Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice / Edition 1

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This book provides a reading of Kant's theory of the construction of mathematical concepts through a fully contextualised analysis. In this work the author argues that it is only through an understanding of the relevant eighteenth century mathematics textbooks, and the related mathematical practice, that the material and context necessary for a successful interpretation of Kant's philosophy can be provided.

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Product Details

  • ISBN-13: 9780415939553
  • Publisher: Taylor & Francis
  • Publication date: 9/2/2002
  • Series: Studies in Philosophy Ser.
  • Edition number: 1
  • Pages: 190
  • Product dimensions: 6.10 (w) x 9.10 (h) x 0.60 (d)

Meet the Author

Lisa Shabel is Assistant Professor of Philosophy at Oho State University.

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Table of Contents

Introduction 3
Pt. 1 Euclid: The Role of the Euclidean Diagram in the Elements
1.0 Euclid: An Introduction 9
1.1 Characterizing the Euclidean Diagram: Plane Geometry 11
1.2 Reading the Euclidean Diagram: Warranting Implicit Assumptions 21
1.3 Countering Common Objections to the Euclidean Method 28
1.4 Characterizing and Reading the Euclidean Diagram: the Arithmetic Books 34
1.5 The Role of the Euclidean Diagram in Indirect Proof: A Special Case of "Pre-Formal" Demonstration 36
1.6 Euclid: Conclusion 38
Pt. 2 Wolff: The Elementa and Early Modern Mathematical Practice
2.0 Wolff: An Introduction 41
2.1 Euclid's Elements in the Early Modern Period 44
2.2 Geometry and Arithmetic in Wolff's Elementa and Other Early Modern Textbooks 49
2.3 Algebra and Analysis in Wolff's Elementa: The Tools that Relate Arithmetic and Geometry in the Early Modern Period 62
2.4 Wolff: Conclusion 87
Pt. 3 Kant: Mathematics in the Critique of Pure Reason
3.0 Kant: An Introduction 91
3.1 Pure and Empirical Intuitions 93
3.2 The "Schematism" 109
3.3 Algebraic Cognition 115
3.4 Kant: Conclusion 131
Endnotes 135
References 169
Index 175
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