New Zeno and Actual Infinity
Casper Storm Hansen
.
DOI: 10.4236/ojpp.2011.12010   PDF   HTML     4,617 Downloads   7,384 Views   Citations

Abstract

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.

Share and Cite:

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

Conflicts of Interest

The authors declare no conflicts of interest.

References

[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

Copyright © 2021 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.