Zeno of Elea

by

John Palmer

• LAST REVIEWED: 10 March 2015
• LAST MODIFIED: 10 March 2015
• DOI: 10.1093/obo/9780195389661-0186

Introduction

Zeno of Elea (c. 490–post-450 BCE) is an early Greek philosopher famous for developing a set of ingenious paradoxes that challenge ordinary assumptions regarding plurality and motion. In Plato’s Parmenides, Zeno is made to endorse a description of his arguments as all aiming to show that there are not many things. Simplicius in his commentary on Aristotle’s Physics quotes one such argument and substantial portions of another. However, Zeno’s most famous paradoxes, reported and criticized by Aristotle in Physics 6, purport to show the incoherence of ordinary assumptions regarding the occurrence of motion rather than the existence of a plurality of things. In these paradoxes of motion, Zeno argued that it is impossible to traverse a stadium, that Achilles can never overtake the tortoise, that the moving arrow is actually at rest, and that a scenario involving bodies moving in opposite directions past one another shows that half the time is equal to its double. Because Aristotle’s reporting is often quite brief and comes amidst his own critical responses, reconstruction of Zeno’s original reasoning is challenging and controversial. A problem with some reconstructions is that, by trying to make Zeno’s arguments proof against Aristotle’s criticisms or by otherwise introducing notions he is unlikely to have employed, they produce arguments that are merely Zenonian rather than plausibly those of the historical Zeno. Zeno’s brilliance and stunning originality are nevertheless apparent. His paradoxes have had a lasting impact through the attempts, from Aristotle down to the present day, to respond to the problems they raise. They have spurred natural philosophers, mathematicians, and scientists to deploy ever more sophisticated tools and to develop more precise conceptions of space, time, motion, and material structure in order to respond to their challenges. We may never know just what led Zeno to develop his famous paradoxes. Because his paradoxes tend to problematize the application of quantitative conceptions to physical bodies and to extensions as ordinarily conceived, they may have originated in reflection upon Pythagorean efforts to apply mathematical notions to the natural world. While it is typically said that Zeno aimed to defend the paradoxical monism of his Eleatic mentor, Parmenides, the Platonic evidence on which this view has resided ultimately fails to support it. A more plausible view, going back to Aristotle, regards Zeno as an influential precursor of sophistic antilogic and eristic disputation whose paradoxical arguments were not driven by a specific doctrinal agenda.

General Overviews

The items in this section provide comprehensive overviews of what is known of Zeno and his paradoxes. The works may be consulted for an orientation to the evidence, the arguments, and the issues they raise before delving more deeply into particular problems and controversies. In his studies of the stadium and the arrow, Gregory Vlastos sets a new standard of analytic precision in the reconstruction of Zeno’s paradoxes that is reflected in Vlastos 1967, which remains worth consulting. Makin 1998 is similar in scope and style but has the advantage of having taken account of more-recent developments in scholarship. The fuller treatment in Barnes 1982 not only provides judicious reconstructions but also assesses responses to the major paradoxes from antiquity to the modern era. Kirk, et al. 1983, cited under Texts, Translations, and Commentaries, also provides a good overview along with its presentation of the Greek text of the source material. There are also several useful overviews online. Palmer 2012 presents the evidence for Zeno’s life and writings and for both the major and minor paradoxes followed by discussion of Zeno’s purposes. Less historically focused are the overviews in Huggett 2010 and Dowden 2013, both of which focus on modern mathematical resolutions of the paradoxes.

• Barnes, Jonathan. 1982. The Presocratic philosophers. 2d ed. London: Routledge & Kegan Paul.

  Chapters 12 and 13 on Zeno are among the best in this study of reason in early Greek philosophy. Barnes discusses all the extant arguments attributed to Zeno and concisely surveys lines of response to the major paradoxes from antiquity to the modern era.

• Dowden, Bradley. 2013. Zeno’s paradoxes. Internet encyclopedia of philosophy.

  An account of the paradoxes followed by review of their treatment from Aristotle to the modern era. The focus here is on the “standard solution,” based on calculus, the rest of standard real analysis, and classical mechanics, and various problems it raises.

• Huggett, Nick. 2010. Zeno’s paradoxes. In The Stanford encyclopedia of philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford Univ.

  Provides reconstructions of the paradoxes that take them from their commonsense formulations to their resolutions made possible by the resources of modern mathematics.

• Makin, Stephen. 1998. Zeno of Elea. In The Routledge encyclopedia of philosophy. Vol. 9. Edited by Edward Craig, 843–853. London and New York: Routledge.

  Provides solid reconstructions of the major paradoxes and briefly explores strategies for response.

• Palmer, John. 2012. Zeno of Elea. In the Stanford encyclopedia of philosophy. Edited by Edward N. Zalta. Stanford, CA: Stanford Univ.

  Surveys the evidence for Zeno’s life and writings, presents the primary evidence for the major and minor paradoxes with reconstructions of their logic, and discusses Zeno’s likely purposes in propounding the paradoxes.

• Vlastos, Gregory. 1967. Zeno of Elea. In The encyclopedia of philosophy. Vol. 8. Edited by Paul Edwards, 369–379. New York and London: Macmillan.

  Provides reconstructions and discussions of all the extant paradoxes that aim to isolate their more questionable premises, followed by a brief discussion of their influence. Reprinted in Gregory Vlastos, Studies in Greek Philosophy, Volume 1: The Presocratics, edited by Daniel W. Graham (Princeton, NJ: Princeton Univ. Press, 1993), pp. 241–263.