 Wittgenstein, however, does not endeavour to refute Platonism. His aim, instead, is to clarify what Platonism is and what it says, implicitly and explicitly (including variants of Platonism that claim, e.g., that if a proposition is provable in an axiom system, then there already exists a path [i.e., a proof] from the axioms to that proposition (RFM I, §21; Marion 1998: 13–14, 226; Steiner 2000: 334). Platonism is either “a mere truism” (LFM 239), Wittgenstein says, or it is a ‘picture’ consisting of “an infinity of shadowy worlds” (LFM 145), which, as such, lacks ‘utility’ (cf. PI §254) because it explains nothing and it misleads at every turn.