An Essay on the Foundations of Geometry

Bertrand Russell

University Press, 1897 - Geometry - 201 pages

Contents

• INTRODUCTION: 1
• Metageometry has upset the first line of argument not: 5
• A SHORT HISTORY OF METAGEOMETRY: 7
• 17 The first work of this period that of Riemann invented: 14
• CHAPTER II: 54
• Modern Logic regards every judgment as both synthetic: 55
• He therefore unduly neglected the qualitative adjectives: 61
• A criticism of representative modern theories need not begin: 64
• And his definition of measurement applies only to space: 67
• And his assertion of the dependence of measurement on rigid: 74
• Geometry deals with an abstract matter whose physical: 80
• Projective Geometry does not deal with magnitude: 102
• Recent French speculation on the foundations of Geometry: 112
• applies to all spaces alike: 117
• The quadrilateral construction is essential to the projective: 123
• And are required for qualitative spatial comparison: 124
• What is meant by qualitative equivalence in Geometry? 129 119 Two pairs of points on one straight line or two pairs: 129
• of space: 133
• The conception of a form of externality: 134
• The resulting doctrine of extension will be for the moment hypothetical: 136
• And homogeneous: 137
• It must have a finite integral number of dimensions: 139
• Owing to its passivity and homogonoity: 140
• A onedimensional form alone would not suffice for ex porionoo: 141
• Since its elements would be immovably fixed in a series: 142
• Two positions have a rotation indopondont of other positions: 143
• Hence projective Geometry is wholly A prion: 146
• Section B the axioms of metrical geometry 141 Metrical Geometry is distinct from projective but has the same fundamental postulate: 147
• It introduces the new idea of motion and has three A priori axioms: 148
• Measurement requires a criterion of spatial equality: 149
• The denial of this axiom involves an action of empty space on things: 151
• There is a mathematically possible alternative to the axiom: 152
• Which however is logically and philosophically untenable: 163
• There can be only one such relation: 166
• Hence the axiom of distance also is a priori in a doable: 172
• But these three are necessary to the direct measurement: 178
• To prove that experience requires a form of externality I: 184

Bibliographic information

• Title: An Essay on the Foundations of Geometry
• Author: Bertrand Russell
• Publisher: University Press, 1897
• Original from: Harvard University
• Digitized: Jul 28, 2007
• Length: 201 pages