Clearly, a 1-year-old man is young. Moreover, if someone is young at a given time, he is also young 1 second later—youth doesn’t vanish in 1 second. You can then infer that also a 1-year-and-1-second old man is young. But now take this conclusion and apply to it again the idea that youth doesn’t vanish in 1 second: you can then infer that also a 1-year-and-2-second old man is young. But now take this further conclusion and apply to it once again the idea that youth doesn’t vanish in 1 second: you can then infer that also a 1-year-and-3-second old man is young… By iterating this reasoning enough times, you can thus reach any age you like, so that, for example, you can conclude that also a 100-year-old man is young! This simple and yet arresting argument is in essence one of the most venerable and difficult philosophical paradoxes: the Sorites Paradox.

The Sorites Paradox targets the concepts that we mostly use in thinking about, experiencing and interacting with the world—that is, vague concepts, which categorise objects as falling on one side or the other of a distinction that seems not to depend on small differences (such as the concept of youth, redness, baldness etc.). The paradox boldly attempts to show that all such concepts are incoherent, in that what is supposed to fall on their negative side (e.g. a 100-year-old man is supposed not to be young) is also allegedly shown to have to fall on their positive side by the kind of paradoxical little-by-little reasoning just presented (e.g. a 100-year-old man is allegedly shown to have to be young by the particular reasoning just presented). Just as radical as this challenge is, work on the paradox has given rise to a vast array of groundbreaking theories in areas as diverse as formal and philosophical logic, philosophy of language, epistemology, metaphysics, practical philosophy, linguistics and psychology.

This book is the first one ever published to focus exclusively on the Sorites Paradox: it intends, on the one hand, to take stock of the vertiginous developments in thought about the paradox that have taken place in the last half century and, on the other hand, to address some of the new challenges that have arisen in the context of such developments. From a more structural point of view, the book represents an absolute novelty also in two other respects. Firstly, it provides a systematic treatment of the paradox, by devoting exactly one chapter to each main type of solution to the paradox and to each area where the paradox has exerted a profound influence. Secondly, each chapter is so conceived as to be accessible to novices in its topic, by gradually leading them from an introductory presentation of its general subject to a discussion of some open problems at the edge of contemporary research. From a more thematic point of view, the book also constitutes a substantial novelty, in that it extensively covers fairly recent solutions (i.e. dialetheism and non-transitivism) and somewhat underrepresented areas (i.e. practical philosophy and psychology). Even for those solutions and areas that have already received sustained attention in previous publications, the relevant chapter not only provides the state of the art, but also pushes research further on that front, by putting forth new ideas on some selected issues.