Logical Studies of Paraconsistent Reasoning in Science and Mathematics

✍ Scribed by Holger Andreas, Peter Verdée (eds.)

• Publisher: Springer
• Year: 2016
• Tongue: English
• Leaves: 221
• Series: Trends in logic 45
• Edition: 1st ed.
• Category: Library

✦ Synopsis

This book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives, they shed a new light on the question of whether paraconsistent logics can function as the underlying logics of inconsistent but useful scientific and mathematical theories. The great variety of paraconsistent logics gives rise to various, interrelated questions, such as what are the desiderata a paraconsistent logic should satisfy, is there prospect of a universal approach to paraconsistent reasoning with axiomatic theories, and to what extent is reasoning about sets structurally analogous to reasoning about truth. Furthermore, the authors consider paraconsistent logic’s status as either a normative or descriptive discipline (or one which falls in between) and which inconsistent but non-trivial axiomatic theories are well understood by which types of paraconsistent approaches. This volume addresses such questions from different perspectives in order to (i) obtain a representative overview of the state of the art in the philosophical debate on paraconsistency, (ii) come up with fresh ideas for the future of paraconsistency, and most importantly (iii) provide paraconsistent logic with a stronger philosophical foundation, taking into account the developments within the different schools of paraconsistency

✦ Table of Contents

Front Matter....Pages i-vi
Paraconsistent Reasoning in Science and Mathematics: Introduction....Pages 1-16
Adaptive Proofs for Networks of Partial Structures....Pages 17-45
Inconsistency in Ceteris Paribus Imagination....Pages 47-63
On the Preservation of Reliability....Pages 65-80
Prospects for Triviality....Pages 81-89
On Gluts in Mathematics and Science....Pages 91-101
Contradictoriness, Paraconsistent Negation and Non-intended Models of Classical Logic....Pages 103-109
From Paraconsistent Logic to Dialetheic Logic....Pages 111-134
Paradoxes of Expression....Pages 135-144
Dialetheism in the Structure of Phenomenal Time....Pages 145-157
Saving Proof from Paradox: Gödel’s Paradox and the Inconsistency of Informal Mathematics....Pages 159-173
On the Methodology of Paraconsistent Logic....Pages 175-204
Paraconsistent Computation and Dialetheic Machines....Pages 205-221

✦ Subjects

Logic, Symbolic and mathematical