Euclid's Heritage. Is Space Three-Dimensional?

1993
ISBN: 978-0-7923-2025-8
Verlag: Springer Netherlands

Buch, Englisch, Band 52, 231 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1160 g

Reihe: The Western Ontario Series in Philosophy of Science

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.

Zielgruppe

Research

Autoren/Hrsg.

Janich, P.

Weitere Mitwirkende

Zook, David

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Geisteswissenschaften Philosophie Erkenntnistheorie
• Geisteswissenschaften Philosophie Wissenschaftstheorie, Wissenschaftsphilosophie
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Geschichte der Naturwissenschaften, Formalen Wissenschaften & Technik
• Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines Wissenschaften: Theorie, Epistemologie, Methodik
• Mathematik | Informatik Mathematik Mathematik Allgemein Geschichte der Mathematik

Inhaltsverzeichnis

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.