Topology (philosophy)

The topology ( ancient Greek τόπος tópos , German 'place' and λόγος lógos , German 'doctrine' ) in philosophy primarily describes a theory of the geometric description of places and fields in space as the sphere of the outside world . Depending on its form, it can be viewed as a sub-area of philosophical metaphysics , phenomenology or social and cultural philosophy .

Particularly due to the “ topological turn ” in the humanities, the consideration of place, field and space categories in philosophy has attracted attention. This also creates a connection to Japanese philosophy , in which the place ( 場所 basho ) has played a central role since the beginning of the 20th century. The term bashoron ( 場所論 'doctrine of place' ) used there denotes this type of philosophical topology.

history

A first approach to the geometric description of a place in space is the Cartesian coordinate system . Topological approaches were developed to distinguish them from Descartes' analytical geometry in order to find a coordinate-free representation. Instead of just calculating something, one wanted to find the intrinsic structure and movement possibilities. So it was about the replacement of quantitative geometry by a modal one. In the 17th century and into the 19th century, the term Geometria situs , Geometria situs , or Analysis situs, was used instead of topology . B. in Leibniz , who in the work De analysi situs examined the relationship of spatial points to one another independently of the metrical relationships. An application example for the Geometria situs is the investigation of the properties of geometrical bodies as in the polyhedron substitution , which is attributed to both René Descartes (1639) and Leonhard Euler .

The term "topology" was first used by Johann Benedict Listing in 1847 in the publication Preliminary Studies on Topology . Like August Ferdinand Möbius, he described the Möbius strip . Möbius developed a "theory of elementary relationship", with which one can describe topologically equivalent objects that emerge from one another through reversible, clear and continuous distortion. In the context of the Erlangen program , Felix Klein defined topology as an invariant theory of reversible unique transformations. Finally, Henri Poincaré ( algebraic topology ) and Georg Cantor (set theoretical topology ) contributed to the further development of the topology .

In 2009 Dieter Pfister and Thomas Latka founded the Institute for Topology in Munich and Basel, which is dedicated to the interdisciplinary research of spatial, spatial and field phenomena.

literature

Heribert Boeder : Topology of Metaphysics. Alber, Freiburg im Breisgau / Munich 1980, ISBN 3-495-47437-4 .
Edward S. Casey: The Fate of Place. A Philosophical History . University of California Press, Berkeley CA 1997, ISBN 0-520-20296-1 .
IM James (Ed.): History of Topology . Elsevier, Amsterdam 1999, ISBN 978-0-08-053407-7 .
Thomas Latka: Topical social system. The introduction of the Japanese theory of place into systems theory and its consequences for a theory of social systems . Publishing house for systemic research in the Carl-Auer-Systeme-Verlag, Heidelberg 2003, ISBN 3-89670-321-8 , (also: Munich, University of Philosophy, Diss., 2002/03).
Kitarō Nishida : logic of the place. The beginning of modern philosophy in Japan . Translated and edited by Rolf Elberfeld . Scientific Book Society, Darmstadt 1999, ISBN 3-534-13703-5 .
Wolfram Pichler, Ralph Ubl (Ed.): Topology. Folds, knots, nets, evertings in art and theory . Turia + Kant, Vienna 2009, ISBN 978-3-85132-556-0 .

Web links

Individual evidence

↑ Gottfried Wilhelm Leibniz: De analysi situs. 1693, Mathematische Schriften, ed. By CI Gerhardt, 1858, German: Hauptschriften zur Grundführung der Philosophie , translated by A. Buchenau, ed. by Ernst Cassirer, Volume 1, 1904, 69, see Marie-Luise Heuser : Historical observations on the term "topology". Leibniz and Listing. In: Kurt Maute (Ed.): Topology. An approach to developing alternative structures. Sprint, Stuttgart 1994, pp. 1-13.
↑ K. Mainzer: Keyword topology. In: Historical Dictionary of Philosophy . Volume 10, pp. 1289-1290.
↑ On Leibniz and Listing see Marie-Luise Heuser: The beginnings of topology in mathematics and natural philosophy. In: Stephan Günzel (Ed.): Topology. For the description of space in cultural and media studies. transcript Verlag, Bielefeld 2007, ISBN 978-3-89942-710-3 , pp. 183-202.

[1] Gottfried Wilhelm Leibniz: De analysi situs. 1693, Mathematische Schriften, ed. By CI Gerhardt, 1858, German: Hauptschriften zur Grundführung der Philosophie , translated by A. Buchenau, ed. by Ernst Cassirer, Volume 1, 1904, 69, see Marie-Luise Heuser : Historical observations on the term "topology". Leibniz and Listing. In: Kurt Maute (Ed.): Topology. An approach to developing alternative structures. Sprint, Stuttgart 1994, pp. 1-13.

[2] K. Mainzer: Keyword topology. In: Historical Dictionary of Philosophy . Volume 10, pp. 1289-1290.

[3] On Leibniz and Listing see Marie-Luise Heuser: The beginnings of topology in mathematics and natural philosophy. In: Stephan Günzel (Ed.): Topology. For the description of space in cultural and media studies. transcript Verlag, Bielefeld 2007, ISBN 978-3-89942-710-3 , pp. 183-202.