Showing Space, or: Can there be Sciences of the Non-Discursive?

Abstract

In the Tractatus Wittgenstein argues that what is expressed through language cannot be represented in language, but only shown. He was thinking of logic, but complex spatial relations seem a clearer case. They are present in both minds and worlds, in that human beings live in spatial complexes like buildings and cities, and deal with them competently, but their patterns are nondiscursive and cannot be described in natural language. What language does have, of course, are terms for simple spatial relations involving two or three entities (‘inside’, ‘between’, ‘through’, ‘beyond’ etc), and these relations can be represented graphically, and so shown. However, by isolating their elementary concepts, it was possible to develop graphical representations of complex spatial relations which first showed how spatial complexity was structured, and then permitted it to be quantified, so in effect rendering space analysable and the nondiscursive discursive. But when we do this, we encounter Wittgenstein again in two senses. First, we find that Wittgenstein’s arguments against overarching structures in the Untersuchungen turn out not to be true for spatial relations, since culturally differentiated ‘spatial games’ can be shown again and again to generate universal emergent structures in the forms of cities, showing that for all its variation in cultural expression, these is a single underlying language of space. But second, although these emergent structures can be represented graphically, and tested against functional evidence, they cannot (so far!) be described within the formal language. So we are back to the Tractatus!