Towards a topological philosophy |
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| Authors: | Bartłomiej Skowron Janusz Kaczmarek Krzysztof Wójtowicz |
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| Institution: | 1. Faculty of Administration and Social Sciences, Warsaw University of Technology, Poland;2. Department of Logic and Methodology of Sciences, University of Lodz, Poland;3. Faculty of Philosophy, University of Warsaw, Poland |
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| Abstract: | This article examines the use of mathematical concepts in philosophy, focusing on topology, which may be viewed as a modern supplement to geometry. We show that Plato and Parmenides were already employing geometric ideas in their research, and discuss three examples of the application of topology to philosophical problems: the first concerns the analysis of the Cartesian distinction between res extensa and res cogitans, the second the ontology of possible worlds of Wittgenstein's Tractatus, and the third Leibniz's monadology. We also consider the role of topology in mathematical explanations of the sort found in science, arguing that it can perform a role in philosophy that is of comparable importance. |
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| Keywords: | geometry and philosophy mathematical philosophy topological explanations topological ontology topological philosophy topology and philosophy |
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