Zeno’s Paradoxes and the Notion of Point
DOI:
https://doi.org/10.47850/RL.2022.3.4.33-39Keywords:
movement paradoxes, point-free geometry, pointless topology.Abstract
Zeno’s movement paradoxes stem from the notion of point as an object that has no size. The ambiguity of point as «a place taking no place» leads in some cases to questions having no clear answers. The article discusses solutions of such paradoxes in the framework of point-free geometry or pointless topology. These approaches consider point as a derived notion which doesn’t permit the paradoxical questions mentioned. The lesson we can draw from the movement paradoxes discussed in I. Berestov’s article is that infinity and limit notions similar to that of point are not always clear enough to base on them our formalization.
References
Берестов, И. В. (2022). Как Ахиллес с Гектором разминулся: затруднение в теории движения, разводящей прохождение открытого интервала и его замыкания. Respublica Literaria. Т. 3. № 4. С. 5-27. DOI: 10.47850/RL.2022.3.4.5-27
Berestov, I. V. (2022). How Achilles and Hector Missed Each Other: A Difficulty in the Theory of Motion That Distinguish the Passage of an Open Interval and the Passage of its Closure. Respublica Literaria. Vol. 3. no. 4. С. 5-27. DOI: 10.47850/RL.2022.3.4.5-27 (In Russ.)
Gerla, G. (1994). Pointless geometries. In Buekenhout, F. and Kantor, W. (eds.). Handbook of Incidence Geometry. North-Holland. pp. 1015-1031. [Online]. Available at: http://www.dipmat2.unisa.it/people/gerla/www/Down/point-free.pdf (Accessed: 21 October 2022).
Johnstone, P. T. (Jan. 1983). The Point of Pointless Topology. Bulletin of the American Mathematical Society (New Series). Vol. 8. no. 1. pp. 41-53. [Online]. Available at: http://www.ams.org/mathscinet-getitem?mr=682820 (Accessed: 21 October 2022).
Shapiro, S. and Hellman, G. (eds.) (2021). The History of Continua. Philosophical and Mathematical Perspectives. Oxford University Press.
Suárez, F. (1861) Disputationes metaphysicae. In Opera Omnia (ed. by C. Berton), vols. 25-26, Paris: Vivès.
Thomson, J. F. (Oct. 1954). Tasks and Super-Tasks. Analysis. Vol. 15. no. 1. pp. 1-13. DOI: 10.1093/analys/15.1.1.
Whitehead, A. N. (1919). An Inquiry Concerning the Principles of Natural Knowledge. Cambridge. Cambridge University Press. 216 p.
Whitehead, A. N. (1920). The Concept of Nature. Cambridge. Cambridge University Press. [Online]. Available at: http://www.gutenberg.org/files/18835/18835-h/18835-h.htm (Accessed: 21 October 2022).
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
https://oc.philosophy.nsc.ru/remote.php/webdav/%D0%94%D0%BE%D0%B3%D0%BE%D0%B2%D0%BE%D1%80%20%D1%81%20%D0%B0%D0%B2%D1%82%D0%BE%D1%80%D0%BE%D0%BC%20RL-%D0%BF%D1%80%D0%B0%D0%B2.doc
