Motivating Non-Contingency

This chapter takes up the question of how to motivate the crucial ‘Non-Contingency’ premise in the Tolerance Puzzles introduced in Chapter 2, a question that has received surprisingly little attention in the literature on these puzzles. We articulate and set aside some dubious motivations for the premise, including motivations which assimilate Tolerance Puzzles to the well-known Sorites Paradox. In place of these, we develop a ‘Security Argument’ for Non-contingency, based on the thought that it is not just a matter of chance or luck that we avoid error in believing the Tolerance premise.

The Riddle of Vagueness

This anthology includes fourteen of Crispin Wrights’s highly influential essays on the phenomenon of vagueness in natural language, collectively representing almost half a century of cutting-edge systematic research. Key issues addressed include whether or under what assumptions vague expressions’ apparent tolerance of marginal changes in things to which they apply indicates that they are governed by inconsistent semantic rules, the varieties of Sorites paradox and the roots of the plausibility of their respective major premises, what it is for something to be a borderline case of a vague expression, whether vagueness should be viewed as fundamentally a semantic or an epistemic phenomenon, whether there is ‘higher-order’ vagueness, and what should be the appropriate logic for vague statements. The essays reprinted here jointly document the development of a distinctively original treatment of the philosophy and logic of vagueness, broadly analogous to the intuitionistic philosophy and logic for pure mathematics. Richard Kimberly Heck contributes an extended introductory essay, providing both an insightful critical overview of the development of the distinctive elements of Wright’s thought about vagueness, and indeed an invaluable advanced introduction to the topic.

Intuitionism and the Sorites Paradox

This chapter revisits and further develops all the principle themes and concepts of the preceding chapters. Epistemicism about vagueness postulates a realm of distinctions drawn by basic vague concepts that transcend our capacity to know them. Its treatment of their subject matter is thus broadly comparable to the Platonist philosophy of mathematics. An intuitionist philosophy of vagueness, as do many philosophies of the semantics and metaphysics of vague expressions, finds this idea merely superstitious and rejects it. The vagueness-intuitionist, however, credits the epistemicist with a crucial insight: that vagueness is indeed a cognitive, rather than a semantic, phenomenon—something that is not a consequence of some kind of indeterminacy, or open-endedness in the semantics of vague expressions but rather resides in our brute inability to bring, for example, yellow and orange right up against one another, so to speak, so as to mark a sharp and stable boundary. A solution to the Sorites paradox is developed that is consonant with this basic idea but, by motivating a background logic that observes (broadly) intuitionistic restrictions on the proof theory for negation, allows us to treat the paradoxical reasoning as a simple reductio of its major premise, without the unwelcome implication, sustained by classical logic, of sharp cut-offs.

Introduction

Crispin Wright’s work on vagueness has been extremely influential. This piece provides an overview of his contributions and the ways his views have changed over the forty-plus years he has been writing about the topic. Heck argues that Wright’s discussion of the Tachometer paradox provides us with the resources to disarm the Sorites paradox. Sadly, that still leaves us remarkably far from any positive account of the semantics of vague concepts. In his most recent work, Wright has pursued an ‘intuitionistic’ account of vagueness whose virtues and vices are described.

On Being in a Quandary

This chapter addresses three problems: the problem of formulating a coherent relativism, the Sorites paradox, and a seldom noticed difficulty in the best intuitionistic case for the revision of classical logic. A response to the latter is proposed which, generalized, contributes towards the solution of the other two. The key to this response is a generalized conception of indeterminacy as a specific kind of intellectual bafflement—Quandary. Intuitionistic revisions of classical logic are merited wherever a subject matter is conceived both as liable to generate Quandary and as subject to a broad form of evidential constraint. So motivated, the distinctions enshrined in intuitionistic logic provide both for a satisfying resolution of the Sorites paradox and a coherent outlet for relativistic views about, for example, matters of taste and morals. An important corollary of the discussion is that an epistemic conception of vagueness can be prised apart from the strong metaphysical realism with which its principal supporters have associated it, and acknowledged to harbour an independent insight.

Further Reflections on the Sorites Paradox

This chapter revisits certain of the issues of Chapters 1 and 2. It is argued that Dummett’s ‘incoherentist’ response to the Sorites is unacceptable, and urges that we should distinguish a variety of types of Sorites, as individuated by the differing motivations for their various respective major premises, including what are here termed the No Sharp Boundaries paradox and the Tachometer paradox. The chapter rejects Christopher Peacocke’s contention that the major premises for Sorites can be motivated under the aegis of a behaviouristic conception of linguistic competence, so that jettison of the Governing View is beside the point as a response to Sorites paradoxes. It musters six objections to Peacocke’s own treatment of the Sorites, as representative of degree-theoretic approaches to vagueness in general. The chapter includes further discussion of the relationship between tolerance and observationality.

Language-Mastery and the Sorites Paradox

This chapter, originally written for Gareth Evans’s and John McDowell’s edited anthology of papers, Truth and Meaning, on the philosophical issues raised by Davidsonian truth-theoretic semantics for natural language, reprises the key arguments of Chapter 1, but with a more explicit focus on the question: what is the nature of linguistic competence? Can it, at least at the most basic level, be viewed as consisting in propositional knowledge of, and a consequent ability to follow, semantic and syntactic rules? The suggestion is that the Davidsonian programme is implicitly invested in a positive answer to that question, and that one lesson of the Sorites is to make that answer seriously doubtful, mandating a ‘more purely behaviouristic’ conception of basic linguistic competence.

Enriched category as a model of qualia structure based on similarity judgements

Qualitative relationships between two instances of conscious experiences can be quantified through the perceived similarity. Previously, we proposed that by defining similarity relationships as arrows and conscious experiences as objects, we can define a category of qualia in the context of category theory. However, the example qualia categories we proposed were highly idealized and limited to cases where perceived similarity is binary: either present or absent without any gradation. When similarity is graded, a situation can arise where A0 is similar to A1, A1 is similar to A2, and so on, yet A0 is not similar to An, which is called the Sorites paradox. Here, we introduce enriched category theory to address this situation. Enriched categories generalize the concept of a relation between objects as a directed arrow (or morphism) in ordinary category theory to a more flexible notion, such as a measure of distance. As an alternative relation, here we propose a graded measure of perceived dissimilarity between the two objects. These measures combine in a way that addresses the Sorites paradox; even if the dissimilarity between Ai and Ai+1 is small for i = 0 … n, hence perceived as similar, the dissimilarity between A0 and An can be large, hence perceived as different. In this way, we show how dissimilarity-enriched categories of qualia resolve the Sorites paradox. We claim that enriched categories accommodate various types of conscious experiences. An important extension of this claim is the application of the Yoneda lemma in enriched category; we can characterize a quale through a collection of relationships between the quale and the other qualia up to an (enriched) isomorphism.