Medieval Finitism

Discussing various versions of two medieval arguments for the impossibility of infinity, this Element sheds light on early stages of the evolution of the notion of INFINITIES OF DIFFERENT SIZES. The first argument is called 'the Equality Argument' and relies on the premise that all infinities are equal. The second argument is called 'the Mapping Argument' and relies on the assumption that if one thing is mapped/ superposed upon another thing and neither exceeds the other, the two things are equal to each other. Although these arguments were initially proposed in the context of discussions against the possibility of infinities, they have played pivotal roles in the historical evolution of the notion of INFINITIES OF DIFFERENT SIZES.

List of contents

1. Introduction; 2. Definition and characteristics of infinity; 3. The equality argument; 4. The mapping argument; 5. Conclusion; List of abbreviations; List of ancient and medieval thinkers discussed in this element; References.

Summary

This Element explores medieval arguments for the impossibility of infinity, focusing on the early stages of the development of the notion of 'infinities of different sizes'. The Equality Argument and Mapping Argument, initially proposed in opposition to infinity, have played significant roles in the historical evolution of this concept.

Foreword

This Element explores early stages of evolution of the notion of 'infinities of different sizes' via  medieval arguments for finitism!

Product details

• Authors: Mohammad Saleh Zarepour, Mohammad Saleh (The University of Manche Zarepour
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.01.2025
• EAN: 9781009618434
• ISBN: 978-1-0-0961843-4
• No. of pages: 80
• Series: Elements in the Philosophy of Mathematics
• Subjects: Humanities, art, music > Philosophy; Non-fiction book > Philosophy, religion > Philosophy: general, reference works; PHILOSOPHY / General, Philosophy, Philosophy of Mathematics, Discrete Mathematics, Ancient Greek and Roman philosophy, Medieval Western philosophy