Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-04T20:34:43.787Z Has data issue: false hasContentIssue false
  • English
  • Français

Leibniz on Continuity

Published online by Cambridge University Press:  31 January 2023

Richard T.W. Arthur
Richard T.W. Arthur*
Affiliation:
Middlebury College
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Leibniz never tired of stressing the fundamental importance of the concept of continuity for philosophy, nor was he shy of attributing major importance to his own struggle through “the labyrinth of the continuum” for the subsequent development of his whole system of thought. Unfortunately, however, his own thought on the subject is something of a labyrinth itself, and from a modern point of view many of his pronouncements are apt to seem blatantly contradictory.

Certain quotations seem to commit him unambiguously to atomism. Thus to de Voider he writes: “Matter is not continuous, but discrete…. The same holds for changes, which are not truly continuous.” (To de Voider, 11th October 1705: G.II.279).2

Type
Part II. History and Philosophy of Science
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1986 , Issue 1: Volume One: Contributed Papers 1986 , 1986 , pp. 105 - 115
Copyright
Copyright © Philosophy of Science Association 1986

Footnotes

1

The latter part of this paper is based on joint research on the relation between Leibniz’s work and Combinatorial Topology, which I have been undertaking with Graham Solomon (Philosophy, University of Western Ontario) over the last several months.

References

Alexander, James W. (1930). “The Combinatorial Theory of Complexes.” Annals of Mathematics , Series II, 31: 292–320.CrossRefGoogle Scholar
Alexander, James W. (1932). “Some Problems in Topology.” In Proceedings of the International Congress of Mathematicians r Series II. 4 th Congress--Zurich. Pages 249–257.Google Scholar
Bos, H.J. (1971-5). “Differentials, Higher-Order Differentials and the Derivative iri the Leibnizian Calculus.” Archive for History of Exact Sciences 14: 1–90.CrossRefGoogle Scholar
Cauchy, Augustine. (1813). Journal de l’Ecole Polytechnique 9.Google Scholar
Descartes, René (1644). Principles of Philosophy. (As reprinted in Oeuvres de Descartes. Volume VIII. (eds.) Adams, Charles and Tannery, Paul. Paris: Libraire Philosophique J. Vrin, 1973.)Google Scholar
Drake, Stillman. (1974). Galileo Galilei: Two New Sciences. Madison: University of Wisconsin Press.Google Scholar
Gerhardt, C. (ed.). (1849-55). Leibnizens Mathematisohe Schriften. 7 vols. Berlin and Halle.Google Scholar
Gerhardt, C. (ed.). (1875-90). Die Philosophische Sohriften von Gottfried Wilhelm Leibniz. 7 vols. 1978 edition. Hildeheim, New York: Georg Olms Verlag.Google Scholar
Kline, Morris. (1972). Mathematical Thought from Ancient to Modern Times. New York: Oxford University Press.Google Scholar
Leibniz, Gottfried Wilhelm (1676). Pacidius Philalethi. (In Oppuscles et fragments inédits de Leibniz , (ed.) Louis Couturat. Paris: Presses Universitaires de France, 1903. Pages 594–627.)Google Scholar
Loemker, Leroy E. (1969). Gottfried Wilhelm Leibniz: Philosophical Papers and Letters. Dordrecht-Holland: D. Reidel.Google Scholar
Newman, M.H.A. (1962). “Geometrical Topology.” In Proceedings of the International Congress of Mathematicians—Stockholm. Pages 139–146.Google Scholar
Parkinson, G.H.R. (1973). Leibniz: Philosophical Writings. London: J.M. Dent & Sons Ltd.Google Scholar
Russell, Bertrand. (1900). A Critical Exposition of the Philosophy of Leibniz. Cambridge: Cambridge University Press.Google Scholar
Veblen, Oswald. (1925). “Remarks on the Foundation of Geometry.” Bulletin of the American Mathematical Society 31: 121–141.CrossRefGoogle Scholar