Axiomathes 22 (1):5-30 (2012)
Abstract |
Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl’s ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl
|
Keywords | Husserl Spatial representation Perceptual space Physical space Mathematical space Geometry Pure geometry Applied geometry Euclidean geometry Non-Euclidean geometries Intentional constitution Weyl |
Categories | (categorize this paper) |
ISBN(s) | |
DOI | 10.1007/s10516-011-9161-0 |
Options |
![]() ![]() ![]() ![]() |
Download options
References found in this work BETA
The Crisis of European Sciences and Transcendental Phenomenology: An Introduction to Phenomenological Philosophy.Edmund Husserl - 1970 - Evanston: Northwestern University Press.
Logical Investigations.Edmund Husserl & J. N. Findlay - 1972 - Journal of Philosophy 69 (13):384-398.
View all 13 references / Add more references
Citations of this work BETA
The Constitution of Weyl’s Pure Infinitesimal World Geometry.C. D. McCoy - 2022 - Hopos: The Journal of the International Society for the History of Philosophy of Science 12 (1):189–208.
Mathematics and Its Applications, A Transcendental-Idealist Perspective.Jairo José da Silva - 2017 - Springer.
Similar books and articles
Edmund Husserl on the Applicability of Formal Geometry.René Jagnow - 2006 - In Emily Carson & Renate Huber (eds.), Intuition and the Axiomatic Method. Springer. pp. 67-85.
Geometry and Spatial Intuition: A Genetic Approach.Rene Jagnow - 2003 - Dissertation, Mcgill University (Canada)
An Enhanced Argument for Innate Elementary Geometric Knowledge and its Philosophical Implications.Helen3 De Cruz - 2007 - In Bart Van Kerkhove (ed.), New perspectives on mathematical practices. Essays in philosophy and history of mathematics. World Scientific.
The Fate of Mathematical Place: Objectivity and the Theory of Lived-Space From Husserl to Casey.Edward Slowik - 2010 - In Vesselin Petkov (ed.), Space, Time, and Spacetime. Berlin: Springer Verlag. pp. 291-312.
Time, Topology and Physical Geometry.Tim Maudlin - 2010 - Aristotelian Society Supplementary Volume 84 (1):63-78.
Concepts and Intuitions in Kant's Philosophy of Geometry.Joongol Kim - 2006 - Kant-Studien 97 (2):138-162.
Some Open Problems in the Philosophy of Space and Time.Patrick Suppes - 1972 - Synthese 24 (1-2):298 - 316.
Analytics
Added to PP index
2011-09-26
Total views
64 ( #176,937 of 2,499,017 )
Recent downloads (6 months)
1 ( #419,059 of 2,499,017 )
2011-09-26
Total views
64 ( #176,937 of 2,499,017 )
Recent downloads (6 months)
1 ( #419,059 of 2,499,017 )
How can I increase my downloads?
Downloads