 Whether or not it is ultimately defensible—and this is an absolutely crucial question for Wittgenstein’s Philosophy of Mathematics—this strongly counter-intuitive aspect of Wittgenstein’s account of algorithmic decidability, proof, and the sense of a mathematical proposition is a piece with his rejection of predeterminacy in mathematics. Even in the case where we algorithmically decide a mathematical proposition, the connections thereby made do not pre-exist the algorithmic decision, which means that even when we have a “mathematical question” that we decide by decision procedure, the expression only has a determinate sense qua proposition when it is decided. On Wittgenstein’s account, both middle and later, “[a] new proof gives the proposition a place in a new system” (RFM VI, §13), it “locates it in the whole system of calculations”, though it “does not mention, certainly does not describe, the whole system of calculation that stands behind the proposition and gives it sense” (RFM VI, §11).