What is it to have visual intuition? Can we obtain geometrical knowledge by
using visual reasoning? And if we can, is this because we have a faculty of
intuition?
This book addresses these questions. It shows how mainstream philosophers
since Leibniz have wrongly ignored visual reasoning as a source of
knowledge; and how even basic geometrical reasoning that uses diagrams can be
explained without using any appeal to a faculty of intuition. In so doing,
this book helps to rehabilitate an ancient but long-disregarded tradition as
it presents the first detailed philosophical case study of that branch of
mathematical reasoning.
Jesse Norman is honorary research fellow in philosophy at University College
London.
- Preface
- 1 Introduction: An Old Kind of Reasoning
- 2 The Euclidean Presentation
- 3 The Framework of Alternatives
- 4 Crude Empiricism: Ross's Plato
- 5 Subtle Empiricism: Mill
- 6 Leibniz and the Denial of Epistemic Value
- 7 Kant: A Proto-Theory of Geometrical Reasoning
- 8 Making Room for Neo-Kantian View
- 9 The Competing Logics of Prop.I.32
- 10 The Epistemology of Euclid's Argument
- 11 Conclusions: Value Restored
- References
- Index
6/1/2006