The Price of True Contradictions About the World

  • Jonas R. Becker ArenhartEmail author
Part of the Trends in Logic book series (TREN, volume 47)


We examine an argument advanced by Newton C. A. da Costa according to which there may be true contradictions about the concrete world. This is perhaps one of the few arguments advancing this kind of thesis in full generality in the context of a scientifically-oriented philosophy. Roughly put, the argument holds that contradictions in the concrete world may be present where paradoxes require controversial solutions, solutions which in general are radically revisionary on much of the body of established science. We argue that the argument may be successfully challenged in the face of the actual practice of science; as a consequence, commitment to true contradictions about the world may be correctly dismissed as unnecessary, at least if the route to contradictions is the one advanced in the argument. We finish by highlighting a parallel between da Costa’s argument and another typical dialetheist argument by Graham Priest to the effect that paradoxes of self-reference are true contradictions.



We would like to thank two anonymous referees for their constructive criticisms and comments which helped to improve the paper.


  1. 1.
    Ardourel, V. 2015. A discrete solution for the paradox of Achilles and the tortoise. Synthese 192 (9): 2843–2861.CrossRefGoogle Scholar
  2. 2.
    Arenhart, J.R.B. 2012. Ontological frameworks for scientific theories. Foundations of Science 17: 339–356.CrossRefGoogle Scholar
  3. 3.
    Arenhart, J.R.B., and D. Krause. 2016. Contradiction, quantum mechanics, and the square of opposition. Logique et Analyse 59 (235): 301–315.Google Scholar
  4. 4.
    Barker, S., and M. Jago. 2012. Being positive about negative facts. Philosophy and Phenomenological research 85: 117–138.CrossRefGoogle Scholar
  5. 5.
    Beall, J. C. 2004. Introduction: At the intersection of truth and falsity. In The Law of Non-Contradiction: New Philosophical Essays, ed. G. Priest, J.C. Beall, and B. Armour-Garb, 1–19. Oxford: Clarendon Press.Google Scholar
  6. 6.
    Beall, J.C. 2009. Spandrels of truth. Oxford: Oxford University Press.CrossRefGoogle Scholar
  7. 7.
    Berto, F. 2012. How to rule out things with words: Strong paraconsistency and the algebra of exclusion. In New waves in philosophical logic, ed. G. Restall, G. K. Russell, 169–189. New York: Palgrave Macmillan.CrossRefGoogle Scholar
  8. 8.
    Bobenrieth, A. 2007. In Paraconsistency and the Consistency or Inconsistency of the World, ed. J.Y. Béziau, W. Carnielli, and D. Gabbay, Handbook of Paraconsistent Logic, 493–512. London: College Publications.Google Scholar
  9. 9.
    da Costa, N.C.A. 1997. Logiques Classiques et Non Classiques. Essai sur les fondements de la logique. Paris: Masson.Google Scholar
  10. 10.
    da Costa, N.C.A. 2002. Logic and Ontology. Principia 6 (2): 279–298.Google Scholar
  11. 11.
    da Costa, N.C.A., and C. de Ronde. 2013. The paraconsistent logic of superpositions. Foundations of Physics 43 (7): 845–858.CrossRefGoogle Scholar
  12. 12.
    Deguchi, Y., J.L. Garfield, and G. Priest. 2013. The contradictions are true – and it’s not out of this world! a response to Takashi Yagisawa. Philosophy East and West 63 (3): 370–372.CrossRefGoogle Scholar
  13. 13.
    de Ronde, C. 2015. Modality, potentiality, and contradiction in quantum mechanics. In New Directions in Paraconsistent Logic, ed. J.-Y. Béziau, M. Chakraborty, and S. Dutta, 249–265. New Delhi: Springer.CrossRefGoogle Scholar
  14. 14.
    Grim, P. 1991. The Incomplete Universe: Totality, Knowledge, and Truth. Cambridge: MIT Press.Google Scholar
  15. 15.
    Horsten, L. 2015. One hundred years of semantic paradox. Journal of Philosophical Logic 44: 681–695.CrossRefGoogle Scholar
  16. 16.
    Mares, E. D. 2004. Semantic dialetheism. In The Law of Non-Contradiction: New Philosophical Essays, ed. G. Priest, J.C. Beall, and B. Armour-Garb, 264–275. Oxford: Clarendon Press.Google Scholar
  17. 17.
    Michael, M. 2016. On a most telling argument for paraconsistent logic. Synthese 193 (10): 3347–3362.CrossRefGoogle Scholar
  18. 18.
    Morganti, M., and T.E. Tahko. 2017. Moderately naturalistic metaphysics. Synthese 194 (7): 2557–2580.CrossRefGoogle Scholar
  19. 19.
    Morrison, M. 2011. One phenomenon, many models: inconsistency and complementarity. Studies in History and Philosophy of Science 42: 342–351.CrossRefGoogle Scholar
  20. 20.
    Mosterín, J. 2011. The role of consistency in empirical science. Manuscrito: revista internacional de filosofia 34(1):293–305.CrossRefGoogle Scholar
  21. 21.
    Priest, G. 1998. What is so bad about contradictions? The Journal of Philosophy 95 (8): 410–426.CrossRefGoogle Scholar
  22. 22.
    Priest, G. 2006. In Contradiction: A Study of the Transconsistent, 2nd ed. Oxford: Oxford University Press.CrossRefGoogle Scholar
  23. 23.
    Priest, G. 2006. Doubt Truth to be a Liar. Oxford: Oxford University Press.Google Scholar
  24. 24.
    Priest, G. 2014. Contradictory concepts. In Logic, Reasoning, and Rationality, ed. E. Weber, D. Wouters, and J. Meheus, 197–215. Berlin: Springer.Google Scholar
  25. 25.
    Priest, G., and R. Routley. 1989. The philosophical significance and inevitability of paraconsistency. In Paraconsistent Logic: Essays on the Inconsistent, ed. G. Priest, R. Routley, and J. Norman, 483–537. Munich: Philosophia Verlag.Google Scholar
  26. 26.
    Tahko, T. 2009. The law of non-contradiction as a metaphysical principle. Australasian Journal of Logic 7: 32–47.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Federal University of Santa CatarinaFlorianópolisBrazil

Personalised recommendations