Contradictions arise in the everyday, from the smallest points to the widest boundaries. In this book, Zach Weber uses 'dialetheic paraconsistency' – a formal framework where some contradictions can be true without absurdity – as the basis for developing this idea rigorously, from mathematical foundations up.
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. This Element provides a selective introductory survey of this research program, distinguishing between moderate' and radical' approaches.