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Free Variation and the Intuition of Geometric Essences: Some Reflections on Phenomenology and Modern Geometry

Richard Tieszen
Philosophy and Phenomenological Research
Vol. 70, No. 1 (Jan., 2005), pp. 153-173
Stable URL: http://www.jstor.org/stable/40040783
Page Count: 21
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Free Variation and the Intuition of Geometric Essences: Some Reflections on Phenomenology and Modern Geometry
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Abstract

Edmund Husserl has argued that we can intuit essences and, moreover, that it is possible to formulate a method for intuiting essences. Husserl calls this method 'ideation'. In this paper I bring a fresh perspective to bear on these claims by illustrating them in connection with some examples from modern pure geometry. I follow Husserl in describing geometric essences as invariants through different types of free variations and I then link this to the mapping out of geometric invariants in modern mathematics. This view leads naturally to different types of spatial ontologies and it can be used to shed light on Husserl's general claim that there are different ontologies in the eidetic sciences that can be systematically related to one another. The paper is rounded out with a consideration of the role of ideation in the origins of modern geometry, and with a brief discussion of the use of ideation outside of pure geometry.

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