Logical Studies of Paraconsistent Reasoning in Science and Mathematics

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This volume features contributions from leading scholars across various schools within the research area of paraconsistency. The authors critically examine how contemporary paraconsistent logics can enhance our understanding of human reasoning in science and mathematics. They explore whether these logics can serve as the foundation for inconsistent yet valuable scientific and mathematical theories. The diversity of paraconsistent logics raises interrelated questions, including the desiderata a paraconsistent logic should fulfill, the potential for a universal approach to paraconsistent reasoning with axiomatic theories, and the structural similarities between reasoning about sets and truth. Additionally, the authors discuss the status of paraconsistent logic as a normative or descriptive discipline and identify which inconsistent but non-trivial axiomatic theories are best understood through various paraconsistent approaches. This work aims to provide a representative overview of the current philosophical debate on paraconsistency, generate innovative ideas for its future, and strengthen the philosophical foundation of paraconsistent logic by considering developments across different schools.