 The Tractarian conceptions of genuine (contingent) propositions and the (original and) core concept of truth are used to construct theories of logical and mathematical ‘propositions’ by contrast. Stated boldly and bluntly, tautologies, contradictions and mathematical propositions (i.e., mathematical equations) are neither true nor false—we say that they are true or false, but in doing so we use the words ‘true’ and ‘false’ in very different senses from the sense in which a contingent proposition is true or false. Unlike genuine propositions, tautologies and contradictions “have no ‘subject-matter’” (6.124), “lack sense”, and “say nothing” about the world (4.461), and, analogously, mathematical equations are “pseudo-propositions” (6.2) which, when ‘true’ (‘correct’; ‘richtig’ (6.2321)), “merely mark … [the] equivalence of meaning [of ‘two expressions’]” (6.2323). Given that “[t]autology and contradiction are the limiting cases—indeed the disintegration—of the combination of signs” (4.466; italics added), where 