Frege on Vagueness and Ordinary Language

Frege supposedly believed that vague predicates have no Bedeutung. But given other things he evidently believes, such a position would seem to commit him to a suspect nihilism according to which assertoric sentences containing vague predicates are neither true nor false. I argue that we have good reason to resist ascribing to Frege the view that vague predicates have no Bedeutung and thus good reason to resist seeing him as committed to the suspect nihilism. In some comments on his classic essay Über Sinn und Bedeutung, Frege affirms what has come to be known as his sharpness requirement on concepts: “It must be determinate for every object whether it falls under a concept or not; a concept word that does not meet this requirement on its Bedeutung is bedeutungslos” (NS 1:133/PW 122).1 This text and others like it have given rise to something of a scholarly consensus according to which Frege endorses what I will call SHARPNESS: (SHARPNESS) Vague or otherwise incompletely defined predicates have no Bedeutung.2 Editions of Frege’s works are cited using the following abbreviations: B: The Frege Reader, ed. M. Beaney (Boston: Blackwell, 1997); BS: Conceptual Notation, ed. T. W. Bynum (Oxford: Oxford University Press, 1972), cited by section number; CP: Collected Papers on Mathematics, Logic, and Philosophy, ed. B. McGuinness (New York: B. Blackwell, 1984); FA: The Foundations of Arithmetic (Evanston: Northwestern University, 1980); GG: Grundgesetze der Arithmetik, vol. 2, cited by section number; KS: Kleine Schriften, ed. I. Angelelli (Hildesheim: Georg Olms, 1967); NS: Nachgelassene Schriften, ed. H. Hermes, F. Kambartel, and F. Kaulbach (Hamburg: Felix Meiner, 1969), cited by volume and page number; PMC: Philosophical and Mathematical Correspondence (Chicago: University of Chicago, 1980); PW: Posthumous Writings, trans. P. Long and R. White (Chicago: University of Chicago, 1979). I follow contemporary usage in calling vague only those predicates lacking well-