Hostname: page-component-6dbcb7884d-fw45b Total loading time: 0 Render date: 2025-02-14T08:47:15.765Z Has data issue: false hasContentIssue false
  • English
  • Français

Points and Spaces

Published online by Cambridge University Press:  20 November 2018

L. E. J. Brouwer
L. E. J. Brouwer*
Affiliation:
Blaricum, Holland
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The gradual disengagement of mathematics from logic. Beginning with a historical review of the development of mathematical thought, we have to consider successively (cf. 10, pp. 139-140):

(1) The observational period. For some familiar regularities of (outer or inner) experience of time and space, which, to any attainable degree of approximation, seemed invariable, absolute and sure invariability was postulated. These regularities were called axioms and were put into language. Thereupon extensive systems of properties were developed from the linguistic substratum of the axioms by means of reasoning, guided by experience but linguistically following and using the principles of classical logic. This logic was considered autonomous, and mathematics was considered more or less dependent on logic.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 6 , 1954 , pp. 1 - 17
Copyright
Copyright © Canadian Mathematical Society 1954

References

1. Weyl, H., Über die neue Grundlagenkrise der Mathematik, Math. Z., 10 (1921), 39–79.Google Scholar
2. Dresden, A., Brouwer's contributions to the foundations of mathematics, Bull. Amer. Math. Soc, 30(1924), 31–40.Google Scholar
3. Wavre, R., Y a-t-il une crise des mathématiques? Revue de Métaphysique et de Morale, 31(1924), 435–470.Google Scholar
4. Wavre, R., Logique formelle et logique empiriste, Revue de Métaphysique et de Morale, 33(1926), 65–75.Google Scholar
5. Lévy, P., Wavre, R., and Borel, E., Discussions, Revue de Métaphysique et de Morale, 33(1926), 253–258, 425–430, 545–551; 34 (1927), 271–276.Google Scholar
6. Brouwer, L. E. J., Über Definitionsbereiche von Funktionen, Math. Ann., 97(1921), 60–75.Google Scholar
7. Brouwer, L. E. J. f Wissenschaft, Mathematik uni Sprache, Monatsh. Math. Phys., 36(1928), 153–164.Google Scholar
8. Mannoury, G., La question vitale: A ou B?, Nieuw Archief Wisk. (2), 21(1943), 161–167.Google Scholar
9. Brouwer, L. E. J., Consciousness, philosophy and mathematics, Proc. Tenth International Congress of Philosophy (Amsterdam, 1948), 1235–1249.Google Scholar
10. Brouwer, L. E. J., Historical background, principles and methods of intuitionism, South African J. Sci., Oct.-Nov. 1952, 139–146.Google Scholar