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Paraconsistency: Introduction

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Paraconsistency: Logic and Applications

Part of the book series: Logic, Epistemology, and the Unity of Science ((LEUS,volume 26))

Abstract

It is a natural view that our intellectual activities should not result in positing contradictory theories or claims: we ought to keep our theories and claims as consistent as possible. The rationale for this comes from the venerable Law of Non-Contradiction, to be found already in Aristotle’s Metaphysics, and which can be formulated by stating: for any truth-bearer A, it is impossible for both A and ¬A to be true.

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Notes

  1. 1.

    Dialetheism itself has a venerable tradition in the history of Western philosophy: Heraclitus and other pre-Socratic philosophers were arguably dialetheists, for instance; and so were Hegel and Marx, who placed the obtaining and overcoming (Aufhebung) of contradictions at the core of their ‘dialectical method’. For an introduction to dialetheism, see Berto and Priest (2008). A notable collection of essays on the Law of Non-Contradiction is Priest et al. (2004).

  2. 2.

    See Priest (2005), Chap. 7.

  3. 3.

    Trivialism finds, however, a recent, brilliant defence in Kabay (2010).

  4. 4.

    See Béziau (2000).

  5. 5.

    See Berto (2007) Chap. 5 and Priest and Tanaka (2009).

  6. 6.

    Even dialetheists accept this. See, for example, Priest (2005) Chap. 8. For paraconsistent belief revision, see Mares (2002) and Tanaka (2005).

  7. 7.

    For surveys, besides Priest and Tanaka (2009), see Priest (2002) and Brown (2002).

  8. 8.

    See Jaśkowski (1948).

  9. 9.

    See for instance Schotch and Jennings (1980).

  10. 10.

    For a general overview of adaptive logics, see Batens (2001).

  11. 11.

    A classic paper in this tradition is Da Costa (1974).

  12. 12.

    See Asenjo (1966).

  13. 13.

    See Priest (1979).

  14. 14.

    For Belnap’s logic, see Belnap (1977). The interpretation of the truth values of FDE in terms of sets of classical truth values has been suggested by Dunn (1976).

  15. 15.

    See Anderson and Belnap (1975) and Anderson et al. (1992).

  16. 16.

    For a general introduction to relevant logics, see Mares (2006) and, for a philosophical interpretation, Mares (2004). On non-normal or impossible worlds, see Berto (2009).

  17. 17.

    On substructural logics, see Restall (2000) and Paoli (2002).

  18. 18.

    For instance, Bohr’s atomic theory assumed that energy comes in discrete quanta, and also assumed Maxwell electromagnetic equations to make predictions on atomic behaviour. The two assumptions are inconsistent, but the theory was quite successful—and, more importantly, nobody would find intuitively acceptable that the theory entails that everything is true. On this story, see Brown (1993).

  19. 19.

    For instance, Priest (1997a) is a story centred on an inconsistent box which is both empty and not empty; the contradiction is only true in the fiction, of course, but if we bracketed the inconsistency we would miss the whole point of the narration. And intuitively, not everything happens in the story.

  20. 20.

    For an overview of applications of paraconsistency, see Priest and Routley (1989). Specifically on the metaphysics of change, see Priest (1987), Chaps. 11, 12 and 15.

  21. 21.

    See Brady (1989) for a proof of the non-triviality of paraconsistent set theory, and Brady (2006) for a general account.

  22. 22.

    See Meyer (1976), Friedman and Meyer (1992), Meyer and Mortensen (1984) and, for a general characterization, Priest (1997b) and Priest (2000).

  23. 23.

    Sub-valuational semantics have been proposed by Hyde (1997) and Varzi (1997).

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Authors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Koji Tanaka

  2. University of Aberdeen, Aberdeen, UK

    Francesco Berto

  3. Victoria University of Wellington, Wellington, New Zealand

    Edwin Mares

  4. University of Cagliari, Cagliari, Italy

    Francesco Paoli

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  1. Koji Tanaka
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  2. Francesco Berto
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  3. Edwin Mares
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  4. Francesco Paoli
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Correspondence to Koji Tanaka .

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Editors and Affiliations

  1. , Department of Philosophy, University of Auckland, Arts 2, 18 Symonds Street, Auckland, 1142, New Zealand

    Koji Tanaka

  2. , Department of Philosophy, University of Aberdeen, King's College, High Street, Aberdeen, AB24 3UB, United Kingdom

    Francesco Berto

  3. , Department of Philosophy, Victoria University of Wellington, Murphy 518, Kelburn Parade, Wellington, New Zealand

    Edwin Mares

  4. , Department of Education, University of Cagliari, Via Is Mirrionis 1, Cagliari, 09123, Italy

    Francesco Paoli

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Tanaka, K., Berto, F., Mares, E., Paoli, F. (2013). Paraconsistency: Introduction. In: Tanaka, K., Berto, F., Mares, E., Paoli, F. (eds) Paraconsistency: Logic and Applications. Logic, Epistemology, and the Unity of Science, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4438-7_1

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