There is More to Negation than Modality
- 460 Downloads
There is a relatively recent trend in treating negation as a modal operator. One such reason is that doing so provides a uniform semantics for the negations of a wide variety of logics and arguably speaks to a longstanding challenge of Quine put to non-classical logics. One might be tempted to draw the conclusion that negation is a modal operator, a claim Francesco Berto (Mind, 124(495), 761–793, 2015) defends at length in a recent paper. According to one such modal account, the negation of a sentence is true at a world x just in case all the worlds at which the sentence is true are incompatible with x. Incompatibility is taken to be the key notion in the account, and what minimal properties a negation has comes down to which minimal conditions incompatibility satisfies. Our aims in this paper are twofold. First, we wish to point out problems for the modal account that make us question its tenability on a fundamental level. Second, in its place we propose an alternative, non-modal, account of negation as a contradictory-forming operator that we argue is superior to, and more natural than, the modal account.
KeywordsNegation Compatibility Modality Contradictory
We would like to thank Brendan Balcerak Jackson, Francesco Berto, Thomas Müller, Heinrich Wansing, and an anonymous referee for helpful discussion. We would also like to thank the participants of the Munich Centre for Mathematical Philosophy (MCMP) Colloquium.
- 1.Batens, D. (1980). Paraconsistent extensional propositional logics. Logique et Analyse, 90–91, 195–234.Google Scholar
- 2.Batens, D., & De Clercq, K. (2004). A rich paraconsistent extension of full positive logic. Logique et Analyse, 185-188, 227–257.Google Scholar
- 3.Beall, J. (2009). Spandrels of truth. Oxford University Press.Google Scholar
- 4.Belnap, N. (1976). How a computer should think. In: G. Ryle (ed.) Contemporary aspects of philosophy, pp. 30-55. Oriel Press.Google Scholar
- 6.Béziau, J.Y. (2006). Paraconsistent logic! (a reply to Slater). Sorites, 17, 17–25.Google Scholar
- 8.Carnielli, W., Marcos, J., & de Amo, S. (2000). Formal inconsistency and evolutionary databases. Logic and Logical Philosophy, 8, 115–152.Google Scholar
- 11.De, M. (2011). Negation in context. Scotland: Ph.D. thesis, University of St Andrews.Google Scholar
- 13.De, M., & Omori, H. (2014). More on empirical negation. In: Advances in modal logic, vol. 10, pp. 114-133. College publications.Google Scholar
- 15.Dunn, J.M. (1999). A comparative study of various model-theoretic treatments of negation: A history of formal negation. In: H. Wansing (ed.) What is Negation?, pp. 23-51. Kluwer Academic Publishers.Google Scholar
- 19.Horn, L.R., & Wansing, H. (2015). Negation. In: E.N. Zalta (ed.) The Stanford Encyclopedia of Philosophy, Spring 2015 edn. http://plato.stanford.edu/entries/negation/.
- 20.Lenzen, W. (1996). Necessary conditions for negation operators. In: H. Wansing (ed.) Negation: A Notion in Focus, Perspective in Analytical Philosophy, pp. 3758. Walter de Gruyter.Google Scholar
- 28.Priest, G. (2006). Doubt truth to be a liar. Oxford University Press.Google Scholar
- 29.Priest, G. (2006). In Contradiction: A Study of the Transconsistent, 2nd edn. Oxford University Press.Google Scholar
- 30.Priest, G. (2008). Introduction to non-classical logics: From ifs to is, second edn. Cambridge University Press.Google Scholar
- 31.Quine, W.V. (1970). Philosophy of logic. Prentice Hall Inc.Google Scholar
- 32.Routley, R. (1980). Exploring Meinong’s jungle and beyond. McMaster University.Google Scholar
- 35.Wansing, H. (2006). Contradiction and contrariety: Priest on negation. In Malinowski, J., & Pietruszczak, A. (Eds.), Essays in Logic and Ontology (p. 8193). New York, NY: Rodopi.Google Scholar
- 36.Wansing, H. (2016). On split negation, strong negation, information, falsification, and verification. In: K. Bimbó (ed.) J. Michael Dunn on Information Based Logics, pp. 161-189. Springer.Google Scholar