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After Euclid cover

After Euclid

Visual Reasoning & the Epistemology of Diagrams

Jesse Norman

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.

Contents

  • 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

ISBN (Paperback): 1575865106 (9781575865102)
ISBN (Cloth): 1575865092 (9781575865096)
ISBN (Electronic): 1575869055 (9781575869056)

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