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E-raamat: Paraconsistency: Logic and Applications

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A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.

Here is a comprehensive overview of paraconsistent logical systems, offering chapters contributed by many authorities in the field. The focus is on big picture ideas: different treatments of paradoxes, and application to mathematics, language and metaphysics.
1 Paraconsistency: Introduction
1(14)
Koji Tanaka
Francesco Berto
Edwin Mares
Francesco Paoli
Part I Logic
2 Making Sense of Paraconsistent Logic: The Nature of Logic, Classical Logic and Paraconsistent Logic
15(12)
Koji Tanaka
3 On Discourses Addressed by Infidel Logicians
27(16)
Walter Carnielli
Marcelo E. Coniglio
4 Information, Negation, and Paraconsistency
43(14)
Edwin D. Mares
5 Noisy vs. Merely Equivocal Logics
57(24)
Patrick Allo
6 Assertion, Denial and Non-classical Theories
81(20)
Greg Restall
7 New Arguments for Adaptive Logics as Unifying Frame for the Defeasible Handling of Inconsistency
101(22)
Diderik Batens
8 Consequence as Preservation: Some Refinements
123(18)
Bryson Brown
9 On Modal Logics Defining Jaskowski's D2-Consequence
141(22)
Marek Nasieniewski
Andrzej Pietruszczak
10 FDE: A Logic of Clutters
163(10)
R.E. Jennings
Y. Chen
11 A Paraconsistent and Substructural Conditional Logic
173(28)
Francesco Paoli
Part II Applications
12 An Approach to Human-Level Commonsense Reasoning
201(22)
Michael L. Anderson
Walid Gomaa
John Grant
Don Perlis
13 Distribution in the Logic of Meaning Containment and in Quantum Mechanics
223(34)
Ross T. Brady
Andrea Meinander
14 Wittgenstein on Incompleteness Makes Paraconsistent Sense
257(20)
Francesco Berto
15 Pluralism and "Bad" Mathematical Theories: Challenging our Prejudices
277(32)
Michele Friend
16 Arithmetic Starred
309(6)
Chris Mortensen
17 Notes on Inconsistent Set Theory
315(14)
Zach Weber
18 Sorting out the Sorites
329(20)
David Ripley
19 Are the Sorites and Liar Paradox of a Kind?
349(18)
Dominie Hyde
20 Vague Inclosures
367(12)
Graham Priest
Index 379