Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T07:22:20.810Z Has data issue: false hasContentIssue false

ABSOLUTE CONTRADICTION, DIALETHEISM, AND REVENGE

Published online by Cambridge University Press:  25 February 2014

FRANCESCO BERTO*
Affiliation:
Department of Philosophy, University of Amsterdam and Northern Institute of Philosophy, University of Aberdeen
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF AMSTERDAM OUDE TURFMARKT 141-147, 1012 GC AMSTERDAM, NETHERLANDS E-mail:[email protected].

Abstract

Is there a notion of contradiction—let us call it, for dramatic effect, “absolute”—making all contradictions, so understood, unacceptable also for dialetheists? It is argued in this paper that there is, and that spelling it out brings some theoretical benefits. First it gives us a foothold on undisputed ground in the methodologically difficult debate on dialetheism. Second, we can use it to express, without begging questions, the disagreement between dialetheists and their rivals on the nature of truth. Third, dialetheism has an operator allowing it, against the opinion of many critics, to rule things out and manifest disagreement: for unlike other proposed exclusion-expressing-devices (for instance, the entailment of triviality), the operator used to formulate the notion of absolute contradiction appears to be immune both from crippling expressive limitations and from revenge paradoxes—pending a rigorous nontriviality proof for a formal dialetheic theory including it.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

BIBLIOGRAPHY

Batens, D. (1990). Against global paraconsistency. Studies in Soviet Thought, 39, 209229.Google Scholar
Beall, J. C. (2008). Curry’s paradox. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy. Stanford, CA: CSLI. Available from: htto://plato.stanford.eduGoogle Scholar
Beall, J. C. (2009). Spandrels of Truth. Oxford, UK: Oxford University Press.Google Scholar
Beall, J. C., & Murzi, J. (forthcoming). Two flavors of Curry paradox. Journal of Philosophy.Google Scholar
Berto, F. (2007). How to Sell a Contradiction. The Logic and Metaphysics of Inconsistency, Studies in Logic 6, London: College Publications.Google Scholar
Berto, F. (2008). Adynaton and material exclusion. Australasian Journal of Philosophy, 86, 165190.Google Scholar
Berto, F., & Priest, G. (2013). Dialetheism. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy. Stanford, CA: CSLI. Available from: htto://plato.stanford.eduGoogle Scholar
Birkoff, G., & von Neumann, J. (1936). The logic of quantum mechanics. Annals of Mathematics, 37, 823843.Google Scholar
Brady, R. (1983). The simple consistency of set theory based on the logic CSQ. Notre Dame Journal of Formal Logic, 24, 431439.Google Scholar
Brady, R. (1989). The non-triviality of dialectical set theory. In Priest, G., Routley, R., and Norman, J., editors. Paraconsistent Logic. Essays on the Inconsistent, München, Germany: Philosophia Verlag, pp. 437471.Google Scholar
Dunn, J. M. (1996). Generalized ortho negation. In Wansing, H., editor. Negation. A Notion in Focus, Berlin-New York: De Gruyter, pp. 326.Google Scholar
Field, H. (2008). Saving Truth from Paradox. Oxford, UK: Oxford University Press.Google Scholar
Fine, K. (2009). The question of ontology. In Chalmers, D., Manley, D., and Wasserman, R., editors. Metametaphysics, Oxford, UK: Clarendon Press, pp. 157–77.Google Scholar
Fodor, J. A. (1975). The Language of Thought. Cambridge, MA: Harvard University Press.Google Scholar
Goldblatt, R. I. (1974). Semantic analysis of orthologic. Journal of Philosophical Logic, 3, 1935.Google Scholar
Kabay, P. (2010). On the Plenitude of Truth: A Defense of Trivialism. Saarbrücken, Germany: Lambert Academic Publishing.Google Scholar
Kripke, S. (1972). Naming and necessity. In Davidson, D., and Harman, G., editors. Semantics of Natural Language, Dordrecht: Reidel, pp. 253355 and 762–799, second edition, expanded ed., Oxford, UK: Blackwell, 1980.Google Scholar
Lewis, D. (1982). Logic for equivocators. Noûs, 16, 431441.Google Scholar
Lewis, D. (2004). Letters to Beall and Priest. In Priest, G., Beall, J. C., and Armour-Garb, B., editors. The Law of Non-Contradiction. New Philosophical Essays, Oxford, UK: Clarendon Press, pp. 176177.Google Scholar
Littman, G., & Simmons, K. (2004). A critique of dialetheism. In Priest, G., Beall, J. C., and Armour-Garb, B., editors. The Law of Non-Contradiction. New Philosophical Essays, Oxford, UK: Clarendon Press, pp. 314335.Google Scholar
Mares, E. (2004). Semantic dialetheism. In Priest, G., Beall, J. C., and Armour-Garb, B., editors. The Law of Non-Contradiction. New Philosophical Essays, Oxford, UK: Clarendon Press, pp. 264275.Google Scholar
Meyer, R. K., Routley, R., & Dunn, J. M. (1979). Curry’s paradox. Analysis, 39, 124128.Google Scholar
Parsons, T. (1984). Assertion, denial and the Liar paradox. Journal of Philosophical Logic, 13, 137152.Google Scholar
Parsons, T. (1990). True contradictions. Canadian Journal of Philosophy, 20, 335354.Google Scholar
Priest, G. (1987). In Contradiction: A Study of the Transconsistent. The Hague: Martinus Nijhoff, second edition, revised ed. Oxford, UK: Oxford University Press, 2006.Google Scholar
Priest, G. (1989). Reductio ad Absurdum et Modus Tollendo Ponens. In Priest, G., Routley, R., and Norman, J., editors. Paraconsistent Logic. Essays on the Inconsistent, München, Germany: Philosophia Verlag, pp. 613626.Google Scholar
Priest, G. (1991). Intensional paradoxes. Notre Dame Journal of Formal Logic, 32,193211.Google Scholar
Priest, G. (1998). What is so bad about contradictions? Journal of Philosophy, 8, 410426.Google Scholar
Priest, G. (2001). An Introduction to Non-Classical Logic. From If to Is. Cambridge: Cambridge University Press, second edition, Expanded edition, 2008.Google Scholar
Priest, G. (2002). Paraconsistent logic. In Gabbay, D. M., and Guenthner, F., editors. Handbook of Philosophical Logic, second edition, Vol. 6, Dordrecht, Netherlands: Kluwer, pp. 287393.Google Scholar
Priest, G. (2006). Doubt Truth to Be a Liar. Oxford, UK: Oxford University Press.Google Scholar
Priest, G. (2010). Hopes fade for saving truth. Philosophy, 85, 109140. Critical notice of Field (2008).Google Scholar
Quine, W. V. O. (1951). Mathematical Logic. New York, NY: Harper & Row.Google Scholar
Restall, G. (1993). How to be really contraction-free. Studia Logica, 52, 381391.Google Scholar
Restall, G. (1999). Negation in relevant logics. In Gabbay, D. M., and Wansing, H., editors. What Is Negation?, Dordrecht, Netherlands: Kluwer, pp. 5376.Google Scholar
Restall, G. (2000). An Introduction to Substructural Logics, New York, NY: Routledge.Google Scholar
Shapiro, S. (2004). Simple truth, contradiction, and consistency. In Priest, G., Beall, J. C., and Armour-Garb, B., editors. The Law of Non-Contradiction. New Philosophical Essays, Oxford, UK: Clarendon Press, pp. 336354.Google Scholar
Shapiro, L. (2011). Deflating logical consequence. The Philosophical Quarterly, 61, 320342.Google Scholar
Slaney, J. K. (1989). RWX is not Curry-paraconsistent. In Priest, G., Routley, R., and Norman, J., editors. Paraconsistent Logic. Essays on the Inconsistent, München, Germany: Philosophia Verlag, pp. 472481.Google Scholar
Slater, B. H. (1995). Paraconsistent logics? Journal of Philosophical Logic, 24, 451454.Google Scholar
Slater, B. H. (2007). Dialetheias are mental confusions. In Béziau, J.-Y., Carnielli, W., and Gabbay, D., editors. Handbook of Paraconsistency, London: College Publications, pp. 457466.Google Scholar
Smiley, T. (1993). Can contradictions be true? I. Proceedings of the Aristotelian Society, 67, 1734.Google Scholar
Sorensen, R. (2003). A Brief History of the Paradox. Philosophy and the Labyrinths of the Mind. Oxford, UK: Oxford University Press.Google Scholar
Tappenden, J. (1999). Negation, denial and language change in philosophical logic. In Gabbay, D. M., and Wansing, H., editors. What is Negation?, Dordrecht, Netherlands: Kluwer, pp. 261298.Google Scholar
Varzi, A. (2004). Conjunction and contradiction. In Beall, J. C., Priest, G., andArmour-Garb, B., editors. The Law of Non-Contradiction, Oxford, UK: Clarendon Press, 2004, pp. 93110.Google Scholar
Weber, Z. (2010). Extensionality and restriction in naïve set theory. Studia Logica, 94, 87104.Google Scholar
Weber, Z. (2012). Notes on inconsistent set theory. In Tanaka, K., Berto, F., Mares, E., and Paoli, F., editors. Paraconsistency: Logic and Applications, Dordrecht, Netherlands: Springer, pp. 313325.Google Scholar
Williamson, T. (2007). The Philosophy of Philosophy, Oxford, UK: Blackwell.Google Scholar
Zardini, E. (2011). Truth without contra(di)ction. Review of Symbolic Logic, 4, 498535.Google Scholar