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What does it mean to have visual intuition? Can we gain geometrical knowledge by using visual reasoning? And if we can, is it because we have a faculty of intuition? In After Euclid, Jesse Norman reexamines the ancient and long-disregarded concept of visual reasoning and reasserts its potential as a formidable tool in our ability to grasp various kinds of geometrical knowledge. The first detailed philosophical case study of its kind, this text is essential reading for scholars in the fields of mathematics and philosophy.

Table of 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 a Neo-Kantian View
9.  The Competing Logics of Prop. I.32
10.  The Epistemology of Euclid’s Argument
11.  Conclusions:  Value Restores
 
References
Index

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