Abstract
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?
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Bibliography
W. Hurewicz and H. Wallman, Dimension Theory, Princeton, 1941.
H. P. Manning, Geometry of Four Dimensions, New York, 1956.
I. Kant, Thoughts on the True Estimation of Living Forces (first published 1747), §§ 9–10. A translation by N. Kemp-Smith appears in Kant’s Inaugural Dissertation and Early Writings on Space (trans. John Handyside), Chicago and London, 1929.
I. Kant, Prolegomena to any Future Metaphysics (first published 1783) (trans. P. G. Lucas), Manchester, 1953, §§ 11–13.
H. Reichenbach, The Philosophy of Space and Time (originally published 1928) (trans. M. Reichenbach and J. Freund), New York, 1958, § 44.
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.
M. Jammer, Concepts of Space, Cambridge, Mass., 1954, pp. 172–84.
E. A. Abbott, Flatland, 2nd and revised ed., London, 1884. Republished Oxford, 1962.
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© 1968 Richard Swinburne
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Swinburne, R. (1968). The Dimensions of Space. In: Space and Time. Palgrave Macmillan, London. https://doi.org/10.1007/978-1-349-00581-9_8
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DOI: https://doi.org/10.1007/978-1-349-00581-9_8
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