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The genesis and essence of Hermann Günther Graßmann’s philosophical views in the Extension Theory of 1844

  • Hans-Joachim Petsche

Abstract

Hermann Graßmann’s philosophical and methodological views were directly on the path his father had traced for him. His father had been influenced by Pestalozzi’s pedagogy, Leibniz’ combinatorial and synthetic approach, Kant’s constructive view of mathematics and the dialectics of Romantic philosophy of nature. Merged together, these were the elements of Justus Graßmann’s unique philosophical and mathematical position. These impulses — modified by Schleiermacher’s dialectics — also shaped Hermann Graßmann’s way of thinking.

Keywords

Pure Mathematic Extension Theory Formal Science Philosophical Concept Philosophical Method 
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.

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Notes

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    In this context, see the statistical analyses of works published by Graßmann’s followers on the one hand, and Hamilton’s on the other, ranging from the second half of the 19th century to the early 20th century. In: Crowe 1994, p. 109–149.Google Scholar
  117. 149.
    There is a reference to Schweitzer in Lewis 2004. But when Lewis points out that Paul Carus, who was a pupil of Graßmann in Stettin, also was strongly familiar with Graßmann’s way of thinking, this is only partly true, because Carus strongly opposed the mathematical concept of n-dimensional spaces as late as the 1880s (Carus 1881): “But the whole enterprise has no other significance than to show that what in fact is impossible may still be correct from a logical point of view. It is a scientific equivalent to a paradoxical piece of fiction and only confirms the undeniable fact that one cannot contradict the careful liar by his own words alone, because one will find no contradiction there.” (Carus 1881, p. 54) Carus changed his mind 25 years later (Carus 1908), when he published a foundation of a philosophy of geometry, in which he praised Graßmann enthusiastically. So Paul Carus and Victor Schlegel seem to share the same attitude. Both Carus and Schlegel admired Graßmann’s ideas only after having left Stettin.Google Scholar
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    Schleiermacher wrote Gaß about Bartholdy: “In Berlin, he told me about his plans for a seminar, which made me very happy, and from which I conclude that I share his view of Pestalozzi’s idea and its essential importance. Here, as well, the combination of Lutheran and Reformed higher schools is the next step.” Letter from Schleiermacher to Gaß, May 1805. In: Schleiermacher 1852, p. 23.Google Scholar
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    Letter from J. Chr. Gaß to Schleiermacher, 13 July 1805. In: Schleiermacher 1852, p. 25sq.Google Scholar
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    “With much gratitude I return your copy of the Dialectic ..., my dear friend.” Letter from J. Chr. Gaß to Schleiermacher, 31 March 1816. In: Schleiermacher 1852, p. 125sq.Google Scholar
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    Justus Graßmann wrote in the preface to the Geometry for Elementary Schools (1817): “Enough has already been said about the justification and usefulness of this work in the foreword to Bartholdy’s ‘Versuch einer Sprachbildungslehre für Deutsche’, which has appeared recently. Its general outlines have something to do with some local schools for the poor, which I and some dear friends, now passed away, most notably councilor Bartholdy, have helped to found and establish, apart from preparing these school’s teachers for the sake of doing a good deed, voluntarily and without pay.” (Graßmann 1817, p. iii).Google Scholar
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  125. 158.
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    A2, p. xvii.Google Scholar

Copyright information

© Birkhäuser Verlag AG 2009

Authors and Affiliations

  • Hans-Joachim Petsche
    • 1
  1. 1.PotsdamGermany

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