Preface

According to orthodoxy the study of vagueness belongs to the domain of the phil­osophy of language. According to that paradigm, solving the paradoxes of vagueness involves investigating the nature of words like ‘heap’ and ‘bald’ in English, and parallel words in other languages.

By contrast, the theory I advocate in this book is a theory ofpropositional vagueness.

Let me begin with a bit of autobiography. This project started off in 2009 as a 30,000 word essay written for the thesis portion of the Oxford BPhil examination. Over the next eight years the project turned into my DPhil thesis, and eventually this book. However, the project changed a great deal over that period. Many of the views criticized in the following pages are views I once held, and the end result no doubt bears the marks of this. Indeed, the original purpose of the thesis was to investigate the epistemology of vagueness in the context of a linguistic theory of vagueness. While my primary focus was on the epistemological aspects of vagueness, I was working with the background assumption that vagueness was fundamentally a linguistic phenomenon. My hope was that it would be possible to use game-theoretic concepts—specifically, certain sorts of mixed strategy equilibria—within a broadly Lewisian account of the conventions of language to explain why we are ignorant about the vague.

Thus, despite the prevailing orthodoxy that vagueness has at least something to do with language, I found the alternative non-linguistic picture had a lot to recommend itself. What follows is particular way of spelling out that picture.

Here is a brief overview of the structure of the book. In chapter 1, I argue against the nihilist responses to the sorites paradox and against responses that reject classical logic, setting up one of the fundamental presuppositions of this book: that sorites sequences have cutoff points. In chapter 2, I move on to the debate over classical theories of vagueness—the two most prominent of which are epistemicism and supervaluationism. I outline some widely discussed questions in the philosophy of vagueness, and look at how epistemicism and supervaluationism are typically taken to engage with them. I argue, however, that these questions on the whole do not really carve the philosophical view-space at its joints and that the classification of views as supervaluationist and epistemicist is often not always that insightful.

My positive view starts in chapter 6. This chapter tells us what the role in thought of a vague proposition is, and introduces the Principle of Plenitude that states, roughly, that there's a vague propositions for every possible role in thought. Chapter 7 takes an in-depth look at an alternative, but related, view that is due to Hartry Field. One of the primary differences between the views is that, unlike Field, I accept probabilism—the thesis that rational credences are governed by the axioms of the probability calculus. In this chapter I defend that commitment, and discuss the connection between credences and higher-order vagueness. Chapter 8 introduces the principle Rational Supervenience, that captures a sense in which all disagreements about the vague boil down to disagreements about the precise. Chapter 9 introduces Jeffrey's decision theory in a context where vague propositions are among your preferences and are among the things you can make true. Here I discuss the thought that attitudes with vague contents are superfluous for practical reasoning. Chapter 10 introduces the principle Indifference, stating that it is irrational to care intrinsically about the vague.

In the third part of the book I turn to a number of logical and metaphysical issues relating to the nature of propositions, modality, possible worlds and the semantics for propositional vagueness.

that we should take the former as the primitive notion, rather than the latter. Chap­ter 13 introduces the central notion of a symmetry—roughly an automorphism on the algebra of propositions that preserves their role in thought—and shows how it can provide an illuminating analysis of vagueness. Chapter 14 discusses the relation between fundamental propositions, vagueness, and possible worlds, and argues that certain uses of the ideology of fundamentally and possible worlds lead to paradoxes of higher-order vagueness. Chapter 15 discusses the interaction between the deter- minacy and modal operators, the supervenience of the vague on the precise, and compares the supervaluationist approach to these questions to the present approach. Chapter 16 examines the notion of a vague object, and shows how it fits naturally into my theory of vagueness. Finally, chapter 17 discusses cases of indeterminacy (not vagueness) that seem like they genuinely have to do with language; I argue that they can be naturally accounted for within a theory of propositional vagueness such as my own.

There are several ways to read this book. There is, of course, the most Straight­forward route: to read it from beginning to end. Readers wishing to get a relatively self-contained, albeit compressed, introduction to my positive account, however, may take the following route:

1.       Chapter 3 for a broad overview of my theory.

2.New Roman">       Chapter 6 for the Principle of Plenitude.

3.       Chapter 8 for the principle Rational Supervenience.

4.       Chapter 10 for the principle Indifference.

5.        Chapter 12 for the distinction between vagueness and borderlineness, and problems for a supervaluational approach to propositional vagueness.

6.       Chapter 13 for an explanation of symmetry semantics.

For those not already relatively familiar with decision theory, I would also recommend adding chapter 9—at least section 9.1—to this route: the proper interpretation of decision theory when vague propositions are among the things you can make true is a delicate matter.

The third part of the book addresses a number of issues concerning the proper logical and semantic treatment of propositional vagueness. These chapters explore ways in which the existence of propositional vagueness forces a radical departure from conventional thinking about concepts such as worlds, precisifications, funda- mentality, and similar concepts. One of the running themes of these chapters is that it's not possible to isolate the objective ‘worldly’ divisions in logical space from those divisions ‘merely having to do with vagueness’. One instance of this idea is a natural supervaluational way of modelling propositions as sets of world-precisification pairs. In this framework logical space can be decomposed straightforwardly into ‘worldly’ and ‘non-worldly’ components. For readers wanting to skip straight to these topics, one could read chapter 3 for an overview of the theory, and chapters 11-16.

Any book on vagueness will surely have been influenced heavily by the vast literature that has come before it. In my case, the most easily traced influences have been in the work of Tim Williamson and Hartry Field. While I often oppose Williamson’s epistemicism, it was reading his work that first made me see clearly how hard it was to avoid some of his main conclusions—that vague predicates have sharp cutoff points, and that we don’t know where they lie. Again, although I criticize a lot of Field’s work in this book, there are clear commonalities between his approach and mine. Although the view I develop goes in a very different direction, thinking about his approach to vagueness and the liar has greatly helped me sharpen my own ideas, and led me to raise many of the questions I address in this book. It is also worth emphasizing that the literature has evolved a lot as I was writing this book; I have attempted to discuss new work where it is relevant, but there are omissions nonetheless.

This book has been mostly written from scratch.

Many people, both in print and in conversation, have shaped my thinking on vagueness. I would like in particular to thank the graduate students and faculty at Oxford during my time there and audiences at Barcelona, Bristol, Brown, Dubrovnik, Leeds, Munich, Oxford, USC, Yale, and a symposium on vagueness and belief at the 2015 Central APA, at which I presented various versions of the ideas developed in this book. I received lots of helpful feedback from these people. I also owe a debt of gratitude to two anonymous referees for OUP, both of whom made extremely helpful suggestions about the structure of the book, which led me to significantly reorganize the content.

In 2013, I took part in an online reading group on this book. Participants included Mike Caie, Andreas Ditter, Cian Dorr, Hartry Field, Peter Fritz, Jeremy Goodman, and Harvey Lederman. The results of these discussions greatly improved the book. I’d also like to thank Shieva Kleinschmidt, Ofra Magidor, Jeff Russell, Bernard Salow, Mark Schroeder, and Robbie Williams from whose conversations I have benefited over the years (Robbie was the external examiner for the aforementioned DPhil thesis from which this book evolved, and Ofra, I later discovered, was the examiner for the BPhil thesis; both their comments lead to some important improvements).

I would like, in particular, to thank Mike Caie, who sent me incredibly detailed comments on the book. Apart from providing many on point criticisms of the central philosophical claims of the book, Mike worked his way through all of the technical material, spotting several mistakes and gave me many helpful suggestions about presentation.

Special thanks are also due to John Hawthorne and Tim Williamson. Apart from his influence in print, Tim, as my secondary supervisor for the DPhil, has provided me with lots of insightful feedback and comments on my work during my time at Oxford; both his teaching and writing have been a great source of inspiration for me. Many ideas in this book (and, indeed, many ideas not in this book) have been filtered through John in one form or another. In 2015, I co-taught a seminar on vagueness with John which covered a large portion of this book. His comments during this seminar improved the book in a great number of matters of detail, but also helped me see the book in the context of the bigger picture.

My deepest debt of gratitude is to my supervisor and mentor, Cian Dorr. Although he holds completely opposing views on the topic of vagueness, his influence on this project is too pervasive to be properly credited. His mark can be found on most of the central ideas in this book.

I would also like to thank Peter Momtchiloff for his support on this project. Id especially like to thank Tanya Kostochka and Brian North: Tanya for spotting countless errors and offering several helpful suggestions about making the content more accessible, and Brian North for his meticulous work in copy-editing the book.

Lastly, thanks to the Pasadena branch of Oh My Pan! Taiwanese bakery, and the LA metro Gold and Expo lines, where a non-trivial portion of this book was written.

Gratitude of another kind is owed to my wife, Helen, without whom I would have probably never finished this thing.