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Euclid's Heritage. Is Space Three-Dimensional? : WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE - Peter Janich

Euclid's Heritage. Is Space Three-Dimensional?


By: Peter Janich, David Zook (Translator)

Hardcover Published: 30th November 1992
ISBN: 9780792320258
Number Of Pages: 231

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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.

The History of the Problemp. 1
The Purely Spatial Approachesp. 7
What Does "Purely Spatial" Mean?
The Distinction of the Number Three
Divisibility and Definability: Aristotle
Ancient Geometry and Three-Dimensionality
The Place of a Body: From Aristotle to Galileo
Spatial Form and Measurability
Grounding Three-Dimensionality in Motionp. 27
Preliminary Remarks
Kant and the Incongruent Counterparts
The Analogy Argument Against the Fourth Dimension
Three-Dimensionality and Orientation
Imagined Motion
Argument for Three-Dimensionality from Laws of Forcep. 57
Preliminary Remarks
Kant and the True Estimation of Living Forces
Ehrenfest and the Stability of Orbits
Three-Dimensionality and Modern Physics
Causalistic Explanations and Three-Dimensionalityp. 69
Preliminary Remarks
Three-Dimensionality as the Condition for Everyday Causal Experience
Three-Dimensionality and Causality in Physics
The Biological and Perception-Theoretical Approachesp. 83
Preliminary Remarks
The Physical Continuum versus the Mathematical Continuum (Henri Poincare)
The Dimension Number of the Merkwelt and the Wirkwelt (Jakob von Uexkull)
The Evolution of Three-Dimensional Knowledge
Euclid's Heritage: A Review of the History of the Problemp. 110
Space Is Three-Dimensional: What Does It Mean, and Why Is It True?p. 117
Knowledge about Spacep. 121
"Space" as Object
The Reliability of Knowledge about Space
The Generation of Spatial Forms Upon Bodies
Poiesis and Reenactability: the Principle of Methodical Order
The Construction of the Terminologyp. 136
Bodies, Cuts, Spatial Forms
Halving Bodies
The Continued Cutting of Bodies
The Basic Theorem of Dimension Theory
The Spatial Concept of Dimension and Its Universalityp. 173
The Definition of "Dimension" and the Three-Dimensionality of the Body
Unequivocality and Prototype-Free Reproducibility
The Intuitive Certainty of the Layman and the Scientist
The Epistemological Status of Three-Dimensionality: Drawing a Balance
Bibliographyp. 211
Index of Namesp. 215
Subject Indexp. 217
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792320258
ISBN-10: 0792320255
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 231
Published: 30th November 1992
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 16.51  x 1.91
Weight (kg): 0.52