Kantian Euclidean Space and Husserlian Material Ontologies

"When considering the relevance of Kant's transcendental position on Euclidean space, one widespread complaint goes something like this: In what concerns the transcendental validity of mathematics in experience, Kant failed to distinguish between pure and applied geometry the way we do today. Pure geometry, as Hilbert showed, is a mere mathematical multiplicity, an axiomatic system interwoven by means of formal relationships where a priori intuition plays no role at all. Its claims have no empirical content whatsoever. Applied geometry, on the other hand, as exemplified by the use of non-Euclidean geometries by Einstein, has to do with the application of a formal geometrical structure as a means of depicting the empirical world. This application is done under certain theoretical assumptions and the postulation of an empirical spatial congruence. Once the coordination of the geometrical structure with the empirical phenomena is established, it can be empirically tested. There is no place for the idea that Euclidean geometry is a priori and synthetic, a transcendental constitutive of experience. Euclidean geometry is just a possible 'mathematical multiplicity', a formal structure whose correspondence with the physical world is not imposed. Thus, the transcendental a priori validity of geometry for all possible experience as implicitly ascertained in the mathematical principles of the pure understanding appears to have been refuted."

(José Ruiz Fernández, 2003)

Essays in Celebration of the Founding of the Organization of Phenomenological Organizations. Ed. CHEUNG, Chan-Fai, Ivan Chvatik, Ion Copoeru, Lester Embree, Julia Iribarne, & Hans Rainer Sepp. Web- Published at www.o-p-o.net, 2003

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