From Religion to Dialectics and Mathematics

Schleiermacher’s Theological Contribution to the Development of Modern Tensor Calculus in Grassmann’s Ausdehnungslehre

Wolfgang Achtner 1
  • 1 Justus Liebig University, Gießen, Germany

Abstract

Hermann Grassmann is known to be the founder of modern vector and tensor calculus. Having as a theologian no formal education in mathematics at a university he got his basic ideas for this mathematical innovation at least to some extent from listening to Schleiermacher’s lectures on Dialectics and, together with his brother Robert, reading its publication in 1839. The paper shows how the idea of unity and various levels of reality first formulated in Schleiermacher’s talks about religion in 1799 were transformed by him into a philosophical system in his dialectics and then were picked up by Grassmann and operationalized in his philosophical-mathematical treatise on the extension theory (German: Ausdehnungslehre) in 1844.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Johannes M. Dittmer, Schleiermachers Wissenschaftslehre als Entwurf einer prozessualen Metaphysik in semiotischer Perspektive. Triadizität im Werden. DeGruyter, Berlin 2001.

  • Albert Einstein, Aus meinen späteren Jahren, Ullstein Verlag, Frankfurt 41993.

  • Hermann Grassmann, Gesammelte Mathematische und Physikalische Werke, Bd. I, 1. Friedrich Engel (ed.), Teubner, Leipzig 1894.

  • M.B. Green, J.H. Schwarz, E. Witten, Superstring theory, Vol., 1, Introduction, Cambridge Monographs on mathematical physics, Cambridge University Press 2002.

  • Inken Mädler, Kirche und bildende Kunst der Moderne. Ein an F. D. E. Schleiermacher orientierter Beitrag zur theologischen Urteilsbildung, Verlag Mohr Siebeck, Tübingen 1997.

  • Hans-Joachim Petsche, “Ernst Abbe’s reception of Grassmann in the light of Grassmann’s reception of Schleiermacher”, in: Hans-Joachim Petsche et al. (ed.), Hermann Graßmann. From Past to Future: Graßmann’s Work in Context. Graßmann Bicentennial Conference, September 2009, Birkhäuser, Springer, Basel 2011

  • Friedrich Schleiermacher, Dialektik, Justus Jonas (ed.), Dialektik aus Schleiermachers handschriftlichem Nachlasse, Friedrich Schleiermacher’s sämtliche Werke, Dritte Abteilung zur Philosophie, Vierten Bandes zweiter Theil, Reimer Verlag, Berlin 1839.

  • Friedrich Schleiermacher, Reden über die Religion an die Gebildeten unter ihren Verächtern, Reclam Verlag, Stuttgart 2010,

  • Alfred North Whitehead, A treatise on universal algebra: with applications, The University Press, Cambridge 1898.

OPEN ACCESS

Journal + Issues

Search