Paradoxes and Inconsistent Mathematics

Why are there paradoxes? This book uses paraconsistent logic to develop the mathematics to find out.

List of contents

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.

About the author

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

Summary

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.

Product details

• Authors: Zach Weber, Zach (University of Otago Weber
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Paperback / Softback
• Released: 31.03.2024
• EAN: 9781108995009
• ISBN: 978-1-108-99500-9
• No. of pages: 337
• Subjects: Humanities, art, music > Philosophy > General, dictionaries; Natural sciences, medicine, IT, technology > Mathematics > Basic principles; Non-fiction book > Philosophy, religion > Philosophy: general, reference works; PHILOSOPHY / Logic, MATHEMATICS / History & Philosophy, MATHEMATICS / Logic, Philosophy of Mathematics, Mathematical logic, Philosophy: logic