Yes, idea axioms make Hume’s concern explicit. Let’s explore.
David Hume’s famous is–ought problem points out that we cannot logically derive what ought to be from what is without an additional value judgment. The solution is to make that missing value explicit: is → value → ought. For example, we observe that some people go hungry. That’s the is. We know we should feed them, that’s the ought. But why? That’s all Hume was saying is to fill in the value driving our is-ought principles. We value reducing unnecessary suffering. That’s the value. Therefore, we conclude that we ought to help feed those in need when we can.
Now, consider the close relationship between values, virtues, and principles. A value is something you consider good or important. A virtue is a character trait. A trait you likely wish to cultivate. Perhaps in favor of a value. A principle is a rule that guides your decisions and actions. And that too can be aligned with one of your goods, one of your values in your value system. For example, we value reducing suffering, cultivate compassion as a virtue, and adopt the principle of helping those in need. With this close relationship, you can see that idea axioms are closely related to the is–value–ought structure of normative philosophy.
Idea axioms are a practical thinking tool. Starting with a core idea, we identify a value, a virtue, and a principle that guides us toward action—an ought. They don’t guarantee that the resulting action is right. A questionable value can lead to a questionable conclusion. But they make our reasoning visible, allowing us to examine, challenge, and improve it. Idea axioms are useful across many areas of thought, and Hume’s is–ought problem is one place where they shine.