Über drei Erscheinungen von Unterschied in der Mathematik

On Three Appearances of Difference in Mathematics. This article proposes to examine three types of relations between man and equality, as they are embodied in the relation to the minimal condition of the mathematical: the sentence of identity: I=I. Starting our examination from the current common conception of science and mechanism, we aim to reveal that behind the dominating logic of identity there are two other systems of logic, which have arisen during the history of humanity and that of mathematics. Following Serres, the first one might be revealed during the passage from the Babylonian mathematics to the interaction between Thales and the Greek gnomon. The Babylonian epoch marks an era, in which the logic of sameness operates; logic which offers a place for the mathematician. This era is followed by a science, working under the second logic: the logic of identity, which consecrates an axiomatic definition-based approach, at the expense of the human being. The third logic looms after the discovery of Gödel's incompleteness theorems: that an undecidable statement can be derived within every arithmetical system. Under this logic, the roles of man and the allegedly mathematical automatic machine become even more intertwined: the newly found logic promises instability not only for man, but also for the machinic-mathematics.