Comparative Anaphora: comparing alternatives

A common assumption in degree semantics is that there is a functionargumentrelationship betwen the comparative morpheme er and the overt standard.Drawing on observations from comparatives without an overt standard, I argue forreconsiderations of this assumption and offer a reanalysis of er, where it directlycompares to the alternative in the second dimension of meaning.

Being tall compared to compared to being tall and being taller

This paper investigates the semantics of implicit comparatives (Alice is tall compared to Bob) and its connections to the semantics of explicit comparatives (Alice is taller than Bob) and sentences with adjectives in plain positive form (Alice is tall). We consider evidence from two experiments that tested judgments about these three kinds of sentence, and provide a semantics for implicit comparatives from the perspective of degree semantics.

Degree semantics, polarity, and the grammaticalization of comparative operators into complementizers

Focusing on German, the paper presents a cross-linguistic study of the diachronic development of comparatives, providing a formal account for why comparative operators generally grammaticalise into complementisers in degree equatives more readily than in comparatives proper. It is argued that this is so because comparatives mark degree inequality overtly in a head position. This feature must be acquired by the original operator during grammaticalisation, while in equatives the operator has all the features necessary for grammaticalisation and must only lose any additional features incompatible with a complementiser. The extension of an equative complementiser into a general comparative complementiser is possible only if the relevant functional head undergoes feature change, in line with the Borer–Chomsky Conjecture. The changes under scrutiny can be well observed in the history of German and Hungarian, and similar asymmetries surface in synchronic patterns in many other languages, too.

The limiting theory

This chapter considers how the compositional theory argued for in the preceding chapters might apply to a variety of additional cases where a lexical, degree-theoretic semantics has been proposed. For example, the analysis of attitude verbs like “to want”, nouns like “idiot”, and verbs like “to cool”. The chapter suggests that, rather than diagnosing scalar structure, the kinds of data motivating lexical degree-theoretic interpretation here should be understood as diagnostic of order-theoretic properties on the relevant expression’s domain of predication. Supporting the idea of a general recipe for how such cases should be addressed, the chapter raises theoretical questions like the following: do any lexical categories natively have a degree semantics? When is a degree-theoretic treatment appropriate? Should there be morphosyntactic requirements (e.g., overt or covert “much”) for an interpretation based on degrees, or not? What alternative analyses of extant cases are available?

Measuring occasions

While much of the tradition in degree semantics has focused on the distribution and interpretation of comparatives targeting adjectives, this chapter discusses a class of adjectival comparatives that appears to have gone unnoticed. That is, traditional accounts focus on the interpretation of phrases like “more patient”, while the present chapter considers how such phrases differ from minimally different targets like “patient more”. Probing the meaning of the latter sort of case, this chapter suggests an analysis in which they are interpreted rather like plural verbal comparatives—i.e., as comparisons between numbers of events. This proposal includes a novel approach to the distinction between stage-level and individual-level adjectival predications, such that the former allows for its (base) stative property to be mapped to a plurality of discrete (i.e., maximal and non-overlapping) occasions during which the relevant state(s) hold.

Measurement theory and the typology of scales

Most previous work on graded modality has relied on qualitative orderings, rather than degree semantics. This chapter introduces Representational Theory of Measurement (RTM), a framework which makes it possible to translate between qualitative and degree-based scales. I describe a way of using RTM to extend the compositional degree semantics introduced in chapter 1 to qualitative scales. English data are used to motivate the application of the RTM discussion between ordinal, interval, and ratio scales to scalar adjectives, with special attention to the kinds of statements that are semantically interpretable relative to different scale types. I also propose and motivate empirically a distinction between ‘additive’ and ‘intermediate’ scales, which interact differently with the algebraic join operation (realizing sum formation or disjunction, depending on the domain). This distinction is reflected in inferential properties of non-modal adjectives in English, and is also important for the analysis of graded modality in later chapters.