 In discussions of the provability of mathematical propositions it is sometimes said that there are substantial propositions of mathematics whose truth or falsehood must remain undecided. What the people who say that don’t realize is that such propositions, if we can use them and want to call them “propositions”, are not at all the same as what are called “propositions” in other cases; because a proof alters the grammar of a proposition. (PG 367)