Written by two of the leading figures in the field, this is a lucid and systematic introduction to semantics as applied to transformational grammars of the ...

Aspectual particles (the term is due to (König 1991)) appear to come in groups, related by negation, and therefore have attracted the attention of formal semanticists. The following examples list the particles of English, German and Hebrew; they show that the system is semantically transparent in various degrees.

The notion of measurement plays a central role in human cognition. We measure people’s height, the weight of physical objects, the length of stretches of time, or the size of various collections of individuals. Measurements of height, weight, and the like are commonly thought of as mappings between objects and dense scales, while measurements of collections of individuals, as implemented for instance in counting, are assumed to involve discrete scales. It is also commonly assumed that natural language makes use of (...) both types of scales and subsequently distinguishes between two types of measurements. This paper argues against the latter assumption. It argues that natural language semantics treats all measurements uniformly as mappings from objects (individuals or collections of individuals) to dense scales, hence the Universal Density of Measurement (UDM). If the arguments are successful, there are a variety of consequences for semantics and pragmatics, and more generally for the place of the linguistic system within an overall architecture of cognition. (shrink)

The sentence Irving was closer to me than he was to most of the others contains a quantifier, most of the other, in the scope a comparative. The first part of this paper explains the challenges presented by such cases to existing approaches to the semantics of the comparative. The second part presents a new analysis of comparatives based on intervals rather than points on a scale. This innovation is analogized to the move from moments to intervals in tense semantics. (...) The remainder of the paper is concerned with an interval-based semantics of degree in relation to issues other than the comparative proper. The paper begins with a discussion of the role negative polarity has played in studies on the semantics of comparatives. (shrink)

This paper uses the distribution and interpretation of antonymous adjectives in comparative constructions as an empirical basis to argue that abstract representations of measurement, or ‘degrees’, must be modeled as intervals on a scale, rather than as points, as commonly assumed. I begin by demonstrating that the facts in this domain must be accounted for in terms of the interaction of the semantics of adjectival polarity and the semantics of the comparative, rather than principles governing the (overt) expression of particular (...) types of adjectives in comparatives. I then show that a principled account of the full range of data under consideration can be constructed within a model in which degrees are formalized as intervals on a scale and adjectival polarity is characterized in terms of two structurally distinct and complementary sorts of `positive' and `negative' degrees. (shrink)

The paper takes up the objections raised in van der Auwera (1993) against the joint analysis of the German particles schon, noch and erst published in Löbner (1989). Central to my analysis is the claim that the particles are organized in duality groups of four to which essentially the same type of analysis applies. Van der Auwera (1993) claims that already/schon, in its basic use, is different from the other three particles in having a more complex meaning which results in (...) an opposition of the particle to finally/endlich. As to the narrow-focus temporal uses he argues that the duality approach is inadequate in including improper members on the one hand, and excluding relevant particles on the other.The criticism will be refuted. After a recollection of the duality analysis in Section 2, van der Auwera's arguments against the general design of my analysis are dealt with in Section 3. It will be argued that his own analysis of already/schon and its group, as far as it is supported by the data, does not really differ from my approach. In Section 4, I will deal with the claim that finally/endlich contradicts already/schon, which if correct would provide an indirect argument against the duality analysis of schon and noch. I will argue that endlich is set apart from the particles of the schon group by the presence of a non-descriptive, expressive, meaning component. For its descriptive meaning, endlich logically entails schon and belongs to a parallel duality group of its own together with noch immer. The apparent incompatibility of finally/endlich and already/schon can be explained as a conflict between what is foregrounded by each particle, respectively. In Section 5, I will argue that, contrary to van der Auwera's claims, the narrow focus uses of schon and its kin do form proper duality groups. The existence of such uses of noch, not treated in Löbner (1989), does not invalidate the duality analysis of schon and erst. Rather, noch in its relevant narrow-focus use belongs to yet another duality group together with its dual nur noch. (shrink)

In this paper, I provide a compositional semantics for sentences with enough and too followed by a to-infinitive clause and for resultative constructions with so... that within the framework of possible world semantics. It is proposed that the sentential complement of these constructions denotes an incomplete conditional and is explicitly or implicitly modalized, as if it were the consequent of a complete conditional. Enough, too, and so are quantifiers that relate an extent predicate and the incomplete conditional (expressed by the (...) sentential complement) and are interpreted as comparisons between two extents. The first extent is the maximal extent that satisfies the extent predicate. The second extent is the minimal or maximal extent of a set of extents that satisfy the (hidden) conditional, where the sentential complement supplies the consequent and the main clause the antecedent. This approach permits to predict (a) the context-dependent interpretation of these constructions and (b) the duality relations between the degree words. (shrink)