Paraconsistency in Mathematics
“Paraconsistency in Mathematics” by Zach Weber, published by Cambridge University Press on August 11, 2022, is a concise exploration of paraconsistent logic and its applications in mathematics. This 75-page work delves into the study of inconsistent theories, presenting a framework that allows for the coherent examination of abstract objects and structures where contradictions may exist without leading to incoherence.
Readers will find a selective introductory survey of the evolution of paraconsistent mathematics, which has emerged as a significant area of non-classical mathematics since its inception in the mid-20th century. The book distinguishes between moderate and radical approaches to this field, focusing on the philosophical issues and future challenges that arise within this research program. Through its examination of the intersection of science, philosophy, and mathematics, this work offers insights into the complexities of dealing with inconsistencies in mathematical theories.
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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.
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