1 Peirce and the Specification of Borderline Vagueness David W. Agler A version of this paper appeared in Semiotica 193: 195–215 Abstract Scholarship on the historical development of the concept of vagueness pinpoints Russell’s 1923 essay titled “Vagueness” and later articles in the 1930s, 40s, and 50s by Max Black, Carl Hempel, et alia as the starting point for a rigorous analysis of borderline vagueness. What accounts for the importance of these papers over and above earlier discussions of indeterminacy in antiquity and in the modern period is that Russell and others explicitly distinguish borderline vagueness from indeterminacies that are thought not to threaten classical logic. This paper argues that historical propriety concerning the analysis of borderline vagueness belongs to Peirce since he was the first to show that borderline vagueness is not only distinct from other forms of indeterminacy (generality, unspecificity, and uninformativeness), but also that the application of vague predicates involve an intrinsic uncertainty when applied to borderline cases. Keywords: Peirce, Russell, Vagueness, Indeterminacy, Semantics, Sorites ‘Vagueness’ is highly polysemous term. In common parlance, the term is used to indicate that something is unclear, obscure, ambiguous, too general, indeterminate, uninformative, fuzzy, obtuse, abstract, indistinct, inexact, unspecific, or elusive. In discussions about logic, semantics, and ontology, great pain is taken to conceptually distinguish the multitude of meanings associated with ‘vagueness’ from a type of indeterminacy thought to threaten classical logic and ontology. This latter form of indeterminacy is known as ‘borderline vagueness’. Characterizing vagueness is problematic for there is disagreement about the nature of the phenomenon (whether it is epistemic, contextual, or a semantic). 1 1 For some recent attempts to characterize the nature of vagueness, see (Rayo 2010:23–27; Soames 2010:46–48; Weatherson 2010:78–82) In order to avoid question-begging, the phenomenon is generally introduced by example. Consider a monotonically-increasing set of women arranged from shortest to tallest, where the shortest woman is 4’4 and the tallest woman is 7’7. While the predicate ‘tall’ clearly applies to the tallest woman and clearly does not apply to the shortest woman, there are a variety of in-between or borderline cases where it is indeterminate whether ‘tall’ applies or does not apply. That is, it is indeterminate whether the extension of ‘tall’ sharply classifies every woman in the set into a distinct category. Generally, it is agreed upon that the predicate ‘tall’ is vague in the sense of ‘borderline vague’ because (1) the indeterminacy of interpretation issues from the presence of borderline cases, (2) the indeterminacy is due to an intrinsic uncertainty concerning its application and not a subjective indeterminacy, and (3) this objective indeterminacy is not eliminable by an increase of information about either the object to which the predicate applies (e.g. the heights of the woman) or the intentions of the speaker.