On a “most telling” argument for paraconsistent logic
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Priest and others have presented their “most telling” argument for paraconsistent logic: that only paraconsistent logics allow non-trivial inconsistent theories. This is a very prevalent argument; occurring as it does in the work of many relevant and more generally paraconsistent logicians. However this argument can be shown to be unsuccessful. There is a crucial ambiguity in the notion of non-triviality. Disambiguated the most telling reason for paraconsistent logics is either question-begging or mistaken. This highlights an important confusion about the role of logic in our development of our theories of the world. Does logic chart good reasoning or our commitments? We also consider another abductive argument for paraconsistent logics which also is shown to fail.
KeywordsPhilosophy of logic Classical logic Challenges to classical logic
Thanks are due to Aislinn Batstone, Wylie Breckenridge, John P. Burgess, Adam Dickerson, Lloyd Humberstone, Toby Meadows, Marcus Rossberg, Max Rabie, and Lionel Shapiro. I would also like to thank and acknowledge the comments of anonymous referees.
- Anderson, A. R., & Belnap, N. (1975). Entailment: The logic of relevance and necessity (Vol. 1). Princeton, NJ: Princeton University Press.Google Scholar
- Harman, G. (1986). Change in view. Cambridge, MA: MIT Press.Google Scholar
- Jaśkowski, S. (1948). Rachunek zdań dla systemów dedukcyjnych sprzecznych (S. Jaśkowski (1969), Trans.). Studia Societatis Scientiarum Torunensis (Section A), 1(5), 55–77.Google Scholar
- Milne, P. (2009). What is the normative role of logic? Proceedings of the Aristotelian Society Supplementary, LXXXIII, 269–298.Google Scholar
- Priest, G., & Tanaka, K. (1997). Paraconsistent logic. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy (Fall 1997 Edition). Retrieved from http://plato.stanford.edu/archives/fall1997/entries/logic-paraconsistent/.
- Priest, G., Tanaka, K. & Weber, Z. (2015). Paraconsistent logic. In E. N. Zalta (ed.), The Stanford encyclopedia of philosophy (Spring 2015 Edition). Retrieved from http://plato.stanford.edu/archives/spr2015/entries/logic-paraconsistent/.
- Routley, R., Plumwood, V., Meyer, R. K., & Brady, R. T. (1982). Relevant logics and their rivals. Atascedero, CA: Ridgeview.Google Scholar
- Sextus Empiricus. (1993). Outlines of Pyrrhonism. (R. G. Bury, Trans., Loeb editions, p. 283). London: W. Heinemann.Google Scholar