Paraconsistency in Mathematics

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.