This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites Paradox and challenges classical logic and semantics.
The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, or neither one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates.
Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case.
In fragments of the lost Protrepticus, preserved in Iamblichus, Aristotle responds to Isocrates’ worries about the excessive demandingness of theoretical philosophy. Contrary to Isocrates, Aristotle holds that such philosophy is generally feasible for human beings. In defense of this claim, Aristotle offers the progress argument, which appeals to early Greek philosophers’ rapid success in attaining exact understanding. In this paper, I explore and evaluate this argument. After making clarificatory exegetical points, I examine the argument’s premises in light of pressing worries that the argument reasonably faces in its immediate intellectual context, the dispute between Isocrates and Aristotle. I also relate the argument to modern concerns about philosophical progress. I contend that the argument withstands these worries, and thereby constitutes a reasonable Aristotelian response to the Isocratean challenge.