 To best understand Wittgenstein’s intermediate Philosophy of Mathematics, one must fully appreciate his strong variant of formalism, according to which “[w]e make mathematics” (WVC 34, note 1; PR §159) by inventing purely formal mathematical calculi, with ‘stipulated’ axioms (PR §202), syntactical rules of transformation, and decision procedures that enable us to invent “mathematical truth” and “mathematical falsity” by algorithmically deciding so-called mathematical ‘propositions’ (PR §§122, 162).