A Certain Version of Preservationism

• Authors: Makaś Michał
• Languages of publication: EN

Abstracts

EN

A certain approach to paraconsistency was initiated by works of R. Jennings and P. Schotch. In their “Inference and necessity” [4] they proposed a notion of a level of inconsistency (incoherence) of a given set of premises. This level is a measure that assigns to a given set of premises X, the least number of elements of covers of X that consist of consistent subsets of X. The idea of the level of inconsistency allows to formulate a paraconsistent inference relation called by the authors forcing, while the ob- tained approach  preservationism. Similarly as classical inference relation is truth-preserving, the obtained inference relation is preserving the level of inconsistency. We will discuss some examples of inferences that are valid in the sense of Jennings-Schotch inference relation and rise some questions on them. Based on that we formulate an inference relation as an answer to the mentioned doubts. As regards forcing inference relation, the set of premises needed to de- rive a given conclusion can vary when changing covers from one to another. Our proposal is to stipulate to have some common set of relevant premises

Keywords

EN

preservationism; inconsistency; Jennings; Schotch; Canadian school of paraconsistency; incoherence; level of inconsistency

• Publisher: Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń)
• Journal: Logic and Logical Philosophy
• Year: 2017
• Volume: 26
• Issue: 1
• Pages: 63-77

Dates

published

2017-03-15

online

2017-08-30

Contributors

author

Makaś Michał

• Uniwersytet Mikołaja Kopernika (Nicolaus Copernicus University in Toruń), Department of Logic Faculty of Humanities

References

• Payette, G., and P. Schotch, “On preserving“, Logica Universalis, 1, 2 (2007): 295–310. DOI: 10.1007/s11787-007-0015-x
• Priest, G., “Paraconsistent logic”, Chapter 4, pages 287–393, in D. Gabbay and F. Guenthner (eds.), Handbook of Philosophical Logic (Second Edition), Vol. 6, Kluwer Academic Publishers, Dordrecht, 2002. DOI: 10.1007/978-94-017-0460-1_4
• Schotch, P., B. Brown, and R. Jennings (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic, University of Toronto Press, Toronto, 2009.
• Schotch, P., and R. Jennings, “Inference and necessity”, Journal of Philosophical Logic, 9, 3 (1980): 327–340. DOI: 10.1007/BF00248398
• Schotch, P., and R. Jennings, “On detonating”, pages 306–327 in G. Priest, R. Routley, and J. Norman (eds.), Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, München, 1989.

Identifiers

DOI

10.12775/LLP.2016.027