Infinity Metaphors, Idealism, and the Applicability of Mathematics

Abstract

I open this text by analyzing some conceptions of mathematical infinity in order to point out the rich variety of metaphors and analogies that they involve. Then I go into Hoëné-Wronski’s nineteenth-century philosophy of mathematics, which is closely related to German idealism, for a further evaluation of the role of notions of infinity in shaping our world. Finally, building on these discussions, I propose that Steiner’s question concerning the applicability of mathematics can be answered by combining a rich anthropocentric mathematical language with an anthropocentric process where reason and practice form our way of inhabiting the world.