Bertrand Russell, the famous philosopher, Nobel prize winning author, and, with Alfred North Whitehead, writer of the "Principia mathematica" which attempted to establish the foundations of mathematics, referred to the difficulties surrounding the notions of infinity and continuity as "one of the greatest of philosophical problems." Indeed, at some time or other in mathematics, physics or philosophy classes, students are confronted by the paradoxes of motion, first presented in the Ancient World by Zeno, which deal with the issues of infinity and continuity. A typical example of Zeno's riddles is the paradox of how one can ever start a journey if, in order to get somewhere, one must first go half way; but then to get half way, one must traverse half of that distance, etc. Since these divisions can go on forever, one can never even begin the journey. Hence, motion is impossible. Zeno's paradoxes not only provide an easy lesson plan for introductory science or philosophy classes, but are still debated in learned texts in the foundations of mathematics. Ancient and modern solutions are well known. Not so well known, however, are the ingenious and perceptive answers involving discussions of sophisticated concepts of infinity and continuity which medieval scholars gave to these problems. It is these little known developments which Professor Murdoch is examining. He will investigate the late medieval treatment of the notions of infinity and continuity and the various problems that were then seen as intimately involved with these notions and with their interaction with other aspects of medieval science and philosophy. The results will be two fold. First, Professor Murdoch will provide an essentially topical history of the medieval discussions of the problems surrounding the infinite and the continuous with an in-depth treatment of the context of these medieval discussions and an intensive analysis of the various medieval topics and aspects of infinity and continuity themselves. Secondly, he will prepare a number of separate articles on each of the major individuals who contributed to these discussions. These articles will locate the relevant examinations within the structure of a single work and within the overall thought of the author of these individual works. This analysis will greatly expand our understanding of the development of these vexing issues of infinity and continuity and will greatly inform contemporary discussions.

National Science Foundation (NSF)
Division of Biological Infrastructure (DBI)
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Alicia Armstrong
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Harvard University
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