Euclid's Heritage. Is Space Three-Dimensional?

Overview

The three spatial characteristics of length, height and depth are used in the same unreflective way by laymen, technicians and scientists alike to describe the forms, positions and measure of bodies and hollow bodies. But how do we know that the space we live in has just these three dimensions? The question has occupied philosophers and scientists since antiquity. The answers proposed have become ever more presumptuous and have increasingly lost sight of everyday intuitions and have sacrificed explanatory power. ...

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Paperback (Softcover reprint of hardcover 1st ed. 1993)
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Overview

The three spatial characteristics of length, height and depth are used in the same unreflective way by laymen, technicians and scientists alike to describe the forms, positions and measure of bodies and hollow bodies. But how do we know that the space we live in has just these three dimensions? The question has occupied philosophers and scientists since antiquity. The answers proposed have become ever more presumptuous and have increasingly lost sight of everyday intuitions and have sacrificed explanatory power. In Euclid's Heritage Janich shows that all explanations of three-dimensionality hinge on an unreflective geometrical language which seems to accept the lack of an alternative for the three sorts of entities — points, lines and planes — that bound the three extended entities — lines, planes and solids. This is a Euclidean heritage in a dual sense: Euclid himself adopted a geometrical language from the art of figure drawing, and left a tradition of doing geometry as planimetry and of doing stereometry by rotating plane figures.
The systematic approach offered here starts out from operational definitions of the spatial forms — plane, straight edge and perpendicularity — and proofs that only three planes can intersect pairwise orthogonally. This is the constructive solution in the frame theory of action, providing an unequivocal characterisation of spatial relations in the physical world. The traditional order of geometric concepts turns out to be the most important obstacle to the methodical ordering of everyday scientific concepts.

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Product Details

  • ISBN-13: 9789048142170
  • Publisher: Springer Netherlands
  • Publication date: 1/5/2011
  • Series: The Western Ontario Series in Philosophy of Science, #52
  • Edition description: Softcover reprint of hardcover 1st ed. 1993
  • Edition number: 1
  • Pages: 231
  • Product dimensions: 6.00 (w) x 9.00 (h) x 0.51 (d)

Table of Contents

One The History of the Problem.- One / The Purely Spatial Approaches.- Two / Grounding Three-Dimensionality in Motion.- Three / Argument for Three-Dimensionality from Laws of Force.- Four / Causalistic Explanations and Three-Dimensionality.- Five / The Biological and Perception-Theoretical Approaches.- Six / Euclid’s Heritage: A Review of the History of the Problem.- Two Space Is Three-Dimensional: What Does It Mean, and Why Is It True?.- Seven / Knowledge about Space.- Eight / The Construction of the Terminology.- Nine / The Spatial Concept of Dimension and Its Universality.- Appendices.- Index of Names.

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