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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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