Geometric and intuitive space in Husserl
Moving from the reformulation of the meaning of geometry, achieved in the first half of the Nineteenth Century (principally by Lobachevsky, Bolyai and Riemann), which also implied a new definition of the relationship between formal and empirical understanding of the space (e.g. in the investigations of von Helmholtz), Husserl starts, since the Philosophy of arithmetic, a deep reflection on the definition of space, which would have led to a new philosophical theory of Euclidean geometry (Hua XII, p. 8). Husserl took the view that the clarification of scientific concepts must be made back to the intuitive ground from whence they sprang. In what the author himself called the Raumbuch, the book of the space, Husserl makes a clear distinction between space and intuitive geometric space, believing that this was a conceptual construct, of which there is not an intuitive representation. In fact, peculiar to geometrical concepts is ideation. For this reason the setting of Husserlian problem differs markedly from that of Kant: for Kant, «the representation of space behind the geometry is an intuition, not a concept» (Hua XXI, 268). Despite this "freedom" of the products of idealization, geometry, for Husserl, is deep-rooted in intuition, because in his opinion, and following Gauss, there is a clear difference between arithmetic and geometry. Or within the experience they are structured all the possibilities of various geometric multiplicity. From the idea, here implied, that Euclidean geometry should be assumed, Husserl take distances as early as the Logical Investigations. But despite the changes of perspective, the reference to the intuition remains constant along the entire Husserlian research. The clarification of the relationship between geometry and intuitive space presupposes a long preparatory work related to the supply of light in space structures intuitive, because the processes of idealization not happen—this is the specificity of reflection Husserl—upon the intuitive world, but are prepared in it. In this context Husserl will confront for a long time with contemporary research about the psychology of the space, and in particular with those of Stumpf. For Stumpf, the space (intended as an extension) is an absolute content that inheres essentially to the quality of sensations, for example to color. From this setting Husserl definitely takes the distances, because its base is the confusion between field of view and representation of the surface. The central point is therefore that «the visual field is not some sort of objective surface in space» (TS, 141). In the constitution of three-dimensional thingness and of the deep space play also an essential role the kinesthetic sensations. There is in fact a definite correlation between the visual field and kinesthetic course, since even in the changing of the contents of the field of view, we can show. from the perspective of phenomenological-transcendental, a stable association between sensation kinesthetic and visual content. The manifold of places is never given without a kinaesthetic sensation, and neither is a kinaesthetic sensation given without the total manifold of places, which is merely fulfilled in a changing manner. All this is not yet sufficient to constitute three-dimensional space, as «the Objects here are still not things» (TS, 193). And this marks the end of the most problematic attempt to Husserl: to follow the strata in the constitution of the thing and the constitution of a «visual space for Euclidean space» and, therefore, of a Riemannian manifold (TS, 274).
Costa, V. (2017)., Geometric and intuitive space in Husserl, in F. Masi (ed.), The changing faces of space, Dordrecht, Springer, pp. 125-137.
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