The Philosophy Department and the Spetnagel Development Fund present Dr. Stewart Shapiro discussing “Potential Infinity: A Modal Account” on Sept. 26 at 4 p.m. in Scripps 111.
Shapiro is the O’Donnell Professor of Philosophy at Ohio State University. His lecture is part of the Ohio University History and Philosophy of Science Lecture Series.
Abstract: Beginning with Artistotle, almost every major philosopher and mathematician before the nineteenth century rejected the notion of the actual infinite. They all argued that the only sensible notion is that of potential infinity. The list includes some of the greatest mathematical minds ever. Due to Georg Cantor’s influence, the situation is almost the opposite nowadays (with some intuitionists as notable exceptions). The received view is that the notion of a merely potential infinity is dubious: it can only be understood if there is an actual infinity that underlies it. After a sketch of some of the history, our aim is to analyze the notion of potential infinity, in modal terms, and to assess its scientific merits.
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