Space and Time pp 136-156 | Cite as

The Dimensions of Space

  • Richard Swinburne


THE pure geometer generalising Euclid’s system constructs self-consistent geometries of any number of dimensions.1 Which of these can be physical geometries, viz. can have application to physical space when ‘point’, ‘line’, ‘plane’, etc., have the senses described in Chapters 4 and 6?


Physical Space Material Object Euclidean Geometry Unique Identification Perpendicular Distance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    W. Hurewicz and H. Wallman, Dimension Theory, Princeton, 1941.Google Scholar
  2. [2]
    H. P. Manning, Geometry of Four Dimensions, New York, 1956.Google Scholar
  3. [3]
    I. Kant, Thoughts on the True Estimation of Living Forces (first published 1747), §§ 9–10. A translation by N. Kemp-Smith appears in Kants Inaugural Dissertation and Early Writings on Space (trans. John Handyside), Chicago and London, 1929.Google Scholar
  4. [4]
    I. Kant, Prolegomena to any Future Metaphysics (first published 1783) (trans. P. G. Lucas), Manchester, 1953, §§ 11–13.Google Scholar
  5. [5]
    H. Reichenbach, The Philosophy of Space and Time (originally published 1928) (trans. M. Reichenbach and J. Freund), New York, 1958, § 44.Google Scholar
  6. [6]
    H. Brotman, ‘Could Space be Four-dimensional?’, Mind, 1952, reprinted in Essays in Conceptual Analysis (ed. A. Flew), London, 1956. My page reference refers to latter volume.Google Scholar
  7. [7]
    M. Jammer, Concepts of Space, Cambridge, Mass., 1954, pp. 172–84.Google Scholar
  8. [8]
    E. A. Abbott, Flatland, 2nd and revised ed., London, 1884. Republished Oxford, 1962.Google Scholar

Copyright information

© Richard Swinburne 1968

Authors and Affiliations

  • Richard Swinburne
    • 1
  1. 1.University of HullUK

Personalised recommendations