The precautionary principle, presented as a guide to environmental policy decisions in the presence of uncertainty, has been the subject of vigorous debate. However, the has generally not been discussed in relation to formal theories of choice under uncertainty developed as generalizations of the expected utility model. In this paper, it is argued that a formal basis for the precautionary principle may be found in an incompleteness hypothesis regarding formal models of choice under uncertainty. The incompleteness hypothesis states that estimates derived from formal models of choice under uncertainty will generally be over-optimistic and that the errors will be greater, the less well-understood is the problem in question.