An essay on the foundations of geometry
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About This Book
Discover Bertrand Russell's enlightening perspectives on mathematics and philosophy, providing fresh insights into the connection between the two disciplines.Mathematics Philosophy Top Reads by Bertrand Introduction to Mathematical Philosophy/An Essay on the Foundations of Geometry by Bertrand Russell by Bertrand Delve into the intersection of mathematics and philosophy with Bertrand Russell's "Mathematics Philosophy Top Reads." This collection features two of Russell's seminal "Introduction to Mathematical Philosophy" and "An Essay on the Foundations of Geometry." These essays explore the ph...
Chapters (229)(click to expand)
- AN ESSAY ON THE FOUNDATIONS OF GEOMETRY
- PREFACE.
- TABLE OF CONTENTS.
- INTRODUCTION. OUR PROBLEM DEFINED BY ITS RELATIONS TO LOGIC, PSYCHOLOGY AND MATHEMATICS.
- FOOTNOTES:
- CHAPTER I. A SHORT HISTORY OF METAGEOMETRY.
- First Period.
- Second Period.
- Third Period.
- FOOTNOTES:
- CHAPTER II. CRITICAL ACCOUNT OF SOME PREVIOUS PHILOSOPHICAL THEORIES OF GEOMETRY.
- Kant.
- Riemann.
- Helmholtz.
- Erdmann.
- Lotze.
- Delbœuf.
- FOOTNOTES:
- CHAPTER III.
- Section A. THE AXIOMS OF PROJECTIVE GEOMETRY.
- Section B. THE AXIOMS OF METRICAL GEOMETRY.
- I. The Axiom of Free Mobility.
- II. The Axiom of Dimensions[163].
- III. The Axiom of Distance.
- FOOTNOTES:
- CHAPTER IV. PHILOSOPHICAL CONSEQUENCES.
- Conclusion.
- FOOTNOTES:
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