Vol. 32 No. 1 (2012)
Symposium

Anti-Realism and Infinitary Proofs

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  • Diego Tajer
Diego Tajer
Universidad de Buenos Aires / CONICET
DOI: https://doi.org/10.36446/af.2012.108

Published 2012-05-01

Keywords

  • Anti-realism,
  • Realism,
  • Infinitary logic
  • Anti-realismo,
  • Realismo,
  • Lógica infinitaria
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Abstract

In the discussion about Yablo’s Paradox, a debated topic is the status of infinitary proofs. It is usually considered that, although a realist could (with some effort) accept them, an anti-realist could not do it at all. In this paper I will argue that there are plausible reasons for an anti-realist to accept infinitary proofs and rules of inference.

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References

  1. Beall, JC. (2001), ‘Is Yablo’s paradox non circular?’, Analysis, 61, pp. 176-187.
  2. Bringsjord, S. and van Heuveln, B. (2003), ‘The ‘mental eye’ defense of an infinitized version of Yablo’s paradox’, Analysis, 63, pp. 61-70.
  3. Brouwer, l. (1928), 'Mathematics, science and language', in Ewald, W. (1996), From Kant to Hilbert, vol. 2, Oxford University Press, pp.1170-1785.
  4. Cook, R. (forthcoming), Yablo’s Paradox: An Essay on Circularity, Oxford, Oxford University Press.
  5. Dummett, M. (1975), 'Wang’s Paradox’, Synthese, 30, pp. 301-324.
  6. Hilbert, D. (1931), ‘The grounding of elementary number theory’, in Ewald, W. (1996), From Kant to Hilbert, vol. 2, Oxford UniversityPress, pp. 1148-1157.
  7. Ignjatovic, A. (1992), ‘Hilbert’s program and the omega-rule’, Journal of Symbolic Logic, 59 (1), pp. 322-343.
  8. Ketland, J. (2005), ‘Some more curious inferences’, Analysis, 65, pp 18-24.
  9. Moore, A. (1990), ‘A problem for intuitionism: The apparent possibility of performing infinitely many tasks in a finite time’, Proceedings of the Aristotelian Society, 90, pp. 17-34.
  10. Sorensen, R. (1998), ‘Yablo’s paradox and kindred infinite liars’, Mind, 107, pp. 137-155.
  11. Tarski, A. (1936), 'On the Concept of following logically', Stroińska, M. and Hitchcock, D. (trads.), History and Philosophy of Logic, 2002, 23, pp. 155-196.
  12. Tennant, N. (1997), The taming of the true, Oxford, Oxford University Press.
  13. van Dantzig, D. (1956), ’Is 101010a finite number?’, Dialectica, 10, pp.273-277.
  14. Wittgenstein, l. (1964), Remarks on the Foundations of Mathematics, von Wright, G. H., Rhees, R. and anscombe, G. E. M. (eds), Anscombe, G. E. M. (trad.), Oxford, Blackwell.
  15. Wright, C. (1982), ‘Strict finitism’, Synthese, 51 (2), pp. 203-282.

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