the event e.
11
See Asher (1992: 475). In other terms, what is problematic, in my opinion, is the idea that 'plausibility' is a neces sary condition for the truth of a
12
Since the event at issue is realized in the actual world w, this kind of situation is not problematic for Asher's theory because one can refer to the 'perspec tive' which coincides with the singleton of w. Nevertheless, at the end of the
progressive sentence.
(1 992). (1992: 486).
See Asher Asher
previous section we saw that referring
The need for a stronger connection
between s and e (instead of the temporal
connection in (24)) is mentioned in Asher (1992: 486): the suggestion is that s must be causally necessary for the production of e.
9
Leo will smoke tomorrow at 3.15 p.m., then it is true that he is smoking now, because there is an event of Leo's smoking which is later than the state of Leo's being sleeping. Once more, what
to this type of perspective raises some problems in Asher's theoretical frame work.
13
Provided that (28) is considered on its genuine progressive reading, and not on its 'future' or 'imrninential' reading (which is ruled out by the context). This
stereotype of a complex event whose realization is considered improbable.
is even clearer in Italian, where the progressive cannot have this second
kind of reading. The Italian translation of (28), i.e. L'acqua sta bagnando il prato cannot have an 'imrninential' reading and this sentence is false even if uttered
The existence of a stereotype does not entail that the realisation of the event at issue must be highly probable or 'plau sible' in the sense of default reasonings Asher's theory refers to. For instance, in the case of example (3 1) we have the
14
See Kratzer
(1981)
for a treatment of
this notion in terms of a possible
world semantics. In the present framework, stereotypical conversational
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to check whether there is an event e of type ¢ which is cotemporaneous or later than s. As a consequence, if it is true that
a socialist mayor' the indefinite description can be interpreted as refer ring to a city which has a socialist mayor at the evaluation time or at the (future) moment at which Leo goes to that city. But notice that, in the former case, we can infer that there is a city with the intended characteristics; in the latter, we can infer that there will be a city with the intended character istics. (Interestingly enough, a similar reasoning can be repeated if the future
Let s be any current state in the real world w, say the state of Leo's being sleepy, and 1r a perspective that selects some arbitrary property that s has in w.
Andrea Bonomi
tuality. For the sake of simplicity, from now on we shall ignore the temporal
backgrounds are considered from the point of view of event semantics.
IS
Actually, this is a very rough stipulation of the temporal relation between the rime of evaluation and the whole eventuality J. See Klein {I994) for an. accurate description of the relations between the time of utterance, the 'topic' time and the time of the even-
205
parameter.
I6
The argument I am going to develop also applies to (non-permanent} states compatible with the use of the pro gressive.
I7
See Moltmann
{I99I}
for this principle
and for the necessary restrictions.
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