MoL-2002-01: Stand Over There, Please: The Dynamics of Vagueness, the Origins of Vagueness, and How Pie-Cutting Relates to Ancient Heaps of Sand

MoL-2002-01: Cable, Seth (2002) Stand Over There, Please: The Dynamics of Vagueness, the Origins of Vagueness, and How Pie-Cutting Relates to Ancient Heaps of Sand. [Report]

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Abstract

Stand Over There, Please The Dynamics of Vagueness, the Origins of Vagueness, and How Pie-Cutting Relates to Ancient Heaps of Sand Seth Cable Abstract: This thesis is an investigation into the semantics of vague expressions, although vague predicates are predominantly discussed. It proposes an analysis of vague predicates within the framework of dynamic semantics, and argues that this analysis predicts the observed relationship between the properties of having borderline cases, of being susceptible to sorites paradoxes, and of being context-dependent. The first, introductory chapter concerns the questions of what, precisely, a "theory of vagueness" is and what it can hope to achieve. The material here is intended to provide the lens through which the more technical work of the following chapters should be viewed, and it is hoped that the characterization offered here of a program for the study of vagueness clarifies and unifies the existing literature on this subject. In outline, the chapter explains first the concept of "vagueness" as it appears in the linguistic and philosophical literature, and then discusses the necessary limits to any scientific study of this property. In regards to those limits, it is argued that a complete explanation of the semantics and logic of vague language is logically impossible, and that the most we as theorists can hope for is a set of increasingly refined approximations. These necessarily limitations, moreover, affect how one should describe the study of vagueness as an intellectual activity, and so how the reader should understand the material of the next three chapters. In Chapter 2, the basic semantic analysis for vague predicates is proposed. This analysis uses the formal techniques of dynamic semantics to capture the unique information change potential of predications employing vague language. Moreover, the analysis is argued to correctly predict the relationship between the context dependency of a predicate and its having "borderline cases." Some basic properties of the resulting logic of vague predicates are then discussed, including its wide retention of classical logic and its ability to grab hold of "penumbral connections." Finally, the vagueness operator "definitely" is introduced, as well as its proposed information change potential, and some effects on our logic of adding the operator to our language are proven. Chapter 3 begins with a host of difficulties for the basic analysis of the previous chapter. In particular, the analysis allows for the possibility of unnaturally precise uses of vague predicates and fails to predict the relationship between the presence of borderline cases and so-called "higher-order vagueness." It is suggested that these problems may be overcome if a more sophisticated theory of the origins of linguistic vagueness is adopted. The concept of a "vague selection" is introduced, as well as the hypothesis that all vagueness in language may be reduced to the "vagueness" of these selections. This hypothesis is spelled out formally within our dynamic semantics, and the resulting analysis is demonstrated to overcome the challenges raised at the chapter's beginning. The fourth and final chapter concerns the sorites paradox. The basic questions concerning the sorites are reviewed, as well as some reasons against accepting it as a genuine paradox. It is then argued that the reductive theory of vagueness put forth in the previous chapter provides a unique perspective on what is occurring within the sorites argument, a perspective from which one spies a potential "resolution" to the paradox. Finally, it is argued that this analysis of the sorites, when combined with our reductive theory of vagueness, predicts that predicates are susceptible to sorites arguments if and only if they are vague.

Item Type: Report
Report Nr: MoL-2002-01
Series Name: Master of Logic Thesis (MoL) Series
Year: 2002
Uncontrolled Keywords: vagueness
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/729

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