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Logics of Formal Inconsistency

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Book cover Handbook of Philosophical Logic

Part of the book series: Handbook of Philosophical Logic ((HALO,volume 14))

In traditional logic, contradictoriness (the presence of contradictions in a theory or in a body of knowledge) and triviality (the fact that such a theory entails all possible consequences) are assumed inseparable, granted that negation is available. This is an effect of an ordinary logical feature known as ‘explosiveness’: According to it, from a contradiction ‘α and ¬α’ everything is derivable. Indeed, classical logic (and many other logics) equate ‘consistency’ with ‘freedom from contradictions’. Such logics forcibly fail to distinguish, thus, between contradictoriness and other forms of inconsistency. Paraconsistent logics are precisely the logics for which this assumption is challenged, by the rejection of the classical ‘consistency presupposition’.

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Authors
  1. Walter Carnielli
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  2. Marcelo E. Coniglio
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  3. João Marcos
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Editors and Affiliations

  1. King’s College, London, U.K

    D.M. Gabbay

  2. Centrum für Informations- und Sprachverarbeitung, Ludwig-Maximilians-Universität München, Germany

    F. Guenthner

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© 2007 Springer

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Carnielli, W., Coniglio, M.E., Marcos, J. (2007). Logics of Formal Inconsistency. In: Gabbay, D., Guenthner, F. (eds) Handbook of Philosophical Logic. Handbook of Philosophical Logic, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-6324-4_1

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