Very, Many, Small, Penguins
Harald A. Bastiaanse
Abstract:
This thesis is divided into five separate chapters, each of which deals with an issue related to vagueness. These chapters are adaptations of manuscripts to be published as papers in various journals. Their abstracts as they (will) appear in these journals are repeated below (but with 'paper' replaced by 'chapter') so as to comply with standard conventions.
Chapter 1 - The Rationality of Round Interpretation
Expanding on a point made by Krifka (Krifka 2007, p.7-8), I show that the fact that a round number has been used significantly increases the posterior probability that that number was intended as an approximation.
This increase should typically be enough to make assuming that an approximation was indeed intended a rational choice, and thereby helps explain why round numbers are often seen as simply having an approximate meaning.
Generalization into non-number words is also discussed, resulting in a possible origin of (some) vagueness.
Chapter 2 - The Intensional Many
Following on Westerstahl's argument that many is not Conservative (Westerstahl 1985), I propose an intensional account of Conservativity as well as intensional versions of EXT and Isomorphism closure. I show that an intensional reading of many can easily possess all three of these, and provide a formal statement and proof that they are indeed proper intensionalizations.
It is then discussed to what extent these intensionalized properties apply to various existing readings of many.
Chapter 3 - A Syllogistic for Subsective Adjectives
I introduce a syllogistic logic for reasoning about subsective adjectives, and prove that it is complete relative to an appropriate class of models.
Chapter 4 - A Syllogistic Characterization of Gradable Adjectives
Building on an existing syllogistics for subsective adjectives (Chapter 3), I show that if gradable adjectives are defined as those subsective adjectives which are based on a weak order, this notion can be characterized in a natural logic without prior access to that weak order.
Furthermore, generalizing this characterization allows for the characterization of a useful notion of commensurability of groups of adjectives into a single scale.
Chapter 5 - Making the Right Exceptions
Conflicts among default rules are very common. This chapter provides a principled answer to the question of how to deal with them. It does so in two ways: semantically within a circumscriptive theory, and syntactically by supplying an algorithm for inheritance networks. Arguments that can be expressed in both frameworks are valid on the circumscriptive account if and only if the inheritance algorithm has a positive outcome.