The "discovery" of non-Euclidean geometries had profound repercussions on the sciences and philosophy alike and opened a heated debate on the nature of space and on the origin of geometry and its axioms. At the heart of the discussion lay Kant’s doctrine of space. Nelson took part in this debate, rejecting the three main theories of time: the logical, the empirical and the conventionalist. Referring to J.F. Fries’ philosophy, he tried to demonstrate the a priori, synthetic nature of Euclidean axioms and the merely logical character of non-Euclidean geometries. His attempt, though interesting, ended according to the Author of this essay in failure.
Keywords: Non-Euclidean geometries, logical interpretation, empiricism, conventionalism, ontological relativity, L. Nelson