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Leibniz and Topological Equivalence

Published online by Cambridge University Press:  13 April 2010

Graham Solomon
Graham Solomon
Affiliation:
Wilfrid Laurier University
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Extract

Did Leibniz invent or, if you prefer, discover topology with his analysis situs? Yes, urge Nicholas Rescher (1978, p. 70), George MacDonald Ross (1984, p. 29) and Ian Hacking (1984, p. 213). No, urge Hans Freudenthal (1954/1972), Benson Mates (1986, p. 240) and Michael Otte (1989, p. 24). James Alexander (1932/1967, p. 249), drawing a distinction between point set and combinatorial methods, cautiously remarked that combinatorial topology “is more nearly a development of Leibniz's original idea.” Less cautiously, Morris Kline (1972, p. 1163) remarked that “to the extent that he was at all clear, Leibniz envisioned what we now call combinatorial topology.” Louis Couturat (1961, p. 429), Rudolf Carnap (1922, p. 81) and Ernst Cassirer (1950, p. 49) proposed projective geometry as the realization of Leibniz's project. Dennis Martin (1983, p. 5) sees topology as a development from analysis situs. Javier Echeverria (1988, p. 218), reporting on his archival research, argues that Leibniz “successfully introduced very general geometrical notions that boil down to what is known today as topology.” And a good many others, for and against, might be cited.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 32 , Issue 4 , Fall 1993 , pp. 721 - 724
Copyright
Copyright © Canadian Philosophical Association 1993

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References

Alexander, J. W. 1967 “Some Problems in Topology.” Rpt. 1932. In Verhandlungen des Internationalen Mathematiker-Kongresses Zurich 1932, Band I. Nendeln, Liechtenstein: Kraus, pp. 249–57.Google Scholar
Arnol'd, V. I. 1990 Huygens and Barrow, Newton and Hooke. Translated by Primrose, Eric J. F.. Basel: Birkhauser.CrossRefGoogle Scholar
Carnap, R. 1922 Der Raum; ein Beitrag zur Wissenshaftslehre. Kantstudien Erganzunsheft Nr. 56. Berlin: Reuther und Reichard.Google Scholar
Cassirer, E. 1950 The Problem of Knowledge: Philosophy, Science, and History since Hegel. Translated by Woglom, W. H. and Hendel, C. W.. New Haven: Yale University Press.Google Scholar
Couturat, L. 1961 La Logique de Leibniz d'apres documents inedits. 1901. Rpt. Hildensheim: G. Olms.Google Scholar
Couturat, L. 1966 Opuscles et Fragments inedits de Leibniz. 1903. Rpt. Hildensheim: G. Olms.Google Scholar
Echeverrfa, J. 1988 “Geometrie et topologie chez Leibniz.”In Proceedings of the 5th International Leibniz Conference,Hanover, pp. 213–20.Google Scholar
Freudenthal, H. 1972 “Leibnitz und die Analysis Situs.” Rpt. 1954. Studia Leibnitiana 4 (1972): 61–69. Reprinted from Homénaje à Millas-Villicrosa, I. Barcelona: C.S.J.S., 1954, pp. 611–21.Google Scholar
Hacking, I. 1984 “Leibniz and Descartes: Proof and Eternal Truth.” In Philosophy Through Its Past. Edited by Honderich, T.. Harmondsworth: Penguin, pp. 211–24.Google Scholar
Kline, M. 1972 Mathematical Thought from Ancient to Modern Times. Oxford: Oxford University Press.Google Scholar
Loemker, L. 1969 G. W. Leibniz: Philosophical Papers and Letters, 2nd ed.Dordrecht: Reidel.Google Scholar
MacDonald Ross, G. 1984 Leibniz- Oxford: Oxford University Press.Google Scholar
Martin, D. J. 1983 “Leibniz's Conception of Analysis Situs and Its Relevance to the Problems of the Relationship between Mathematics and Philosophy.” Ph.D. dissertation, Atlanta, GA: Emory University.Google Scholar
Mates, B. 1986 The Philosophy of Leibniz. New York: Oxford University Press.Google Scholar
Otte, M. 1989 “The Ideas of Hermann Grassmann in the Context of the Mathematical and Philosophical Tradition since Leibniz.” Historia Mathematica, 16: 1–35.CrossRefGoogle Scholar
Rescher, N. 1978 “Some Observations on Leibniz's Theory of Space.” In L'Espacel Space, edited by Svilar, M. and Mercier, A.. Berne: Peter Lang, pp. 64–72.Google Scholar
Stillwell, J. 1989 Mathematics and Its History. New York: Springer Verlag.CrossRefGoogle Scholar
Weyl, H. 1939 The Classical Groups. Princeton: Princeton University Press.Google Scholar