Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century


The seventeenth century saw dramatic advances in mathematical theory and practice. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, the rules of analytic geometry, geometry of indivisibles, arithmetic of infinites, and calculus were developed. Although many technical studies have been devoted to these innovations, Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the philosophy of mathematics of the period. Starting with the Renaissance debates on the certainty of mathematics, Mancosu leads the reader through the foundational issues raised by the emergence of these new mathematical techniques, including the influence of the Aristotelian conception of science in Cavalieri and Guldin, the foundational relevance of Descartes' Geometrie, the relation between geometrical and epistemological theories of the infinite, and the Leibnizian calculus and the opposition to infinitesimalist procedures. In the process Mancosu draws a sophisticated picture of the subtle dependencies between technical development and philosophical reflection in seventeenth century mathematics.


The present book is the result of several years' work in the history of the philosophy of mathematics in the seventeenth century. While doing research for it I have come into contact with several scholars whose help and encouragement it is a pleasure to acknowledge here. I began work on this subject while I was a graduate student at Stanford University. At that time I had the opportunity to talk a great deal with Wilbur Knorr, Nancy Cartwright, and Ezio Vailati. Ezio kindly agreed to my using a joint article in chapter 5 of this book. I also owe a great deal to my Ph.D. advisor, Solomon Feferman. Although we rarely spoke about the seventeenth century (we were too busy discussing theories of operations and classes) his point of view on the foundations of mathematics has greatly influenced my outlook on the subject. And that influence goes far beyond purely technical knowledge; Sol has been a model as a scholar and as a human being.

A great deal of the archival research for the book was made possible by a stipendiary junior research fellowship in the history and philosophy of science and mathematics at Wolfson College, Oxford. During those three years (1989-91) I had access to the treasures of the Bodleian Library. In addition to the joy of being at Oxford, I also experienced the wonderful friendship and intellectual support provided by Daniel Isaacson.

The book was completed in Germany thanks to an Alexander von Humboldt-Stiftung fellowship and a Morse fellowship (from Yale), which allowed me to take time off from my teaching duties at Yale University. During my stay at the Institut für Philosophie, Wissenschaftstheorie, Wissenschaftsund Technikgeschichte of the Technische Universität in Berlin, Eberhard Knobloch has been a most wonderful host and a critical reader of my work.

Other scholars have also helped me with the project or have invited me to give seminars. I will simply list them in alphabetical order, confident that they are aware of my gratitude even if I cannot express their merits individually: Ruth Barcan-Marcus, Philip Beeley, Patricia Blanchette, George Boolos, Fabio Bosinelli, Herbert Breger, Peter Cramer, Lisa Downing, Michael Dummett, Luciano Floridi, Sergio Galvan, Donald Gillies, Giulio Giorello, Anthony Grafton, Karsten Harries, Jonathan Lear, Ernan McMullin, Giuseppe Micheli, Siegmund Probst, Neil Ribe, Carlos Sá.

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