Frege: Vagueness

Frege supposedly believes that vague predicates have no referent (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 the process, I call (...) attention to several under-appreciated texts in which Frege suggests that a vague predicate, though lacking a Bedeutung of its own, can come to acquire a Bedeutung in certain contexts. The upshot of this suggestion is that vague predicates can serve the purposes of ordinary communication quite well, even if they are useless for logical purposes. (shrink)

Controversy exists concerning the consequences of Frege's sharpness requirement for concepts and functions. Some say that the sharpness requirement, if taken to be a necessary condition for truth functional language use, renders most of our natural language discourse meaningless. This is because most if not all natural language concepts and predicates are not sharp. In this essay I argue first that Frege does indeed see the sharpness requirement as a necessary condition on a language's truth- functionality in all contexts in (...) which language is used, and that the attempt to eschew the difficulty that this requirement presents by stipulating within a metalanguage what the extensions of our natural language concepts and predicates shall be is fundamentally at odds with Frege's conception of logic. I then turn to a possible application of Frege's notion of sharpness as a set of metaphysical presuppositions underlying the everyday use of concepts in contexts in which truth is being addressed. (shrink)

The purpose of this paper is to discuss Frege’s view on vagueness, and to draw some relevant consequences of it. By examining what exactly Frege has in mind each time he complains about vagueness and advocates the sharpness requirement, I argue that he shows preoccupation with different kinds of vagueness in different periods of his thought. I also discuss the scope of the sharpness requirement, and argue that it is intended as applying primarily to mathematics and logic. Finally, I try (...) and argue that some of Frege’s remarks on incomplete functions suggest a view that is close in spirit to the contemporary supervaluationist approach to vagueness. (shrink)

If you’ve read the first five hundred pages of this book, you’ve read most of it (we assume that ‘most’ requires more than ‘more than half’). The set of natural numbers n such that the first n pages are most of this book is nonempty. Therefore, by the least number principle, it has a least member k. What is k? We do not know. We have no idea how to find out. The obstacle is something about the term ‘most’. It (...) is recognisably the same feature as the feature of ‘heap’ that prevents us from finding an answer to the question ‘How many grains make a heap?’ and the feature of many other expressions that prevents us from finding answers to similar questions involving them. Call this feature, whatever its underlying nature, vagueness. (shrink)