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Logic and Logical Philosophy

A Certain Version of Preservationism
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A Certain Version of Preservationism

Authors

  • Michał Makaś Nicolaus Copernicus University in Toruń

DOI:

https://doi.org/10.12775/LLP.2016.027

Keywords

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

Abstract

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 obtained 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 derive 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.

Author Biography

Michał Makaś, Nicolaus Copernicus University in Toruń

Department of Logic

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.

Logic and Logical Philosophy

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Published

2016-08-30

How to Cite

1.
MAKAŚ, Michał. A Certain Version of Preservationism. Logic and Logical Philosophy. Online. 30 August 2016. Vol. 26, no. 1, pp. 63-77. [Accessed 4 July 2025]. DOI 10.12775/LLP.2016.027.
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Vol. 26 No. 1 (2017): March

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Articles

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