David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Oxford University Press (1996)
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, arithmatic 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.
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Citations of this work BETA
Paolo Mancosu (2009). Measuring the Size of Infinite Collections of Natural Numbers: Was Cantor's Theory of Infinite Number Inevitable? Review of Symbolic Logic 2 (4):612-646.
Eric Schliesser (2013). Newtonian Emanation, Spinozism, Measurement and the Baconian Origins of the Laws of Nature. Foundations of Science 18 (3):449-466.
Jeremy Avigad, Edward Dean & John Mumma (2009). A Formal System for Euclid's Elements. Review of Symbolic Logic 2 (4):700--768.
Willem R. de Jong & Arianna Betti (2010). The Classical Model of Science: A Millennia-Old Model of Scientific Rationality. Synthese 174 (2):185-203.
Kajsa Bråting & Johanna Pejlare (2008). Visualizations in Mathematics. Erkenntnis 68 (3):345 - 358.
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