A Soundness Analysis of Zeno’s of Elea Dichotomy
- Authors: Berestov I.V.1
-
Affiliations:
- Institute of Philosophy and Law SB RAS
- Issue: Vol 2, No 4 (2021)
- Pages: 27-42
- Section: PHILOSOPHY
- URL: https://ogarev-online.ru/2713-3125/article/view/380073
- DOI: https://doi.org/10.47850/RL.2021.2.4.27-42
- ID: 380073
Cite item
Full Text
Abstract
We are studying three basic interpretations of the Dichotomy aporia, in which Zeno tries to prove the impossibility of movement. In all these interpretations, the key assumption is the dubious statement about the impossibility of performing an infinite sequence of actions in a finite time. However, weshow that in the two interpretations of the Dichotomy it is possible to get rid of the dubious key assumption, replacing it with the seemingly much more reliable assumption that covering the distance is representable as a sequence of displacements. Our approach is based on the thesis proved by P. Benacerraf that completing an infinite sequence of movements in an interpretation of the Dichotomy is not sufficient to arrive to the end of the distance.
About the authors
I. V. Berestov
Institute of Philosophy and Law SB RAS
Email: berestoviv@yandex.ru
ORCID iD: 0000-0003-0782-761X
Candidate of Philosophy, Senior Researcher Novosibirsk
References
- Берестов, И. В. (2021). Содержит ли современный анализ затруднений с зеноновскими последовательностями решение Дихотомии? Respublica Literaria. Т. 2. № 1. С. 28-36. doi: 10.47850/RL.2021.2.1.28-36. Berestov, I. V. (2021). Does Contemporary Analysis of Difficulties with Zeno Sequences Contain a Solution to the Dichotomy? Respublica Literaria. Vol. 2. no. 1. pp. 28-36. doi: 10.47850/RL.2021.2.1.28-36. (In Russ.)
- Берестов, И. В. (2020). Специфика преемственности концепций в элейской философской школе. Respublica Literaria. Т. 1. № 2. С. 28-51. doi: 10.47850/RL.2020.1.2. 28-51. Berestov, I. V. (2020). A Feature of the Conception Inheritance in the Eleatic School of Philosophy. Respublica Literaria. Vol. 1. no. 2. pp. 28-51. doi: 10.47850/RL.2020.1.2.28-51. (In Russ.)
- Фрагменты ранних греческих философов. Ч. 1. (1989). Ред. и пер. А. В. Лебедев. М.: Наука. Lebedev, A. V. (1989). (ed. and transl.). Fragments of Early Greek Philosophers. Part 1. Moscow. (In Russ.)
- Benacerraf, P. (2001). Tasks, Supertasks, and the Modern Eleatics. In Salmon, W. C. (ed.) Zeno’s Paradoxes. Indianapolis. Hacklett. pp. 103-129. (Originally published in 1962).
- Diels H., Kranz W. (Hrsg.). (1951-1952). Die Fragmente der Vorsokratiker (=DK). Bd I–II. Die sechste Auflage. Hildesheim. Weidmannsche Verlagsbuchhandlung.
- Hawthorne, J. (2000). Before-Effect and Zeno Causality. Noûs. Vol. 34. no. 4. pp. 622-633.
- Laks, A, Most, G.W. (eds. and transl.). (2016). Early Greek Philosophy. Vol. V. Part 2. Cambridge (Mass., USA). London (UK). Harvard University Press. 801 p. (Loeb Classical Library; Vol. 528)
- Lee, H. P. D. (ed. and transl.) (1936). Zeno of Elea. Text, with Translation and Notes (= Lee). Cambridge. Cambridge University Press. Pp. vi, 125. (Ser. Cambridge Classical Studies)
- Papa-Grimaldi, A. (1996). Why Mathematical Solutions of Zeno’s Paradoxes Miss the Point: Zeno’s One and Many Relation and Parmenides’ Prohibition. Review of Metaphysics. Vol. 50. no. 2. pp. 299-314.
- Thomson, J. F. (1954). Tasks and Super-Tasks. Analysis. Vol. 15. pp. 1-13.
Supplementary files
