In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. Toronto: University of Toronto Press. pp. 85-104 (2009)

Authors
Gillman Payette
University of British Columbia
Peter Schotch
Dalhousie University
Abstract
In this essay Gillman Payette and Peter Schotch present an account of the key notions of level and forcing in much greater generality than has been managed in any of the early publications. In terms of this level of generality the hoary notion that correct inference is truth-preserving is carefully examined and found wanting. The authors suggest that consistency preservation is a far more natural approach, and one that can, furthermore, characterize an inference relation. But an examination of the usual account of consistency reveals problems that, in general, can be corrected by means of an auxiliary notion of inference (forcing) which relies upon a kind of generalization of consistency, called level. Preservation of the latter is shown to be another of the properties which characterize a logic and forcing is shown to preserve it. The essay ends with a sketch of a result which locates forcing among all possible level-preserving inference relations.
Keywords preservationism  Philosophy of Logic  Logical Consequence
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DOI 10.3138/9781442688742-007
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The Inapplicability of (Selected) Paraconsistent Logics.Rafal Urbaniak & Paweł Siniło - 2014 - Journal of Applied Non-Classical Logics 24 (4):368-383.

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Similar books and articles

On Preserving.Gillman Payette & Peter K. Schotch - 2007 - Logica Universalis 1 (2):295-310.
7. Preserving Logical Structure.Gillman Payette - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. Toronto: University of Toronto Press. pp. 105-144.
2. Paraconsistency: Who Needs It?Peter Schotch & Ray Jennings - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press. pp. 17-32.
9. Forcing and Practical Inference.Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press. pp. 161-174.
Contents.Raymond Jennings, Bryson Brown & Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press.
Frontmatter.Raymond Jennings, Bryson Brown & Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press.
Contributors.Raymond Jennings, Bryson Brown & Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press. pp. 203-203.
Nomenclature.Raymond Jennings, Bryson Brown & Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press. pp. 189-194.
Acknowledgments.Raymond Jennings, Bryson Brown & Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press.
References.Raymond Jennings, Bryson Brown & Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press. pp. 195-198.
Index.Raymond Jennings, Bryson Brown & Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press. pp. 199-202.
1. Introduction to the Essays.Peter Schotch - 2009 - In Raymond Jennings, Bryson Brown & Peter Schotch (eds.), On Preserving: Essays on Preservationism and Paraconsistent Logic. University of Toronto Press. pp. 1-16.

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