 When, therefore, Wittgenstein says (PG 368) that if “[the Law of the Excluded Middle] is supposed not to hold, we have altered the concept of proposition”, he means that an expression is only a meaningful mathematical proposition if we know of an applicable decision procedure for deciding it (PG 400). If a genuine mathematical proposition is undecided, the Law of the Excluded Middle holds in the sense that we know that we will prove or refute the proposition by applying an applicable decision procedure (PG 379, 387).