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 OJPP  Vol.1 No.2 , November 2011
New Zeno and Actual Infinity
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.
Cite this paper: nullHansen, C. (2011). New Zeno and Actual Infinity. Open Journal of Philosophy, 1, 57-60. doi: 10.4236/ojpp.2011.12010.
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

 
 
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