Abstract
Wittgenstein developed his notion of “logical space” in late 1914 in the second of his wartime notebooks (MS 102). The paper is discussing this development with respect to possible earlier prototypes (Hertz’s “configuration space” and Boltzmann’s “phase space”) and the role logical space plays in the Prototractatus and the Tractatus itself. It is argued that the use is not a mere metaphorical one but can be understood as a concrete mathematical structure given by the logical relationship between truth-arguments, truth-possibilities and truth-conditions. In this perspective the underlying structure is best made visible with the help of three connected representational spaces (called “parameter space”, “state space” and “propositional space”) and the possible mappings between them instead of studying the one logical space directly.
On the basis of this analysis a proposal is presented to reconstruct Wittgenstein’s elementary propositions as a certain iterative decision procedure or alternatively as filters connected in series acting on state space.With this understanding the colour-exclusion problem can be fully resolved within the logical framework of the Tractatus.
© 2017 by Walter de Gruyter Berlin/Boston