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- Type of Document: M.Sc. Thesis
- Language: Farsi
- Document No: 44280 (42)
- University: Sharif University of Technology
- Department: Philosophy of Science
- Advisor(s): Shahshahani, Siavash
- Abstract:
- The meaning and the nature of space and it’s essential properties seems to be one of the oldest problems which has been continuing to occupy human’s mind during centuries. It can be counted as a common ground between philosophy, mathematics, physics and even art. However this thesis concentrates on the philosophical and mathematical attitudes, neglecting the other aspects of the issue. Prima facie, it appears that the concept of space is essentially mingled with geometry, the science which seems to investigate the essentials of space. Taking it for granted, Kant regarded space, and so Euclidean geometry which dominates it, as an indispensible and necessary structure of the human’s mind. After the emergence of Non-Euclidean geometries, Kant’s philosophy encountered a serious problem, the problem of multiplicity of possible geometries. Mathematicians appealed to various methods to solve the problem. Klein’s Erlangen Program, Hilbert’s formalism and Riemann’s theory of manifolds, to name but a few, are such endeavors. Riemann was the irst who drew a sharp distinction between space and the geometry which dominates it. He entirely distinguished the physical space from the geometrical space, regarding the geometry as not an essential and fundamental property of space, but rather an external, accidental one. One can reconstitute Kant’s philosophy in the light of Riemann’s theory, the task which this thesis is going to perform
- Keywords:
- Geometry ; Manifold ; A Priori ; A Posteriori ; Time ; Kant ; Geometric Space ; Synthetic ; Analytical Method
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