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.
General
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