Method versus calculus in Newton's criticisms to Descartes and Leibniz


  • Niccolò Guicciardini Universidad de Siena



17th Century, philosophy of mathematics, Newton, Descartes, Leibniz


In this paper I will consider Newton’s views on mathematical method. Newton never wrote extensively about this issue. However, in his polemic writings addressed against Descartes and Leibniz he expressed the idea that his method was superior to the ones proposed by the French and the German. Considering these writings can help us in understanding the role attributed to algebra and calculus in Newton’s mathematical thought.

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Author Biography

Niccolò Guicciardini, Universidad de Siena

Departamento de Filosofía y Ciencias Sociales
Universidad de Siena
Siena, Italia


BOS, H. J. M., Redefining Geometrical Exactness: Descartes ’Transformation of the Early Modern Concept of Construction. Springer-Verlag, New York, Berlin, Heidelberg, Tokyo, 2001.

COHEN, I. B. The Newtonian Revolution. Cambridge University Press, Cambridge, 1980.

DESCARTES, R. The Geometry of René Descartes with a Facsimile of the First Edition Ed. por D. E. Smith y M. L. Latham. Dover, NewYork, 1954.

GALUZZI, M., “I marginalia di Newton alla seconda edizione latina della Geometria di Descartes e i problemi ad essi collegati”, in: Belgioioso, G., Cimino, G., Costabel, P., Papuli, G. (eds.) Descartes: il Metodo e i Saggi. Istituto dell’Enciclopedia Italiana, Roma 1990, 387–417.

GUICCIARDINI, N. Reading the Principia: the Debate on Newton’s Mathematical Methods for Natural Philosophy from 1687 to 1736. Cambridge University Press, Cambridge, 1999.

GUICCIARDINI, N. Isaac Newton on mathematical certainty and method. MIT Press, Cambridge, Mass., 2009.

HALL, A. R. Philosophers at War: the Quarrel between Newton and Leibniz. Cambridge University Press, Cambridge, 1980.

JONES, Alexander (ed.). Pappus de Alejandria. Book 7 of the Collection. Sources in the History of Mathematics and the Physical Sciences. Springer-Verlag Berlin and Heidelberg GmbH & Co. K., 1986.

LEIBNIz, G.W. Leibnizens mathematische Schriften, 7 Vols. Olms, Hildesheim, 1971.

NEWTON, I. The Principia: Mathematical Principles of Natural Philosophy. Traducción de I. Bernard Cohen y Anne Whitman con la asistencia de Julia Budenz, precedida de A guide to Newton’s Principia por I. Bernard Cohen. University of California Press, Berkeley, Los Angeles, London, 1999.

NEWTON, I., Philosophiae Naturalis Principia Mathematica. The Third Edition (1726) with Variant Readings. Ed. Alexandre Koyré and I. Bernard Cohen, con la asistencia de Anne Whitman. Cambridge University Press, Cambridge, 1972.

NEWTON,I. The Correspondence of Isaac Newton, 7 Vols. Ed. by H. W. Turnbull et al. Cambridge University Press, Cambridge, 1959–1977.

NEWTON,I. The Mathematical Papers of Isaac Newton, 8 Vols. Ed. por Derek T. Whiteside. Cambridge University Press, Cambridge, London, New York, 1967–1981.

NEWTON, I., The Mathematical Works of Isaac Newton, 2 Vols. Ed. por Derek T. Whiteside. Johnson Reprint Corp., NewYork, London, 1964–1967.

PANZA, M. Newton et les Origines del’Analyse: 1664–1666.Blanchard, Paris 2005.

PASINI, E. Il Reale e l’Immaginario: la Fondazione del Calcolo In nitesimale nel Pensiero di Leibniz. Sonda, Torino, 1993.

SHAPIRO, A., Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton’sTheories of Colored Bodies and Fits of Easy Reflection. Cambridge University Press, Cambridge, 1993.

SMITH, G. E., “The methodology of the Principia”, in: Cohen, I. B. and Smith, George E. (eds.) The Cambridge Companion to Newton. Cambridge University Press, Cambridge, 2002, pp. 137–173.

STEIN, H. “Newton’s metaphysics”, in: Cohen, I. B. and Smith, George E. (eds.) The Cambridge Companion to Newton. Cambridge University Press, Cambridge, 2002, pp. 256–307.

WESTFALL, R. S., Never at Rest: a Biography of Isaac Newton. Cambridge University Press, Cambridge, 1980.



How to Cite

Guicciardini, N. (2009). Method versus calculus in Newton’s criticisms to Descartes and Leibniz. Estudios De Filosofía, (39), 9–38.



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