According to the plurivaluationist, our vague discourse doesn’t have a single meaning. Instead, it has many meanings, each of which is precise—and it is this plurality of meanings that is the source of vagueness. I believe plurivaluationist positions are underdeveloped and for this reason unpopular. This paper attempts to correct this situation by offering a particular development of plurivaluationism that I call supersententialism. The supersententialist leverages lessons from another area of research—the Problem of the Many—in service of the plurivaluationist (...) position. The Problem reveals theoretical reasons to accept that there are many cats where we thought there was one; the supersententialist claims that we are in a similar situation with respect to languages, propositions and sentences. I argue that the parallel suggested by the supersententialist reveals unappreciated advantages and lines of defense for plurivaluationism. (shrink)

In VAGUENESS AND DEGREES OF TRUTH, Nicholas Smith develops a new theory of vagueness: fuzzy plurivaluationism. -/- A predicate is said to be VAGUE if there is no sharply defined boundary between the things to which it applies and the things to which it does not apply. For example, 'heavy' is vague in a way that 'weighs over 20 kilograms' is not. A great many predicates -- both in everyday talk, and in a wide array of theoretical vocabularies, from (...) law to psychology to engineering -- are vague. -/- Smith argues, based on a detailed account of the defining features of vagueness, that an accurate theory of vagueness must involve the idea that truth comes in degrees. The core idea of degrees of truth is that while some sentences are true and some are false, others possess intermediate truth values: they are truer than the false sentences, but not as true as the true ones. Degree-theoretic treatments of vagueness have been proposed in the past, but all have encountered significant objections. In light of these, Smith develops a new type of degree theory. Its innovations include a definition of logical consequence that allows the derivation of a classical consequence relation from the degree-theoretic semantics, a unified account of degrees of belief and their relationships with degrees of truth and subjective probabilities, and the incorporation of semantic indeterminacy -- the view that vague statements need not have unique meanings -- into the degree-theoretic framework. -/- As well as being essential reading for those working on vagueness, Smith's book provides an excellent entry-point for newcomers to the area -- both from elsewhere in philosophy, and from computer science, logic and engineering. It contains a thorough introduction to existing theories of vagueness and to the requisite logical background. (shrink)

The major reason given in the philosophical literature for dissatisfaction with theories of vagueness based on fuzzy logic is that such theories give rise to a problem of higherorder vagueness or artificial precision. In this paper I first outline the problem and survey suggested solutions: fuzzy epistemicism; measuring truth on an ordinal scale; logic as modelling; fuzzy metalanguages; blurry sets; and fuzzy plurivaluationism. I then argue that in order to decide upon a solution, we need to understand the true (...) nature and source of the problem. Two possible sources are discussed: the problem stems from the very nature of vagueness—from the defining features of vague predicates; or the problem stems from the way in which the meanings of predicates are determined—by the usage of speakers together with facts about their environment and so on. I argue that the latter is the true source of the problem, and on this basis that fuzzy plurivaluationism is the correct solution. (shrink)

Nicholas Smith argues that an adequate account of vagueness must involve\ndegrees of truth. The basic idea of degrees of truth is that while\nsome sentences are true and some are false, others possess intermediate\ntruth values: they are truer than the false sentences, but not as\ntrue as the true ones. This idea is immediately appealing in the\ncontext of vagueness--yet it has fallen on hard times in the philosophical\nliterature, with existing degree-theoretic treatments of vagueness\nfacing apparently insuperable objections. Smith seeks to turn the\ntide in (...) favor of a degree-theoretic treatment of vagueness, by motivating\nand defending the basic idea that truth can come in degrees, by arguing\nthat no theory of vagueness that does not countenance degrees of\ntruth can be correct, and by developing a new degree-theoretic treatment\nof vagueness--fuzzy plurivaluationism--that solves the problems plaguing\nearlier degree theories. (shrink)

Vagueness is one of the most persistent and challenging topics in the intersection of philosophy and logic. At least five other noteworthy books on vagueness have been written by philosophers since 1991 [2, 6, 11, 12, 15]. A (necessarily incomplete) bibliography that has been compiled for the Arché project Vagueness: its Nature and Logic (2004-2006) of the University of St Andrews lists more than 350 articles and books on vagueness until 2005.1 Many new and interesting contributions have appeared since. The (...) book under review is much more than yet another addition to this prolific discourse. Nicholas Smith manages to tackle two different tasks that are potentially in tension. On the one hand, he provides a comprehensive, systematic and well written account of various approaches to vagueness that have been debated so far. On the other hand, Smith carefully explains and defends his own theory of vagueness, called fuzzy plurivaluationism. Given the complex and almost unsurmountably large amount of relevant literature and the fact that theories of vagueness based on fuzzy logic have almost universally been rejected by philosophers so far this is no simple feat. In the comments below, I will largely follow the structure of book. If along the way I cannot resist to make side remarks or even take issue with some of.. (shrink)