Is higher-order uncertainty needed?

In the artificial intelligence and decision making communities, there seems to be agreement on the calculations used in most problems that are solved using 'higher-order uncertainty', but disagreement on the terminology used. The purpose here is to show that these problems can be modeled using traditional first-order beliefs, and that, when they are modeled this way, the calculations are the same as the 'higher-order' calculations. The disagreements arise because researchers rephrase first-order beliefs in various guises of higher-order uncertainty. I argue that we should stay with the traditional first-order formulations of the problems.