If you’ve read the first five hundred pages of this book, you’ve read most of it (we assume that ‘most’ requires more than ‘more than half’). The set of natural numbers n such that the first n pages are most of this book is nonempty. Therefore, by the least number principle, it has a least member k. What is k? We do not know. We have no idea how to find out. The obstacle is something about the term ‘most’. It (...) is recognisably the same feature as the feature of ‘heap’ that prevents us from finding an answer to the question ‘How many grains make a heap?’ and the feature of many other expressions that prevents us from finding answers to similar questions involving them. Call this feature, whatever its underlying nature, vagueness. (shrink)

This paper supersedes an ealier version, entitled "A Non-Standard Semantics for Inexact Knowledge with Introspection", which appeared in the Proceedings of "Rationality and Knowledge". The definition of token semantics, in particular, has been modified, both for the single- and the multi-agent case.

There are many examples in the literature that suggest that indistinguishability is intransitive, despite the fact that the indistinguishability relation is typically taken to be an equivalence relation (and thus transitive). It is shown that if the uncertainty perception and the question of when an agent reports that two things are indistinguishable are both carefully modeled, the problems disappear, and indistinguishability can indeed be taken to be an equivalence relation. Moreover, this model also suggests a logic of vagueness that seems (...) to solve many of the problems related to vagueness discussed in the philosophical literature. In particular, it is shown here how the logic can handle the sorites paradox. (shrink)

In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. (...) We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity. (shrink)

Williamson (2000a) has argued that posi- tive introspection is incompatible with in- exact knowledge. His argument relies on a margin-for-error requirement for inexact knowledge based on a intuitive safety prin- ciple for knowledge, but leads to the counter- intuitive conclusion that no possible creature could have both inexact knowledge and posi- tive introspection. Following Halpern (2004) I put forward an alternative margin-for-error requirement that preserves the safety require- ment while blocking Williamson’s argument. I argue that the infallibilist conception of knowledge (...) that underlies the new require- ment provides a better account of inexact knowledge and higher-order knowledge than both Williamson’s and Halpern’s. (shrink)

I address Peter Mott's 'Margins for Error and the Sorites Paradox' , pp. 494–503). Mott criticizes my account of inexact knowledge, on which it satisfies margin for error principles of the form 'If one knows in a given case, one avoids false belief in sufficiently similar cases'. Mott's arguments are shown to be fallacious because they ignore the fact that our knowledge of inexact knowledge is itself inexact. In the examples discussed, the first-level inexact knowledge is perceptual. Since my defense (...) of an epistemicist theory of vagueness explains our ignorance of truth-values in borderline cases as the result of knowledge the inexactness of which has a conceptual source, the paper also contributes to the defense of epistemicism about vagueness. (shrink)