Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in (...) 1998 and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems. (shrink)

Salmon was the first to speak explicitly of paradoxes of kinematics. In this short note I introduce a new class of infinity puzzles. Following natural terminology, they should actually be called static paradoxes.

In this paper, I propose that the debate in epistemology concerning the nature and value of understanding can shed light on the role of scientific idealizations in producing scientific understanding. In philosophy of science, the received view seems to be that understanding is a species of knowledge. On this view, understanding is factive just as knowledge is, i.e., if S knows that p, then p is true. Epistemologists, however, distinguish between different kinds of understanding. Among epistemologists, there are those who (...) think that a certain kind of understanding—objectual understanding—is not factive, and those who think that objectual understanding is quasi-factive. Those who think that understanding is not factive argue that scientific idealizations constitute cognitive success, which we then consider as instances of understanding, and yet they are not true. This paper is an attempt to draw lessons from this debate as they pertain to the role of idealizations in producing scientific understanding. I argue that scientific understanding is quasi-factive. (shrink)

Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf’s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in 1998 (...) and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems. (shrink)

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of (...) part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason. (shrink)