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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Stand Over There, Please
The Dynamics of Vagueness, the Origins of Vagueness, and How Pie-Cutting
Relates to Ancient Heaps of Sand
Seth Cable

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

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

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