Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2025-01-05T19:46:43.203Z Has data issue: false hasContentIssue false
  • English
  • Français

Zeno's Metrical Paradox Revisited

Published online by Cambridge University Press:  01 April 2022

David M. Sherry
David M. Sherry*
Affiliation:
Department of Philosophy, Northern Arizona University
Get access Rights & Permissions [Opens in a new window]

Abstract

Professor Grünbaum's much-discussed refutation of Zeno's metrical paradox turns out to be ad hoc upon close examination of the relevant portion of measure theory. Although the modern theory of measure is able to defuse Zeno's reasoning, it is not capable of refuting Zeno in the sense of showing his error. I explain why the paradox is not refutable and argue that it is consequently more than a mere sophism.

Type
Research Article
Information
Philosophy of Science , Volume 55 , Issue 1 , March 1988 , pp. 58 - 73
Copyright
Copyright © 1988 by the Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

I owe thanks to John Hagood for discussions of measure theory which helped me to avoid a number of infelicities.

References

REFERENCES

Aristotle, (1941), The Basic Works of Aristotle. Edited by McKeon, R. New York: Macmillan.Google Scholar
Grünbaum, A. (1952), “A Consistent Conception of the Extended Linear Continuum as an Aggregate of Unextended Elements”, Philosophy of Science 19: 288–306.CrossRefGoogle Scholar
Grünbaum, A. (1968), Modern Science and Zeno's Paradoxes. London: George Allen and Unwin.Google Scholar
Grünbaum, A. (1973), Philosophical Problems of Space and Time, 2nd ed. Dordrecht: Reidel.CrossRefGoogle Scholar
Massey, G. (1969), “Toward Clarification of Grünbaum's Conception of an Intrinsic Metric”, Philosophy of Science 36: 331–345.CrossRefGoogle Scholar
Normore, C. (1982), “Walter Burley on Continuity”, in Kretzmann, N. (ed.), Infinity and Continuity in Ancient and Medieval Thought. Ithaca and London: Cornell University Press, pp. 258–269.Google Scholar
Sherry, D. (1986), “On Instantaneous Velocity”, History of Philosophy Quarterly 3: 391–406.Google Scholar
Skyrms, B. (1983), “Zeno's Paradox of Measure”, in Cohen, R. and Laudan, L. (eds.), Physics, Philosophy, and Psychoanalysis, Dordrecht: Reidel, pp. 223–254.CrossRefGoogle Scholar