This paper discusses Gordon Baker’s interpretation of the later Wittgenstein, in particular his interpretation of the notion of Wittgensteinian philosophical conceptions (Auffassungen) and the notions of non-exclusivity, local incompatibility, non-additivity and global pluralism which Baker uses to characterize Wittgensteinian conceptions. On the basis of this discussion, and a critique of certain features of Baker’s interpretation of Wittgensteinian conceptions, I introduce the notion of a multidimensional logical description of language use, explaining how this notion, which Baker’s interpretation excludes, constitutes and important element of the later Wittgenstein’s philosophical method of clarification and perspicuous representation. I conclude by explaining how Baker’s problematic notions of local incompatibility and non-additivity, if they are seen in the light of Wittgenstein’s criticisms of certain views of the completeness of philosophical or logical accounts, nevertheless point in the right direction
