Project Gutenberg #52091
An Essay on the Foundations of Geometry
Bertrand Russell
1897Russell's first philosophical book: a history of non-Euclidean geometry and an inquiry into which geometric axioms are known a priori.
Project Gutenberg #52091 Public domain in the United States Cover source Local typographic cover created for The Missing Workbook from public-domain source metadata
Section 2 of 6 Page 2 of 2
Introduction: Our Problem Defined by Its Relations to Logic, Psychology and Mathematics
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knowledge of such a form is to be freed from contradictions, of wholly abstracting this knowledge from all reference to the matter contained in the form.
I shall hope to have touched, with this discussion, on all the main points relating to the Foundations of Geometry.
FOOTNOTES: [1] Cf. Erdmann, Axiome der Geometrie, p. 111: "Für Kant sind Apriorität und ausschliessliche Subjectivität allerdings Wechselbegriffe." [2] I use "experience" here in the widest possible sense, the sense in which the word is used by Bradley. [3] Where the branch of experience in question is essential to all experience, the resulting apriority may be regarded as absolute; where it is necessary only to some special science, as relative to that science. [4] I have given no account of these empirical proofs, as they seem to be constituted by the whole body of physical science. Everything in physical science, from the law of gravitation to the building of bridges, from the spectroscope to the art of navigation, would be profoundly modified by any considerable inaccuracy in the hypothesis that our actual space is Euclidean. The observed truth of physical science, therefore, constitutes overwhelming empirical evidence that this hypothesis is very approximately correct, even if not rigidly true.