On Topology

Theory, Culture and Society 30 (5):122-152 (2013)
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Recent arguments asserting a topological turn in culture also identify a range of topologically informed interventions in social and cultural theory. Talk of a topological turn evokes both the enduring interest that the field of mathematics presents and the business of analysis in the cultural sphere. This article questions the novelty of this ‘becoming topological of culture’ and digs into a deeper historicity in order to identify the trends that may be said to support the development of topology in the current situation. It also examines the relationship between mathematics considered ontologically and mathematics considered epistemologically, in order to better grasp the significance of the practical abstractions that mathematics as technics manifests. Discussions of Cantor, Russell, Poincaré, Lévi-Strauss, Lacan and others address the background of contemporary mathematical topology. The article goes on to examine Alain Badiou’s principle that mathematics is ontology and concludes with a discussion of the mathematics of Martin Heidegger.



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Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.
The linguistic turn, Recent essays in philosophical method.Richard Rorty - 1970 - Revue Philosophique de la France Et de l'Etranger 160:501-502.
Nearness and Da-sein: The Spatiality of Being and Time.Peter Sloterdijk - 2012 - Theory, Culture and Society 29 (4-5):36-42.

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