Paradoxes of Transfinite Cosmology

Abstract

The first section of the article presents a short survey of the main historical concepts of infinity, especially in Aristotel, Kant and Cantor. In the second section the question is considered whether the modern cosmology has solved the first Kant’s antinomy, i.e., whether (our) universe is finite or infinite in space and time, and some issues of modern topology are discussed (torus etc.). In the third section the concept of “multiverse” is introduced, and the methodology of cosmological theories of multiverse(s) is connected with the theory of sets; from this point of view, the concept of “Multiverse of all multiverses” yields to be paradoxical. In the last section of the article, we consider Cantor’s “Absolute” as a possible solution of the paradoxes of infinity, and we state the closeness of this approach to Kant’s conception of the whole(ness) as a “regulative idea”.