Peirce and the specification of borderline vagueness

Abstract

Scholarship on borderline vagueness pinpoints Russell's 1923 essay titled "Vagueness" as the starting point for rigorous analysis. The importance of Russell's work over and above discussions of indeterminacy in antiquity and in the modern period is that Russell isolated borderline vagueness from indeterminacies that do not 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 distinct from other forms of indeterminacy (e.g., generality, unspecificity, and uninformativeness) and that the application of vague predicates to borderline cases involves an intrinsic uncertainty.

Peirce’s three-dimensional notion of vagueness

“…Bergman (2004;2009) focused more closely on the pragmatic-contextual role that the two figures of indeterminacy (vagueness and generality) play in the communicative context. Agler (2010;2013) placed the Peircean perspective in dialogue with contemporary theories of vagueness that focus on the analysis of predicates and the problematic Sorites paradox that vague predicates seem to generate. As already mentioned, Tiercelin (1986;1989;1992) examined the problem of vagueness from both a semiotic and an ontological point of view, arguing that a comprehensive treatment of vagueness must also address the epistemological implications within Peircean architecture.…”

“…The incompatibility of the two approaches is supported by almost all Peircean commentators, perhaps with the sole exception of Agler (2010;2013) and Tiercelin (in particular, 2019). However, this is not to argue that a comparison between Peircean vagueness and vagueness understood in the contemporary sense is not possible, but that it should first be recontextualized.…”