The Structure And Logic Of Boundary Vague Categories
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The Structure and Logic of Boundary-vague Categories
My thesis concerns the phenomenon of vagueness familiar to many via the paradox of the heap or the sorites paradox. The paradox arises via a clash of intuitions. On the one hand, there is the belief that there are things that are heaps and things that aren't: or that the expression "heap" can be true of things and false of things. On the other, there are a pair of intuitions which may ultimately be identical, which say that "heap" draws no sharp boundaries between things to which it does and doesn't apply and that "heap" is tolerant to small changes, which is to say that if something is a heap, it must remain so after the removal of a single composing element. -- In chapter 1, I isolate the vagueness in question - boundary-vagueness - via these intuitions and by a distinctive type of borderline cases that boundary-vague categories such as "heap" allow for. I introduce the sorites paradox in order to lay out possible lines of attack In chapter 2, I consider arguments by Crispin Wright that there are (a) various compelling reasons for certain expressions to be tolerant and that (b) paradoxes are thus derivable only if we work within a realist semantic framework Wright argues from vagueness to a rejection of the realist framework I argue that the case is not made. -- In chapter 3, I develop a model for vagueness in terms of categories. I treat our intuitions as stemming from a basic principle which, roughly states that closely-similar things must be co-categorised. I argue that our capacity to categorise is in certain ways limited, autonomous and context-dependent, which accounts for why it functions in such a way that does not lead to paradox. The paradoxes arise through the way we analyse what we do. In chapter 4,1 consider the relationship of vagueness to truth and the issue of higher-order vagueness. I argue not for a particular logic but a framework I call "flexible trivalentism".
Vagueness, Logic and Ontology
The topic of vagueness re-emerged in the twentieth century from relative obscurity. It deals with the phenomenon in natural language that manifests itself in apparent semantic indeterminacy - the indeterminacy, for example, that arises when asked to draw the line between the tall and non-tall, or the drunk and the sober. An associated paradox emphasises the challenging nature of the phenomenon, presenting one of the most resilient paradoxes of logic. The apparent threat posed for orthodox theories of the semantics and logic of natural language has become the focus of intense philosophical scrutiny amongst philosophers and non-philosophers alike. Vagueness, Logic and Ontology explores various responses to the philosophical problems generated by vagueness and its associated paradox - the sorites paradox. Hyde argues that the theoretical space in which vagueness is sometimes ontologically grounded and modelled by a truth-functional logic affords a coherent response to the problems posed by vagueness. Showing how the concept of vagueness can be applied to the world, Hyde's ontological account proposes a substantial revision of orthodox semantics, metaphysics and logic. This book will be of particular interest to readers in philosophy, linguistics, cognitive science and geographic information systems.
Frege's Conception of Logic
Author: Patricia A. Blanchette
language: en
Publisher: Oxford University Press
Release Date: 2012-04-01
In Frege's Conception of Logic Patricia A. Blanchette explores the relationship between Gottlob Frege's understanding of conceptual analysis and his understanding of logic. She argues that the fruitfulness of Frege's conception of logic, and the illuminating differences between that conception and those more modern views that have largely supplanted it, are best understood against the backdrop of a clear account of the role of conceptual analysis in logical investigation. The first part of the book locates the role of conceptual analysis in Frege's logicist project. Blanchette argues that despite a number of difficulties, Frege's use of analysis in the service of logicism is a powerful and coherent tool. As a result of coming to grips with his use of that tool, we can see that there is, despite appearances, no conflict between Frege's intention to demonstrate the grounds of ordinary arithmetic and the fact that the numerals of his derived sentences fail to co-refer with ordinary numerals. In the second part of the book, Blanchette explores the resulting conception of logic itself, and some of the straightforward ways in which Frege's conception differs from its now-familiar descendants. In particular, Blanchette argues that consistency, as Frege understands it, differs significantly from the kind of consistency demonstrable via the construction of models. To appreciate this difference is to appreciate the extent to which Frege was right in his debate with Hilbert over consistency- and independence-proofs in geometry. For similar reasons, modern results such as the completeness of formal systems and the categoricity of theories do not have for Frege the same importance they are commonly taken to have by his post-Tarskian descendants. These differences, together with the coherence of Frege's position, provide reason for caution with respect to the appeal to formal systems and their properties in the treatment of fundamental logical properties and relations.