Paraconsistency in Mathematics
Zach Weber
Abstract
Paraconsistent logic makes it possible to study inconsistent theories in a coherent way. From its modern start in the mid-20th century, paraconsistency was intended for use in mathematics, providing a rigorous framework for describing abstract objects and structures where some contradictions are allowed, without collapse into incoherence. Over the past decades, this initiative has evolved into an area of non-classical mathematics known as inconsistent or paraconsistent mathematics. This Element provides a selective introductory survey of this research program, distinguishing between `moderate' and `radical' approaches. The emphasis is on philosophical issues and future challenges.
Topics & Concepts
Paraconsistent logicComputer scienceEpistemologyMathematics educationCalculus (dental)Algebra over a fieldMathematicsTheoretical computer sciencePure mathematicsPhilosophyHigher-order logicMedicineDentistryDescription logicComputability, Logic, AI AlgorithmsMathematical and Theoretical AnalysisQuantum Mechanics and Applications