Foundations of geometry and induction : containing Geometry in the sensible world and the logical problem of induction

This is Volume of IV eight on a series on the Philosophy of Logic and Mathematics. Originally published in 1930, this study contains sections on geometry in the sensible world and the logical problem of induction. Dedication Contents Preface • Bertrand Russell GEOMETRY IN THE PERCEIVED WORLD Introduction Part One: Geometric Order I. Pure Geometry Is an Exercise in Logic II. Formal Relationship of Various Systems of Geometry III. Material Consequences of This Relationship IV. Points and Volumes Part Two: Terms and Relations Introduction I. Spatio-Temporal Relations Independent of the Distinction Between Extension and Duration; The Notion of a Sense-Datum Temporal Relations and the Hypothesis of Durations (Durées) III. Global Resemblance IV. Qualitative Similarity and Local Similarity V. Relations of the Group of Local Similarities Part Three: Some Geometries of Sensation Introduction I. Succession and Global Resemblance (Data of any external sense) II. Succession and Global Resemblance (Kinesthetic data and data of any external sense) III. Introduction of Local Diversity in Sense Data IV. Relations of Position (Visual Data) V. Limitations of the Hypothesis of a Natural Spatial Symbolism VI. Relations of Position, Simultaneity, Qualitative Similarity, Local Similarity (Visual Data) VII. Reflections on the Preceding Universe VIII. Elimination of the Relations of Position IX. The Geometry of Perspectives Summary and Conclusion THE LOGICAL PROBLEM OF INDUCTION Contents Preface Introduction Preliminary Notions Hypothesis Concerning the Two Elementary Relations of a Fact to a Law Induction by Invalidation Induction by Confirmation Index to Geometry in the Sensible World Index to Logical Problem of Induction