Online research in philosophy

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken.

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.

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken.

Degree theories of vagueness build on the observation that vague predicates such as 'tall' and 'red' come in degrees. They employ an infinite-valued logic, where the truth values correspond to degrees of truth and are typically represented by the real numbers in the interval [0,1]. In this paper, the success with which the numerical assignments of such theories can capture the phenomenon of vagueness is assessed by drawing an analogy with the measurement of various physical quantities using real numbers. I argue that degree theories of vagueness are undermined by the failure of the necessary connectedness principle. Moreover, the semantics for the connectives entail that there must be a uniquely correct numerical assignment for the sentences, and this is implausible. Different senses of 'coming in degrees' are then distinguished; I argue that a confusion between them could be the source of the degree theorist's error, and the distinction illuminates the problem cases described earlier in the paper.

Supervaluational treatments of vagueness are currently quite popular among those who regard vagueness as a thoroughly semantic phenomenon. Peter Unger's 'problem of the many' may be regarded as arising from the vagueness of our ordinary physical-object terms, so it is not surprising that supervaluational solutions to Unger's problem have been offered. I argue that supervaluations do not afford an adequate solution to the problem of the many. Moreover, the considerations I raise against the supervaluational solution tell also against the solution to the problem of the many which is suggested by adherents of the epistemic theory of vagueness.

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.

In this paper I criticize a version of supervaluation semantics. This version is called "Region-Valuation" semantics. It's developed by Pablo Cobreros. I argue that all supervaluationists, regionalists in particular, and truth-value gap theorists of vagueness more generally, are commited to the validity of D-intro, the principle that every sentence entails its definitization (the truth of "Paul is tall" guarantees the truth of "Paul is definitely tall"). The principle embroils one in a paradox that's distinct from, but related to, the sorites paradox. I call it the "gap-principles paradox".

We argue that standard definitions of ‘vagueness’ prejudice the question of how best to deal with the phenomenon of vagueness. In particular, the usual understanding of ‘vagueness’ in terms of borderline cases, where the latter are thought of as truth-value gaps, begs the question against the subvaluational approach. According to this latter approach, borderline cases are inconsistent (i.e., glutty not gappy). We suggest that a definition of ‘vagueness’ should be general enough to accommodate any genuine contender in the debate over how to best deal with the sorites paradox. Moreover, a definition of ‘vagueness’ must be able to accommodate the variety of forms sorites arguments can take. These include numerical, total-ordered sorites arguments, discrete versions, continuous versions, as well as others without any obvious metric structure at all. After considering the shortcomings of various definitions of ‘vagueness’, we propose a very general non-question-begging definition.

The main question of the paper is that ofwhat vagueness consists in. This question must be distinguished from other questions about vagueness discussed in the literature. It is argued that familiar accounts of vagueness for general reasons failto answer the question ofwhat vagueness consists in. A positive view is defended, according to which, roughly, the vagueness of an expression consists in it being part ofsemantic competence to accept a tolerance principle for the expression. Since tolerance principles are inconsistent, this is an inconsistency view on vagueness.

The two standard theories of vagueness—vagueness-as-ignorance and vagueness-asindeterminacy—agree on the following principle: if you are certain that it is clearly vague whether p, then you clearly should not believe p and you clearly should not believe not-p. I argue against the principle, and thus against the two standard theories. I offer an explanation of the initial appeal of the principle. And I show how a rival principle helps to better explain a recalcitrant trio of widely accepted data.