Paraconsistency in Mathematics

An accessible survey of a programme in logic that allows mathematics to be inconsistent.

Zach Weber (Author)

9781108995412, Cambridge University Press

Paperback / softback, published 11 August 2022

75 pages
22.8 x 15.2 x 0.5 cm, 0.14 kg

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.

1. Invitation to Paraconsistency in Mathematics: Why and How?
2. Set Theory
3. Arithmetic
4. Calculus, Topology, and Geometry
5. Whither Paraconsistency in Mathematics?

Subject Areas: Philosophy of science [PDA], Philosophy of mathematics [PBB], Mathematics [PB], Mathematics & science [P], Philosophy [HP]