Paraconsistent Logics from a Philosophical Point of View
Keywords:
Logic, paraconsistency, explosion, law of non-contradiction, dialetheismAbstract
This article begins with a general and abstract definition of logic and, particularly, of paraconsistent logics, to establish a common ground for the discussion. Briefly stating, these kinds of logics have the property of being non-explosive, that is, it is not possible to infer any conclusion from contradictories premises. Using these definitions, it is possible to analyze some of the philosophical aspects of paraconsistent logics, in particular, the relation between the notion of explosion and the law of non-contradiction, as well as the syntactic/semantic possibility and, above all, the metaphysical possibility of paraconsistent logics. I further analyze a stronger position towards paraconsistency, namely: the claim that there are true contradictions. This articles concludes with some possible critiques to paraconsistent logics – and their refutations as well –, and pose some open questions for further work.References
HORN, L. R. Contradiction. In: The Stanford Encyclopedia of Philosophy (Winter 2010 Edition). Available in: http://plato.stanford.edu/entries/contra diction. Date of access: 30/01/12.
MORTENSEEN, C. Inconsistent Mathematics. Dordrecht: Kluwer Academic Publishers, 1995.
PRIEST, G. Paraconsistency and Dialetheism. In: GABBAY, D., WOODS, J. (eds.), Handbook of the History of Logic: The Many Valued and Nonmonotonic Turn in Logic, Vol. 8. Oxford: Elsevier, 2007.
______. Paraconsistent Logic. In: GABBAY, D., GUENTHNER, F. (eds.), Handbook of philosophical logic, vol. 6. Dordrecht: Kluwer Academic Publishers, 2002.
______. The logic of paradox, Journal of Philosophical Logic 1979.
PRIEST, G.; BERTO, F. “Dialeteísmo”, The Stanford Encyclopedia of Philosophy (Summer, 2010 Edition). Available in http://plato.stanford.edu/en tries/dialetheism. Date of access: 30/01/12.
PRIEST, G.; TANAKA, K. “Paraconsistent Logic”, The Stanford Encyclopedia of Philosophy (Summer, 2009 Edition). Available in: http://plato.stanford.edu/ entries/logic-paraconsistent. Date of acess: 30/01/12.
SAINSBURY, R. M. Paradoxes. Third Edition. Cambridge: Cambridge University Press, 2009.
