The Concepts of Infinity and Continuity
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{'SignBlockName': 'Alicia Armstrong', 'PO_EMAI': 'aarmstro@nsf.gov', 'PO_PHON': '7032924743'}
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.
{'FirstName': 'John', 'LastName': 'Murdoch', 'PI_MID_INIT': 'E', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'John E Murdoch', 'EmailAddress': 'murdoch@fas.harvard.edu', 'NSF_ID': '000339863', 'StartDate': '08/01/1987', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
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{'Code': '1353', 'Text': 'Hist & Philosophy of SET'}
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