Carter (Noûs 55(1):171–198, 2021) argued that while most simple positive numerical sentences are literally false, they can communicate true contents because relevance has a weakening effect on their literal contents. This paper presents a challenge for his account by considering entailments between the imprecise contents of numerical sentences and the imprecise contents of comparatives. I argue that while Carter's weakening mechanism can generate the imprecise contents of plain comparatives such as `A is taller than B', it cannot generate the imprecise (...) contents of comparatives that quantify the difference between their arguments, such as `A is exactly n times as tall as B'. I then propose an alternative theory on which intervals serve as both thick degrees on a scale and denotations of numerical expressions. I argue that the alternative theory can account for the imprecise contents of both forms of comparatives as well as the data that motivate Carter's theory. (shrink)

Multidimensional adjectives are ubiquitous in natural language. An adjective F is multidimensional just in case whether F applies to an object or pair of objects depends on how those objects stand with respect to multiple underlying dimensions of F-ness. Developing a semantics for multidimensional adjectives requires us to address the problem of dimensional aggregation: how do the application conditions of an adjective F in its positive and comparative forms depend on its underlying dimensions? Here we develop a semantics for multidimensional (...) adjectives that incorporates aggregation functions. We then explore an analogy between dimensional aggregation and preference aggregation, bringing results from social choice theory to bear on the number and kind of aggregation functions that are admissible in a context. These results suggest that, for any given adjective, there will often be multiple aggregation functions admissible, meaning that multidimensional comparatives are often vague. (shrink)

Ruth Chang and Joseph Raz have both drawn far-reaching consequences for agency from the phenomenon of incommensurability. After criticizing their arguments, I outline an alternative view: if incommensurability is vagueness, then there are no substantial implications for agency, except perhaps a limited form of naturalistic voluntarism if our reasons are provided by desires.

We argue that all comparative expressions in natural language obey a principle that we call Comparability: if x and y are at least as F as themselves, then either x is at least as F as y or y is at least as F as x. This principle has been widely rejected among philosophers, especially by ethicists, and its falsity has been claimed to have important normative implications. We argue that Comparability is needed to explain the goodness of several patterns (...) of inference that seem manifestly valid, that the purported failures of Comparability would have absurd consequences, and that the influential arguments against Comparability are less compelling than they may have initially seemed. (shrink)

We advocate and develop a states-based semantics for both nominal and adjectival confidence reports, as in "Ann is confident/has confidence that it's raining", and their comparatives "Ann is more confident/has more confidence that it's raining than that it's snowing". Other examples of adjectives that can report confidence include "sure" and "certain". Our account adapts Wellwood's account of adjectival comparatives in which the adjectives denote properties of states, and measure functions are introduced compositionally. We further explore the prospects of applying these (...) tools to the semantics of probability operators. We emphasize three desirable and novel features of our semantics: (i) probability claims only exploit qualitative resources unless there is explicit compositional pressure for quantitative resources; (ii) the semantics applies to both probabilistic adjectives (e.g., "likely") and probabilistic nouns (e.g., "probability"); (iii) the semantics can be combined with an account of belief reports that allows thinkers to have incoherent probabilistic beliefs (e.g. thinking that A & B is more likely than A) even while validating the relevant purely probabilistic claims (e.g. validating the claim that A & B is never more likely than A). Finally, we explore the interaction between confidence-reporting discourse (e.g., "I am confident that...") and belief-reports about probabilistic discourse (e.g.,"I think it's likely that.."). (shrink)

This paper explores the hypothesis that all comparative sentences— nominal, verbal, and adjectival—contain instances of a single morpheme that compositionally introduces degrees. This morpheme, sometimes pronounced much, semantically contributes a structure-preserving map from entities, events, or states, to their measures along various dimensions. A major goal of the paper is to argue that the differences in dimensionality observed across domains are a consequence of what is measured, as opposed to which expression introduces the measurement. The resulting theory has a number (...) of interesting properties. It characterizes the notion of ‘measurement’ uniformly across comparative constructions, in terms of non-trivial structure preservation. It unifies the distinctions between mass/count nouns and atelic/telic verb phrases with that between gradable and non-gradable adjectives. Finally, it affords a uniform characterization of semantically anomalous comparisons across categories. (shrink)

This paper discusses comparison classes—sets that relativize the interpretation of gradable adjectives, often specified with for-clauses as in John is smart for a linguist. Such a discussion ultimately lends support to the thesis that scales, degrees, measure functions, and linear orders are grammatically derived from more basic relations between individuals. Three accounts of comparison classes are compared and evaluated. The first proposes that such classes serve as an argument to a function that determines a standard of comparison. The second maintains (...) that these classes restrict the domain of a measure function used to map entities to degrees. The third proposes that these classes limit the kind of individuals that participate in a binary relation; this relation is then used in the construction of a scale and a measure function. It is this third account that is most consistent with the empirical data. It can explain how comparison classes fix a standard of comparison, induce presuppositions concerning the comparative subjects, and induce incommensurability in comparative constructions. (shrink)

A long-standing tension in semantic theory concerns the reconciliation of positive gradable adjective (GA) ascriptions and comparative GA ascriptions. Vagueness-based ap- proaches derive the comparative from the positive, and face non-trivial challenges with incommensurability and non-GA comparatives. Classic degree-based approaches effectively derive the positive from the comparative, out of sync with the direction of evidence from morphology, and create some difficulties in accounting for GA scale-mates with differing thresholds (e.g., cold ∼ warm ∼ hot). We propose a new reconciliation that (...) capitalizes on recent proposals analyzing GAs as predicates of states. On our account, GAs lexically involve both a threshold property and a background state structure. Positive occurrences of GAs make use of the threshold property, while comparative occurrences make use of degrees representing elements of the background structure. Our approach preserves the virtues of classic degree-based approaches while offering a natural account of scale-mates, and without appeal to covert morphemes like POS or related devices. As we show, it is possible to inject our solution back into the classic degree-based approach, but we find reasons to prefer our states-based account. (shrink)

We offer a novel account of metalinguistic comparatives, such as 'Al is more wise than clever'. On our view, metalinguistic comparatives express comparative commitments to conventions. Thus, 'Al is more wise than clever' expresses that the speaker has a stronger commitment to a convention on which Al is wise than to a convention on which she is clever. This view avoids problems facing previous approaches to metalinguistic comparatives. It also fits within a broader framework—independently motivated by metalinguistic negotiations and convention-shiftingexpressions— (...) that gives linguistic conventions a role in the semantics. (shrink)

In this paper I focus on a recently discussed phenomenon illustrated by sentences containing predicates of taste: the phenomenon of " perspectival plurality " , whereby sentences containing two or more predicates of taste have readings according to which each predicate pertains to a different perspective. This phenomenon has been shown to be problematic for (at least certain versions of) relativism. My main aim is to further the discussion by showing that the phenomenon extends to other perspectival expressions than predicates (...) of taste and by proposing a general solution to the problem raised by it on behalf of the relativist. The core claim of the solution (" multiple indexing ") is that utterances of sentences containing perspectival expressions should be evaluated with respect to (possibly infinite) sequences of perspective parameters. (shrink)

This paper presents a novel semantic analysis of unit names (like pound and meter) and gradable adjectives (like tall, short and happy), inspired by measurement theory (Krantz et al. In Foundations of measurement: Additive and Polynomial Representations, 1971). Based on measurement theory’s four-way typology of measures, I claim that different adjectives are associated with different types of measures whose special characteristics, together with features of the relations denoted by unit names, explain the puzzling limited distribution of measure phrases, as well (...) as unit-based comparisons between predicates (as in the table is longer than it is wide). All considered, my analyses support the view that the grammar of natural languages is sensitive to features of measurement theory. (shrink)

Degree readings of size adjectives, as in big stamp-collector, cannot be explained away as merely the consequence of some extragrammatical phenomenon. Rather, this paper proposes that they actually reflect the grammatical architecture of nominal gradability. Such readings are available only for size adjectives in attributive positions, and systematically only for adjectives that predicate bigness. These restrictions can be understood as part of a broader picture of gradable NPs in which adnominal degree morphemes—often overt—play a key role, analogous to their role (...) in the extended AP. Size adjectives acquire degree readings through a degree morpheme similar to the one that licenses AP-modifying measure phrases. Its syntax gives rise to positional restrictions on the availability of these readings, and the semantics of degree measurement interacts with the scale structure of size adjectives to give rise to restrictions on the adjective itself. (shrink)

According to what I call the Traditional View, there is a fundamental semantic distinction between counting and measuring, which is reflected in two fundamentally different sorts of scales: discrete cardinality scales and dense measurement scales. Opposed to the Traditional View is a thesis known as the Universal Density of Measurement: there is no fundamental semantic distinction between counting and measuring, and all natural language scales are dense. This paper considers a new argument for the latter, based on a puzzle I (...) call the Fractional Cardinalities Puzzle: if answers to ‘how many’-questions always designate cardinalities, and if cardinalities are necessarily discrete, then how can e.g. ‘2.38’ be a correct answer to the question ‘How many ounces of water are in the beaker?’? If cardinality scales are dense, then the answer is obvious: ‘2.38’ designates a fractional cardinality, contra the Traditional View. However, I provide novel evidence showing that ‘many’ is not uniformly associated with the dimension of cardinality across contexts, and so ‘how many’-questions can ask about other kinds of measures, including e.g. volume. By combining independently motivated analyses of cardinal adjectives, measure phrases, complex fractions, and degrees, I develop a semantics intended to defend the Traditional View against purported counterexamples like this and others which have received a fair amount of recent philosophical attention. (shrink)

Cognitive Science, Volume 46, Issue 3, March 2022.

This paper looks at one area of potential crosslinguistic variation in comparatives. It has recently been claimed that Japanese clausal comparatives lack degree abstraction structures in the complement of yori ‘than’. Based on data from several empirical domains such as predicative adjectival comparatives, intensional contexts, and negative islands, this paper shows that Japanese clausal comparatives do not in general contrast with their English counterparts in the way predicted by the above claim. The syntactic and semantic phenomena observed in Japanese clausal (...) comparatives receive straightforward accounts if we assume that they do involve degree abstraction and degree comparison, along the lines familiar from analyses of their English counterparts. (shrink)

Although there is no consensus about what kinds are, there is a common understanding that kinds can be regarded as collections of objects that share certain properties. What these properties exactly are is often left unspecified. This paper explores the semantics of ad hoc kind-referring terms, where the determination of the relevant set of shared properties does not rely on “natural” properties or world knowledge. Rather, information provided by a nominal modifier, typically a relative clause, is used to impute the (...) required regular behavior on the kind-referring NP. Building on Carlson’s disjointness condition, I show that we can not only account for the ubiquity of these expressions, but we can also extend the analysis to other constructions that have traditionally not been taken to be kind referring, such as Amount and Degree Relative constructions. (shrink)

This paper provides a new account of positive versus negative antonyms. The data includes well-known linguistic generalizations regarding negative adjectives, such as their incompatibility with measure phrases (cf. two meters tall/ *short) and ratio phrases (twice as tall/ #short) as well as the impossibility of truly crosspolar comparisons (*Dan is taller than Sam is short). These generalizations admit a variety of exceptions, e.g., positive adjectives that do not license measure phrases (cf. #two degrees warm/cold) and rarely also negative adjectives that (...) do (cf. two hours late/early). Furthermore, new corpus data is presented regarding the use of twice with positive and negative adjectives. The analysis the paper presents supposes that grammar associates gradable adjectives with measure functions—mapping of entities to a set of degrees isomorphic to the real numbers (Kennedy, Projecting the adjective: The syntax and semantics of gradability and comparison, 1999). On this analysis, negative adjectives map entities to values that are linearly reversed and linearly transformed in comparison with their values in the positive antonyms. As shown, the generalizations, as well as their exceptions, directly follow. Negative polarity is explained in terms of function reversal, and non-licensing of measure phrases is explained in terms of transformation by an unspecified value. (shrink)

Although there is no consensus about what kinds are, there is a common understanding that kinds can be regarded as collections of objects that share certain properties. What these properties exactly are is often left unspecified. This paper explores the semantics of ad hoc kind-referring terms, where the determination of the relevant set of shared properties does not rely on “natural” properties or world knowledge. Rather, information provided by a nominal modifier, typically a relative clause, is used to impute the (...) required regular behavior on the kind-referring NP. Building on Carlson’s disjointness condition, I show that we can not only account for the ubiquity of these expressions, but we can also extend the analysis to other constructions that have traditionally not been taken to be kind referring, such as Amount and Degree Relative constructions. (shrink)

Although there is no consensus about what kinds are, there is a common understanding that kinds can be regarded as collections of objects that share certain properties. What these properties exactly are is often left unspecified. This paper explores the semantics of ad hoc kind-referring terms, where the determination of the relevant set of shared properties does not rely on “natural” properties or world knowledge. Rather, information provided by a nominal modifier, typically a relative clause, is used to impute the (...) required regular behavior on the kind-referring NP. Building on Carlson’s disjointness condition, I show that we can not only account for the ubiquity of these expressions, but we can also extend the analysis to other constructions that have traditionally not been taken to be kind referring, such as Amount and Degree Relative constructions. (shrink)

On the received view, the Representational Theory of Measurement reduces measurement to the numerical representation of empirical relations. This account of measurement has been widely criticized. In this article, I provide a new interpretation of the Representational Theory of Measurement that sidesteps these debates. I propose to view the Representational Theory of Measurement as a library of theorems that investigate the numerical representability of qualitative relations. Such theorems are useful tools for concept formation that, in turn, is one crucial aspect (...) of measurement for a broad range of cases in linguistics, rational choice, metaphysics, and the social sciences. (shrink)

The construction we are discussing is a recent American English construction with an individual-denoting noun phrase in the predicate position modified by a degree modifier that typically occurs with gradable adjectives, as in 'This is so Obama!' We attempt to look deeper into the structure and compositional semantics of this construction, and though we do not provide a complete analysis of it, we believe that the study of this construction can contribute to questions of gradable predicate semantics, multidimensionality, degree constructions (...) and proper name semantics. (shrink)

This paper presents a new logical analysis of quantity comparatives (i.e. More linguists than philosophers came to the party.) within the Delineation Semantics approach to gradability and comparison (McConnell-Ginet in Comparison constructions in English. PhD thesis, University of Rochester, Rochester, 1973; Kamp in Formal semantics of natural language. Cambridge University Press, Cambridge, 1975; Klein in Linguist Philos 4:1–45, 1980) among many others. Along with the Degree Semantics framework (Cresswell in Montague grammar. Academic Press, New York, 1976; von Stechow in J (...) Semant 3:1–77, 1984; Kennedy in Projecting the adjective. PhD thesis. University of California, Santa Cruz, 1997, among many others) Delineation Semantics is one of the dominant logical frameworks for analyzing the meaning of gradable constituents of the adjectival syntactic category; however, there has been very little work done investigating the application of this framework to the analysis of gradability outside the adjectival domain. This state of affairs distinguishes the Delineation Semantics framework from its Degree Semantics counterpart, where such questions have been investigated in great deal since the beginning of the twenty-first century. Nevertheless, it has been observed [for example, by Doetjes (Seventeenth amsterdam colloquium. University of Amsterdam, Amsterdam, 2011); van Rooij (The vagueness handbook. Springer, Dordrecht, 2011c)] that there is nothing inherently adjectival about the way that the interpretations of scalar predicates are calculated in Delineation Semantics, and therefore that there is enormous potential for this approach to shed light on the nature of gradability and comparison in the nominal and verbal domains. This paper is a first contribution to realizing this potential within a Mereological extension of a simple version of the DelS system. (shrink)