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Review of  Vagueness, Gradability and Typicality

Reviewer: Luca Sbordone
Book Title: Vagueness, Gradability and Typicality
Book Author: Galit W. Sassoon
Publisher: Brill
Linguistic Field(s): Pragmatics
Subject Language(s): English
Issue Number: 24.5004

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Sassoon's book offers the results of a comprehensive analysis of linguistic gradability in the interpretation of adjectival and nominal predicates. The book is primarily aimed at scholars in formal semantics, but because psychological literature is discussed thoroughly and a fruitful conciliation between psychological and linguistic approaches is explicitly attempted, it will also be of great interest for researchers in cognitive psychology and cognitive pragmatics.

Part I is intended as an introduction to the topics of vagueness, gradability and typicality, both from a linguistic and a psychological perspective and with an eye on highlighting the divergences between the two approaches. The discussion of the various theories is mainly critical: extant accounts are presented and then criticized in detail. The sum of the objections is intended to open a theoretical space for Sassoon's own proposal which is presented in the second part of the book. Part II is a gradual introduction to the author’s complex and complete model. The theory hinges on the proposed distinction between nominal and adjectival predicates. While both are shown to be associated with sets of dimensions, the processing of such dimensions is demonstrated to depend on completely different strategies: a version of prototype theory is integrated for processing nominal dimensions, while logical rules are invoked in the case of adjectives. With such a dichotomy, claimed to be reflected in grammar, Sassoon shows how problematic linguistic data laid out in the first part can be accounted for. In the same way, psychological findings thought to contradict standard semantic analyses are shown to be straightforwardly predicted by the proposed model.

Chapter 1 introduces basic notions and summarizes the individual chapters.

Chapter 2 defines and explores the notions of vagueness, gradability and typicality, including an extensive overview of the linguistic and psychological literature, aimed at highlighting both commonalities and especially points of contrast between the two fields. The linguistic phenomenon of vagueness is defined classically and understood as a ‘pervasive feature of adjectives’ (21) while it is noted that usually most nominal predicates are regarded as sharp. Gradability is a property of most adjectival predicates, enabling entities to possess the properties denoted by the predicate by different degrees. Empirical tests for gradability are listed, the most prominent being compatibility with degree morphology. A crucial distinction is made between dimensional and multidimensional gradable adjectives.

The correlation between polarity and gradability is introduced (concerning e.g. different patterns of combination with degree modifiers in positive and negative predicates). It is shown that adjectives are typically more felicitous than nouns in within-predicate comparison ('the table is longer than the sofa') while conversely nouns license between-predicate comparison ('the table is longer than the sofa is wide') more freely.

In line with the findings of many psychological studies, nominal predicates are also shown to be vague, conceptually gradable (i.e. they show typicality effects) and associated with sets of dimensions. Sasson thus argues that the similarity between nouns and adjectives is stronger than the linguistic literature usually acknowledges.

Prototype theory is supported as a better theoretical alternative to explain the existence of nominal dimensions as compared with classic (definitional) theory of concepts.

Chapter 3 is a survey of the dominant extant accounts of gradability and typicality and their interconnections from a linguistic perspective. This chapter presents the popular view in formal semantics of gradability as vagueness-dependent, and shows how the semantic analysis of gradable predicates is approached in simplified vagueness models making use of supervaluations. A number of problems arising from vagueness-based approaches to gradability are discusses: importantly, the morphological complexity of the comparative form with respect to the positive form of gradable adjectives is left unexplained. Also, the very idea that gradability is vagueness-dependent is questioned following the distinction between absolute (and presumably non-vague) and relative (vague) gradable predicates (Kennedy (2007) Kennedy and MacNally (2005)).

Concerning the nature of the degrees associated with gradable predicates, two main families of approaches are discusses: the ‘ordinal scale’ analysis and the ‘interval scale’ analysis. Several problems concerning the adequacy of both these alternatives are raised.

Furthermore, the chapter presents treatments of polarity effects in gradable predicates. The so-called 'extent theory' is presented and criticized and Landman's (2010) 'Supremum theory' is introduced as a more convincing (if not unproblematic) alternative.

Moreover, it is contended that standard formal semantics approaches assume that nouns are non-gradable and that this assumption must be abandoned in light of 'robust and pervasive' (114) evidence to the contrary. Then, the author turns to the critical discussion of one remarkable but still inadequate exception to this consensus view, i.e. Kamp and Partee's (1995) 'Supermodel theory'.

Chapter 4 is a comprehensive overview of the family of psychological prototype theories of concepts. The chapter introduces and criticizes various extant views concerning the appropriate representation and computation of relevant conceptual dimensions in the prototype structure. In relation to classic prototype theory, competing categorization criteria are introduced. Standard-based categorization predicts the link between likelihood of categorization of an entity and its similarity to the prototype. Categorization based on a contrast-set accounts for the facts that sometimes membership likelihood may be not monotonically related to similarity.

On the other hand, an exemplar theory of concepts gives importance to the separate dimension sets of entities or subcategories. The section discusses advantages of exemplar theory (e.g. prediction of the exemplar effects and concept variability) and its disadvantages (e.g. failure to predict summary-representation effects). Finally, inconsistent predictions stemming from the two theories are argued to be accommodated in a more comprehensive approach.

The problem of the compatibility of psychological theories and formal semantic theories is discussed. Many psychological theories reject the idea of truth-conditional semantics (Murphy 2002, Lakoff 1987), regarding phenomena such as conjunction fallacies, subtype effects, overextension effects as counterexamples to truth-conditional compositional semantic theories. However, experimental findings suggest that incorporating logical rules makes a theory more explanatory.

Finally, 'knowledge theory' is presented whereby typicality is not based on statistical regularities (in contrast with the so called 'probabilistic view') but on prior knowledge. However, there are several problems related to the representation of knowledge structures.

The author criticizes experimental data, questioning the idea that categorization is based on typicality: she maintains that there is a 'tight coupling' between typicality and membership, apparent dissociations notwithstanding.

Chapter 5 introduces Sassoon's proposed model. In contrast to extant vagueness-based models, this approach assumes a full vagueness model explicitly representing partiality of information and the relation between learning and gradability. Degree functions are incorporated into the model on a par with denotations.

The ontology of the model is a dimension space consisting of a set of entities and a function mapping these entities to real numbers (degrees). Objects are identified with 'real' not conceptual/linguistic properties (whose extension varies across contexts). In such a framework, proper names are not rigid designators, but are identified with positive or negative denotations.

The crux of the model is the characterization of the degree functions: these are general and not predicate-specific; constrains over the scales follows from the characterization of the functions and need not be stipulated. In turn, predicate dimensions are regarded as normal predicates.

For nominal concepts, prototype theory is integrated into the system. Nominal concepts map entities to their weighted means in a set of dimensions. For adjectives a rule-based analysis is incorporated. The distinction between similarity-based and rule-based categories is well supported by neuropsychological data. It is hypothesized that such a distinction is grammaticalized as two separate categories: nouns and adjectives. As a corollary, the theory correctly predicts that the meaning of the positive predicate is more basic than that of the comparative.

Chapter 6 presents a vagueness model incorporating dimensions and degrees. First, recursive syntactic and semantics definitions are given. One important characteristic is that the ontology of the language includes a set of mappings from n-tuples of entities to degrees understood as real numbers. In such a view, 'each possible individual-tuple can be described as a unique maximal, consistent assignment of degrees, the degrees assigned to it by all of the possible degree functions' (200).

The complete vagueness model formalizes the idea that every intermediate context in the model represents a possible 'real' context, representing e.g. the knowledge shared by the participants in a certain discourse. Importantly, in the model the interpretation of proper names is not rigid, by contrast partial information about proper names is represented, making identity statement informative. Additional notions required for the interpretation of a predicate in a total context (and discussed in the remainder of the book) include functions assigning to the predicate the relevant degree function, transformation value, standard of membership, local domain, dimension set, weight and ideal value of membership.

Chapter 7's main thesis is that the noun-adjective distinction functions as a cue to how to process dimensions. Nominal predicates are associated with a dimension set which is by default processed as a prototype (i.e. by averaging). In contrast, adjectival predicates are associated with a dimension set processed by default as a set of rules (by means of Boolean operations of union and intersection). It follows that, unlike nominal dimensions, dimensions of adjectives can be accessed by grammatical operators.

The proposed analysis of adjectives correlates positivity in the adjectival domain with universal quantification over dimensions (i.e. dimensions are integrated conjunctively) and negativity with existential quantification (i.e. disjunctively, signaling the existence of a counterexample).

Sassoon presents results of both corpus studies and judgment experiments. It is argued that the results generally support the proposal. The proposal is economic in that dimensions need to be lexically specified only for positive adjectives, thereby explaining their cognitive prominence. The negated character of dimensions in negative adjectives explains their intuitive negative connotation and relative complexity.

A corollary hypothesis is that, provided that nouns are less cognitively demanding in terms of dimension processing, across languages nouns will occur more frequently than adjectives.

Sassoon sees the present proposal as a cluster theory without the limits classically imputed to cluster theories: in Sassoon's model, clusters are implemented within an intensional and entirely compositional theory.

Chapter 8 introduces and formalizes the learning principle, the idea that properties of earlier acquired entities are selected for the dimension set. The choice for a full vagueness model allows to associate predicate gradability with the order in which vagueness is resolved, i.e. with the order in which entities are learnt to be part of the predicate denotation.

Psychological data is provided to support the idea that typicality of entities is coupled with such a learning order. Additional data shows that the learning principle functions as a cue to specify the relevant degree function of a predicate, especially in nominal concepts. She contends that the learning principle is more psychologically realistic as a default strategy of categorization than the probabilistic criterion advocated in classic prototype theory. Also, the learning constraint provides us with means to account for familiarity effects and typicality effects in individual concepts (e.g. proper names).

Finally, the learning principle makes an intuitive prediction about negated predicates and negative antonyms: it accounts for the fact that the denotation of the negated concept can be contextually restricted and not correspond to the complement of the positive predicate while retaining the intuition that ordering of entities in positive and negative categories is reversed.

Interaction between the learning constraint and standard logical rules of formal semantic theories helps making correct predictions with respect to phenomena taken to contradict these rules, e.g. conjunction fallacies and emergent features. This shows that a theory which incorporates logical rules is more explanatory than one which refutes them.

Chapter 9 presents a fully compositional analysis for predicate constructions with different gradability morphemes. The section thus represents a formal specification of the proposal aimed at showing that the model is able to predict correct truth-conditions for a number of constructions involving degree modifiers.

With respect to polarity effects, the chapter retains the intuition that the entity ordering of a negative predicate is reversed with respect to that of its positive counterpart. However, it is also shown that the information we have about the kind of reversing function responsible for producing the degrees of negative adjectives is very poor. The chapter pursues the hypothesis that the value of such a transformational constant is undetermined. Crucially, indeterminacy of the degree function of negative predicates explains linguistic data related to polarity, such as unacceptability of measure phrase modification in negative antonyms as compared with their acceptability in positive adjectives and in negative adjectives in the comparative form, and the infelicity of modification with multipliers in negative adjectives.

Chapter 10 presents general conclusions, summing up the main points of the proposed model and highlighting the importance of the analysis of nominal concepts as incorporating a version of prototype theory in the semantic representation of nominal dimensions. Furthermore, it explores some of the main themes for future research in light of the results of contemporary linguistic studies on gradability.

Overall, the book undoubtedly represents a major contribution to the understanding of linguistic gradability. The author has mastery of the relevant literature, both linguistic and psychological. Importantly, the reciprocal acknowledgment of the relevant findings in the two fields drives the author towards an extremely balanced and cognitively realistic theory of predicate interpretation. Psychological and linguistic data are always counterbalanced: the fact that the predictions of the proposed model converge towards the findings of the two fields represents a crucial point of strength of the theory. Not only does Sassoon manage to fruitfully integrate linguistic and psychological theories of gradability and typicality, but she also convincingly bridges the gap between vagueness-based and degree-based approaches to gradability, by showing that degrees and degree-functions can be assumed in the ontology of a vagueness-based formal system without however reducing vagueness to the grammar (as e.g. in Kennedy 2007).

The first part of the book is an extremely comprehensive overview of extant theories of gradability. Sassoon has gone to great lengths to collect, explain and critically discuss an impressive number of contending accounts. The author explicitly states that the aim of this first part is to 'serve as a handbook introduction to the relevant topics' (6). However, the vocabulary is often rather technical even in this introductory section: a number of basic notions are presupposed, for formal semantics and other areas. Moreover, various extant theories are mostly only sketched, with more space dedicated to critical discussion and elaboration of relevant objections. While this is surely a helpful strategy for highlighting the advantages of the proposed model compared to other accounts, it in places interferes with the clarity of exposition. All in all, this section is an excellent sketch of a map of the territory in which Sassoon's own theory inscribes itself and which it helps to fruitfully expand. However, as an introduction to the relevant topics, it is surely best suited for a reader with solid prior knowledge of the subject matter; it is hardly intended for undergraduates or beginning graduate students in linguistics or cognitive psychology.

Moreover, the book’s central focus is on the notion of gradability (typicality, in the nominal domain). In turn, the assumed notion of gradability appears to encompass two distinct but related phenomena: the conceptual gradability of predicates (i.e. the potential for a predicate to permit different degrees of its application) and their grammatical gradability (i.e. the compatibility with degree morphology and modification). While the former is entailed by the latter, and is a property of both vague nouns and adjectives (and, presumably, of arguably vague verbs, e.g. run, Morzycki forthcoming), the latter is specific of adjectives. Gradability, on such a comprehensive understanding, is regarded as vagueness-dependent and so modeled in a full vagueness model (i.e. a complex context structure based on supervaluationism which allows for the representation of partiality and gradual learning of information). However, the book's title notwithstanding, the problem of vagueness itself is not specifically addressed. Undoubtedly, a discussion of the philosophical problem of vagueness and the Sorites paradox would have been beyond the scope of the book. Nonetheless, in line with supervaluationism, vagueness here is reflected in the semantics and the paradoxical conclusion of Sorites reasoning is avoided by means of adjustments in the logical meta-theory. Because such a theoretical position is assumed and not justified, the book would have surely benefitted from a proper defense of supervaluationism and from a critical discussions of competing theories concerning the source of vagueness and its proper linguistic representation.

The second part is a significant contribution to the semantic analysis of gradable predicates. Sassoon's main thesis is at once extremely simple and extraordinarily explanatory. Moreover, as is frequently noted in the book, the theory has the advantage of being more economical compared to other analogous theories, as it hinges on a simple dichotomy between the processing of dimensions in nominal and adjectival concepts and derives from this hypothesis a straightforward explanation of a large set of linguistic data (e.g. polarity effects, compatibility with degree morphemes, etc.). The most interesting sections of the second part are Chapter 7 ('A Degree-Function Based Typology of Predicates') and Chapter 8 ('The Learning Principle and Complex Concepts'), where most of the theoretical hypotheses are introduced and convincingly argued for. In particular, the introduction of the learning constraint, supported with robust empirical data, allows for an elegant explanation of how logical rules can be implemented in a similarity-based account of nominal dimensions.

In conclusion, Sassoon's book is a cornerstone for future work on predicate gradability and typicality, and more generally for all future researches aiming to bridge the gap between semantics and psychology.

Kamp, H. and Partee, B. 1995. Prototype Theory and Compositionality. Cognition 57: 129-191.

Kennedy, C. 2007. Vagueness and Grammar: The semantics of relative and absolute gradable predicates. Linguistics and Philosophy 30: 1-45.

Kennedy, C. and McNally, L. 2005. Scale Structure and the Semantic Typology of Gradable Predicates. Language 81: 345-381.

Lakoff, G. 1987. Women, Fire and Dangerous Things: What categories reveal about the mind. Chicago University Press. Chicago.

Landman, F. 2010. Internal and Interval Semantics for CP-comparatives. In M. Aloni, H. Bastiaanse, T. de Jager, and K. Schulz (Eds.) Proceedings of the Seventeenth Amsterdam Colloquium Conference on Logic, Language and Meaning, Springer Lecture Notes in Computer Science. Springer. Berlin, Heidelberg, pp. 133-142.

Morzycki, M. Forthcoming. Modification. Book manuscript.

Murphy, G. 2002.The Big Book of Concepts. The MIT Press. Cambridge, Massachusetts.

Williamson, T. 1994. Vagueness. Routledge. London.
Luca Sbordone is a Ph.D candidate in Linguistics at the University of Cambridge. He holds an MA in Philosophy at the Scuola Normale Superiore of Pisa (Italy). His research focuses on lexical semantics and pragmatics, with particular attention to the problems of vagueness and imprecision. His research interests include Philosophy of Language and Mind, Cognitive Psychology and Pragmatics.

Format: Hardback
ISBN-13: 9781781902639
Pages: 446
Prices: U.S. $ 157.00