We will spend our last 5 classes discussing Zeno’s paradoxes and philosophical issues that have arisen in connection with them during the last century. This first assignment consists of the beginning of Salmon’s introduction to the anthology he edited. In it, he gives a brief introduction to each of the 5 paradoxes (or 6 depending on how you count them). (He goes on after p. 16 to introduce some of the selections in the anthology; it’s fine to read this further part of the introduction, but I’m not assigning that, and we won’t end reading all of selections he mentions.)

There are two common approaches to thinking about Zeno’s paradoxes, on the one hand trying to see if they expose real problems in our ways of thinking about time, space, and motion and, on the other, trying to see why they might seem to expose such problems even if they do not really do so. Our interest will be focused on the first of these approaches to the paradoxes; but much recent writing about them has had the second aim, and we will occasionally approach them from that perspective, too.

One of the reasons people have pursued the second approach in the last century is that mathematical understanding of infinity and the issues it raises solidified at the end of the 19th century with the work of Georg Cantor (1845-1918). So, for the last century, people have felt they had a good way of thinking about the situations Zeno describes; but this way of thinking seems rather different from Zeno’s, so there has been considerable effort to think through the relation between the two. (I should add that I don’t mean to suggest that there is nothing more to be learned about infintity. For example, although mathematicians have been able to reason about infinitely small quantities with some confidence since the time of Archimedes, who lived about a century after Aristotle or two centuries after Zeno, fully rigorous approaches to reasoning about such “infinitesimals” were worked out only in the 1960s.)