 True, the Tractatus is a notoriously difficult work to interpret. Even the question as to whether the main portion of the book, essentially all of it other than the ‘frame’ of the preface and the end, is to be taken as a serious attempt to present a metaphysics is controversial. If we leave that hermeneutic controversy aside, and consider the metaphysics which is offered to us, the formalistic aspects one finds are twofold. Firstly, mathematical sentences are said to express ‘pseudo-propositions’, and so are devoid of truth value (only contingent propositions have a truth value). Secondly, mathematics is described as a ‘calculus’ which is not to be used to represent the world as it is in itself but whose value is entirely instrumental. To be sure, the most explicit statement of this is not in the Tractatus but in comments Wittgenstein wrote on Ramsey’s copy of it: