Logical Studies of Paraconsistent Reasoning in Science and Mathematics

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This volume features contributions from leading scholars in the field of paraconsistency, exploring how contemporary paraconsistent logics enhance our understanding of human reasoning in science and mathematics. The authors critically examine whether these logics can serve as foundational frameworks for inconsistent yet useful scientific and mathematical theories. They address various interrelated questions, such as the essential criteria a paraconsistent logic must meet, 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, descriptive, or hybrid discipline, and identify which inconsistent but non-trivial axiomatic theories are best understood through specific paraconsistent approaches. By presenting diverse perspectives, this work aims to (i) provide a comprehensive overview of the current philosophical discourse on paraconsistency, (ii) generate innovative ideas for its future, and (iii) strengthen the philosophical foundations of paraconsistent logic, reflecting developments across various schools of thought.