Online research in philosophy

This paper discusses Fara's so-called 'Paradox of Higher-Order Vagueness' concerning supervaluationism. In the paper I argue that supervaluationism is not committed to global validity, as it is largely assumed in the literature, but to a weaker notion of logical consequence I call 'regional validity'. Then I show that the supervaluationist might solve Fara's paradox making use of this weaker notion of logical consequence. The paper is discussed by Delia Fara in the same volume.

In a seminal paper of 1923 on vagueness, Bertrand Russell discussed some of the most important problems concerning the nature of vagueness, its extension within the language, and its relation to truth and logic. The present paper inquires into Russell's theory. The following topics will be analysed and discussed in turn in sections 1?5: Russell's definition of vagueness; his claim that all phrases are vague; his theory of the source of the vagueness in our language; his principles for the transmission of vagueness; and his claim that logic is incompatible with vagueness. This paper is an attempt to give a rational reconstruction of Russell's position as expressed in his paper. Compatible passages in other of his works are also studied.

Vagueness is a familiar but deeply puzzling aspect of the relation between language and the world. It is highly controversial what the nature of vagueness is -- a feature of the way we represent reality in language, or rather a feature of reality itself? May even relations like identity or parthood be affected by vagueness? Sorites arguments suggest that vague terms are either inconsistent or have a sharp boundary. The account we give of such paradoxes plays a pivotal role for our understanding of natural languages. If our reasoning involves any vague concepts, is it safe from contradiction? Do vague concepts really lack any sharp boundary? If not, why are we reluctant to accept the existence of any sharp boundary for them? And what rules of inference can we validly apply, if we reason in vague terms? Cuts and Clouds presents the latest work towards a clearer understanding of these old puzzles about the nature and logic of vagueness. The collection offers a stimulating series of original essays on these and related issues by some of the world's leading experts.

Touching your mother's foot is incest because all the rest is a matter of degree (or so said Diogenes). That's just one expression of the puzzle of vagueness. Here's another: the passage of one second cannot mark the transition from being a pupa to being a butterfly--if something is a pupa at one time then in all close instants it remains a pupa; alas, it follows from this, via trivial logic, that there are no butterflies. Or again: it's vague where the Highlands of Scotland begin and end, so, a small step in the direction of London cannot mark the boundary between the Lowlands and the Highlands. But then it follows, via trivial logic, that one is unable to leave the Highlands (even when in London). What's driving these paradoxical arguments seems to be the very vagueness of the terms involved: such terms as 'incest', 'butterfly', 'pupa', 'The Highlands' are all vague and such vagueness seems to make them tolerant to marginal change. The puzzles of vagueness are not only deep (in that they admit of no uncontroversial and entirely satisfactory solution), they are also broad, for vague language is everywhere. In this course, you will be introduced to the various puzzles of vagueness and whether and how we might best address them. We will tackle such as questions as: Does the possibility of vagueness entail that there simply cannot be a logic of natural language? Does it entail that language is governed by inconsistent rules? Or does vagueness require some special or deviant logic? Is vagueness a special species of ignorance? Is the world, in some sense, vague? Is there an uncontroversial definition of vagueness or can we only isolate the phenomenon from within some substantive and controversial conception? What is higher-order vagueness and why is it considered to be such a puzzling phenomenon? Must the truth about vagueness be so strange? In what exact way are vague expressions tolerant?

The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions (such as ‘borderline’ and ‘definitely’) introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio , it does not fare substantially better with respect to immunity to any form of sorites paradox.

Vagueness provides the first comprehensive examination of a topic of increasing importance in metaphysics and the philosophy of logic and language. Timothy Williamson traces the history of this philosophical problem from discussions of the heap paradox in classical Greece to modern formal approaches such as fuzzy logic. He illustrates the problems with views which have taken the position that standard logic and formal semantics do not apply to vague language, and defends the controversial realistic view that vagueness is a kind of ignorance--that there really is a grain of sand whose removal turns a heap into a non-heap, but we cannot know which one it is.

Most expressions in natural language are vague. But what is the best semantic treatment of terms like 'heap', 'red' and 'child'? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this timely book Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories of vagueness and their supporting arguments, and she offers a powerful and original defence of a form of supervaluationism, a theory that requires almost no deviation from standard logic yet can accommodate the lack of sharp boundaries to vague predicates and deal with the paradoxes of vagueness in a methodologically satisfying way. Her study will be of particular interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics.

We all know that much in our thought and language, as well as much in the law, is vague. We are also reasonably good at recognizing cases of vagueness, even though most of us would be hard pressed to say exactly what vagueness is. In recent decades, there has been a flowering of work in the philosophy of logic and language attempting to do just that. Much of this work focuses on what it is for a word or phrase to be vague. The aim of this effort is to clarify what it is for a claim, question, command, or promise expressed using such a term to be vague, as well as what it is to reason with such terms. Different logico-linguistic theories have different conceptions of the scope of putative laws of classical logic, including bivalence (which states that every declarative sentence or proposition is either true or false) and excluded middle (which asserts all instances of A or ~A). In addition to this work in philosophical logic, recent decades have seen a growing interest in vagueness among legal scholars and philosophers of law. Here the focus is not so much on what legal vagueness is, which is generally assumed to be readily recognizable. Rather, it is on the extent and sources of vagueness in the law, the implications of vagueness for interpretation and adjudication, the systemic effects of vagueness, and the function – i.e. important positive value – of vagueness in certain areas of the law, as opposed to its disutility in others.1 To date, these two investigations of vagueness – in philosophical logic and the philosophy of law – have been largely independent of one another. This independence gives rise to a natural line of questioning. Can work in one domain contribute to work in..

The problem of vagueness and the sorites paradox arise because we try to treat natural language as if it were a unitary formal system. In fact, natural language contains a large variety of representational ontologies that serve different purposes and which cannot be united formally, but which can intuitively be taken as ways of seeing a common basic ontology. Using this framework, we can save classical logic from vagueness and avoid the sorites.

It is common among philosophers who take an interest in the phenomenon of vagueness in natural language not merely to acknowledge higher-order vagueness but to take its existence as a basic datum— so that views that lack the resources to account for it, or that put obstacles in the way, are regarded as deficient just on that score. My main purpose in what follows is to loosen the hold of this deeply misconceived idea. Higher-order vagueness is no basic datum but an illusion, fostered by misunderstandings of the nature of (ordinary, if you will ‘first-order’) vagueness itself. To see through the illusion is to take a step that is prerequisite for a correct understanding of vagueness, and for any satisfying dissolution of its attendant paradoxes.