The precautionary principle (PP) is an influential principle of risk management. It has been widely introduced into environmental legislation, and it plays an important role in most international environmental agreements. Yet, there is little consensus on precisely how to understand and formulate the principle. In this article I prove some impossibility results for two plausible formulations of the PP as a decision‐rule. These results illustrate the difficulty in making the PP consistent with the acceptance of any tradeoffs between catastrophic risks and more ordinary goods. How one interprets these results will, however, depend on one's views and commitments. For instance, those who are convinced that the conditions in the impossibility results are requirements of rationality may see these results as undermining the rationality of the PP. But others may simply take these results to identify a set of purported rationality conditions that defenders of the PP should not accept, or to illustrate types of situations in which the principle should not be applied.