Abstract
THE Academy journal of the 12th of February, 1870 (vol. i. p. 128), contained a paper by Prof. Helmholtz upon the Axioms of Geometry in a philosophical point of view. The opinions set forth by him were based upon the latest speculations of German geometers, so that a new light seemed to be thrown upon a subject which has long been a cause of ceaseless controversy. While one party of philosophers, especially Kant and the great German school, have pointed to the certainty of geometrical axioms as a proof that these truths must be derived from the conditions of the thinking mind, another party hold that they are empirical, and derived, like other laws of nature, from observation and induction. Helrnholtz comes to the aid of the latter party by showing that our Axioms of Geometry will not always be necessarily true; that perhaps they are not exactly true even in this world, and that in other conceivable worlds they would be entirely superseded by a new set of geometrical conditions.
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JEVONS, W. Helmholtz on the Axioms of Geometry . Nature 4, 481–482 (1871). https://doi.org/10.1038/004481a0
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DOI: https://doi.org/10.1038/004481a0