The author elucidates the ontological basis of elementary mathematical theories and thereby assesses their certainty as a foundation for the more complex theories of modern mathematics, such as mathematical analysis and set theory. He adduces arguments in favor of the position of Frege, who held that geometry can provide a sufficiently broad and certain foundation for mathematics.

The article exposes Husserl’s theory of time and provides its detailed comparison with theories of time of I. Kant and F. Brentano. The author first examines the general principles of the phenomenological theory of consciousness, and then analyzes the time concept of F. Brentano and Husserl’s criticism of these ideas, and eventually makes a comparison of Husserl’s and Kant’s theories of time. The author is inclined to conclude that progress in the interpretation of the time made by Husserl, is largely (...) external, based on unacceptable epistemological principles. Critique of these principles the author plans to carry out in one of the next issues of the magazine. (shrink)

The article deals with the philosophical and methodological ideas of N. I. Lobachevsky—one of the creators of non-Euclidean geometries in the first half of the nineteenth century. The author shows that Lobachevsky elaborated a specific system of views on the nature of mathematical concepts and that these views were deeply involved in his mathematical investigation, especially in the creation and justification of the new geometry.

Oholekha Yaʻaḳov -- Et amalenu -- Melekhet H.