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Toward a Clarification of Grünbaum's Conception of an Intrinsic Metric

Published online by Cambridge University Press:  14 March 2022

Gerald J. Massey
Gerald J. Massey*
Affiliation:
Michigan State University
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Abstract

Much of Grünbaum's work may be regarded as a careful development and systematic elaboration of the Riemann–Poincaré thesis of the conventionality of congruence, the thesis that the continuous manifolds of space, time, and space-time are intrinsically metrically amorphous, i.e. are devoid of intrinsic metrics. Therefore, to appreciate Grünbaum's philosophical contributions, one must have a clear understanding of what he means by an intrinsic metric. The second and fourth sections of this paper are exegetical; in them we try to piece together, from his sundry remarks about intrinsic metrics, what Grünbaum means by the term ‘intrinsic metric.’ We shall argue that, the customary carefulness and precision of Grünbaum's writings notwithstanding, there are residual unclarities and difficulties which beset his conception of an intrinsic metric. In the fifth section we shall propose an explication of Grünbaum's notion of an intrinsic metric which seems on the whole faithful to Grünbaum's intuitions and insights and which also seems capable of performing the philosophical services which his work demands of that notion. The third section is a digression on Zeno's metrical paradox of extension.

Type
A Panel Discussion of Grünbaum's Philosophy of Science
Information
Philosophy of Science , Volume 36 , Issue 4 , December 1969 , pp. 331 - 345
Copyright
Copyright © 1969 by The Philosophy of Science Association

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Footnotes

†

Professor Grünbaum's response to the Panel Discussants will appear in a future issue of this journal.

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