The authors argue that the ways in which people-scientists and laymen-use probabilistic reasoning is predicated on a set of often questionable assumptions that are implicit and frequently go untested. They relate to the correspondence between the terms of a theory and the observations used to validate the theory and to the implicit understandings of intention and prior knowledge that arise between the conveyer and the receiver of information. The authors show several ways in which the use of probabilistic reasoning rests on a priori commitments to a partitioning of an outcome space and demonstrate that there are many more assumptions underlying the use of probabilistic reasoning than are usually acknowledged. They unfold these assumptions to show how several different interpretations of the same results in behavioral decision theory and cognitive psychology are equally well supported by "the facts." They then propose a more comprehensive approach to mapping cognitive processes than those currently used, one that is based on the analysis of all of the relevant alternative interpretations presented in the article.