What Verities May Be

Philosophical Perspectives, 1999

Suppose that Harry is a borderline case of baldness. Then the epistemic theory of vagueness has it that it's either true that he's bald or else true that he's not bald, but nothing we do will ever enable us to know the truth about Harry's baldness; and likewise, mutatis mutandis, for every other borderline case of a vague notion. This remarkable thesis is defended with great force and ingenuity by Timothy Williamson in his masterful book Vagueness, 1 but several other extremely able contemporary philosophers also accept the theory in the sense in which I'm about to define it, and they include Roy Sorensen, Paul Horwich, Hartry Field, Vann McGee and Brian McLaughlin. 2 Consequently, this paper will focus not only on Williamson's version of the epistemic theory, but also on the theory in its other guises. More specifically, this paper has the following outline. • Adefinition of the epistemic theory in the sense in which I want to discuss it. • A brief discussion of the motivation for the generic epistemic theory. • Application of the epistemic theory to the two issues that define the philosophical problem of vagueness-the problem of resolving the sorites paradox and the problem of explicating the notion of a borderline case (and, thereby, the notion of vagueness, for vagueness just is the possibility of borderline cases). • The outstanding question for the epistemic theorist is how to explain the ignorance to which she's committed. First I'll discuss how this challenge might be met by those epistemic theorists, such as Williamson, who take the crucial semantic properties to be use dependent. Then I'll discuss how the challenge might be met by those epistemic theorists, such as Hartry Field, who take the crucial semantic properties to be use independent.

At the heart of what the paradox alludes to is humankind’s grappling with the notion of ‘vagueness’ and associated indeterminacy relating to the application of predicates and their extensions. Herein, the paradox applies to those instances where predicates are said to lack ‘sharp boundaries’, despite any efforts to define such. In this paper, particular attention is afforded to the ‘Epistemic Response’ to the paradox in addressing or ‘solving’ the problem of vagueness. To the epistemicist, vagueness is a form of ignorance about these boundaries, and this gap in human knowledge – more than a mere semantic gap – is not able to be reconciled, as is inferred from the philosopher and metaphysician, Parmenides.

Synthese, 2015

This paper engages with a specific problem concerning the relationship between descriptive and normative claims. Namely, if we understand that descriptive claims frequently contain normative assertions, and vice versa, how then do we interpret the traditionally rigid distinction that is made between the two, as 'Hume's law' or Moore's 'naturalistic fallacy' argument offered. In particular, Kripke's interpretation of Wittgenstein's 'rule-following paradox' is specially focused upon in order to reconsider the rigid distinction. As such, the paper argues that if descriptive and normative claims are not mutually exclusive, then we need a new framework with which to understand this relationship. In this regard, the paper borrows from concerns with vagueness, particularly using a degree-theoretic approach in terms of subjective probability, in an attempt to graphically figure out these differences. Consequently, the paper tentatively proposes the hyperbola model in which degrees of normativity and degrees of descriptivity could be expressed and measured. It is hoped, as a result, that this tentative proposal will contribute to deepening the debate on vagueness in general.

philosophy.stanford.edu

Logic, Rationality, and Interaction

The semantic paradoxes and the paradoxes of vagueness ('soritical paradoxes') display remarkable family resemblances. In particular, the same nonclassical logics have been (independently) applied to both kinds of paradoxes. These facts have been taken by some authors to suggest that truth and vagueness require a uni ed logical framework (see e.g. [5,3]). Some authors go further, and argue that truth is itself a vague or indeterminate concept (see e.g. [7,4]). Importantly, however, there currently is no identi cation of what the common features of semantic and soritical paradoxes exactly consist in. This is what we aim to do in this work: we analyze semantic and soritical paradoxes, and develop our analysis into a theory of paradoxicality. The uni cation of the paradoxes of truth and vagueness we propose here has a wide scope, but for the sake of concreteness we focus on four three-valued logics.

Approaching Vagueness, 1983

It is argued in this paper that the vagueness of natural language predicates arises from the fact that they are learned and used always in limited contexts and hence are incompletely defined. A semantics for natural language must take this into account by making the interpretation of predicates context-dependent. It is shown that a context dependent semantics also provides the means for an account of vagueness. These notions are first developed and argued for in abstract terms and are then applied to a solution of the prototype of vagueness puzzles: the paradox of the heap.

Springer, 2024

This book provides an in-depth analysis of the nature and role of hypothetical reasoning about impossibilities. The interest in this subject stems from the simple observation that wondering is an inherent aspect of our experience. Whether one regrets choosing a taxicab over the subway or contemplates the outcome of an election turning out differently, the question 'What would have happened if...?' is a familiar one. While we often focus on possible scenarios, we also ponder impossible ones: What if whales were fish? What if a man could be in two places at once? What if one could draw a round square? Puzzles concerning such questions sparked a heated discussion over the nature and role of hypothetical reasoning about impossibilities. This book goes beyond being an opinionated introduction to this debate. After comparing various approaches to this issue, it proposes a novel perspective that draws on considerations from epistemology and the philosophy of explanation and dependence. Targeting researchers and students interested in the philosophy of modalities, this book delivers an in-depth analysis of a captivating and often overlooked aspect of human reasoning.

Synthese, 1977

A measure of degrees of similarity between possible worlds can be used to generate measures over propositions, or sets of possible worlds. These measures over propositions will count as 'probability measures', at least in the sense that they satisfy the axioms of the probability calculus. In a previous article (Bigelow, 1976), I have outlined one way in which such probability measures can be generated. In the present article I will present a considerably less devious way of generating probability measures. I will draw on two resources. My first resource will be standard techniques of measure theory. I will borrow lavishly from an excellent mathematics textbook by Friedman (1970). My second resource will be provided by concepts originating in modal logic, and also in the analysis of counterfactuals given by David Lewis (1973). The theory I offer rests on a natural extension of standard techniques used in modal logic for the analysis of concepts of necessity and possibility. The semantics of modal logic rest on a relation, called a (strict) accessibility relation on possible worlds. Different accessibility relations provide us with analyses of different concepts of necessity and possibility (see Hughes and Cresswell, 1968). A strict accessibility relation is used to give an analysis of the relationship of necessitation which may hold between propositions. We say it is true, in a given possible world, that one proposition necessitates another, when all the accessible worlds in which the first is true are worlds in which the second is true as well. But there are important relations among propositions which a strict accessibility relation does not illuminate. It may be, in particular, that though one proposition does not strictly necessitate another, yet it does nevertheless provide good inductive support for it. If the first is true, it may be extremely probable that the second will be true as well. This will be so, I will maintain, when most of the worlds in which the first is true are worlds in which the second is true.

Philosophical Studies, 2021

We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams' Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals.

Vassar College Journal of Philosophy, 2018

This article argues that resolutions to the sorites paradox offered by epistemic and supervaluation theories fail to adequately account for vagueness. After explai​ning the paradox, I examine the epistemic theory defended by Timothy Williamson and discuss objections to his semantic argument for vague terms having precise boundaries. I then consider Rosanna Keefe's supervaluationist approach and explain why it fails to accommodate the problem of higher-order vagueness. I conclude by discussing how fuzzy logic may hold the key to resolving the sorites paradox without positing indefensible borders to the correct application of vague terms.