Hellman and Shapiro explore the development of the idea of the continuous, from the Aristotelian view that a true continuum cannot be composed of points to the now standard, entirely punctiform frameworks for analysis and geometry. They then investigate the underlying metaphysical issues concerning the nature of space or space-time.

• 1: The Old Orthodoxy (Aristotle) vs the New Orthodoxy (Dedekind-Cantor)


• 2: The classical continuum without points


• 3: Aristotelian and Predicative Continua


• 4: Real numbers on an Aristotelian continuum


• 5: Regions-based Two Dimensional Continua: The Euclidean Case


• 6: Non-Euclidean Extensions


• 7: The matter of points


• 8: Scorecard

Geoffrey Hellman received his BA and PhD from Harvard (1973). Having published widely in analytic philosophy and philosophy of science, he has, since the 1980s, concentrated on philosophy of quantum mechanics and philosophy and foundations of mathematics. Following the lead of his adviser, Hilary Putnam, Hellman has developed modal-structural interpretations of mathematical theories, including number theory, analysis, and set theory. He has also worked on predicative foundations of arithmetic (with Solomon Feferman) and pluralism in mathematics (with J.L. Bell). In 2007 he was elected as a fellow of the American Academy of Arts and Sciences.
Stewart Shapiro received an MA in mathematics in 1975, and a PhD in philosophy in 1978, both from the State University of New York at Buffalo. He is currently the O'Donnell Professor of Philosophy at The Ohio State University, and he serves as Distinguished Visiting Professor at the University of Connecticut, and as Professorial Fellow at the University of Oslo. He has contributed to the philosophy of mathematics, philosophy of language, logic, and philosophy of logic, publishing monographs on higher-order logic, structuralism, vagueness, and pluralism in logic.