Paradoxes and Inconsistent Mathematics

Zach Weber (University of Otago, New Zealand)

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English

Cambridge University Press
04 April 2024

Philosophy: logic; Philosophy of mathematics; Mathematical logic

Logical paradoxes – like the Liar, Russell's, and the Sorites – are notorious. But in Paradoxes and Inconsistent Mathematics, it is argued that they are only the noisiest of many. 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. In doing so, Weber directly addresses a longstanding open question: how much standard mathematics can paraconsistency capture? The guiding focus is on a more basic question, of why there are paradoxes. Details underscore a simple philosophical claim: that paradoxes are found in the ordinary, and that is what makes them so extraordinary.

By: Zach Weber (University of Otago New Zealand)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Dimensions: Height: 244mm, Width: 170mm, Spine: 18mm
Weight: 584g
ISBN: 9781108995009
ISBN 10: 1108995004
Pages: 337
Publication Date: 04 April 2024
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Part I. What are the Paradoxes?: Introduction to an inconsistent world; 1. Paradoxes; or, 'here in the presence of an absurdity'; Part II. How to Face the Paradoxes?: 2. In search of a uniform solution; 3. Metatheory and naive theory; 4. Prolegomena to any future inconsistent mathematics. Part III. Where are the Paradoxes?: 5. Set theory; 6. Arithmetic; 7. Algebra; 8. Real analysis; 9. Topology. Part IV. Why Are there Paradoxes?: 10. Ordinary paradox.

Zach Weber is Associate Professor of Philosophy at the University of Otago, New Zealand.