Abstract

The crisis of intuition that affected the very foundations of Western knowledge starting in the mid-nineteenth century played itself out on two main sites: the elaboration of pure symbolisms in mathematical logic and electromagnetic field theory in physics, which conceived of communication as something that could no longer be presented intuitively but only described symbolically. The chapter studies both sites in detail. The genesis of mathematics as a science of purely symbolic relationships, which avoided all interpretation of symbols and pursued a previously unthinkable agenda of pure formalism, occupies a key position: it inaugurated the principles of a new system of notation, a new discourse network. Focusing on the archaeology of Boole's exact science of logic, the chapter also describes the collapse of the opposition between thinking and calculating. Hegel had pinpointed this opposition as the salient feature of the presymbolic age just prior to its end, and it continued, in a kind of epistemic belatedness, to structure antimathematical and antitechnological affects well into the twentieth century. In a sort of parallel action, physical field theory, by means of symbolisms, that is, exact notation, cast out the specters of representation that until then had populated the problem of communication and had determined the imaginary of communication. The investigation thus shows what has previously been discussed as a foundational crisis of the sciences to have been a foundational crisis of thinking as such, a crisis that crystallized around the poles of the symbolic and of communication.

Keywords: archeology of the axiomatic age; thinking and calculating; formalism and interpretation; exact science of logic; symbolic knowledge about communication; G. W. F. Hegel; George Boole; Heinrich Hertz

But what in itself is contradictory cannot be.