Share This Article:

New Zeno and Actual Infinity

Abstract Full-Text HTML Download Download as PDF (Size:115KB) PP. 57-60
DOI: 10.4236/ojpp.2011.12010    4,356 Downloads   7,032 Views   Citations


In 1964 José Benardete invented the “New Zeno Paradox” about an infinity of gods trying to prevent a traveller from reaching his destination. In this paper it is argued, contra Priest and Yablo, that the paradox must be resolved by rejecting the possibility of actual infinity. Further, it is shown that this paradox has the same logical form as Yablo’s Paradox. It is suggested that constructivism can serve as the basis of a common solution to New Zeno and the paradoxes of truth, and a constructivist interpretation of Kripke’s theory of truth is given.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Hansen, C. (2011). New Zeno and Actual Infinity. Open Journal of Philosophy, 1, 57-60. doi: 10.4236/ojpp.2011.12010.


[1] Beall, J. C. (ed.) (2007). Revenge of the Liar: New essays on the paradox. Oxford: Oxford University Press.
[2] Benardete, J. (1964). Infinity: An essay in metaphysics. Oxford: Clarendon Press.
[3] Brouwer, L. E. J. (1933). Willen, weten, spreken. Euclides, 9, 177-193. (Translated as “Will, knowledge and speech” in (van Stigt, 1990))
[4] Kripke, S. (1975). Outline of a theory of truth. The Journal of Philoso- phy, 72, 690-716. doi:10.2307/2024634
[5] Priest, G. (1999). On a version of one of Zeno’s paradoxes. Analysis, 59, 1-2. doi:10.1111/1467-8284.00139
[6] Priest, G. (2002). Beyond the limits of thought (2nd ed.). Oxford: Ox- ford University Press. doi:10.1093/acprof:oso/9780199254057.001.0001
[7] van Stigt, W. P. (1990). Brouwer's intuitionism. Amsterdam: North-Ho- lland.
[8] Yablo, S. (1993). Paradox without self-reference. Analysis, 53, 251-252. doi:10.2307/3328245
[9] Yablo, S. (2000). A reply to new Zeno. Analysis, 60, 148-151. doi:10.1111/1467-8284.00217

comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.