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Strict Finitism and the Happy Sorites

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Abstract

Call an argument a ‘happy sorites’ if it is a sorites argument with true premises and a false conclusion. It is a striking fact that although most philosophers working on the sorites paradox find it at prima facie highly compelling that the premises of the sorites paradox are true and its conclusion false, few (if any) of the standard theories on the issue ultimately allow for happy sorites arguments. There is one philosophical view, however, that appears to allow for at least some happy sorites arguments: strict finitism in the philosophy of mathematics. My aim in this paper is to explore to what extent this appearance is accurate. As we shall see, this question is far from trivial. In particular, I will discuss two arguments that threaten to show that strict finitism cannot consistently accept happy sorites arguments, but I will argue that (given reasonable assumptions on strict finitistic logic) these arguments can ultimately be avoided, and the view can indeed allow for happy sorites arguments.

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References

  1. Boolos, G. (1984). Don’t eliminate cut. Journal of Philosophical Logic, 13, 373–378.

    Article  Google Scholar 

  2. Boolos, G. (1991). Zooming down the slippery slope. Nous, 25, 695–706.

    Article  Google Scholar 

  3. Buss, S. (1998a). An introduction to proof theory. In Buss, S. (ed.), Handbook of Proof Theory. Elsevier.

  4. Buss, S. (1998b). First-order proof theory of arithmetic. In Buss, S. (ed.), Handbook of Proof Theory, Elsevier.

  5. Dedekind, R. (1963) Essays on the Theory of Numbers, translated by Beman, W. Dover Publications.

  6. Dummett, M. (1975). Wang’s paradox. Synthese, 30, 301–324.

    Article  Google Scholar 

  7. Dummett, M. (1977). Elements of Intuitionism. Oxford University Press.

  8. Fara, D. (2001). Phenomenal Continua and the Sorites. Mind, 110, 905–935 (Originally published under ‘Delia Graff’).

    Article  Google Scholar 

  9. Frege, G. (1974). The Foundations of Arithmetic, translated by Austin, J.L. Oxford University Press.

  10. Magidor, O. (2007). Strict finitism refuted? Proceedings of the Aristotelian Society, CVII, 403–411.

    Google Scholar 

  11. Read, S., & Wright, C. (1985). Hairier than Putnam thought. Analysis, 45, 56–58.

    Article  Google Scholar 

  12. Tennant, N. (1997). The Taming of the True, Oxford University Press.

  13. Wright, C. (1982). Strict Finitism. Synthese, 51, 203–282.

    Article  Google Scholar 

Download references

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  1. University of Oxford (Balliol College), Oxford, OX1 3BJ, UK

    Ofra Magidor

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  1. Ofra Magidor
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Correspondence to Ofra Magidor.

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Magidor, O. Strict Finitism and the Happy Sorites. J Philos Logic 41, 471–491 (2012). https://doi.org/10.1007/s10992-011-9180-8

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  • DOI: https://doi.org/10.1007/s10992-011-9180-8

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