# Euclid’s Heritage: Is Space Three-Dimensional?

• Peter Janich
Book

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

1. Front Matter
Pages i-xi
2. ### The History of the Problem

1. Front Matter
Pages 1-6
2. Peter Janich
Pages 7-26
3. Peter Janich
Pages 27-56
4. Peter Janich
Pages 57-68
5. Peter Janich
Pages 69-82
6. Henri Poincaré, Jakob von Uexküll
Pages 83-109
7. 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
2. Peter Janich
Pages 121-135
3. Peter Janich
Pages 136-172
4. Peter Janich
Pages 173-208
4. Back Matter
Pages 209-231

### Introduction

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.

### Keywords

Euclid antiquity art concept construction drawing history history of literature history of mathematics knowledge language opera perception space tradition

#### Authors and affiliations

• Peter Janich
• 1
1. 1.Lehrstuhl 1 für PhilosophiePhilipps-Universität MarburgGermany

### Bibliographic information

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