The Reconcilability of Non-Euclidean Geometries with Kant's Philosophy of Mathematics

2021-9-27
Çöteli, Can
This thesis examines Kant’s philosophy of geometry, and the possibility of reconciling non-Euclidean geometries with Kant’s philosophy of geometry. Kant believed that the propositions of Euclidean geometry are necessary and universal. In addition to that, he embraced the view that the character of space is Euclidean and he did not give any credence to the possibility of determining the character of space by using another geometrical structure. He also propounded the view that experience plays no positive role in the acquisition of geometrical knowledge. In this thesis, the views of Helmholtz, Poincaré and Reichenbach as to the positive role experience plays in the genesis of geometry are elaborately discussed. In the light of their views, it is shown that different environmental conditions have the potency to compel sentient beings like us to adopt nonEuclidean geometries. These geometries, in turn, has a proper intuitive content in contradistinction to Kant’s claim that they are only possible logically, not intuitively. Under these considerations, this thesis shows that it is not possible to reconcile Kant’s theory of geometry with non-Euclidean geometries even if undergoes appropriate modifications offered by certain philosophers such as Strawson, who tried to reduce the scope of Kant’s theory of geometry to visual space by arguing that visual space cannot be non-Euclidean. For Strawson, the propositions of Euclidean geometry are necessary and universal as was propounded by Kant, but its validity its limited to our visual space. This thesis also shows the possibility of visualizing non-Euclidean geometries by considering the views of abovementioned philosophers in contradistinction to Strawson’s arguments in support of Kant’s theory of geometry.

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Citation Formats
C. Çöteli, “The Reconcilability of Non-Euclidean Geometries with Kant’s Philosophy of Mathematics,” M.S. - Master of Science, Middle East Technical University, 2021.