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The Constructible and the Intelligible in Newton's Philosophy of Geometry

Published online by Cambridge University Press:  01 January 2022

Mary Domski
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Abstract

In the preface to the Principia (1687) Newton famously states that “geometry is founded on mechanical practice.” Several commentators have taken this and similar remarks as an indication that Newton was firmly situated in the constructivist tradition of geometry that was prevalent in the seventeenth century. By drawing on a selection of Newton's unpublished texts, I hope to show the faults of such an interpretation. In these texts, Newton not only rejects the constructivism that took its birth in Descartes's Géométrie (1637); he also presents the science of geometry as being more powerful than his Principia remarks may lead us to believe.

Type
History of Philosophy of Science
Information
Philosophy of Science , Volume 70 , Issue 5: Proceedings of the 2002 Biennial Meeting of The Philosophy of Science Association. Part I: Contributed Papers , December 2003 , pp. 1114 - 1124
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

My thanks to Michael Friedman for very helpful comments on different versions of this paper.

References

Bos, Henk (1981), “On the Representation of Curves in Descartes's Géométrie”, On the Representation of Curves in Descartes's Géométrie 24:295–339.Google Scholar
Bos, Henk (1996), “Tradition and Modernity in Early Modern Mathematics: Viéte, Descartes and Fermat”, in Goldstein, Catherine, Gray, Jeremy, and Ritter, Jim (eds.), L'Europe mathématique: Histoires, mythes, identités. Paris: Éditions de la Maison des Sciences de l'Homme, 185–204.Google Scholar
Bos, Henk (2001), Redefining Geometrical Exactness: Descartes' Transformation of the Early Modern Concept of Construction. New York: Springer-Verlag.CrossRefGoogle Scholar
Cuomo, S. (2000), Pappus of Alexandria and the Mathematics of Late Antiquity. Cambridge: Cambridge University Press.Google Scholar
Dear, Peter (1995), Discipline and Experience: The Mathematical Way in the Scientific Revolution. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Descartes, René ([1637] 1925), The Geometry of René Descartes. Translated from the French and Latin by D. E. Smith and M. L. Latham (with a facsimile of the first edition, 1637). Chicago and London: Open Court Publishing Company.Google Scholar
Friedman, Michael (2000), “Geometry, Construction, and Intuition in Kant and His Successors”, in Sher, G. and Teiszen, R. (eds.), Between Logic and Intuition: Essays in Honor of Charles Parsons. Cambridge: Cambridge University Press, 186–218.CrossRefGoogle Scholar
Garrison, James (1987), “Newton and the Relation of Mathematics to Natural Philosophy”, Newton and the Relation of Mathematics to Natural Philosophy 48:609–627.Google Scholar
Guicciardini, Nicolò (2002), “Analysis and Synthesis in Newton's Mathematical Work”, in Cohen, I. Bernard and Smith, George E. (eds.), The Cambridge Companion to Newton. Cambridge: Cambridge University Press, 308–328.CrossRefGoogle Scholar
Heath, Thomas (1960), A History of Greek Mathematics in Two Volumes. London: Oxford University Press.Google Scholar
Jones, A. (1986), Pappus of Alexandria: Book 7 of the Collection in Two Parts. New York, Berlin, Heidelberg, and Tokyo: Springer-Verlag.CrossRefGoogle Scholar
Knorr, Wilbur (1985), The Ancient Tradition of Geometric Problems. Boston, Basel, and Stuttgart: Birkhaeuser.Google Scholar
Mahoney, Michael S. (1990), “Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late–Seventeenth Century”, in Lindberg, D. and Westman, R. (eds.), Reappraisals of the Scientific Revolution. Cambridge: Cambridge University Press, 461–491.Google Scholar
Molland, A. G. (1976), “Shifting the Foundations: Descartes's Transformation of Ancient Geometry”, Shifting the Foundations: Descartes's Transformation of Ancient Geometry 3:21–49.Google Scholar
Molland, A. G. (1991), “Implicit Versus Explicit Geometrical Methodologies: The Case of Construction”, in Rashed, R. (ed.), Mathématiques et philosophie de l'antiquité à l'age classique: Hommage à Jules Vuillemin. Paris: Éditions du Centre National de la Recherche Scientifique, 181–196.Google Scholar
Newton, Isaac (1967–1981), The Mathematical Papers of Isaac Newton. 8 vols. Translated and edited by D. T. Whiteside. Cambridge: Cambridge University Press.Google Scholar
Newton, Isaac (1999), Mathematical Principles of Natural Philosophy, 3d ed. Translated by I. Bernard Cohen and Anne Whitman. Berkeley: University of California Press.Google Scholar
Thomas, Ivor (1951), Selections Illustrating the History of Greek Mathematics. Translated by Thomas, Ivor, in 2 vols., Loeb Classical Library. Cambridge: Harvard University Press.Google Scholar
Whiteside, D. T. (1995), “Newton the Mathematician”, in Cohen, I. Bernard and Westfall, Richard S. (eds.), Newton: A Norton Critical Edition. New York and London: W. W. Norton and Company, 406–413. First published@@@@@ in Bechler, Z. (ed.), Contemporary Newtonian Research. Dordrecht: Reidel, 1982.Google Scholar