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Vagueness and Borderline Cases
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Authors Daly, Helen
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VAGUENESS AND BORDERLINE CASESby Helen L. Daly _____________________
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF PHILOSOPHYIn Partial Fulfillment of the Requirements For the Degree of
DOCTOR OF PHILOSOPHYIn the Graduate College
THE UNIVERSITY OF ARIZONA
THE UNIVERSITY OF ARIZONA
Terry Horgan Date: 5/13/2011 _______________________________________________________________________
Shaughan Lavine Date: 5/13/2011 _______________________________________________________________________
Final approval and acceptance of this dissertation is contingent upon the candidate’s submission of the final copies of the dissertation to the Graduate College.
I hereby certify that I have read this dissertation prepared under my direction and recommend that it be accepted as fulfilling the dissertation requirement.
________________________________________________ Date: 5/13/2011 Dissertation Director: Shaughan Lavine ________________________________________________ Date: 5/13/2011 Dissertation Director: Terry Horgan
STATEMENT BY AUTHORThis dissertation has been submitted in partial fulfillment of requirements for an advanced degree at the University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library.
Brief quotations from this dissertation are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permission for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his or her judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.
I am very fortunate to have been a graduate student at the University of Arizona while writing this dissertation. The faculty and graduate students there form a remarkable community of scholars, in whose company my philosophical ideas and skills have improved tremendously. I am grateful for such excellent colleagues, and I am particularly grateful for the steady hand at the helm of the department: Chris Maloney.
I owe hearty thanks to the many philosophers whose profound insights and difficult questions have forced me to refine the ideas presented here. Particular thanks are due to those who were willing to work through significant parts of this work with me, namely, Jacob Caton, Marc Johansen, Stephen Lenhart, Rachana Kamtekar, Marga Reimer, Kevin Vallier, and Robbie Wagoner. This work is also much improved because of the many comments and questions offered to me when I presented portions of this manuscript as part of the University of Arizona colloquium series, as part of the speaker series at Colorado College, and as part of the University of Arizona undergraduate philosophy club’s speaker series. Special thanks to Aeyn Edwards.
My dissertation committee members have been exceptionally generous with their time and talent. Carolina Sartorio’s insightful questions, comments, and suggestions prevented me from making several serious mistakes. And my committee co-chairs could not have done more to help me. Over the years, they spent countless hours thinking about vagueness with me and guiding me through the process of writing my first extended philosophical work. Shaughan Lavine and I began our conversation about vagueness in 2003, and my thinking about vagueness and about many other philosophical issues has come a long way as a result of our very pleasant and productive on-going dialogue. Terry Horgan has read draft after draft of this work with his extraordinary patience and his talent for finding the good idea buried among bad ones. By his example, I learned not just how to do philosophy, but how to be a philosopher. Both Terry and Shaughan stubbornly insisted that I could complete this project. Without their confidence and guidance, I certainly could not have done so.
Finally, I am very grateful to my parents, George and Betty Habermann, for their constant love and support; to my brothers, Greg and Paul Habermann, who first taught me how to argue; and to my loving and patient husband, Jacob Daly, who tolerated my unreasonable schedule while writing this work and frequently reminded me to eat.
Although the ideas presented here have been influenced and improved with the help of many people, responsibility for the errors and infelicities is mine alone.
1. THE NATURE OF VAGUENESS
1.2 Describing vagueness
1.3 Defining vagueness
1.4 The problem of vagueness
1.5 Requirements for an adequate solution to the problem
2. RECENT WORK ON BORDERLINE CASES
2.2 Diana Raffman
2.3 Crispin Wright
2.4 Higher-order borderline cases
2.5 Michael Tye
3. A NEW ACCOUNT OF BORDERLINE CASES
3.2 Borderline case success criteria
3.3 The vocabulary and taxonomy of borderline cases
3.4 My preferred notion of ‘borderline case’
4. A THEORY OF VAGUENESS
4.1 Vagueness as permission
4.1.1 The normal case
4.1.2 The tougher case
4.2 Vagueness as permission and epistemicism
4.3 Vagueness as permission and supervaluationism
4.4 Conclusions and directions for future research
Vagueness is ubiquitous in natural language. It seems incompatible with classical, bivalent logic, which tells us that every statement is either true or false, and none is vaguely true. Yet we do manage to reason using vague natural language. In fact, the majority of our day-to-day reasoning involves vague terms and concepts. There is a puzzle here: how do we perform this remarkable feat of reasoning? I argue that vagueness is a kind of semantic indecision. In short, that means we cannot say exactly who is bald and who is not because we have never decided the precise meaning of the word ‘bald’— there are some borderline cases in the middle, which might be bald or might not. That is a popular general strategy for addressing vagueness. Those who use it, however, do not often say what they mean by ‘borderline case’. It is most frequently used in a loose way to refer to in-between items: those people who are neither clearly bald nor clearly not bald. But under that loose description, the notion of borderline cases is ambiguous, and some of its possible meanings create serious problems for semantic theories of vagueness.
Here, I clarify the notion of a borderline case, so that borderline cases can be used profitably as a key element in a successful theory of vagueness. After carefully developing my account of borderline cases, I demonstrate its usefulness by proposing a theory of vagueness based upon it. My theory, vagueness as permission, explains how classical logic can be used to model even vague natural language.
Vagueness is ubiquitous in natural language. We notice it immediately in words like ‘bald’, ‘tall’, and ‘blue’; a longer look shows us that it is present even in apparently precise terms like ‘now’, ‘six feet tall’, and ‘organism’. For consider, the word ‘now’ does not pick out a precisely bounded moment. A few milliseconds sooner or later make no difference. And so there is some vagueness even in the apparently precise term, ‘now’.
Similarly, a measurement like ‘six feet tall’ initially seems like a fine way to make precise the vague expression ‘tall’. But when I describe my father as six feet tall, I am not using the phrase precisely. I have no idea whether he is 6.000 feet tall, 6.001 feet tall, or some other nearby height, and any ordinary judgment about the truth of my claim does not depend upon his exact height, as measured to the thousandth of a foot. The best explanation is that ‘six feet tall’, as commonly used, is not perfectly precise. It is less vague than ‘tall’, but it is still vague. As for ‘organism’, we might reasonably have supposed that scientific terms, which are commonly defined by stipulation, are not vague.
But in this case we would be wrong. The word ‘organism’ refers to living things. A virus is a borderline case of an organism since it has some features of living things, but lacks DNA and many of the other features normally thought to be required for life. Vagueness is everywhere.
That is not just an idle observation: vagueness creates real trouble. It is apparently incompatible with classical, bivalent logic, which tells us that every statement is either true or false, and none is vaguely true. The point can be put more strongly. Our best model of successful reasoning is classical, bivalent logic, which has exactly two truthvalues: true and false. There is no room for “kind of true.” But we often cannot say whether a claim like ‘Joe is bald’ is true or false—perhaps Joe’s hair is such that we could reasonably go either way. And, supposing my father is not exactly 6.000 feet tall, is it true or false that he is six feet tall? Classical, bivalent logic does not seem well-suited to accommodating ordinary reasoning with vague terms.
Yet we do manage to reason using vague terms. In fact, the majority of our dayto-day reasoning involves vague terms and concepts. There is a puzzle here: how do we perform this remarkable feat of reasoning? Must we wholly revise our understanding of logic to meet the challenge of ubiquitous vagueness? Or should we rather attempt to eliminate vagueness from our language, in order to promote better reasoning? I will argue that neither of those radical measures is needed, or even desirable.
Vagueness, I contend, is a kind of semantic indecision. In short, that means we cannot say exactly who is bald and who is not because we have never decided the precise meaning of the word ‘bald’—there are some borderline cases in the middle, people who might be bald or might not. That is a popular general strategy for addressing vagueness.
Those who use it, however, do not often say just what they mean by ‘borderline case’.
The term is most frequently used as a loose way to refer to in-between items: e.g., those people who are neither clearly bald nor clearly not bald. But under that loose description, I will argue that the notion of borderline cases is ambiguous, and that some of its possible meanings create serious problems for semantic theories of vagueness. In what follows, I clarify the notion borderline cases so that it can be used profitably as a key part of how vagueness is understood. An important consequence of my clarification is that semantic theories of vagueness are provided with a plausible defense against objections regarding their use of borderline cases, and also with an explanation of how we are able to reason so successfully using vague terms and concepts. As evidence for the usefulness of my notion of borderline case, I also develop a theory of vagueness employing my borderline cases as its central explanatory mechanism.
Chapter 1 is an explanation of the problem of vagueness. There is some disagreement about what vagueness is and what a theory of vagueness should do. After describing some of the possibilities, I settle on a reasonably neutral account, reflected in the two success criteria I propose for theories of vagueness. First, a theory of vagueness must explain how we can reason well, even with vague concepts, and so (1) the theory must accurately describe ordinary reasoning and how such reasoning can meet an appropriate standard of logical rigor. Second, a theory of vagueness must be about vagueness, and so it must (2) respect the intuition that vague predicates lack sharp boundaries. (For example, it might either not permit that there is a sharp boundary dividing the bald from the non-bald, or explain why people are prone to feel as if there is no such sharp boundary, even though there is one.) In order to demonstrate the difficulty of meeting both criteria at once, I describe a few ways in which theories of vagueness may fail to do so.
In Chapter 2, I consider three prominent accounts of vagueness that are explicitly concerned with borderline cases. Diana Raffman and Crispin Wright have both recently clarified the notion borderline case. My own account of borderline cases is in part a further development of considerations they have raised. The third account I consider is Michael Tye’s. It is very insightful, but subtly equivocates between two different notions of borderline cases. Such insidious errors illustrate the pressing need for further clarification of the various meanings that may be ascribed to ‘borderline case’.