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Surfaces and Superposition

Field Notes on some Geometrical Excavations

Buildings appear to rest on top of the earth’s surface, yet the surface is actually permeated by the buildings’ foundations-out of view. If a foundation’s blueprints are unavailable, as in archaeology, excavation would be needed to discover what actually supports a specific building. Analogously, the fields of geometry and topology have easily observable concepts resting on the surface of theoretical underpinnings that have not been completely discovered, unearthed or understood. Moreover, geometrical and topological principles of superposition provide insight into probing the connections between accessible superstructures and their hidden underpinnings. This book develops and applies these insights broadly, from physics to mathematics to philosophy. Even analogies and abstractions can now be seen as foundational superpositions.

This book examines the dimensionality of surfaces, how superpositions can make stable frameworks, and gives a quasi-Leibnizian account of the relative `spaces’ that are defined by these frameworks. Concluding chapters deal with problems concerning the spatio-temporal frameworks of physical theories and implications for theories of visual geometry. The numerous illustrations, while surprisingly simple, are satisfyingly clear.

200 pages | 6 x 9 | © 2001

Lecture Notes

Philosophy: Logic and Philosophy of Language

Philosophy of Science

Table of Contents

Patrick Suppes
I: Preliminaries
1. Characteristics of the Approach
2. The Concrete Superficial
3. The Logic of Constructability
4. Remarks on Physical Abstraction
II: Surface Topologies
5. Overview
6. Points on Surfaces
7. Towards a Topology of Physical Surfaces
8. Boundaries
9. Surface Dimensionality
10. Aspects of a Platonic Account of Linearity
III: Superposition
11. The Method of Superposition and Its Problems
12. Phenomena and Topology of Superposition
13. Possible Superpositions
14. Rigidity
15. Rigid Frames and Their Spaces
IV: Miscellaneous Topics
16. Connections with Physical Theory
17. Surface Feature, Sense Datum, and Psychology
18. Objectives, Theses, and Objections

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