"Logic is a geometry of thinking". Space and Spatial Frameworks in Wittgenstein's Writings

Abstract

The thesis investigates the history and functions of space concepts in Wittgenstein’s philosophy. It is based on a Kantian account which conceives of space not as a thing, but as an a priori framework which constitutes possibilities, not facts. The increasing abstraction and formalisation of geometry in the 19th century enabled Wittgenstein in his Tractatus Logico-Philosophicus to extend this formal account and to devise his concept of “logical space” as a universal and necessary manifold for all meaningful states-of-affairs. After his return to philosophy in 1929, he holds up the idea that necessity is not an extraordinary fact, but a feature of the logical framework which constitutes possibilities. Unlike in the Tractatus, however, he then speaks of spaces in the plural and highlights the differences between different “geometries” or “grammars”. I emphasise the plurality of Wittgenstein’s later space concept by presenting the various fields in which spatial terminology is used, as well as the similarity of these various instances by pointing out commonalities in the way in which they are used: the emphasis on possibility instead of truth, the distinction between “geometry” and “physics”(between logic and experience), but also the distinction between different kinds of geometries. These similarities allow me to recognise a number of concepts as closely connected to “space” – and thereby to one another – instead of highlighting their differences. Against views which argue for the complete disappearance of spaces and grammar in the late Wittgenstein’s philosophy, I suggest that these concepts are not dismissed, but transformed after the middle period. The reasons for this transformation are the increasing importance of time, notably the change from static spaces to more dynamic frameworks, and the acknowledgement of empirical factors in logic: instead of an ontological separation of logic and experience it makes more sense to speak of different grammatical roles.