 As radical as the respective #3s are, Brouwer and Wittgenstein agree that an undecided \(\phi\) is a mathematical proposition (for Wittgenstein, of a particular mathematical calculus) if we know of an applicable decision procedure. They also agree that until \(\phi\) is decided, it is neither true nor false (though, for Wittgenstein, ‘true’ means no more than “proved in calculus \(\Gamma\)”). What they disagree about is the status of an ordinary mathematical conjecture, such as Goldbach’s Conjecture. Brouwer admits it as a mathematical proposition, while Wittgenstein rejects it because we do not know how to algorithmically decide it. Like Brouwer (1948 [1983: 90]), Wittgenstein holds that there are no “unknown truth[s]” in mathematics, but unlike Brouwer he denies the existence of “undecidable propositions” on the grounds that such a ‘proposition’ would have no ‘sense’, “and the consequence of this is precisely that the propositions of logic lose their validity for it” (PR §173). In particular, if there are undecidable mathematical propositions (as Brouwer maintains), then at least some mathematical propositions are not propositions of any existent mathematical calculus. For Wittgenstein, however, it is a defining feature of a mathematical proposition that it is either decided or decidable by a known decision procedure in a mathematical calculus. As Wittgenstein says at (PR §151), 