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Euclid's Heritage. Is Space Three-Dimensional?

  • Book
  • © 1992

Overview

Authors:
  1. Peter Janich

    1. Lehrstuhl 1 für Philosophie, Philipps-Universität Marburg, Germany

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Part of the book series: The Western Ontario Series in Philosophy of Science (WONS, volume 52)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xi
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  2. The History of the Problem

    1. Front Matter

      Pages 1-6
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    2. The Purely Spatial Approaches

      • Peter Janich
      Pages 7-26

    3. Grounding Three-Dimensionality in Motion

      • Peter Janich
      Pages 27-56

    4. Argument for Three-Dimensionality from Laws of Force

      • Peter Janich
      Pages 57-68

    5. Causalistic Explanations and Three-Dimensionality

      • Peter Janich
      Pages 69-82

    6. The Biological and Perception-Theoretical Approaches

      • Henri Poincaré, Jakob von Uexküll
      Pages 83-109

    7. Euclid’s Heritage: A Review of the History of the Problem

      • Peter Janich
      Pages 110-115

  3. Space Is Three-Dimensional: What Does It Mean, and Why Is It True?

    1. Front Matter

      Pages 117-120
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    2. Knowledge about Space

      • Peter Janich
      Pages 121-135

    3. The Construction of the Terminology

      • Peter Janich
      Pages 136-172

    4. The Spatial Concept of Dimension and Its Universality

      • Peter Janich
      Pages 173-208

  4. Back Matter

    Pages 209-231
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Keywords

About this book

We live in a space, we get about in it. We also quantify it, we think of it as having dimensions. Ever since Euclid's ancient geometry, we have thought of bodies occupying parts of this space (including our own bodies), the space of our practical orientations (our 'moving­ abouts'), as having three dimensions. Bodies have volume specified by measures of length, breadth and height. But how do we know that the space we live in has just these three dimensions? It is theoreti­ cally possible that some spaces might exist that are not correctly described by Euclidean geometry. After all, there are the non­ Euclidian geometries, descriptions of spaces not conforming to the axioms and theorems of Euclid's geometry. As one might expect, there is a history of philosophers' attempts to 'prove' that space is three-dimensional. The present volume surveys these attempts from Aristotle, through Leibniz and Kant, to more recent philosophy. As you will learn, the historical theories are rife with terminology, with language, already tainted by the as­ sumed, but by no means obvious, clarity of terms like 'dimension', 'line', 'point' and others. Prior to that language there are actions, ways of getting around in the world, building things, being interested in things, in the more specific case of dimensionality, cutting things. It is to these actions that we must eventually appeal if we are to understand how science is grounded.

Authors and Affiliations

  • Lehrstuhl 1 für Philosophie, Philipps-Universität Marburg, Germany

    Peter Janich

Bibliographic Information

  • Book Title: Euclid's Heritage. Is Space Three-Dimensional?

  • Authors: Peter Janich

  • Series Title: The Western Ontario Series in Philosophy of Science

  • DOI: https://doi.org/10.1007/978-94-015-8096-0

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 1992

  • Hardcover ISBN: 978-0-7923-2025-8Published: 30 November 1992

  • Softcover ISBN: 978-90-481-4217-0Published: 28 October 2010

  • eBook ISBN: 978-94-015-8096-0Published: 09 March 2013

  • Series ISSN: 1566-659X

  • Series E-ISSN: 2215-1974

  • Edition Number: 1

  • Number of Pages: XI, 231

  • Additional Information: Originally published in German

  • Topics: Philosophy of Science, History of Mathematical Sciences, Epistemology, Geometry

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