Total Paraconsistency

Bruno Da Ré

Abstract


In the context of non-classical logics, many philosophers have been particularly interested in the paraconsistent logics. In addition to traditional definitions, in recent years, new ways of characterizing the notion of paraconsistency have been proposed. In all of these definitions the rule or the meta-rule of explosion is abandoned. In this article, I present those definitions and evaluate the role that the negation and the transitivity play in each of them. Finally, I propose a new definition of paraconsistency which I call total paraconsistency and show that the rule of weakening plays a crucial role in all of the characterizations of such a concept.


Keywords


negation; transitivity; weakening; paraconsistent logics; explosion

References


Anderson, A., Belnap, N. (1975). Entailment, Vol. I. Princeton: University Press. doi: 10.2307/2272137

Avron, A. (1991). Simple consequence relations. Information and Computation, 92(1): 105-139. doi: 10.1016/0890-5401(91)90023-U

Asenjo, F. G. (1966). A calculus of antinomies. Notre Dame Journal of Formal Logic, 7(1): 103-105. doi:10.1305/ndjfl/1093958482

Barrio, E. (2018). Models & Proofs: LFIs without a Canonical Interpretation. Principia, 22(1): 87-112 doi: 10.5007/1808-1711.2018v22n1p87

Barrio, E., Pailos, F., Szmuc, D. (2018). What is a paraconsistent logic? En W. Carnielli, J. Malinowski (eds.), Contradictions, from Consistency to Inconsistency, pp. 89-108. Cham: Springer. doi: 10.1007/978-3-319-98797-2_5

Barrio, E., Pailos, F., Szmuc, D. (2019). A Hierarchy of Classical and Paraconsistent Logics. Journal of Philosophical Logic. doi.org/10.1007/s10992-019-09513-z

Beall, J. (2011). Multiple-conclusion LP and default classicality. The Review of Symbolic Logic, 4(2): 326-336. doi:10.1017/S1755020311000074

Bobenrieth, A. (1998). Five philosophical problems related to paraconsistent logic. Logique et Analyse, 41(161-163): 21-30.

Carnielli, W., Coniglio, M. (2016). Paraconsistent logic: Consistency, contradiction and negation. Switzerland: Springer International Publishing. doi: 10.1007/978-3-319-33205-5

Cobreros, P., Égré, P., Ripley, D., Van Rooij, R. (2013). Reaching transparent truth. Mind, 122(488): 841-866. doi: 10.1093/mind/fzt110

da Costa, N. (1974). On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic, 15: 497-510. doi: 10.1305/ndjfl/1093891487

da Costa, N., Lewin, R. (1995). Lógica paraconsistente. En C. Alchourrón, J. Méndez, R. Orayen (eds.). Lógica. Enciclopedia IberoAmericana de Filosofía, Vol. 7, pp. 185-204. Madrid: Trotta.

Mares, E., Meyer, R. (2001). Relevant Logics. En Goble, Lou (ed.), The Blackwell Guide to Philosophical Logic. Oxford: Blackwell.

Mares, E. (2004). Relevant Logic: a Philosophical Interpretation. Cambridge: Cambridge University Press. doi:10.1017/CBO9780511520006

Paoli, F. (2002). Substructural logics: a primer. Dortrech: Springer Netherlands. doi: 10.1007/978-94-017-3179-9

Plumwood, V., Routley, R., Meyer, R., Brady, R. (1982). Relevant Logics and its Rivals, Volume I. Atascardero, CA: Ridgeview. doi: https://doi.org/10.2307/2275039

Priest, G. (1979). The logic of paradox. Journal of Philosophical logic, 8(1): 219–241. doi:10.1007/BF00258428

Priest, G. (2006). In Contradiction: A Study of the Transconsistent. Oxford: Oxford University Press. doi: 10.2307/2219835

Ripley, D. (2013). Revising up: Strengthening classical logic in the face of paradox. Philosophers Imprint, 13(5): 1-13. url: http://hdl.handle.net/2027/spo.3521354.0013.005

Routley, R., Meyer, R. (1976). Dialectical logic, classical logic, and the consistency of the world. Studies in East European Thought, 16(1): 1-25. doi: 10.1007/BF00832085

Urbas, I. (1990). Paraconsistency. Studies in Soviet Thought, 39(3-4): 343-354. doi: 10.1007/BF00838045




DOI: https://doi.org/10.22370/rhv2019iss13pp90-101

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