We demonstrate that classes of dependencies among beliefs held with uncertainty cannot be represented in rule-based systems in a natural or efficient manner. We trace these limitations to a fundamental difference between certain and uncertain reasoning. In particular, we show that beliefs held with certainty are more modular than uncertain beliefs. We argue that the limitations of the rule-based approach for expressing dependencies are a consequence of forcing non-modular knowledge into a representation scheme originally designed to represent modular beliefs. Finally, we describe a representation technique that is related to the rule-based framework yet is not limited in the types of dependencies that it can represent.