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Realism, Antirealism, and Paraconsistency

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Book cover The Realism-Antirealism Debate in the Age of Alternative Logics

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 23))

Abstract

The distinction between realism and anti-realism about some topic is often couched in terms of the question of whether classical or intuitionist logic is applicable to it. Is paraconsistent logic realist or anti-realist? In this paper it is shown that the answer depends on the paraconsistent logic in question. This is done by discussing logics with constructible negation.

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Notes

  1. 1.

    For a gentle introduction, see [11, chap. 8].

  2. 2.

    For an introduction to non-classical logics, see Priest [6, 9].

  3. 3.

    See [6, §6.3].

  4. 4.

    On all this, see [9, §9.7a].

  5. 5.

    This and other examples are discussed in [8, chap. 3] (esp. 3.5).

  6. 6.

    In N 4, which we shall meet in the next section, the inference in both directions fails. The fact that ¬ A is true at a world does not entail that A is not true there.

  7. 7.

    N 4 was first proposed by Almukdad and Nelson [1]. N 3 and N 4 are discussed in [13], and also in [9, §9.7a], where they are called L 3 and L 4.

  8. 8.

    The point is made in [4, chap. 1] and further discussed in [10, §2.II.i].

  9. 9.

    Rumfitt [12] argues for treating truth and falsity even-handedly, in the way required by N 3 and N 4. He does so by analysing falsity in terms of a primitive notion of rejection. This will do for N 3, but not for N 4, which would require one the be able to simultaneously accept and reject something.

  10. 10.

    This means that the logic is not closed under uniform substitution. Closure can be regained by dropping the heredity condition for propositional parameters. This produces a system almost identical to that of [5, chap. 6]. The only difference is in the properties of the accessability relation.

  11. 11.

    See [6, chaps. 7 and 8].

  12. 12.

    See [9, chap. 20].

  13. 13.

    For a survey of paraconsistent logics, see [7].

  14. 14.

    The * semantics for negation are very closely related to the relational semantics, and in simple cases are interdefinable with them. See [6, §9.6], and [9, §22.5]. One might therefore reasonably expect the considerations concerning the relational semantics to carry over to the * semantics. For one interpretation of the ternary relation in terms of information, and so broadly sympathetic to an anti-realist reading, see [2, chap. 3].

References

  1. Almukdad, A., and D. Nelson. 1984. “Constructible Falsity and Inexact Predicates.” Journal of Symbolic Logic 49:231–33.

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  2. Mares, E. 2004. Relevant Logic: A Philosophical Interpretation. Cambridge: Cambridge University Press.

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  3. Nelson, D. 1949. “Constructible Falsity.” Journal of Symbolic Logic 14:14–26.

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  5. Priest, G. 1987. In Contradiction. Dordrecht: Martinus Nijhoff; 2nd (extended) Edition, Oxford: Oxford University Press, 2006.

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  6. Priest, G. 2001. Introduction to Non-Classical Logic. Cambridge, MA: Cambridge University Press; revised as Part 1 of G. Priest, Introduction to Non-Classical Logic: From If to Is (Cambridge: Cambridge University Press, 2008).

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  7. Priest, G. 2002. “Paraconsistent Logic.” In Handbook of Philosophical Logic, edited by D. Gabbay and F. Guenthner (2nd Edition), vol. 6, 287–393. Dordrecht: Kluwer.

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  8. Priest, G. 2006. Doubt Truth to Be a Liar. Oxford: Oxford University Press.

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  9. Priest, G. 2008. Introduction to Non-Classical Logic: From If to Is. Cambridge: Cambridge University Press.

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  10. Priest, G., and R. Routley. 1989. “The Philosophical Significance and Inevitability of Paraconsistency.” In Paraconsistent Logic: Essays on the Inconsistent, edited by G. Priest, R. Routley, and J. Norman, ch. 18. Munich: Philosophia Verlag.

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Acknowledgments

Versions of this paper were given at the Universities of Melbourne, St Andrews, and Lille in the second half of 2007. I am grateful to the audiences in those places for their helpful comments.

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Authors and Affiliations

  1. Departments of Philosophy, University of Melbourne, Melbourne, VIC, Australia

    Graham Priest

  2. University of St Andrews, St Andrews, UK

    Graham Priest

  3. The Graduate Center, City University of New York, New York, NY, USA

    Graham Priest

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Correspondence to Graham Priest .

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Editors and Affiliations

  1. , UFR Philosophie/ UMR-STL: 8163, Université de Lille, B.P. 60149, Villeneuve d'Asque, 59653, France

    Shahid Rahman

  2. Centre for Logic & Philosophy of Sc, Philosophy & Moral Science Dept., Ghent University, Blandijnberg 2, Gent, 9000, Belgium

    Giuseppe Primiero

  3. , Département de philosophie, Université du Québec à Montréal, Succursale Centre-Ville 8888 C.P., Montreal, H3C 3P8, Canada

    Mathieu Marion

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Priest, G. (2012). Realism, Antirealism, and Paraconsistency. In: Rahman, S., Primiero, G., Marion, M. (eds) The Realism-Antirealism Debate in the Age of Alternative Logics. Logic, Epistemology, and the Unity of Science, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1923-1_10

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