 Here the ‘conclusion’ of an inductive proof [i.e., “what is to be proved” (PR §164)] uses ‘\(m\)’ rather than ‘\(n\)’ to indicate that ‘\(m\)’ stands for any particular number, while ‘\(n\)’ stands for any arbitrary number. For Wittgenstein, the proxy statement “\(\phi(m)\)” is not a mathematical proposition that “assert[s] its generality” (PR §168), it is an eliminable pseudo-proposition standing proxy for the proved inductive base and inductive step. Though an inductive proof cannot prove “the infinite possibility of application” (PR §163), it enables us “to perceive” that a direct proof of any particular proposition can be constructed (PR §165). For example, once we have proved “\(\phi(1)\)” and “\(\phi(n) \rightarrow \phi(n + 1)\)”, we need not reiterate modus ponens \(m - 1\) times to prove the particular proposition “\(\phi(m)\)” (PR §164). The direct proof of, say, “\(\phi\)(714)” (i.e., without 713 iterations of modus ponens) “cannot have a still better proof, say, by my carrying out the derivation as far as this proposition itself” (PR §165).