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RESTRICTION and SATURATION Sandra Chung and William A. Ladusaw University of California, Santa Cruz August 2001 TABLE OF CONTENTS CHAPTER 1. MODES OF COMPOSITION 1 1.1 The Calculus of Saturation 3 1.2 Predicate Restriction 5 1.3 Syntactic Versus Semantic Saturation 8 1.4 Saturation at the Event Level 14 1.5 Scope Constraints 17 1.6 The Property Theory of Inde®nites 18 1.7 Summary 23 Notes 26 CHAPTER 2. INDEFINITES IN MAORI 28 2.1 A Dash of Maori Grammar 31 2.2 The Syntax of He and TeÅtahi 35 2.3 Their Semantic Similarity 40 2.3.1 Wide Scope in Episodic Sentences 40 2.3.2 Narrow Scope in Quanti®cational Constructions 44 2.4 Some Semantic Contrasts 52 2.4.1 Wide Scope in Quanti®cational Constructions 52 2.4.2 The Existential Construction 54 2.5 Our Account 58 2.5.1 Restrict Versus Specify 60 Contents Chung & Ladusaw 2.5.2 Some Approaches Not Taken 70 2.6 Two Further Semantic Contrasts 72 2.6.1 A Constraint on Subjects 72 2.6.2 Two Types of Predicates 78 2.7 A Dash of Pragmatics 84 2.7.1 In Narrative Discourse 84 2.7.2 In the Museum 88 2.8 Conclusion 89 Notes 95 CHAPTER 3. OBJECT INCORPORATION IN CHAMORRO 102 3.1 A Dash of Chamorro Grammar 105 3.2 Incorporation 110 3.3 The Incorporated Object is Semantically Incomplete 114 3.4 The Extra Object 119 3.4.1 The Extra Object is a Syntactic Adjunct 121 3.5 The Extra Object is a Semantic Argument 125 3.5.1 A De®niteness Effect 126 3.5.2 An Af®rmative Polarity Item 133 3.5.3 A Curious Restriction 137 3.6 Our Account 142 3.7 Restriction Without Saturation 155 3.8 Conclusion 165 Contents Chung & Ladusaw Notes 172 APPENDIX A. THE SYNTAX OF CHAMORRO INCORPORATION 177 A.1 Previous Approaches 178 A.2 Some Inconclusive Results 180 A.2.1 The Extra Object is a Syntactic Adjunct 181 A.2.2 The Incorporated Object Originates Within NP 181 A.2.2.1 Incorporation in Maori 183 A.2.2.2 Summary 189 A.3 Some More Conclusive Results 189 A.3.1 Coordinate NP's 190 A.3.2. The Word Order of the Incorporated Object 191 A.3.3 The Word Order of the Subject 193 A.3.4 The Overall Situation 195 A.4 The Attachment Site of the Extra Object 196 Notes 199 APPENDIX B. MAORI AND CHAMORRO 200 REFERENCES 204 Chapter 1 Chung & Ladusaw CHAPTER 1. MODES OF COMPOSITION Strawson's (1959) discussion of `subject and predicate' examines the received view of the basis for distinguishing between the semantics of predicates and terms with reference to Frege's (1997[1862]) distinction between objects and concepts. Frege characterizes the distinction between A4s [terms] and B4s [predicates] by means of a metaphor. Objects, he says, are complete, concepts incomplete or unsaturated. ªNot all parts of a thought can be complete; at least one must be `unsaturated' or predicative; otherwise they would not hold together.º Of B2s [predicates] he says that it is only because their sense is unsaturated that they are capable of serving as a link. (1959: 152-153) The idea that semantic predicates are unsaturated (to various degrees) and that this semantic incompleteness is made complete by composing them with semantically complete terms (of appropriate types) is fundamental to formal semantic analyses of natural language. It is the basis of Montague's (1973) application of type theory in his classic PTQ analysis of English, where all predicative expressions are assigned functional types and the fundamental composition operation is function application. Strawson's discussion portrays the opposition between complete objects and incomplete concepts as a unifying theme that can be played out at the level of linguistic acts, linguistic categories, and propositional roles. He considers various approaches to the basis for this metaphor, noting The main thing which I wish to carry away from consideration of Frege and Geach is the fact that both writers make an absolute distinction between two mutually exclusive classes of expressions, members of each of which can be 1 Chapter 1 Chung & Ladusaw combined with suitable members of the other to yield an assertion. Members of the two classes of expressions alike introduce terms; but members of one class introduce them assertively, and members of the other class do not. The List IV distinction of non-linguistic terms merely mirrors, in a confused way, this discussion in the style of introduction. Essentially the distinction we have arrived at is a distinction between styles of introduction of terms [Emphasis added]. It says nothing of any distinction between types or categories of terms, between kinds of object. (1959: 153) This monograph is an investigation of different `styles of introduction' or what we will term modes of composition in the syntax and semantics of inde®nites, and their application in two Austronesian languages (Maori and Chamorro). We start from the assumption that underlying the semantic composition of predicates with their arguments is a calculus of saturation. However, we question the assumption that what may appear syntactically to be a predicate-argument relation is uniformly interpreted by a mode of composition that saturates the predicate. We conclude that introducing a nonsaturating mode of composition, (predicate) restriction, allows consideration of analyses that illuminate constructions in many languages. In this Chapter we discuss the calculus of saturation and introduce predicate restriction. We relate these notions to other semantic proposals about the property theory of inde®nites, existential closure, and so-called semantic incorporation. We introduce a general principle that forces saturation of predicates within a designated domain. The resulting system permits several options for the semantic composition of inde®nites with their predicates. We show that the calculus of saturation allows for the possibility that an argument position of a predicate may be targeted by both modes of composition in one 2 Chapter 1 Chung & Ladusaw construction. 1.1 The Calculus of Saturation What we are calling the calculus of saturation is illustrated by the standard type assignments assumed in the simple example (1). (1) John fed Fido. (2) λyλx [feed'(y)(x)] (f) (j) The logical translation in (2) shows the semantic composition. The verb is given a function (of type <e,<e,t>> that represents it as semantically incomplete in two respects, corresponding to argument roles assigned by the predicate. In the underlying type theory, semantic completeness is represented by the two types e (for entities) and t (for truth-values, standing in for a proposition). The type of the expression in (2) is t, showing that this composition achieves semantic completeness by resolving the two degrees of incompleteness in the predicate by combining the two semantically complete objects f and j with the predicate's semantic content, a function equivalent to a two-place relation between entities. An important part of (2) is the mode of composition that achieves this semantic completeness by saturating the predicate. This is the operation of function application. This is rendered more explicit by (3), which represents that operation explicitly as FA, an operation that takes two arguments, the ®rst of which is a function of domain type σ and an expression of semantic type σ. The value of the operation is an object of type τ, the range type of the function. (3) FA (FA (λyλx [feed'(y)(x)], f), j) The boldface portion of (3) represents the ®rst function application, whose value is a 3 Chapter 1 Chung & Ladusaw function of type <e,t>. Underlying the talk of saturation is the Fregean metaphor of unsaturation. The saturation of the predicate removes an incompleteness, yielding a complete thought (a proposition). From this underlying metaphor derives the fundamental effect of saturation: (4) A saturated argument position is no longer available to semantic composition. (4) states the obvious fact that the ®rst instance of function application in (3) renders the y position unavailable for further composition. The next instance of function application must target the only remaining source of incompleteness: the x argument position. Function application represents one mode of composition that saturates, but it is not the only one. Let us consider the semantic operation of `existential closure'. The functional incompleteness of the verb above can likewise be remedied by an operation that simply removes the incompleteness in favor of an existential quanti®cation over the argument, as illustrated in (5), with EC representing the (unary) composition operation generally represented by ∃ν: (5) EC (EC (λyλx [feed'(y)(x)])) If we track the type changes in the expression in (5), we see that they parallel those in (3). The boldface portion represents a reduction from <e,<e,t>> to <e,t> and the whole expression is of the complete type t. The principle in (4) shows that existential closure likewise saturates the predicate, removing semantic incompleteness. The expression in (6), an attempt to provide individuals for composition after closure, does not cohere into a well-formed logical expression. (6) FA (EC (EC (λyλx [feed'(y)(x)])), f) 4 Chapter 1 Chung & Ladusaw It consists of a proposition (truth-value) and an entity. In Frege's terms, they `do not hold together'.1 Both of the saturating modes of composition are illustrated when we consider a Davidsonian version of (2). (7) λyλxλe [feed'(y)(x)(e)] (f) (j) Two instances of functional application yield the lambda reduced expression in (8). (8) λe [feed'(f)(j)(e)] However, this expression is not semantically complete.
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