Abstract

Jacob Klein’s account of the original phenomenon of formalization accomplished by the innovators of modern mathematics, when they transformed the Greek arithmos into the modern concept of number, and his suggestion that the essential structure of this historically located formalization has become paradigmaticfor the concept formation of non-mathematical concepts (and therefore the most salient characteristic of the “modern consciousness”), is situated within the context of Husserl’s and Heidegger’s understanding of formalization. I show that from the perspective of Klein’s account of formalization the questions thatinform Husserl’s and Heidegger’s phenomenological responses to the problem of formalization are derivative, insofar as both phenomenologists presuppose that the essence of formalization is something that is knowable independent of its historicity. I then show that Klein’s philosophical achievement consists in his account of formalization and the formality of the concepts that it generates as being ungraspable so long as thinking approaches them as something is knowable, independent of its historicity.