Palavras-chave: Paraconsistent logics. Logics of formal inconsistency. Philosophy of paraconsistency. Non-classical logics


In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order to philosophically justify paraconsistency there is no need to endorse dialetheism, the thesis that there are true contradictions. Furthermore, we show that mbC, a logic of formal inconsistency based on classical logic, may be enhanced in order to express the basic ideas of an intuitive interpretation of contradictions as conflicting evidence.


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Biografia do Autor

Walter Carnielli, State University of Campinas

Walter Alexandre Carnielli (Campinas, 11 de janeiro de 1952) é um matemático, lógico e filósofo brasileiro. É professor de lógica na Universidade Estadual de Campinas, onde foi bacharel mestre e doutor, em 1984, orientado por Newton da Costa. Posdoutorado naUniversidade da Califórnia em Berkeley, convidado por Leon Henkin.

Abílio Rodrigues, Federal University of Minas Gerais
Possui graduação em filosofia pela Universidade do Estado do Rio de Janeiro (2000), mestrado em filosofia pela Universidade do Estado do Rio de Janeiro (2002) e doutorado em filosofia pela Pontifícia Universidade Católica do Rio de Janeiro (2007), com estágio de doutoramento na Brown University, EUA. Desde fevereiro de 2009 é professor Adjunto da Universidade Federal de Minas Gerais. Suas áreas de interesse são lógica e filosofia da lógica (com ênfase em lógica intuicionista e paraconsistente), filosofia da linguagem e Frege. É membro da Sociedade Brasileira de Lógica e da Associação Latino-Americana de Filosofia Analítica


ARNAULD, A.; NICOLE, P. Logic or the Art of Thinking. Cambridge University Press, 1996.

ARISTOTLE. Metaphysics. The Complete Works of Aristotle, Oxford University Press, 1996.

BROUWER, L.E.J. “On the Foundations of Mathematics” 1907. Collected Works vol. I. (ed. A. Heyting), North-Holland Publishing Company, 1975.

CARNIELLI, W. “The Single-minded Pursuit of Consistency and its Weakness” in Studia Logica, v. 97, p. 81-100, 2011.

CARNIELLI, W.; CONIGLIO, M.; MARCOS, J. “Logics of Formal Inconsistency”. Handbook of Philosophical Logic, vol. 14, pp.15- 107, (eds.: D. Gabbay; F. Guenthner). Springer, 2007.

CARNIELLI, W.; MARCOS, J. “A Taxonomy of C-systems”. Paraconsistency: the logical way to inconsistency, Proceedings of the Second World Congress on Paraconsistency. New York: Marcel Dekker, 2002.

CHATEAUBRIAND, O. Logical forms vol. 1. Campinas: UNICAMP-CLE, 2001.

DA COSTA, N. “The philosophical import of paraconsistent logic”. Journal of Non-Classical Logics, number 1, pp. 1-19, 1982.

DA COSTA, N.; FRENCH, S. Science and Partial Truth. Oxford University Press, 2003.

FREGE, G. The Basic Laws of Arithmetic, 1893. Transl. M. Furth. University of California Press, 1964.

FREGE, G. “The Thought”, 1918. The Frege Reader. Oxford: Blackwell Publishers, 1997.

HEYTING, A. Intuitionism: an Introduction. London: North-Holland Publishing Company, 1956.

HUNTER, G. Metalogic. University of California Press, 1973.

NICKLES, T. ‘From Copernicus to Ptolemy: inconsistency and method’ in Inconsistency in Science (Ed. J. Meheus). Dordrecht: Springer, 2002.

POPPER, K. Conjectures and Refutations, New York: Harper, 1963.

PRIEST, G. In Contradiction. Oxford University Press, 2006.

PRIEST, G.; BERTO, F. “Dialetheism” in Stanford Encyclopedia of Philosophy. , 2013.

RAATIKAINEN, P. “Conceptions of Truth in Intuitionism”. History and Philosophy of Logic, 25: 131–145, 2004.

ROBBIN, J.W. Mathematical Logic: A First Course. New York: Dover, 1997.

VELLEMAN, D.J.; ALEXANDER GEORGE, A. Philosophies of Mathematics. Oxford: Blackwell Publishers, 2002.

Como Citar
Carnielli, W., & Rodrigues, A. (2015). TOWARDS A PHILOSOPHICAL UNDERSTANDING OF THE LOGICS OF FORMAL INCONSISTENCY. Manuscrito, 38(2), 155-184. Recuperado de