Exactness,inexactness, and the non-transitivity of perceptual indiscriminability

I defend, to a certain extent, the traditional view that perceptual indiscriminability is non-transitive. The argument proceeds by considering important recent work by Benj Hellie: Hellie argues that colour perception represents ‘inexactly’, and that this results in violations of the transitivity of colour indiscriminability. I show that Hellie’s argument remains inconclusive, since he does not demonstrate conclusively that colour perception really does represent inexactly. My own argument for the non-transitivity of perceptual indiscriminability uses inexactness instead as one horn of a dilemma: the key idea is that there is a class of perceptual experiences which might plausibly be supposed either to represent inexactly or to represent exactly—but which demonstrate the non-transitivity of perceptual indiscriminability either way.     

Vagueness and Context

A number of recent accounts for vague terms postulate a kind of context-sensitivity, one that kicks in after the usual ‘external’ contextual factors like comparison class are established and held fixed. In a recent paper, ‘Vagueness without Context Change’(Mind 116 (2007): 275–92), Rosanna Keefe criticizes all such accounts. The arguments are variations on considerations that have been brought against context-sensitive accounts of knowledge, predicates of personal taste, epistemic modals, and the like. The issues are well known and there are variety of options available in reply. More important, the arguments rely on an overly narrow conception of context-sensitivity, suggesting that one size fits all. If Keefe’s arguments were cogent, they would tell against the context-sensitivity of just about any expression, beyond the typical indexicals, including the variation of vague terms with comparison class. However, the criticisms raised by Keefe do highlight certain questions that must be answered by an advocate of a context-sensitive account of vagueness, essentially the same sorts of questions that must be answered by a contextualist or relativist about knowledge, epistemic modals, predicates of personal taste, etc. The main purpose of this paper is to use replies to the relevant objections raised by Keefe as a springboard for further articulation of the underlying view of vagueness.     

Vagueness and Quantification

This paper deals with the question of what it is for a quantifier expression to be vague. First it draws a distinction between two senses in which quantifier expressions may be said to be vague, and provides an account of the distinction which rests on independently grounded assumptions. Then it suggests that, if some further assumptions are granted, the difference between the two senses considered can be represented at the formal level. Finally, it outlines some implications of the account provided which bear on three debated issues concerning quantification.     

Vagueness and Naturalness

I attempt to accommodate the phenomenon of vagueness with classical logic and bivalence. I hold that for any vague predicate there is a sharp cut-off between the things that satisfy it and the things that do not; I claim that this is due to the greater naturalness of one of the candidate meanings of that predicate. I extend the thought to the problem of the many and Benacerraf cases. I go on to explore the idea that it is ontically indeterminate what the most natural meanings are, and hence ontically indeterminate where the sharp cut-off in a sorites series is.     

Quantum Vagueness

It has been suggested that quantum particles are genuinelyvague objects (Lowe 1994a). The present work explores thissuggestion in terms of the various metaphysical packages that areavailable for describing such particles. The formal frameworksunderpinning such packages are outlined and issues of identityand reference are considered from this overall perspective. Indoing so we hope to illuminate the diverse ways in whichvagueness can arise in the quantum context.     

Vagueness and revision sequences

Theories of truth and vagueness are closely connected; in this article, I draw another connection between these areas of research. Gupta and Belnap’s Revision Theory of Truth is converted into an approach to vagueness. I show how revision sequences from a general theory of definitions can be used to understand the nature of vague predicates. The revision sequences show how the meaning of vague predicates are interconnected with each other. The approach is contrasted with the similar supervaluationist approach.     

Event Location and Vagueness

Most event-referring expressions are vague it is utterly difficult, if not impossible, to specify the exact spatiotemporal location of an event from the words that we use to refer to it. We argue that in spite of certain prima facie obstacles, such vagueness can be given a purely semantic (broadly supervaluational) account.     

Vagueness and Blurry Sets

This paper presents a new theory of vagueness, which is designed to retain the virtues of the fuzzy theory, while avoiding the problem of higher-order vagueness. The theory presented here accommodates the idea that for any statement S ₁ to the effect that Bob is bald is x true, for x in [0,1], there should be a further statement S ₂ which tells us how true S ₁ is, and so on – that is, it accommodates higher-order vagueness – without resorting to the claim that the metalanguage in which the semantics of vagueness is presented is itself vague, and without requiring us to abandon the idea that the logic – as opposed to the semantics – of vague discourse is classical. I model the extension of a vague predicate P as a blurry set, this being a function which assigns a degree of membership or degree function to each object o, where a degree function in turn assigns an element of [0,1] to each finite sequence of elements of [0,1]. The idea is that the assignment to the sequence 0.3,0.2, for example, represents the degree to which it is true to say that it is 0.2 true that o is P to degree 0.3. The philosophical merits of my theory are discussed in detail, and the theory is compared with other extensions and generalisations of fuzzy logic in the literature.