 There are no mathematical facts just as there are no (genuine) mathematical propositions. Repeating his intermediate view, the later Wittgenstein says (MS 121, 71v; 27 Dec., 1938): “Mathematics consists of [calculi | calculations], not of propositions”. This radical constructivist conception of mathematics prompts Wittgenstein to make notorious remarks—remarks that virtually no one else would make—such as the infamous (RFM V, §9): “However queer it sounds, the further expansion of an irrational number is a further expansion of mathematics”.