Part I: The History
1. Early Greek Thought
2. Aristotle
3. Medieval and Renaissance Thought
4. The Calculus
5. The Rationalists and the Empiricists
6. Kant
7. Post-Kantian Metaphysics of the Infinite
8. The Mathematics of the Infinite, and the Impact of Cantor
9. Reactions
Part II: Infinity Assessed
10. Transfinite Mathematics
11. The Lowenheim–Skolem theorem
12. Gödel’s Theorem
13. Saying and Showing
14. Infinity Assessed. The History Reassessed
15. Human Finitude
Part III: Infinity Superseded
16. Infinity Reassessed. The History Reassessed Anew
17. Learning How to be Finite
Biography
A.W. Moore is Professor of Philosophy and Lecturer in Philosophy at the University of Oxford, UK, and Tutorial Fellow of St Hugh’s College, Oxford. He is joint editor, with Lucy O’Brien, of the journal Mind. In 2016 he wrote and presented the series A History of the Infinite on BBC Radio 4.
Praise for previous editions
'Moore provides a splendid guide through the intellectual history of this powerful and far-reaching idea ... [He] offers a fascinating consideration of the mystical aspects of infinity and the issues of human finitude and death ... very highly recommended for all readers.' - CHOICE
'Moore's book provides us with an instructive and authoritative overview of a topic of considerable philosophical importance.' - Roger Penrose, Times Literary Supplement
'Moore's book points to deep and unresolved issues in the philosophy of mathematics, and even deeper issues in general philosophy ... It deserves serious study by both mathematicians and philosophers.' - Thomas Tymoczko, Philosophia Mathematica
'[Moore's treatment of] the problems with which the history of thought about the infinite confronts us today ... shows that questions concerning the nature and existence of the infinite are still very much alive. [A] highly stimulating account of the nature of infinity and its bold defence of finitism.' - W. L. Craig, International Philosophical Quarterly
'In the last three thought-provoking chapters of his book Moore draws heavily, but creatively, on Kant and Wittgenstein. Moore presents an analysis and proposed resolution of the issues that are both stimulating and accessible.' - Mary Tiles, Times Higher Education Supplement
