 If, e.g., we succeed in proving GC by mathematical induction (i.e., we prove “\(G(1)\)” and “\(G(n) \rightarrow G(n + 1)\)”), we will then have a proof of the inductive step, but since the inductive step was not algorithmically decidable beforehand (PR §§148, 155, 157; PG 380), in constructing the proof we have constructed a new calculus, a new calculating machine (WVC 106) in which we now know how to use this new “machine-part” (RFM VI, §13) (i.e., the unsystematically proved inductive step). Before the proof, the inductive step is not a mathematical proposition with sense (in a particular calculus), whereas after the proof the inductive step is a mathematical proposition, with a new, determinate sense, in a newly created calculus. This demarcation of expressions without mathematical sense and proved or refuted propositions, each with a determinate sense in a particular calculus, is a view that Wittgenstein articulates in myriad different ways from 1929 through 1944.