One of the central components of formal linguistic semantics is the interpretation of predicates as characteristic functions: functions that assign truth to individuals who have a certain property and falsity to any other individual. For instance, being a bird is true of birds, and false of other animals. Clearly, however, something special is needed for predicates like being tall, for apart from being tall or not tall, individuals can be very tall, extremely tall, quite tall etc. Analysing a predicate like tall as a simple function from individuals to truth values is too simplistic. It is a popular strategy to analyse such predicates as predicating not only of an individual, but also of a degree. Degree expressions like very, extremely, etc. thus have the specialised function of addressing this degree argument. On this view, gradability involves predicates that have a degree argument and operators that target such arguments. The current proposal is motivated by the following hypothesis, which goes counter this general view. Our first working hypothesis is that gradability is a general feature of predication. That is, gradability does not require specialised predicates, nor does it require specialised degree operators. This hypothesis is motivated by examples like:

(1)            Jasper is an unbelievable nerd.

This example not only expresses that Jasper is a nerd, it clearly states that he is so to a considerable degree. This meaning is intriguing for two reasons. First of all, adjectives, not nouns, are the stereotypical gradable predicates. Yet, nouns like nerd and indefinites like a nerd are clearly gradable as well. I can think that someone is plainly a nerd, or that he is quite a nerd , or exclaim what a nerd he is. A second striking fact about (1) is that there is no degree operator to express to what extent Jasper is a nerd. Unbelievable is a regular adjective without a function of grading, so from a semantic point of view it remains a mystery how the degree-reinforcing reading of (1) comes about.

Cases like (1) are not rare exceptions. A closer look at the ways in which natural language allows for the expression of degree reveals a wealth of variation. Except for specialised degree modifiers like very, there are many expressions that can play a role in grading while their core meaning does not deal with degree at all. Examples are epistemic adverbs (really tall, truly tall), evaluative adverbs (surprisingly tall) and expressives (fucking tall). In fact, the grading of a predicate is possible without modifying the predicate itself, for instance, by using emotive sentence modifiers (Man, Billy is tall) or sentence mood (How tall Billy is! ). The observation is that the function of degree modification is widespread over a large and varied range of expressions and constructions. It would be highly surprising were so much of language ambiguous between degree related and non-degree related meanings. This brings us to our second working hypothesis: degree is not a purely semantic phenomenon. That is, the expression of degree does not exclusively result from a semantic process. We will assume that languages have means to augment a non-degree meaning with a pragmatic inference about the degree to which a predication holds. For example, sentence mood can express grading without the core semantic function of mood being degree modification (Zanuttini & Portner 2003). Similarly, an evaluative adverb like surprisingly does not express degree directly, rather it does so by attributing a state of surprise to the speaker (Nouwen 2005). Very little is known about the mechanisms underlying the interaction between the semantics and the pragmatics of gradability. The main theoretic objective of this project is therefore to find the semantic and pragmatic basis of degree and to spell out the constraints that govern it.

The degree-based approach to the semantics of gradable adjectives, which takes such adjectives to predicate over degrees (e.g. Cresswell 1974, von Stechow 1984, Kennedy 1997, Kennedy 2007), is without doubt one of the success stories of present-day formal linguistics. According to working hypothesis 1, however, the empirical coverage of such an approach is too limited. Hypothesis 2, moreover, states that such semantic theories cannot do without a complementary pragmatic analysis. In particular, this project takes gradability to be deeply connected to secondary information provided by utterances. For instance, (2a) is vague and imprecise; it fails to state exactly how many professors were at my party. While the example in (2b) is just as vague, it does give more information, for it conveys that the speaker expected there to be fewer professors.

(2a)          There were many professors at my party.

(2b)         There were surprisingly many professors at my party.

We take such examples to be illustrative of the core function of degree. As such, the view to be developed is related to theories of the interaction of vagueness with context (Kyburg & Morreau 2000, Barker 2002) and to theories that take vagueness and gradability to be context-dependence phenomena (e.g. Fine 1975, Kamp 1975, Klein 1980). Such approaches are the main contenders to the degree approach. However, as theories of vagueness they can be seen to be complementary to the degree-based semantics (cf. Barker 2002, Kennedy 2007). By pursuing the relation between context, vagueness and gradability, this proposal will develop a synthesis of the available approaches. The result will be a timely integration of linguistic and philosophical perspectives on predication.

 

 Approach

 

Theoretically, the project has three specific objectives, each pursued in one of three sub-projects:

 

-        The development of a model of how degree is encoded in natural languages

-        The development of a model of how degree interacts with expressive content

-        The development of a framework for the interaction between gradability, vagueness and context

 

 

Project 1 (PhD student): The role of scales in the broader view of gradability

Traditionally, gradability is thought to be a property of a select class of adjectives. This was challenged by Bolinger (1974) and, more recently, by an increasing number of linguists (e.g. Neeleman et al. 2004). It is now a common semantic assumption that for a predicate to be gradable, it needs to correspond to some (abstract) measurement scale (see e.g. Kennedy 2007 for an overview). This is easy to see for a predicate like tall which is intimately linked to the measure of height. For other predicates, like for instance nerd, there seems to be no single measure available. Still, such predicates are gradable. What governs this kind of gradability, however, is completely unknown.

Recently, several authors have identified properties of measurement scales that determine the class of degree expressions a predicate is compatible with (Paradis 2001, Rotstein & Winter 2004, Kennedy & McNally 2005). There is, for instance, a difference between the scale of height, which is an open-ended scale, and the closed scale of how full something is. Only the latter kind of scale is compatible with degree expressions like half, which is why something can be half full but not half tall. For other gradable predicates it is not clear what the corresponding scale is, nor what its properties are. This sub-project intends to find this out.

Tasks:

1.     Collect data on what the acceptable forms of grading are for a wider class of gradable predicates

2.     Develop a model of what kinds of scales are associated with gradable predicates, how these scales correspond to other properties of the predicate, and how they constrain grading

Task 1 The goal of this task is to outline relevant subclasses of degree modifiers and relevant subclasses of gradable expressions and to clarify the relations between these. To this end, a comparison is made between (I) classically scalar adjectives (tall, full ), (II) concepts with prototypes (a nerd), and (III) (semi-)functional items like prepositions and quantifiers (e.g. existential quantifiers tend to be modifiable by degree moderators like quite as in quite some in English). We have advanced knowledge about the semantics of such expressions, but with respect to degree modification, only scalar adjectives have received thorough investigation. The fact that syntactic constraints on degree modifiers are well understood (Corver 1997, Neeleman et al. 2004) helps the process of filtering out semantic generalisations.

The data will be collected on the basis of carefully constructed questionnaires. The advantage of questionnaires over, for instance, corpus research is that questionnaires allow one to discover the full paradigm for degree expressions. In a corpus, no conclusion can be drawn from not finding a specific combination, for certain acceptable forms of grading may be expected to be too infrequent to be occur.

The task involves a cross-linguistic examination. This is necessary to obtain robust generalisations, filtering out ways of expressing degree that are highly specific idiosyncrasies. It will be part of the task to decide what languages are ideally to be included. To connect to existing research, the set will include some Germanic languages, but moreover contain languages that are markedly different from Germanic in instructive ways.

Task 2 The result of task 1 will be a set of generalisations that are outside the realm of existing theories of gradability. The theoretical part of this sub-project consists of developing a model that does justice to these findings. To construct this model, the generalisations have to be matched to properties of predicates. Such properties, however, could go beyond aspects of denotational semantics. For concept nouns like nerd, for instance, it is essential to look into fine-grained theories of predication such as those found in conceptual semantics (Gaerdenfors 2000) or prototype theory (see, e.g. Kamp & Partee 1995). For functional expressions like quantifiers, it will be helpful to study their role in scalar reasoning.

Project 2 (PhD student): Expressives: degree modification without predicate modification

This sub-project focuses on the least studied forms of degree modification, namely those that do not involve predicate modification. One of the most striking examples is that of emotive language. For instance, the emotive marker man (similarly boy, gosh, etc.), together with a specifically marked intonation, results in a reading for (3) which reinforces the degree to which Jasper is tall.

                  (3)            Man, Jasper is tall!

Markers like man are called expressives. They do not give information about what is said in an utterance, but rather provide the perspective from which something is said. Intuitively, the degree reading of (3) results from on the one hand the assertion that Jasper is tall (to a certain degree) and on the other the secondary information provided by the expressive that the speaker has a marked attitude towards that assertion. From a theoretical point of view, it is as yet unclear how to do justice to this intuition. The role of expressive meaning in grading is unexplored territory. Cases like (3) are not isolated, however, witness the degree-intensifying use of a sentence-internal expressive marker like fucking in fucking tall , or the use of evaluative markers like surprisingly in surprisingly tall . Also, exclamation (How tall he is!) has long since been associated with emotive language (Zanuttini & Portner 2003). The relation between indicators of speaker's attitude and the expression of a degree is far from trivial, as becomes clear from contrasts such as He is surprisingly tall (high degree) and Surprisingly, he is tall (no intensified degree). Such contrasts show that a theory of gradability cannot do without a model of how expressive content interacts with degree.

Tasks:

1.    Empirical investigation into emotional language interacting with degree

2.     Develop a theory of how expressive content interacts with degree

Task 1 The empirical investigation in this sub-project is less rigorous than the systematic scrutiny of sub-project 1. That is, the goal here is to gain an initial data set, which indicates how widespread the interaction between expressive content and degree is. To this end, the focus will be on a single language (Dutch).

The PhD applicant will perform a corpus study on the `corpus gesproken Nederlands' (corpus spoken Dutch). The advantages of using this corpus are: (i) it is spoken and partly spontaneous, which removes the natural inhibition written text carries for the use of expressive language, (ii) it has partly been given prosodic annotation. This latter feature is important given that intonation plays a significant role in the expression of degree as (see e.g. Bolinger 1972, Paradis 1997, McCready 2005).

Task 2 This task involves a detailed investigation of different kinds of ways to provide information about (the speaker's) emotion. Why do degree-affected readings only occur when adverbs like surprisingly immediately modify a predicate? How does this relate to the fact that expressive markers like man are immune to such a requirement? It is particularly interesting to compare the data on expressive and evaluative adverbs to whether and how degree interacts with evidentiality. Some languages have mirative forms that mark unexpectedness (Aikhenwald 2004). Such languages provide completely new data which is particularly valuable, complementing that found for Dutch in task 1.

For a long time, it was commonly thought that expressives fall outside any formal inquiry into natural language semantics and pragmatics, simply because they seem to resist formalisation. It is becoming increasingly clear, however, that a `semantics of use' (rather than of meaning) can be made explicit for such expressions (Kaplan 1999, see McCready 2005, Potts 2007 for a development of that view). That is, the meaning of an expressive is a set of conditions of use. This explains how it can provide information about utterances. This domain is largely unexplored. Luckily, some considerable foundational work on devising tools for this goal has already been done, such as the invention of expressive indices (Potts 2007) and work on multi-dimensional semantics (Potts 2005, Jayez & Rossari 2005, Jayez 2006, Nouwen 2007). Such tools enable us to connect what is known about the compositional semantics of predication to expressive content.

A specific application of the resulting framework is to the semantics of exclamation. The PhD candidate will use the devised framework to analyse what regular wh-exclamatives (What a nerd! ) have in common with other forms of exclamation.

 

 

Project 3 (Principle Investigator): Vagueness, Gradability, Context-dependence

When learning that Jasper is tall one either learns something of Jasper's height (namely that it is considerable) or, in case Jasper's height is known, one finds out what in the given context counts as tall (cf. Kyburg & Morreau 2000, Barker 2002). This shows that the interaction of vagueness and context is no straightforward matter. In fact, there is emerging consensus that vagueness has a communicative function (e.g. Parikh 1994, Krifka 2002, de Jaegher 2003). But what kinds of information are provided by grading, and how do these relate to kinds of vague information exchange? In this sub-project, the relation between vagueness and gradability takes centre stage. In particular, the goal is to spell out how the expression of degree interacts with context.

Tasks:

1.     Compare alternative models of vagueness and gradability

2.      Reconsider the relation between vagueness and gradability

3.     Develop a model of context and context-dependence for gradability phenomena

4.    Develop an account of degree anaphora

Task 1 In some sense, degree expressions can be seen as vagueness regulators, introducing, eliminating, reinforcing or reducing vagueness. This is not the complete story, though. Surprisingly many is just as vague as many (cf. (2a/b) in ¤2a), but provides additional information about the context, namely that the speaker is surprised about the amount. In this task, we investigate what notion of context and what form of contextual interpretation best suits these different roles of grading. The philosophical literature on vagueness and context-dependence pays little attention to the role of gradability. A notable exception is Kennedy 2007, who offers a promising degree-based approach to vagueness (cf. Graff 2000), but leaves the connection with context-based approaches open. The existing theories of vagueness and of gradability form a landscape of possible frameworks. This task involves exploring that landscape by identifying the properties of various options.

Task 2 Most applications of supervaluation theory (Fine 1975) to vagueness result in a tight connection between vagueness and gradability. For instance, it follows from Kamp's 1975 analysis of the comparative that any vague predicate has a comparative form. This is an unwelcome prediction since there are examples of vague predicates that are not easily gradable (e.g. colour terms). Bierwisch (1989) assumes a reverse relation, namely that gradability entails vagueness. However, there exist many gradable adjectives whose positive form is non-vague (Engel 1989, Williamson 1994, Kennedy 2007). For instance, acidic is a crisp concept, but nevertheless some substance can be said to be more acidic than another. The conclusion is that vagueness and gradability are distinct concepts. This is a rather unsatisfying result, for one would like to know exactly in what cases vagueness and gradability correlate. This is particularly so since one of the classic telltale signs of vagueness, the existence of a Sorites paradox, connects vagueness to some salient scale of degrees. This suggests that certain kinds of vagueness are related to (certain kinds of) gradability afterall. The main goal of this task is to give substance to this link.

Part of this task involves co-operation with sub-project 1. Scale structure interacts with vagueness. Adjectives with a closed scale (full) have an absolute standard of comparison for their positives form (Kennedy & McNally 2004) and therefore differ from other adjectives (like tall) w.r.t. vagueness. Sub-project 1 provides a new range of data on the interaction between scalarity, gradability and vagueness. Part of the task is therefore to spell out the consequences for the representation of degree and vagueness. Can degree-based theories of predication be extended to cover the broadened empirical domain? Or does the semantics need to interface with theories of conceptual structure or vague predication?

Task 3 According to approaches like supervaluation theory, vagueness can be reduced to context-dependence. The precise relation between predication and context involves more than supervaluations, however. Particularly, the data in sub-project 2 suggest that information about the context (such as speaker emotion, attitude, etc.) can interact with the expression of degree. That is, gradability cannot be studied by focusing on simple assertions only; one needs to spell out different ways of manipulating the context. In this task, the applicant will cooperate with the PhD student of project 2. The data of that sub-project will be used to specify a model of context-dependence of gradable and vague predication.

Task 4 An important yet understudied clue about the interaction of gradability with context comes from anaphora to degrees. Dutch zo has a double role: on the one hand, they are demonstrative pronouns that pick up degrees (4a), on the other hand they are part of the equative construction (4b).

(4a) Jasper is ouder dan Pierre. Sjeng is ook zo oud.

J. is older than P. S. is also so old

(Jasper is older than Pierre. Sjeng is that old as well.)

(4b) Jasper is zo oud als Pierre.

J. is so old as P.

(Jasper is as old as Pierre.)

It will be a null hypothesis that these uses of zo are related. Such data thus offer an insight in how degree is contextually represented. This phenomenon is used as a testing ground and linguistic application of the model of context developed in the previous tasks.

 

 Innovation

 

Sub-project 1 The study of scale structure is extended beyond scalar adjectives, which results in a more complete understanding of the role played by scales in gradability. Moreover, the sub-project attempts to link such scales to independent properties of expressions. In particular, the combination of conceptual and denotational semantics has never been applied to gradability. The classification of measurement scales and its connection to vagueness (Kennedy 2007) was a first step toward understanding how degree is based on conceptual structures underlying predication. This sub-project sets out to achieve more general results by comparing different kinds of gradable items.

 

Sub-project 2 Most work on gradability focuses on the expression of degree by means of predicate modification. This sub-project turns to a neglected form of gradability, one which involves no modification at all. If our hypothesis is correct and this form of expressing degree is not uncommon, then this sub-project will represent a major shift in empirical focus. The data will be out of reach of conventional theories of degree and will thus enforce a rethinking of how gradability comes about. The project enters new territory by assuming that a semantics of use interacts with a notion of degree. This will have the side-effect of contributing to the emerging knowledge of the use of expressives.

 

Sub-project 3 This sub-project reopens the debate about the relation between vagueness and gradability in the light of a broader perspective on the latter. Moreover, it extends the discussion about the context-dependence of vague expressions by focusing on the role played by degree expressions. This new perspective is exactly what is currently needed, since it will give insight not only into what is vague and what is non-vague, but also into how vagueness is regulated in context. It moreover incorporates new data into old discussions, namely data pertaining to degree anaphora.

 

Method A further innovative aspect of this proposal is the use of questionnaires and corpus research to gain access to a more complete picture of the meaning and use of gradability. Moreover, the use of new (linguistic) data for tackling long-standing philosophical debates is both new and promising.

 

General This project studies degree from a novel, wide empirical perspective. As such, it promises to rid the theoretical debate on gradability from conceptions that are the result of an overly narrow data set. Theoretically, it advocates that gradability can only be understood when adopting a broadened notion of meaning. We believe that just like any pragmatic theory cannot go without addressing semantics, the semantics of degree cannot go without a pragmatic analysis of the data. This creates a fresh interdisciplinary approach, which will contribute new insights into semantics, pragmatics, and philosophy.

 

Literature references

Aikhenvald, A. (2004). Evidentiality. Oxford: Oxford University Press.

Barker, C. (2002). The dynamics of vagueness. Linguistics and Philosophy 25, 1--36.

Bierwisch, M. (1989). The semantics of gradation. In M. Bierwisch and E. Lang (Eds.), Dimensional adjectives, pp. 71--261. Berlin: Springer-Verlag.

Bolinger, D. (1972). Degree Words. Den Haag: Mouton.

Corver, N. (1997). Much-support as a last resort. Linguistic Inquiry 28, 119--164.

Cresswell, M. (1976). The semantics of degree. In B. Partee (Ed.), Montague Grammar, pp. 261--292. Academic Press.

de Jaegher, K. (2003). A game-theoretic rationale for vagueness. Linguistics and Philosophy 26, 637--659.

Engel, R. (1989). On degrees. Journal of Philosophy 86, 23--37.

Fine, K. (1975). Vagueness, truth and logic. Synthese 30, 265--300.

Gaerdenfors, P. (2000). Conceptual Spaces. Cambridge, MA: MIT Press.

Graff, D. (2000). Shifting sands: An interest-relative theory of vagueness. Philosophical Topics 20, 45--81.

Jayez, J. (2006). How many are Ôseveral'? Argumentation, meaning and layers. In S. Vogeleer (Ed.), Bare plurals, indefinites, and the weak-strong distinction. Benjamins.

Jayez, J. and C. Rossari (2005). Parentheticals as conventional implicatures. In F. Corblin and H. de Swart (Eds.), Handbook of French Semantics. Stanford: CSLI Publications.

Kamp, H. (1975). Two theories of adjectives. In E. Keenan (Ed.), Formal semantics of natural language, pp. 123--155. Cambridge: Cambridge University Press.

Kamp, H. and B. Partee (1995). Prototype theory and compositionality. Cognition 75, 129--191.

Kaplan, D. (1999/2004). The meaning of `ouch' and `oops'. Howison Lecture (Berkeley).

Kennedy, C. (1997). Projecting the adjective: the syntax and semantics of gradability and comparison. PhD. Thesis, UCSD.

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

Kennedy, C. and L. McNally (2005). Scale structure, degree modification and the semantics of gradable predicates. Language 81(2), 345--381.

Klein, E. (1980). A semantics for positive and comparative adjectives. Linguistics and Philosophy 4, 1-45.

Krifka, M. (2002). Be brief and vague! In D. Restle and D. Zaefferer (Eds.), Sounds and Systems. Studies in Structure and Change. A Festschrift for Theo Vennemann, pp. 439--458. Berlin: de Gruyter.

Kyburg, A. and M. Morreau (2000). Fitting words: Vague language in context. Linguistics and Philosophy 23, 577--597.

McCready, E. (2005). The Dynamics of Particles. Ph. D. thesis, University of Texas, Austin.

Neeleman, A., H. v. d. Koot, and J. Doetjes (2004). Degree expressions. The Linguistic Review 21(1), 1--66.

Nouwen, R. (2005). Monotone amazement. In P. Dekker and M. Franke (Eds.), Proceedings of the fifteenth Amsterdam Colloquium. ILLC.

Nouwen, R. (2007). On appositives and dynamic binding. Journal of Language and Computation 5(1), 87--102.

Paradis, C. (1997). Degree modifiers of adjectives in spoken British English. Lund Studies in English 92. Lund University Press.

Paradis, C. (2001). Adjectives and boundedness. Cognitive linguistics 12(1), 47--65.

Parikh, R. (1994). Vagueness and utility: the semantics of common nouns. Linguistics and Philosophy 17, 521--535.

Potts, C. (2005). The Logic of Conventional Implicatures, Volume 7 of Oxford Studies in Theoretical Linguistics. Oxford University Press.

Potts, C. (2007). The expressive dimension. Theoretical Linguistics 33(2), 165--197.

Rotstein, C. and Y. Winter (2004). Total adjectives versus partial adjectives: scale structure and higher-order modifiers. Natural Language Semantics 12, 259--288.

von Stechow, A. (1984). Comparing semantic theories of comparison. Journal of Semantics 3, 1--77.

Williamson, T. (1994). Vagueness. Routledge.