Making Sense of Questions in Logic and Mathematics: Mill vs. Carnap

Whether mathematical truths are syntactical (as Rudolf Carnap claimed) or empirical (as Mill actually never claimed, though Carnap claimed that he did) might seem merely an academic topic. However, it becomes a practical concern as soon as we consider the role of questions. For if we inquire as to the truth of a mathematical statement, this question must be (in a certain respect) meaningless for Carnap, as its truth or falsity is certain in advance due to its purely syntactical (or formal-semantical) nature. In contrast, for Mill such a question is as valid as any other. These differing views have their consequences for contemporaryerotetic logic.